Recent Improvements to the Copernicus Trajectory Design and Optimization System

NASA Technical Reports Server (NTRS)

Williams, Jacob; Senent, Juan S.; Ocampo, Cesar; Lee, David E.

2012-01-01

Copernicus is a software tool for spacecraft trajectory design and optimization. The latest version (v3.0.1) was released in October 2011. It is available at no cost to NASA centers, government contractors, and organizations with a contractual affiliation with NASA. This paper is a brief overview of the recent development history of Copernicus. An overview of the evolution of the software and a discussion of significant new features and improvements is given, and how the tool is used to design spacecraft missions

The General Mission Analysis Tool (GMAT): Current Features And Adding Custom Functionality

NASA Technical Reports Server (NTRS)

Conway, Darrel J.; Hughes, Steven P.

2010-01-01

The General Mission Analysis Tool (GMAT) is a software system for trajectory optimization, mission analysis, trajectory estimation, and prediction developed by NASA, the Air Force Research Lab, and private industry. GMAT's design and implementation are based on four basic principles: open source visibility for both the source code and design documentation; platform independence; modular design; and user extensibility. The system, released under the NASA Open Source Agreement, runs on Windows, Mac and Linux. User extensions, loaded at run time, have been built for optimization, trajectory visualization, force model extension, and estimation, by parties outside of GMAT's development group. The system has been used to optimize maneuvers for the Lunar Crater Observation and Sensing Satellite (LCROSS) and ARTEMIS missions and is being used for formation design and analysis for the Magnetospheric Multiscale Mission (MMS).

Application of Modern Fortran to Spacecraft Trajectory Design and Optimization

NASA Technical Reports Server (NTRS)

Williams, Jacob; Falck, Robert D.; Beekman, Izaak B.

2018-01-01

In this paper, applications of the modern Fortran programming language to the field of spacecraft trajectory optimization and design are examined. Modern object-oriented Fortran has many advantages for scientific programming, although many legacy Fortran aerospace codes have not been upgraded to use the newer standards (or have been rewritten in other languages perceived to be more modern). NASA's Copernicus spacecraft trajectory optimization program, originally a combination of Fortran 77 and Fortran 95, has attempted to keep up with modern standards and makes significant use of the new language features. Various algorithms and methods are presented from trajectory tools such as Copernicus, as well as modern Fortran open source libraries and other projects.

Augmenting Parametric Optimal Ascent Trajectory Modeling with Graph Theory

NASA Technical Reports Server (NTRS)

Dees, Patrick D.; Zwack, Matthew R.; Edwards, Stephen; Steffens, Michael

2016-01-01

It has been well documented that decisions made in the early stages of Conceptual and Pre-Conceptual design commit up to 80% of total Life-Cycle Cost (LCC) while engineers know the least about the product they are designing [1]. Once within Preliminary and Detailed design however, making changes to the design becomes far more difficult to enact in both cost and schedule. Primarily this has been due to a lack of detailed data usually uncovered later during the Preliminary and Detailed design phases. In our current budget-constrained environment, making decisions within Conceptual and Pre-Conceptual design which minimize LCC while meeting requirements is paramount to a program's success. Within the arena of launch vehicle design, optimizing the ascent trajectory is critical for minimizing the costs present within such concerns as propellant, aerodynamic, aeroheating, and acceleration loads while meeting requirements such as payload delivered to a desired orbit. In order to optimize the vehicle design its constraints and requirements must be known, however as the design cycle proceeds it is all but inevitable that the conditions will change. Upon that change, the previously optimized trajectory may no longer be optimal, or meet design requirements. The current paradigm for adjusting to these updates is generating point solutions for every change in the design's requirements [2]. This can be a tedious, time-consuming task as changes in virtually any piece of a launch vehicle's design can have a disproportionately large effect on the ascent trajectory, as the solution space of the trajectory optimization problem is both non-linear and multimodal [3]. In addition, an industry standard tool, Program to Optimize Simulated Trajectories (POST), requires an expert analyst to produce simulated trajectories that are feasible and optimal [4]. In a previous publication the authors presented a method for combatting these challenges [5]. In order to bring more detailed information into Conceptual and Pre-Conceptual design, knowledge of the effects originating from changes to the vehicle must be calculated. In order to do this, a model capable of quantitatively describing any vehicle within the entire design space under consideration must be constructed. This model must be based upon analysis of acceptable fidelity, which in this work comes from POST. Design space interrogation can be achieved with surrogate modeling, a parametric, polynomial equation representing a tool. A surrogate model must be informed by data from the tool with enough points to represent the solution space for the chosen number of variables with an acceptable level of error. Therefore, Design Of Experiments (DOE) is used to select points within the design space to maximize information gained on the design space while minimizing number of data points required. To represent a design space with a non-trivial number of variable parameters the number of points required still represent an amount of work which would take an inordinate amount of time via the current paradigm of manual analysis, and so an automated method was developed. The best practices of expert trajectory analysts working within NASA Marshall's Advanced Concepts Office (ACO) were implemented within a tool called multiPOST. These practices include how to use the output data from a previous run of POST to inform the next, determining whether a trajectory solution is feasible from a real-world perspective, and how to handle program execution errors. The tool was then augmented with multiprocessing capability to enable analysis on multiple trajectories simultaneously, allowing throughput to scale with available computational resources. In this update to the previous work the authors discuss issues with the method and solutions.

Optimization of the propulsion for multistage solid rocket motor launchers

NASA Astrophysics Data System (ADS)

Calabro, M.; Dufour, A.; Macaire, A.

2002-02-01

Some tools focused on a rapid multidisciplinary optimization capability for multistage launch vehicle design were developed at EADS-LV. These tools may be broken down into two categories, those related to propulsion design optimization and a computer code devoted to trajectories and under constraints optimization. Both are linked in order to obtain optimal vehicle design after an iterative process. After a description of the two categories tools, an example of application is given on a small space launcher.

Gravity-Assist Trajectories to the Ice Giants: An Automated Method to Catalog Mass- Or Time-Optimal Solutions

NASA Technical Reports Server (NTRS)

Hughes, Kyle M.; Knittel, Jeremy M.; Englander, Jacob A.

2017-01-01

This work presents an automated method of calculating mass (or time) optimal gravity-assist trajectories without a priori knowledge of the flyby-body combination. Since gravity assists are particularly crucial for reaching the outer Solar System, we use the Ice Giants, Uranus and Neptune, as example destinations for this work. Catalogs are also provided that list the most attractive trajectories found over launch dates ranging from 2024 to 2038. The tool developed to implement this method, called the Python EMTG Automated Trade Study Application (PEATSA), iteratively runs the Evolutionary Mission Trajectory Generator (EMTG), a NASA Goddard Space Flight Center in-house trajectory optimization tool. EMTG finds gravity-assist trajectories with impulsive maneuvers using a multiple-shooting structure along with stochastic methods (such as monotonic basin hopping) and may be run with or without an initial guess provided. PEATSA runs instances of EMTG in parallel over a grid of launch dates. After each set of runs completes, the best results within a neighborhood of launch dates are used to seed all other cases in that neighborhood-allowing the solutions across the range of launch dates to improve over each iteration. The results here are compared against trajectories found using a grid-search technique, and PEATSA is found to outperform the grid-search results for most launch years considered.

Gravity-Assist Trajectories to the Ice Giants: An Automated Method to Catalog Mass-or Time-Optimal Solutions

NASA Technical Reports Server (NTRS)

Hughes, Kyle M.; Knittel, Jeremy M.; Englander, Jacob A.

2017-01-01

This work presents an automated method of calculating mass (or time) optimal gravity-assist trajectories without a priori knowledge of the flyby-body combination. Since gravity assists are particularly crucial for reaching the outer Solar System, we use the Ice Giants, Uranus and Neptune, as example destinations for this work. Catalogs are also provided that list the most attractive trajectories found over launch dates ranging from 2024 to 2038. The tool developed to implement this method, called the Python EMTG Automated Trade Study Application (PEATSA), iteratively runs the Evolutionary Mission Trajectory Generator (EMTG), a NASA Goddard Space Flight Center in-house trajectory optimization tool. EMTG finds gravity-assist trajectories with impulsive maneuvers using a multiple-shooting structure along with stochastic methods (such as monotonic basin hopping) and may be run with or without an initial guess provided. PEATSA runs instances of EMTG in parallel over a grid of launch dates. After each set of runs completes, the best results within a neighborhood of launch dates are used to seed all other cases in that neighborhood---allowing the solutions across the range of launch dates to improve over each iteration. The results here are compared against trajectories found using a grid-search technique, and PEATSA is found to outperform the grid-search results for most launch years considered.

Optimization of Low-Thrust Spiral Trajectories by Collocation

NASA Technical Reports Server (NTRS)

Falck, Robert D.; Dankanich, John W.

2012-01-01

As NASA examines potential missions in the post space shuttle era, there has been a renewed interest in low-thrust electric propulsion for both crewed and uncrewed missions. While much progress has been made in the field of software for the optimization of low-thrust trajectories, many of the tools utilize higher-fidelity methods which, while excellent, result in extremely high run-times and poor convergence when dealing with planetocentric spiraling trajectories deep within a gravity well. Conversely, faster tools like SEPSPOT provide a reasonable solution but typically fail to account for other forces such as third-body gravitation, aerodynamic drag, solar radiation pressure. SEPSPOT is further constrained by its solution method, which may require a very good guess to yield a converged optimal solution. Here the authors have developed an approach using collocation intended to provide solution times comparable to those given by SEPSPOT while allowing for greater robustness and extensible force models.

Automated Sensitivity Analysis of Interplanetary Trajectories

NASA Technical Reports Server (NTRS)

Knittel, Jeremy; Hughes, Kyle; Englander, Jacob; Sarli, Bruno

2017-01-01

This work describes a suite of Python tools known as the Python EMTG Automated Trade Study Application (PEATSA). PEATSA was written to automate the operation of trajectory optimization software, simplify the process of performing sensitivity analysis, and was ultimately found to out-perform a human trajectory designer in unexpected ways. These benefits will be discussed and demonstrated on sample mission designs.

Surface Modeling of Workpiece and Tool Trajectory Planning for Spray Painting Robot

PubMed Central

Tang, Yang; Chen, Wei

2015-01-01

Automated tool trajectory planning for spray-painting robots is still a challenging problem, especially for a large free-form surface. A grid approximation of a free-form surface is adopted in CAD modeling in this paper. A free-form surface model is approximated by a set of flat patches. We describe here an efficient and flexible tool trajectory optimization scheme using T-Bézier curves calculated in a new way from trigonometrical bases. The distance between the spray gun and the free-form surface along the normal vector is varied. Automotive body parts, which are large free-form surfaces, are used to test the scheme. The experimental results show that the trajectory planning algorithm achieves satisfactory performance. This algorithm can also be extended to other applications. PMID:25993663

Surface modeling of workpiece and tool trajectory planning for spray painting robot.

PubMed

Tang, Yang; Chen, Wei

2015-01-01

Automated tool trajectory planning for spray-painting robots is still a challenging problem, especially for a large free-form surface. A grid approximation of a free-form surface is adopted in CAD modeling in this paper. A free-form surface model is approximated by a set of flat patches. We describe here an efficient and flexible tool trajectory optimization scheme using T-Bézier curves calculated in a new way from trigonometrical bases. The distance between the spray gun and the free-form surface along the normal vector is varied. Automotive body parts, which are large free-form surfaces, are used to test the scheme. The experimental results show that the trajectory planning algorithm achieves satisfactory performance. This algorithm can also be extended to other applications.

An Automatic Medium to High Fidelity Low-Thrust Global Trajectory Toolchain; EMTG-GMAT

NASA Technical Reports Server (NTRS)

Beeson, Ryne T.; Englander, Jacob A.; Hughes, Steven P.; Schadegg, Maximillian

2015-01-01

Solving the global optimization, low-thrust, multiple-flyby interplanetary trajectory problem with high-fidelity dynamical models requires an unreasonable amount of computational resources. A better approach, and one that is demonstrated in this paper, is a multi-step process whereby the solution of the aforementioned problem is solved at a lower-fidelity and this solution is used as an initial guess for a higher-fidelity solver. The framework presented in this work uses two tools developed by NASA Goddard Space Flight Center: the Evolutionary Mission Trajectory Generator (EMTG) and the General Mission Analysis Tool (GMAT). EMTG is a medium to medium-high fidelity low-thrust interplanetary global optimization solver, which now has the capability to automatically generate GMAT script files for seeding a high-fidelity solution using GMAT's local optimization capabilities. A discussion of the dynamical models as well as thruster and power modeling for both EMTG and GMAT are given in this paper. Current capabilities are demonstrated with examples that highlight the toolchains ability to efficiently solve the difficult low-thrust global optimization problem with little human intervention.

Constraint Force Equation Methodology for Modeling Multi-Body Stage Separation Dynamics

NASA Technical Reports Server (NTRS)

Toniolo, Matthew D.; Tartabini, Paul V.; Pamadi, Bandu N.; Hotchko, Nathaniel

2008-01-01

This paper discusses a generalized approach to the multi-body separation problems in a launch vehicle staging environment based on constraint force methodology and its implementation into the Program to Optimize Simulated Trajectories II (POST2), a widely used trajectory design and optimization tool. This development facilitates the inclusion of stage separation analysis into POST2 for seamless end-to-end simulations of launch vehicle trajectories, thus simplifying the overall implementation and providing a range of modeling and optimization capabilities that are standard features in POST2. Analysis and results are presented for two test cases that validate the constraint force equation methodology in a stand-alone mode and its implementation in POST2.

Computational Approaches to Simulation and Optimization of Global Aircraft Trajectories

NASA Technical Reports Server (NTRS)

Ng, Hok Kwan; Sridhar, Banavar

2016-01-01

This study examines three possible approaches to improving the speed in generating wind-optimal routes for air traffic at the national or global level. They are: (a) using the resources of a supercomputer, (b) running the computations on multiple commercially available computers and (c) implementing those same algorithms into NASAs Future ATM Concepts Evaluation Tool (FACET) and compares those to a standard implementation run on a single CPU. Wind-optimal aircraft trajectories are computed using global air traffic schedules. The run time and wait time on the supercomputer for trajectory optimization using various numbers of CPUs ranging from 80 to 10,240 units are compared with the total computational time for running the same computation on a single desktop computer and on multiple commercially available computers for potential computational enhancement through parallel processing on the computer clusters. This study also re-implements the trajectory optimization algorithm for further reduction of computational time through algorithm modifications and integrates that with FACET to facilitate the use of the new features which calculate time-optimal routes between worldwide airport pairs in a wind field for use with existing FACET applications. The implementations of trajectory optimization algorithms use MATLAB, Python, and Java programming languages. The performance evaluations are done by comparing their computational efficiencies and based on the potential application of optimized trajectories. The paper shows that in the absence of special privileges on a supercomputer, a cluster of commercially available computers provides a feasible approach for national and global air traffic system studies.

Developing Optimized Trajectories Derived from Mission and Thermo-Structural Constraints

NASA Technical Reports Server (NTRS)

Lear, Matthew H.; McGrath, Brian E.; Anderson, Michael P.; Green, Peter W.

2008-01-01

In conjunction with NASA and the Department of Defense, the Johns Hopkins University Applied Physics Laboratory (JHU/APL) has been investigating analytical techniques to address many of the fundamental issues associated with solar exploration spacecraft and high-speed atmospheric vehicle systems. These issues include: thermo-structural response including the effects of thermal management via the use of surface optical properties for high-temperature composite structures; aerodynamics with the effects of non-equilibrium chemistry and gas radiation; and aero-thermodynamics with the effects of material ablation for a wide range of thermal protection system (TPS) materials. The need exists to integrate these discrete tools into a common framework that enables the investigation of interdisciplinary interactions (including analysis tool, applied load, and environment uncertainties) to provide high fidelity solutions. In addition to developing robust tools for the coupling of aerodynamically induced thermal and mechanical loads, JHU/APL has been studying the optimal design of high-speed vehicles as a function of their trajectory. Under traditional design methodology the optimization of system level mission parameters such as range and time of flight is performed independently of the optimization for thermal and mechanical constraints such as stress and temperature. A truly optimal trajectory should optimize over the entire range of mission and thermo-mechanical constraints. Under this research, a framework for the robust analysis of high-speed spacecraft and atmospheric vehicle systems has been developed. It has been built around a generic, loosely coupled framework such that a variety of readily available analysis tools can be used. The methodology immediately addresses many of the current analysis inadequacies and allows for future extension in order to handle more complex problems.

A new optimization tool path planning for 3-axis end milling of free-form surfaces based on efficient machining intervals

NASA Astrophysics Data System (ADS)

Vu, Duy-Duc; Monies, Frédéric; Rubio, Walter

2018-05-01

A large number of studies, based on 3-axis end milling of free-form surfaces, seek to optimize tool path planning. Approaches try to optimize the machining time by reducing the total tool path length while respecting the criterion of the maximum scallop height. Theoretically, the tool path trajectories that remove the most material follow the directions in which the machined width is the largest. The free-form surface is often considered as a single machining area. Therefore, the optimization on the entire surface is limited. Indeed, it is difficult to define tool trajectories with optimal feed directions which generate largest machined widths. Another limiting point of previous approaches for effectively reduce machining time is the inadequate choice of the tool. Researchers use generally a spherical tool on the entire surface. However, the gains proposed by these different methods developed with these tools lead to relatively small time savings. Therefore, this study proposes a new method, using toroidal milling tools, for generating toolpaths in different regions on the machining surface. The surface is divided into several regions based on machining intervals. These intervals ensure that the effective radius of the tool, at each cutter-contact points on the surface, is always greater than the radius of the tool in an optimized feed direction. A parallel plane strategy is then used on the sub-surfaces with an optimal specific feed direction for each sub-surface. This method allows one to mill the entire surface with efficiency greater than with the use of a spherical tool. The proposed method is calculated and modeled using Maple software to find optimal regions and feed directions in each region. This new method is tested on a free-form surface. A comparison is made with a spherical cutter to show the significant gains obtained with a toroidal milling cutter. Comparisons with CAM software and experimental validations are also done. The results show the efficiency of the method.

Nonparametric variational optimization of reaction coordinates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banushkina, Polina V.; Krivov, Sergei V., E-mail: s.krivov@leeds.ac.uk

State of the art realistic simulations of complex atomic processes commonly produce trajectories of large size, making the development of automated analysis tools very important. A popular approach aimed at extracting dynamical information consists of projecting these trajectories into optimally selected reaction coordinates or collective variables. For equilibrium dynamics between any two boundary states, the committor function also known as the folding probability in protein folding studies is often considered as the optimal coordinate. To determine it, one selects a functional form with many parameters and trains it on the trajectories using various criteria. A major problem with such anmore » approach is that a poor initial choice of the functional form may lead to sub-optimal results. Here, we describe an approach which allows one to optimize the reaction coordinate without selecting its functional form and thus avoiding this source of error.« less

Online optimal obstacle avoidance for rotary-wing autonomous unmanned aerial vehicles

NASA Astrophysics Data System (ADS)

Kang, Keeryun

This thesis presents an integrated framework for online obstacle avoidance of rotary-wing unmanned aerial vehicles (UAVs), which can provide UAVs an obstacle field navigation capability in a partially or completely unknown obstacle-rich environment. The framework is composed of a LIDAR interface, a local obstacle grid generation, a receding horizon (RH) trajectory optimizer, a global shortest path search algorithm, and a climb rate limit detection logic. The key feature of the framework is the use of an optimization-based trajectory generation in which the obstacle avoidance problem is formulated as a nonlinear trajectory optimization problem with state and input constraints over the finite range of the sensor. This local trajectory optimization is combined with a global path search algorithm which provides a useful initial guess to the nonlinear optimization solver. Optimization is the natural process of finding the best trajectory that is dynamically feasible, safe within the vehicle's flight envelope, and collision-free at the same time. The optimal trajectory is continuously updated in real time by the numerical optimization solver, Nonlinear Trajectory Generation (NTG), which is a direct solver based on the spline approximation of trajectory for dynamically flat systems. In fact, the overall approach of this thesis to finding the optimal trajectory is similar to the model predictive control (MPC) or the receding horizon control (RHC), except that this thesis followed a two-layer design; thus, the optimal solution works as a guidance command to be followed by the controller of the vehicle. The framework is implemented in a real-time simulation environment, the Georgia Tech UAV Simulation Tool (GUST), and integrated in the onboard software of the rotary-wing UAV test-bed at Georgia Tech. Initially, the 2D vertical avoidance capability of real obstacles was tested in flight. The flight test evaluations were extended to the benchmark tests for 3D avoidance capability over the virtual obstacles, and finally it was demonstrated on real obstacles located at the McKenna MOUT site in Fort Benning, Georgia. Simulations and flight test evaluations demonstrate the feasibility of the developed framework for UAV applications involving low-altitude flight in an urban area.

The Development of NASA's Low Thrust Trajectory Tool Set

NASA Technical Reports Server (NTRS)

Sims, Jon; Artis, Gwen; Kos, Larry

2006-01-01

Highly efficient electric propulsion systems can enable interesting classes of missions; unfortunately, they provide only a limited amount of thrust. Low-thrust (LT) trajectories are much more difficult to design than impulsive-type (chemical propulsion) trajectories. Previous low-thrust (LT) trajectory optimization software was often difficult to use, often had difficulties converging, and was somewhat limited in the types of missions it could support. A new state-of-the-art suite (toolbox) of low-thrust (LT) tools along with improved algorithms and methods was developed by NASA's MSFC, JPL, JSC, and GRC to address the needs of our customers to help foster technology development in the areas of advanced LT propulsion systems, and to facilitate generation of similar results by different analysts.

Automating Initial Guess Generation for High Fidelity Trajectory Optimization Tools

NASA Technical Reports Server (NTRS)

Villa, Benjamin; Lantoine, Gregory; Sims, Jon; Whiffen, Gregory

2013-01-01

Many academic studies in spaceflight dynamics rely on simplified dynamical models, such as restricted three-body models or averaged forms of the equations of motion of an orbiter. In practice, the end result of these preliminary orbit studies needs to be transformed into more realistic models, in particular to generate good initial guesses for high-fidelity trajectory optimization tools like Mystic. This paper reviews and extends some of the approaches used in the literature to perform such a task, and explores the inherent trade-offs of such a transformation with a view toward automating it for the case of ballistic arcs. Sample test cases in the libration point regimes and small body orbiter transfers are presented.

Trajectories for High Specific Impulse High Specific Power Deep Space Exploration

NASA Technical Reports Server (NTRS)

Polsgrove, Tara; Adams, Robert B.; Brady, Hugh J. (Technical Monitor)

2002-01-01

Flight times and deliverable masses for electric and fusion propulsion systems are difficult to approximate. Numerical integration is required for these continuous thrust systems. Many scientists are not equipped with the tools and expertise to conduct interplanetary and interstellar trajectory analysis for their concepts. Several charts plotting the results of well-known trajectory simulation codes were developed and are contained in this paper. These charts illustrate the dependence of time of flight and payload ratio on jet power, initial mass, specific impulse and specific power. These charts are intended to be a tool by which people in the propulsion community can explore the possibilities of their propulsion system concepts. Trajectories were simulated using the tools VARITOP and IPOST. VARITOP is a well known trajectory optimization code that involves numerical integration based on calculus of variations. IPOST has several methods of trajectory simulation; the one used in this paper is Cowell's method for full integration of the equations of motion. An analytical method derived in the companion paper was also evaluated. The accuracy of this method is discussed in the paper.

Variational Trajectory Optimization Tool Set: Technical description and user's manual

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Queen, Eric M.; Cavanaugh, Michael D.; Wetzel, Todd A.; Moerder, Daniel D.

1993-01-01

The algorithms that comprise the Variational Trajectory Optimization Tool Set (VTOTS) package are briefly described. The VTOTS is a software package for solving nonlinear constrained optimal control problems from a wide range of engineering and scientific disciplines. The VTOTS package was specifically designed to minimize the amount of user programming; in fact, for problems that may be expressed in terms of analytical functions, the user needs only to define the problem in terms of symbolic variables. This version of the VTOTS does not support tabular data; thus, problems must be expressed in terms of analytical functions. The VTOTS package consists of two methods for solving nonlinear optimal control problems: a time-domain finite-element algorithm and a multiple shooting algorithm. These two algorithms, under the VTOTS package, may be run independently or jointly. The finite-element algorithm generates approximate solutions, whereas the shooting algorithm provides a more accurate solution to the optimization problem. A user's manual, some examples with results, and a brief description of the individual subroutines are included.

General Mission Analysis Tool (GMAT) Mathematical Specifications

NASA Technical Reports Server (NTRS)

Hughes, Steve

2007-01-01

The General Mission Analysis Tool (GMAT) is a space trajectory optimization and mission analysis system developed by NASA and private industry in the spirit of the NASA Mission. GMAT contains new technology and is a testbed for future technology development.

General Mission Analysis Tool (GMAT) User's Guide (Draft)

NASA Technical Reports Server (NTRS)

Hughes, Steven P.

2007-01-01

4The General Mission Analysis Tool (GMAT) is a space trajectory optimization and mission analysis system. This document is a draft of the users guide for the tool. Included in the guide is information about Configuring Objects/Resources, Object Fields: Quick Look-up Tables, and Commands and Events.

General Mission Analysis Tool (GMAT)

NASA Technical Reports Server (NTRS)

Hughes, Steven P.

2007-01-01

The General Mission Analysis Tool (GMAT) is a space trajectory optimization and mission analysis system developed by NASA and private industry in the spirit of the NASA Mission. GMAT contains new technology and is a testbed for future technology development. The goal of the GMAT project is to develop new space trajectory optimization and mission design technology by working inclusively with ordinary people, universities, businesses, and other government organizations, and to share that technology in an open and unhindered way. GMAT is a free and open source software system licensed under the NASA Open Source Agreement: free for anyone to use in development of new mission concepts or to improve current missions, freely available in source code form for enhancement or further technology development.

Comparison of Low-Thrust Control Laws for Application in Planetocentric Space

NASA Technical Reports Server (NTRS)

Falck, Robert D.; Sjauw, Waldy K.; Smith, David A.

2014-01-01

Recent interest at NASA for the application of solar electric propulsion for the transfer of significant payloads in cislunar space has led to the development of high-fidelity simulations of such missions. With such transfers involving transfer times on the order of months, simulation time can be significant. In the past, the examination of such missions typically began with the use of lower-fidelity trajectory optimization tools such as SEPSPOT to develop and tune guidance laws which delivered optimal or near- optimal trajectories, where optimal is generally defined as minimizing propellant expenditure or time of flight. The transfer of these solutions to a high-fidelity simulation is typically an iterative process whereby the initial solution may nearly, but not precisely, meet mission objectives. Further tuning of the guidance algorithm is typically necessary when accounting for high-fidelity perturbations such as those due to more detailed gravity models, secondary-body effects, solar radiation pressure, etc. While trajectory optimization is a useful method for determining optimal performance metrics, algorithms which deliver nearly optimal performance with minimal tuning are an attractive alternative.

Automation of POST Cases via External Optimizer and "Artificial p2" Calculation

NASA Technical Reports Server (NTRS)

Dees, Patrick D.; Zwack, Mathew R.

2017-01-01

During early conceptual design of complex systems, speed and accuracy are often at odds with one another. While many characteristics of the design are fluctuating rapidly during this phase there is nonetheless a need to acquire accurate data from which to down-select designs as these decisions will have a large impact upon program life-cycle cost. Therefore enabling the conceptual designer to produce accurate data in a timely manner is tantamount to program viability. For conceptual design of launch vehicles, trajectory analysis and optimization is a large hurdle. Tools such as the industry standard Program to Optimize Simulated Trajectories (POST) have traditionally required an expert in the loop for setting up inputs, running the program, and analyzing the output. The solution space for trajectory analysis is in general non-linear and multi-modal requiring an experienced analyst to weed out sub-optimal designs in pursuit of the global optimum. While an experienced analyst presented with a vehicle similar to one which they have already worked on can likely produce optimal performance figures in a timely manner, as soon as the "experienced" or "similar" adjectives are invalid the process can become lengthy. In addition, an experienced analyst working on a similar vehicle may go into the analysis with preconceived ideas about what the vehicle's trajectory should look like which can result in sub-optimal performance being recorded. Thus, in any case but the ideal either time or accuracy can be sacrificed. In the authors' previous work a tool called multiPOST was created which captures the heuristics of a human analyst over the process of executing trajectory analysis with POST. However without the instincts of a human in the loop, this method relied upon Monte Carlo simulation to find successful trajectories. Overall the method has mixed results, and in the context of optimizing multiple vehicles it is inefficient in comparison to the method presented POST's internal optimizer functions like any other gradient-based optimizer. It has a specified variable to optimize whose value is represented as optval, a set of dependent constraints to meet with associated forms and tolerances whose value is represented as p2, and a set of independent variables known as the u-vector to modify in pursuit of optimality. Each of these quantities are calculated or manipulated at a certain phase within the trajectory. The optimizer is further constrained by the requirement that the input u-vector must result in a trajectory which proceeds through each of the prescribed events in the input file. For example, if the input u-vector causes the vehicle to crash before it can achieve the orbital parameters required for a parking orbit, then the run will fail without engaging the optimizer, and a p2 value of exactly zero is returned. This poses a problem, as this "non-connecting" region of the u-vector space is far larger than the "connecting" region which returns a non-zero value of p2 and can be worked on by the internal optimizer. Finding this connecting region and more specifically the global optimum within this region has traditionally required the use of an expert analyst.

Post-Flight Assessment of Low Density Supersonic Decelerator Flight Dynamics Test 2 Simulation

NASA Technical Reports Server (NTRS)

Dutta, Soumyo; Bowes, Angela L.; White, Joseph P.; Striepe, Scott A.; Queen, Eric M.; O'Farrel, Clara; Ivanov, Mark C.

2016-01-01

NASA's Low Density Supersonic Decelerator (LDSD) project conducted its second Supersonic Flight Dynamics Test (SFDT-2) on June 8, 2015. The Program to Optimize Simulated Trajectories II (POST2) was one of the flight dynamics tools used to simulate and predict the flight performance and was a major tool used in the post-flight assessment of the flight trajectory. This paper compares the simulation predictions with the reconstructed trajectory. Additionally, off-nominal conditions seen during flight are modeled in the simulation to reconcile the predictions with flight data. These analyses are beneficial to characterize the results of the flight test and to improve the simulation and targeting of the subsequent LDSD flights.

Flight test trajectory control analysis

NASA Technical Reports Server (NTRS)

Walker, R.; Gupta, N.

1983-01-01

Recent extensions to optimal control theory applied to meaningful linear models with sufficiently flexible software tools provide powerful techniques for designing flight test trajectory controllers (FTTCs). This report describes the principal steps for systematic development of flight trajectory controllers, which can be summarized as planning, modeling, designing, and validating a trajectory controller. The techniques have been kept as general as possible and should apply to a wide range of problems where quantities must be computed and displayed to a pilot to improve pilot effectiveness and to reduce workload and fatigue. To illustrate the approach, a detailed trajectory guidance law is developed and demonstrated for the F-15 aircraft flying the zoom-and-pushover maneuver.

Enabling Parametric Optimal Ascent Trajectory Modeling During Early Phases of Design

NASA Technical Reports Server (NTRS)

Holt, James B.; Dees, Patrick D.; Diaz, Manuel J.

2015-01-01

During the early phases of engineering design, the costs committed are high, costs incurred are low, and the design freedom is high. It is well documented that decisions made in these early design phases drive the entire design's life cycle. In a traditional paradigm, key design decisions are made when little is known about the design. As the design matures, design changes become more difficult -- in both cost and schedule -- to enact. Indeed, the current capability-based paradigm that has emerged because of the constrained economic environment calls for the infusion of knowledge acquired during later design phases into earlier design phases, i.e. bring knowledge acquired during preliminary and detailed design into pre-conceptual and conceptual design. An area of critical importance to launch vehicle design is the optimization of its ascent trajectory, as the optimal trajectory will be able to take full advantage of the launch vehicle's capability to deliver a maximum amount of payload into orbit. Hence, the optimal ascent trajectory plays an important role in the vehicle's affordability posture as the need for more economically viable access to space solutions are needed in today's constrained economic environment. The problem of ascent trajectory optimization is not a new one. There are several programs that are widely used in industry that allows trajectory analysts to, based on detailed vehicle and insertion orbit parameters, determine the optimal ascent trajectory. Yet, little information is known about the launch vehicle early in the design phase - information that is required of many different disciplines in order to successfully optimize the ascent trajectory. Thus, the current paradigm of optimizing ascent trajectories involves generating point solutions for every change in a vehicle's design parameters. This is often a very tedious, manual, and time-consuming task for the analysts. Moreover, the trajectory design space is highly non-linear and multi-modal due to the interaction of various constraints. Additionally, when these obstacles are coupled with The Program to Optimize Simulated Trajectories [1] (POST), an industry standard program to optimize ascent trajectories that is difficult to use, it requires expert trajectory analysts to effectively optimize a vehicle's ascent trajectory. As it has been pointed out, the paradigm of trajectory optimization is still a very manual one because using modern computational resources on POST is still a challenging problem. The nuances and difficulties involved in correctly utilizing, and therefore automating, the program presents a large problem. In order to address these issues, the authors will discuss a methodology that has been developed. The methodology is two-fold: first, a set of heuristics will be introduced and discussed that were captured while working with expert analysts to replicate the current state-of-the-art; secondly, leveraging the power of modern computing to evaluate multiple trajectories simultaneously, and therefore, enable the exploration of the trajectory's design space early during the pre-conceptual and conceptual phases of design. When this methodology is coupled with design of experiments in order to train surrogate models, the authors were able to visualize the trajectory design space, enabling parametric optimal ascent trajectory information to be introduced with other pre-conceptual and conceptual design tools. The potential impact of this methodology's success would be a fully automated POST evaluation suite for the purpose of conceptual and preliminary design trade studies. This will enable engineers to characterize the ascent trajectory's sensitivity to design changes in an arbitrary number of dimensions and for finding settings for trajectory specific variables, which result in optimal performance for a "dialed-in" launch vehicle design. The effort described in this paper was developed for the Advanced Concepts Office [2] at NASA Marshall Space Flight Center

Small Launch Vehicle Trade Space Definition: Development of a Zero Level Mass Estimation Tool with Trajectory Validation

NASA Technical Reports Server (NTRS)

Waters, Eric D.

2013-01-01

Recent high level interest in the capability of small launch vehicles has placed significant demand on determining the trade space these vehicles occupy. This has led to the development of a zero level analysis tool that can quickly determine the minimum expected vehicle gross liftoff weight (GLOW) in terms of vehicle stage specific impulse (Isp) and propellant mass fraction (pmf) for any given payload value. Utilizing an extensive background in Earth to orbit trajectory experience a total necessary delta v the vehicle must achieve can be estimated including relevant loss terms. This foresight into expected losses allows for more specific assumptions relating to the initial estimates of thrust to weight values for each stage. This tool was further validated against a trajectory model, in this case the Program to Optimize Simulated Trajectories (POST), to determine if the initial sizing delta v was adequate to meet payload expectations. Presented here is a description of how the tool is setup and the approach the analyst must take when using the tool. Also, expected outputs which are dependent on the type of small launch vehicle being sized will be displayed. The method of validation will be discussed as well as where the sizing tool fits into the vehicle design process.

Moving-window dynamic optimization: design of stimulation profiles for walking.

PubMed

Dosen, Strahinja; Popović, Dejan B

2009-05-01

The overall goal of the research is to improve control for electrical stimulation-based assistance of walking in hemiplegic individuals. We present the simulation for generating offline input (sensors)-output (intensity of muscle stimulation) representation of walking that serves in synthesizing a rule-base for control of electrical stimulation for restoration of walking. The simulation uses new algorithm termed moving-window dynamic optimization (MWDO). The optimization criterion was to minimize the sum of the squares of tracking errors from desired trajectories with the penalty function on the total muscle efforts. The MWDO was developed in the MATLAB environment and tested using target trajectories characteristic for slow-to-normal walking recorded in healthy individual and a model with the parameters characterizing the potential hemiplegic user. The outputs of the simulation are piecewise constant intensities of electrical stimulation and trajectories generated when the calculated stimulation is applied to the model. We demonstrated the importance of this simulation by showing the outputs for healthy and hemiplegic individuals, using the same target trajectories. Results of the simulation show that the MWDO is an efficient tool for analyzing achievable trajectories and for determining the stimulation profiles that need to be delivered for good tracking.

Minimum deltaV Burn Planning for the International Space Station Using a Hybrid Optimization Technique, Level 1

NASA Technical Reports Server (NTRS)

Brown, Aaron J.

2015-01-01

The International Space Station's (ISS) trajectory is coordinated and executed by the Trajectory Operations and Planning (TOPO) group at NASA's Johnson Space Center. TOPO group personnel routinely generate look-ahead trajectories for the ISS that incorporate translation burns needed to maintain its orbit over the next three to twelve months. The burns are modeled as in-plane, horizontal burns, and must meet operational trajectory constraints imposed by both NASA and the Russian Space Agency. In generating these trajectories, TOPO personnel must determine the number of burns to model, each burn's Time of Ignition (TIG), and magnitude (i.e. deltaV) that meet these constraints. The current process for targeting these burns is manually intensive, and does not take advantage of more modern techniques that can reduce the workload needed to find feasible burn solutions, i.e. solutions that simply meet the constraints, or provide optimal burn solutions that minimize the total DeltaV while simultaneously meeting the constraints. A two-level, hybrid optimization technique is proposed to find both feasible and globally optimal burn solutions for ISS trajectory planning. For optimal solutions, the technique breaks the optimization problem into two distinct sub-problems, one for choosing the optimal number of burns and each burn's optimal TIG, and the other for computing the minimum total deltaV burn solution that satisfies the trajectory constraints. Each of the two aforementioned levels uses a different optimization algorithm to solve one of the sub-problems, giving rise to a hybrid technique. Level 2, or the outer level, uses a genetic algorithm to select the number of burns and each burn's TIG. Level 1, or the inner level, uses the burn TIGs from Level 2 in a sequential quadratic programming (SQP) algorithm to compute a minimum total deltaV burn solution subject to the trajectory constraints. The total deltaV from Level 1 is then used as a fitness function by the genetic algorithm in Level 2 to select the number of burns and their TIGs for the next generation. In this manner, the two levels solve their respective sub-problems separately but collaboratively until a burn solution is found that globally minimizes the deltaV across the entire trajectory. Feasible solutions can also be found by simply using the SQP algorithm in Level 1 with a zero cost function. This paper discusses the formulation of the Level 1 sub-problem and the development of a prototype software tool to solve it. The Level 2 sub-problem will be discussed in a future work. Following the Level 1 formulation and solution, several look-ahead trajectory examples for the ISS are explored. In each case, the burn targeting results using the current process are compared against a feasible solution found using Level 1 in the proposed technique. Level 1 is then used to find a minimum deltaV solution given the fixed number of burns and burn TIGs. The optimal solution is compared with the previously found feasible solution to determine the deltaV (and therefore propellant) savings. The proposed technique seeks to both improve the current process for targeting ISS burns, and to add the capability to optimize ISS burns in a novel fashion. The optimal solutions found using this technique can potentially save hundreds of kilograms of propellant over the course of the ISS mission compared to feasible solutions alone. While the software tool being developed to implement this technique is specific to ISS, the concept is extensible to other long-duration, central-body orbiting missions that must perform orbit maintenance burns to meet operational trajectory constraints.

Interactive orbital proximity operations planning system instruction and training guide

NASA Technical Reports Server (NTRS)

Grunwald, Arthur J.; Ellis, Stephen R.

1994-01-01

This guide instructs users in the operation of a Proximity Operations Planning System. This system uses an interactive graphical method for planning fuel-efficient rendezvous trajectories in the multi-spacecraft environment of the space station and allows the operator to compose a multi-burn transfer trajectory between orbit initial chaser and target trajectories. The available task time (window) of the mission is predetermined and the maneuver is subject to various operational constraints, such as departure, arrival, spatial, plume impingement, and en route passage constraints. The maneuvers are described in terms of the relative motion experienced in a space station centered coordinate system. Both in-orbital plane as well as out-of-orbital plane maneuvering is considered. A number of visual optimization aids are used for assisting the operator in reaching fuel-efficient solutions. These optimization aids are based on the Primer Vector theory. The visual feedback of trajectory shapes, operational constraints, and optimization functions, provided by user-transparent and continuously active background computations, allows the operator to make fast, iterative design changes that rapidly converge to fuel-efficient solutions. The planning tool is an example of operator-assisted optimization of nonlinear cost functions.

Rapid Design of Gravity Assist Trajectories

NASA Technical Reports Server (NTRS)

Carrico, J.; Hooper, H. L.; Roszman, L.; Gramling, C.

1991-01-01

Several International Solar Terrestrial Physics (ISTP) missions require the design of complex gravity assisted trajectories in order to investigate the interaction of the solar wind with the Earth's magnetic field. These trajectories present a formidable trajectory design and optimization problem. The philosophy and methodology that enable an analyst to design and analyse such trajectories are discussed. The so called 'floating end point' targeting, which allows the inherently nonlinear multiple body problem to be solved with simple linear techniques, is described. The combination of floating end point targeting with analytic approximations with a Newton method targeter to achieve trajectory design goals quickly, even for the very sensitive double lunar swingby trajectories used by the ISTP missions, is demonstrated. A multiconic orbit integration scheme allows fast and accurate orbit propagation. A prototype software tool, Swingby, built for trajectory design and launch window analysis, is described.

Hyper-X Stage Separation Trajectory Validation Studies

NASA Technical Reports Server (NTRS)

Tartabini, Paul V.; Bose, David M.; McMinn, John D.; Martin, John G.; Strovers, Brian K.

2003-01-01

An independent twelve degree-of-freedom simulation of the X-43A separation trajectory was created with the Program to Optimize Simulated trajectories (POST II). This simulation modeled the multi-body dynamics of the X-43A and its booster and included the effect of two pyrotechnically actuated pistons used to push the vehicles apart as well as aerodynamic interaction forces and moments between the two vehicles. The simulation was developed to validate trajectory studies conducted with a 14 degree-of-freedom simulation created early in the program using the Automatic Dynamic Analysis of Mechanics Systems (ADAMS) simulation software. The POST simulation was less detailed than the official ADAMS-based simulation used by the Project, but was simpler, more concise and ran faster, while providing similar results. The increase in speed provided by the POST simulation provided the Project with an alternate analysis tool. This tool was ideal for performing separation control logic trade studies that required the running of numerous Monte Carlo trajectories.

Simulation of Trajectories for High Specific Impulse Deep Space Exploration

NASA Technical Reports Server (NTRS)

Polsgrove, Tara; Adams, Robert B.; Brady, Hugh J. (Technical Monitor)

2002-01-01

Difficulties in approximating flight times and deliverable masses for continuous thrust propulsion systems have complicated comparison and evaluation of proposed propulsion concepts. These continuous thrust propulsion systems are of interest to many groups, not the least of which are the electric propulsion and fusion communities. Several charts plotting the results of well-known trajectory simulation codes were developed and are contained in this paper. These charts illustrate the dependence of time of flight and payload ratio on jet power, initial mass, specific impulse and specific power. These charts are intended to be a tool by which people in the propulsion community can explore the possibilities of their propulsion system concepts. Trajectories were simulated using the tools VARITOP and IPOST. VARITOP is a well known trajectory optimization code that involves numerical integration based on calculus of variations. IPOST has several methods of trajectory simulation; the one used in this paper is Cowell's method for full integration of the equations of motion. The analytical method derived in the companion paper was also used to simulate the trajectory. The accuracy of this method is discussed in the paper.

Optimal weight based on energy imbalance and utility maximization

NASA Astrophysics Data System (ADS)

Sun, Ruoyan

2016-01-01

This paper investigates the optimal weight for both male and female using energy imbalance and utility maximization. Based on the difference of energy intake and expenditure, we develop a state equation that reveals the weight gain from this energy gap. We ​construct an objective function considering food consumption, eating habits and survival rate to measure utility. Through applying mathematical tools from optimal control methods and qualitative theory of differential equations, we obtain some results. For both male and female, the optimal weight is larger than the physiologically optimal weight calculated by the Body Mass Index (BMI). We also study the corresponding trajectories to steady state weight respectively. Depending on the value of a few parameters, the steady state can either be a saddle point with a monotonic trajectory or a focus with dampened oscillations.

Evaluation of some significant issues affecting trajectory and control management for air-breathing hypersonic vehicles

NASA Technical Reports Server (NTRS)

Hattis, Philip D.; Malchow, Harvey L.

1992-01-01

Horizontal takeoff airbreathing-propulsion launch vehicles require near-optimal guidance and control which takes into account performance sensitivities to atmospheric characteristics while satisfying physically-derived operational constraints. A generic trajectory/control analysis tool that deepens insight into these considerations has been applied to two versions of a winged-cone vehicle model. Information that is critical to the design and trajectory of these vehicles is derived, and several unusual characteristics of the airbreathing propulsion model are shown to have potentially substantial effects on vehicle dynamics.

Interplanetary Trajectory Design for the Asteroid Robotic Redirect Mission Alternate Approach Trade Study

NASA Technical Reports Server (NTRS)

Merrill, Raymond Gabriel; Qu, Min; Vavrina, Matthew A.; Englander, Jacob A.; Jones, Christopher A.

2014-01-01

This paper presents mission performance analysis methods and results for the Asteroid Robotic Redirect Mission (ARRM) option to capture a free standing boulder on the surface of a 100 m or larger NEA. It details the optimization and design of heliocentric low-thrust trajectories to asteroid targets for the ARRM solar electric propulsion spacecraft. Extensive searches were conducted to determine asteroid targets with large pick-up mass potential and potential observation opportunities. Interplanetary trajectory approximations were developed in method based tools for Itokawa, Bennu, 1999 JU3, and 2008 EV5 and were validated by end-to-end integrated trajectories.

OPTIMAL AIRCRAFT TRAJECTORIES FOR SPECIFIED RANGE

NASA Technical Reports Server (NTRS)

Lee, H.

1994-01-01

For an aircraft operating over a fixed range, the operating costs are basically a sum of fuel cost and time cost. While minimum fuel and minimum time trajectories are relatively easy to calculate, the determination of a minimum cost trajectory can be a complex undertaking. This computer program was developed to optimize trajectories with respect to a cost function based on a weighted sum of fuel cost and time cost. As a research tool, the program could be used to study various characteristics of optimum trajectories and their comparison to standard trajectories. It might also be used to generate a model for the development of an airborne trajectory optimization system. The program could be incorporated into an airline flight planning system, with optimum flight plans determined at takeoff time for the prevailing flight conditions. The use of trajectory optimization could significantly reduce the cost for a given aircraft mission. The algorithm incorporated in the program assumes that a trajectory consists of climb, cruise, and descent segments. The optimization of each segment is not done independently, as in classical procedures, but is performed in a manner which accounts for interaction between the segments. This is accomplished by the application of optimal control theory. The climb and descent profiles are generated by integrating a set of kinematic and dynamic equations, where the total energy of the aircraft is the independent variable. At each energy level of the climb and descent profiles, the air speed and power setting necessary for an optimal trajectory are determined. The variational Hamiltonian of the problem consists of the rate of change of cost with respect to total energy and a term dependent on the adjoint variable, which is identical to the optimum cruise cost at a specified altitude. This variable uniquely specifies the optimal cruise energy, cruise altitude, cruise Mach number, and, indirectly, the climb and descent profiles. If the optimum cruise cost is specified, an optimum trajectory can easily be generated; however, the range obtained for a particular optimum cruise cost is not known a priori. For short range flights, the program iteratively varies the optimum cruise cost until the computed range converges to the specified range. For long-range flights, iteration is unnecessary since the specified range can be divided into a cruise segment distance and full climb and descent distances. The user must supply the program with engine fuel flow rate coefficients and an aircraft aerodynamic model. The program currently includes coefficients for the Pratt-Whitney JT8D-7 engine and an aerodynamic model for the Boeing 727. Input to the program consists of the flight range to be covered and the prevailing flight conditions including pressure, temperature, and wind profiles. Information output by the program includes: optimum cruise tables at selected weights, optimal cruise quantities as a function of cruise weight and cruise distance, climb and descent profiles, and a summary of the complete synthesized optimal trajectory. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6000 series computer with a central memory requirement of approximately 100K (octal) of 60 bit words. This aircraft trajectory optimization program was developed in 1979.

Simulation Propulsion System and Trajectory Optimization

NASA Technical Reports Server (NTRS)

Hendricks, Eric S.; Falck, Robert D.; Gray, Justin S.

2017-01-01

A number of new aircraft concepts have recently been proposed which tightly couple the propulsion system design and operation with the overall vehicle design and performance characteristics. These concepts include propulsion technology such as boundary layer ingestion, hybrid electric propulsion systems, distributed propulsion systems and variable cycle engines. Initial studies examining these concepts have typically used a traditional decoupled approach to aircraft design where the aerodynamics and propulsion designs are done a-priori and tabular data is used to provide inexpensive look ups to the trajectory ana-ysis. However the cost of generating the tabular data begins to grow exponentially when newer aircraft concepts require consideration of additional operational parameters such as multiple throttle settings, angle-of-attack effects on the propulsion system, or propulsion throttle setting effects on aerodynamics. This paper proposes a new modeling approach that eliminated the need to generate tabular data, instead allowing an expensive propulsion or aerodynamic analysis to be directly integrated into the trajectory analysis model and the entire design problem optimized in a fully coupled manner. The new method is demonstrated by implementing a canonical optimal control problem, the F-4 minimum time-to-climb trajectory optimization using three relatively new analysis tools: Open M-DAO, PyCycle and Pointer. Pycycle and Pointer both provide analytic derivatives and Open MDAO enables the two tools to be combined into a coupled model that can be run in an efficient parallel manner that helps to cost the increased cost of the more expensive propulsion analysis. Results generated with this model serve as a validation of the tightly coupled design method and guide future studies to examine aircraft concepts with more complex operational dependencies for the aerodynamic and propulsion models.

Trades Between Opposition and Conjunction Class Trajectories for Early Human Missions to Mars

NASA Technical Reports Server (NTRS)

Mattfeld, Bryan; Stromgren, Chel; Shyface, Hilary; Komar, David R.; Cirillo, William; Goodliff, Kandyce

2014-01-01

Candidate human missions to Mars, including NASA's Design Reference Architecture 5.0, have focused on conjunction-class missions with long crewed durations and minimum energy trajectories to reduce total propellant requirements and total launch mass. However, in order to progressively reduce risk and gain experience in interplanetary mission operations, it may be desirable that initial human missions to Mars, whether to the surface or to Mars orbit, have shorter total crewed durations and minimal stay times at the destination. Opposition-class missions require larger total energy requirements relative to conjunction-class missions but offer the potential for much shorter mission durations, potentially reducing risk and overall systems performance requirements. This paper will present a detailed comparison of conjunction-class and opposition-class human missions to Mars vicinity with a focus on how such missions could be integrated into the initial phases of a Mars exploration campaign. The paper will present the results of a trade study that integrates trajectory/propellant analysis, element design, logistics and sparing analysis, and risk assessment to produce a comprehensive comparison of opposition and conjunction exploration mission constructs. Included in the trade study is an assessment of the risk to the crew and the trade offs between the mission duration and element, logistics, and spares mass. The analysis of the mission trade space was conducted using four simulation and analysis tools developed by NASA. Trajectory analyses for Mars destination missions were conducted using VISITOR (Versatile ImpulSive Interplanetary Trajectory OptimizeR), an in-house tool developed by NASA Langley Research Center. Architecture elements were evaluated using EXploration Architecture Model for IN-space and Earth-to-orbit (EXAMINE), a parametric modeling tool that generates exploration architectures through an integrated systems model. Logistics analysis was conducted using NASA's Human Exploration Logistics Model (HELM), and sparing allocation predictions were generated via the Exploration Maintainability Analysis Tool (EMAT), which is a probabilistic simulation engine that evaluates trades in spacecraft reliability and sparing requirements based on spacecraft system maintainability and reparability.

A Multidisciplinary Performance Analysis of a Lifting-Body Single-Stage-to-Orbit Vehicle

NASA Technical Reports Server (NTRS)

Tartabini, Paul V.; Lepsch, Roger A.; Korte, J. J.; Wurster, Kathryn E.

2000-01-01

Lockheed Martin Skunk Works (LMSW) is currently developing a single-stage-to-orbit reusable launch vehicle called VentureStar(TM) A team at NASA Langley Research Center participated with LMSW in the screening and evaluation of a number of early VentureStar(TM) configurations. The performance analyses that supported these initial studies were conducted to assess the effect of a lifting body shape, linear aerospike engine and metallic thermal protection system (TPS) on the weight and performance of the vehicle. These performance studies were performed in a multidisciplinary fashion that indirectly linked the trajectory optimization with weight estimation and aerothermal analysis tools. This approach was necessary to develop optimized ascent and entry trajectories that met all vehicle design constraints. Significant improvements in ascent performance were achieved when the vehicle flew a lifting trajectory and varied the engine mixture ratio during flight. Also, a considerable reduction in empty weight was possible by adjusting the total oxidizer-to-fuel and liftoff thrust-to-weight ratios. However, the optimal ascent flight profile had to be altered to ensure that the vehicle could be trimmed in pitch using only the flow diverting capability of the aerospike engine. Likewise, the optimal entry trajectory had to be tailored to meet TPS heating rate and transition constraints while satisfying a crossrange requirement.

Tour of Jupiter Galilean moons: Winning solution of GTOC6

NASA Astrophysics Data System (ADS)

Colasurdo, Guido; Zavoli, Alessandro; Longo, Alessandro; Casalino, Lorenzo; Simeoni, Francesco

2014-09-01

The paper presents the trajectory designed by the Italian joint team Politecnico di Torino & Sapienza Università di Roma (Team5), winner of the 6th edition of the Global Trajectory Optimization Competition (GTOC6). In the short time available in these competitions, Team5 resorted to basic knowledge, simple tools and a powerful indirect optimization procedure. The mission concerns a 4-year tour of the Jupiter Galilean moons. The paper explains the strategy that was preliminarily devised and eventually implemented by looking for a viable trajectory. The first phase is a capture that moves the spacecraft from the arrival hyperbola to a low-energy orbit around Jupiter. Six series of flybys follow; in each one the spacecraft orbits Jupiter in resonance with a single moon; criteria to construct efficient chains of resonant flybys are presented. Transfer legs move the spacecraft from resonance with a moon to another one; precise phasing of the relevant moons is required; mission opportunities in a 11-year launch window are found by assuming ballistic trajectories and coplanar circular orbits for the Jovian satellites. The actual trajectory is found by using an indirect technique.

Clustering molecular dynamics trajectories for optimizing docking experiments.

PubMed

De Paris, Renata; Quevedo, Christian V; Ruiz, Duncan D; Norberto de Souza, Osmar; Barros, Rodrigo C

2015-01-01

Molecular dynamics simulations of protein receptors have become an attractive tool for rational drug discovery. However, the high computational cost of employing molecular dynamics trajectories in virtual screening of large repositories threats the feasibility of this task. Computational intelligence techniques have been applied in this context, with the ultimate goal of reducing the overall computational cost so the task can become feasible. Particularly, clustering algorithms have been widely used as a means to reduce the dimensionality of molecular dynamics trajectories. In this paper, we develop a novel methodology for clustering entire trajectories using structural features from the substrate-binding cavity of the receptor in order to optimize docking experiments on a cloud-based environment. The resulting partition was selected based on three clustering validity criteria, and it was further validated by analyzing the interactions between 20 ligands and a fully flexible receptor (FFR) model containing a 20 ns molecular dynamics simulation trajectory. Our proposed methodology shows that taking into account features of the substrate-binding cavity as input for the k-means algorithm is a promising technique for accurately selecting ensembles of representative structures tailored to a specific ligand.

Trajectory Optimization Using Adjoint Method and Chebyshev Polynomial Approximation for Minimizing Fuel Consumption During Climb

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Hornby, Gregory; Ishihara, Abe

2013-01-01

This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.

Dynamic optimization case studies in DYNOPT tool

NASA Astrophysics Data System (ADS)

Ozana, Stepan; Pies, Martin; Docekal, Tomas

2016-06-01

Dynamic programming is typically applied to optimization problems. As the analytical solutions are generally very difficult, chosen software tools are used widely. These software packages are often third-party products bound for standard simulation software tools on the market. As typical examples of such tools, TOMLAB and DYNOPT could be effectively applied for solution of problems of dynamic programming. DYNOPT will be presented in this paper due to its licensing policy (free product under GPL) and simplicity of use. DYNOPT is a set of MATLAB functions for determination of optimal control trajectory by given description of the process, the cost to be minimized, subject to equality and inequality constraints, using orthogonal collocation on finite elements method. The actual optimal control problem is solved by complete parameterization both the control and the state profile vector. It is assumed, that the optimized dynamic model may be described by a set of ordinary differential equations (ODEs) or differential-algebraic equations (DAEs). This collection of functions extends the capability of the MATLAB Optimization Tool-box. The paper will introduce use of DYNOPT in the field of dynamic optimization problems by means of case studies regarding chosen laboratory physical educational models.

Trajectory Design for the Transiting Exoplanet Survey Satellite

NASA Technical Reports Server (NTRS)

Dichmann, Donald J.; Parker, Joel J. K.; Williams, Trevor W.; Mendelsohn, Chad R.

2014-01-01

The Transiting Exoplanet Survey Satellite (TESS) is a National Aeronautics and Space Administration (NASA) mission, scheduled to be launched in 2017. TESS will travel in a highly eccentric orbit around Earth, with initial perigee radius near 17 Earth radii (Re) and apogee radius near 59 Re. The orbit period is near 2:1 resonance with the Moon, with apogee nearly 90 degrees out-of-phase with the Moon, in a configuration that has been shown to be operationally stable. TESS will execute phasing loops followed by a lunar flyby, with a final maneuver to achieve 2:1 resonance with the Moon. The goals of a resonant orbit with long-term stability, short eclipses and limited oscillations of perigee present significant challenges to the trajectory design. To rapidly assess launch opportunities, we adapted the Schematics Window Methodology (SWM76) launch window analysis tool to assess the TESS mission constraints. To understand the long-term dynamics of such a resonant orbit in the Earth-Moon system we employed Dynamical Systems Theory in the Circular Restricted 3-Body Problem (CR3BP). For precise trajectory analysis we use a high-fidelity model and multiple shooting in the General Mission Analysis Tool (GMAT) to optimize the maneuver delta-V and meet mission constraints. Finally we describe how the techniques we have developed can be applied to missions with similar requirements. Keywords: resonant orbit, stability, lunar flyby, phasing loops, trajectory optimization

Primer Vector Optimization: Survey of Theory, new Analysis and Applications

NASA Astrophysics Data System (ADS)

Guzman

This paper presents a preliminary study in developing a set of optimization tools for orbit rendezvous, transfer and station keeping. This work is part of a large scale effort undergoing at NASA Goddard Space Flight Center and a.i. solutions, Inc. to build generic methods, which will enable missions with tight fuel budgets. Since no single optimization technique can solve efficiently all existing problems, a library of tools where the user could pick the method most suited for the particular mission is envisioned. The first trajectory optimization technique explored is Lawden's primer vector theory [Ref. 1]. Primer vector theory can be considered as a byproduct of applying Calculus of Variations (COV) techniques to the problem of minimizing the fuel usage of impulsive trajectories. For an n-impulse trajectory, it involves the solution of n-1 two-point boundary value problems. In this paper, we look at some of the different formulations of the primer vector (dependent on the frame employed and on the force model). Also, the applicability of primer vector theory is examined in effort to understand when and why the theory can fail. Specifically, since COV is based on "small variations", singularities in the linearized (variational) equations of motion along the arcs must be taken into account. These singularities are a recurring problem in analyzes that employ "small variations" [Refs. 2, 3]. For example, singularities in the (2-body problem) variational equations along elliptic arcs occur when [Ref. 4], 1) the difference between the initial and final times is a multiple of the reference orbit period, 2) the difference between the initial and final true anomalies are given by k, for k= 0, 1, 2, 3,..., note that this cover the 3) the time of flight is a minimum for the given difference in true anomaly. For the N-body problem, the situation is more complex and is still under investigation. Several examples, such as the initialization of an orbit (ascent trajectory) and rotation of the line of apsides, are utilized as test cases. Recommendations, future work, and the possible addition of other optimization techniques are also discussed. References: [1] Lawden D.F., Optimal Trajectories for Space Navigation, Butterworths, London, 1963. [2] Wilson, R.S., Howell, K.C., and, Lo, M, "Optimization of Insertion Cost for Transfer Trajectories to Libration Point Orbits", AIAA/AAS Astrodynamics Specialist Conference, AAS 99-041, Girdwood, Alaska, August 16-19, 1999. [3] Goodson, T, "Monte-Carlo Maneuver Analysis for the Microwave Anisotropy Probe", AAS/AIAA Astrodynamics Specialist Conference, AAS 01-331, Quebec City, Canada, July 30 - August 2, 2001. [4] Stern, R.G., "Singularities in the Analytic Solution of the Linearized Variational Equations of Elliptical Motion", Report RE-8, May 1964, Experimental Astronomy Lab., Massachusetts Institute of Technology, Cambridge, Massachusetts.

A Cockpit-Based Application for Traffic Aware Trajectory Optimization

NASA Technical Reports Server (NTRS)

Woods, Sharon E.; Vivona, Robert A.; Roscoe, David A.; LeFebvre, Brendan C.; Wing, David J.; Ballin, Mark G.

2013-01-01

The Traffic Aware Planner (TAP) is a cockpit-based advisory tool designed to be hosted on a Class 2 Electronic Flight Bag and developed to enable the concept of Traffic Aware Strategic Aircrew Requests (TASAR). This near-term concept provides pilots with optimized route changes that reduce fuel burn or flight time, avoids interactions with known traffic, weather and restricted airspace, and may be used by the pilots to request a trajectory change from air traffic control. TAP's internal architecture and algorithms are derived from the Autonomous Operations Planner, a flight-deck automation system developed by NASA to support research into aircraft self-separation. This paper reviews the architecture, functionality and operation of TAP.

Clustering Molecular Dynamics Trajectories for Optimizing Docking Experiments

PubMed Central

De Paris, Renata; Quevedo, Christian V.; Ruiz, Duncan D.; Norberto de Souza, Osmar; Barros, Rodrigo C.

2015-01-01

Molecular dynamics simulations of protein receptors have become an attractive tool for rational drug discovery. However, the high computational cost of employing molecular dynamics trajectories in virtual screening of large repositories threats the feasibility of this task. Computational intelligence techniques have been applied in this context, with the ultimate goal of reducing the overall computational cost so the task can become feasible. Particularly, clustering algorithms have been widely used as a means to reduce the dimensionality of molecular dynamics trajectories. In this paper, we develop a novel methodology for clustering entire trajectories using structural features from the substrate-binding cavity of the receptor in order to optimize docking experiments on a cloud-based environment. The resulting partition was selected based on three clustering validity criteria, and it was further validated by analyzing the interactions between 20 ligands and a fully flexible receptor (FFR) model containing a 20 ns molecular dynamics simulation trajectory. Our proposed methodology shows that taking into account features of the substrate-binding cavity as input for the k-means algorithm is a promising technique for accurately selecting ensembles of representative structures tailored to a specific ligand. PMID:25873944

Real-time immune-inspired optimum state-of-charge trajectory estimation using upcoming route information preview and neural networks for plug-in hybrid electric vehicles fuel economy

NASA Astrophysics Data System (ADS)

Mozaffari, Ahmad; Vajedi, Mahyar; Azad, Nasser L.

2015-06-01

The main proposition of the current investigation is to develop a computational intelligence-based framework which can be used for the real-time estimation of optimum battery state-of-charge (SOC) trajectory in plug-in hybrid electric vehicles (PHEVs). The estimated SOC trajectory can be then employed for an intelligent power management to significantly improve the fuel economy of the vehicle. The devised intelligent SOC trajectory builder takes advantage of the upcoming route information preview to achieve the lowest possible total cost of electricity and fossil fuel. To reduce the complexity of real-time optimization, the authors propose an immune system-based clustering approach which allows categorizing the route information into a predefined number of segments. The intelligent real-time optimizer is also inspired on the basis of interactions in biological immune systems, and is called artificial immune algorithm (AIA). The objective function of the optimizer is derived from a computationally efficient artificial neural network (ANN) which is trained by a database obtained from a high-fidelity model of the vehicle built in the Autonomie software. The simulation results demonstrate that the integration of immune inspired clustering tool, AIA and ANN, will result in a powerful framework which can generate a near global optimum SOC trajectory for the baseline vehicle, that is, the Toyota Prius PHEV. The outcomes of the current investigation prove that by taking advantage of intelligent approaches, it is possible to design a computationally efficient and powerful SOC trajectory builder for the intelligent power management of PHEVs.

Optimal trajectories of aircraft and spacecraft

NASA Technical Reports Server (NTRS)

Miele, A.

1990-01-01

Work done on algorithms for the numerical solutions of optimal control problems and their application to the computation of optimal flight trajectories of aircraft and spacecraft is summarized. General considerations on calculus of variations, optimal control, numerical algorithms, and applications of these algorithms to real-world problems are presented. The sequential gradient-restoration algorithm (SGRA) is examined for the numerical solution of optimal control problems of the Bolza type. Both the primal formulation and the dual formulation are discussed. Aircraft trajectories, in particular, the application of the dual sequential gradient-restoration algorithm (DSGRA) to the determination of optimal flight trajectories in the presence of windshear are described. Both take-off trajectories and abort landing trajectories are discussed. Take-off trajectories are optimized by minimizing the peak deviation of the absolute path inclination from a reference value. Abort landing trajectories are optimized by minimizing the peak drop of altitude from a reference value. Abort landing trajectories are optimized by minimizing the peak drop of altitude from a reference value. The survival capability of an aircraft in a severe windshear is discussed, and the optimal trajectories are found to be superior to both constant pitch trajectories and maximum angle of attack trajectories. Spacecraft trajectories, in particular, the application of the primal sequential gradient-restoration algorithm (PSGRA) to the determination of optimal flight trajectories for aeroassisted orbital transfer are examined. Both the coplanar case and the noncoplanar case are discussed within the frame of three problems: minimization of the total characteristic velocity; minimization of the time integral of the square of the path inclination; and minimization of the peak heating rate. The solution of the second problem is called nearly-grazing solution, and its merits are pointed out as a useful engineering compromise between energy requirements and aerodynamics heating requirements.

Method and Apparatus for Generating Flight-Optimizing Trajectories

NASA Technical Reports Server (NTRS)

Ballin, Mark G. (Inventor); Wing, David J. (Inventor)

2015-01-01

An apparatus for generating flight-optimizing trajectories for a first aircraft includes a receiver capable of receiving second trajectory information associated with at least one second aircraft. The apparatus also includes a traffic aware planner (TAP) module operably connected to the receiver to receive the second trajectory information. The apparatus also includes at least one internal input device on board the first aircraft to receive first trajectory information associated with the first aircraft and a TAP application capable of calculating an optimal trajectory for the first aircraft based at least on the first trajectory information and the second trajectory information. The optimal trajectory at least avoids conflicts between the first trajectory information and the second trajectory information.

Multi-rendezvous low-thrust trajectory optimization using costate transforming and homotopic approach

NASA Astrophysics Data System (ADS)

Chen, Shiyu; Li, Haiyang; Baoyin, Hexi

2018-06-01

This paper investigates a method for optimizing multi-rendezvous low-thrust trajectories using indirect methods. An efficient technique, labeled costate transforming, is proposed to optimize multiple trajectory legs simultaneously rather than optimizing each trajectory leg individually. Complex inner-point constraints and a large number of free variables are one main challenge in optimizing multi-leg transfers via shooting algorithms. Such a difficulty is reduced by first optimizing each trajectory leg individually. The results may be, next, utilized as an initial guess in the simultaneous optimization of multiple trajectory legs. In this paper, the limitations of similar techniques in previous research is surpassed and a homotopic approach is employed to improve the convergence efficiency of the shooting process in multi-rendezvous low-thrust trajectory optimization. Numerical examples demonstrate that newly introduced techniques are valid and efficient.

Air-breathing hypersonic vehicle guidance and control studies; An integrated trajectory/control analysis methodology: Phase 1

NASA Technical Reports Server (NTRS)

Hattis, Philip D.; Malchow, Harvey L.

1991-01-01

A tool which generates optimal trajectory/control histories in an integrated manner is generically adapted to the treatment of single-stage-to-orbit air-breathing hypersonic vehicles. The methodology is implemented as a two point boundary value problem solution technique. Its use permits an assessment of an entire near-minimum-fuel trajectory and desired control strategy from takeoff to orbit while satisfying physically derived inequality constraints and while achieving efficient propulsive mode phasing. A simpler analysis strategy that partitions the trajectory into several boundary condition matched segments is also included to construct preliminary trajectory and control history representations with less computational burden than is required for the overall flight profile assessment. A demonstration was accomplished using a tabulated example (winged-cone accelerator) vehicle model that is combined with a newly developed multidimensional cubic spline data smoothing routine. A constrained near-fuel-optimal trajectory, imposing a dynamic pressure limit of 1000 psf, was developed from horizontal takeoff to 20,000 ft/sec relative air speed while aiming for a polar orbit. Previously unspecified propulsive discontinuities were located. Flight regimes demanding rapid attitude changes were identified, dictating control effector and closed-loop controller authority was ascertained after evaluating effector use for vehicle trim. Also, inadequacies in vehicle model representations and specific subsystem models with insufficient fidelity were determined based on unusual control characteristics and/or excessive sensitivity to uncertainty.

A Time-Regularized, Multiple Gravity-Assist Low-Thrust, Bounded-Impulse Model for Trajectory Optimization

NASA Technical Reports Server (NTRS)

Ellison, Donald H.; Englander, Jacob A.; Conway, Bruce A.

2017-01-01

The multiple gravity assist low-thrust (MGALT) trajectory model combines the medium-fidelity Sims-Flanagan bounded-impulse transcription with a patched-conics flyby model and is an important tool for preliminary trajectory design. While this model features fast state propagation via Keplers equation and provides a pleasingly accurate estimation of the total mass budget for the eventual flight suitable integrated trajectory it does suffer from one major drawback, namely its temporal spacing of the control nodes. We introduce a variant of the MGALT transcription that utilizes the generalized anomaly from the universal formulation of Keplers equation as a decision variable in addition to the trajectory phase propagation time. This results in two improvements over the traditional model. The first is that the maneuver locations are equally spaced in generalized anomaly about the orbit rather than time. The second is that the Kepler propagator now has the generalized anomaly as its independent variable instead of time and thus becomes an iteration-free propagation method. The new algorithm is outlined, including the impact that this has on the computation of Jacobian entries for numerical optimization, and a motivating application problem is presented that illustrates the improvements that this model has over the traditional MGALT transcription.

A Time-Regularized Multiple Gravity-Assist Low-Thrust Bounded-Impulse Model for Trajectory Optimization

NASA Technical Reports Server (NTRS)

Ellison, Donald H.; Englander, Jacob A.; Conway, Bruce A.

2017-01-01

The multiple gravity assist low-thrust (MGALT) trajectory model combines the medium-fidelity Sims-Flanagan bounded-impulse transcription with a patched-conics flyby model and is an important tool for preliminary trajectory design. While this model features fast state propagation via Kepler's equation and provides a pleasingly accurate estimation of the total mass budget for the eventual flight-suitable integrated trajectory it does suffer from one major drawback, namely its temporal spacing of the control nodes. We introduce a variant of the MGALT transcription that utilizes the generalized anomaly from the universal formulation of Kepler's equation as a decision variable in addition to the trajectory phase propagation time. This results in two improvements over the traditional model. The first is that the maneuver locations are equally spaced in generalized anomaly about the orbit rather than time. The second is that the Kepler propagator now has the generalized anomaly as its independent variable instead of time and thus becomes an iteration-free propagation method. The new algorithm is outlined, including the impact that this has on the computation of Jacobian entries for numerical optimization, and a motivating application problem is presented that illustrates the improvements that this model has over the traditional MGALT transcription.

An automated method to find transition states using chemical dynamics simulations.

PubMed

Martínez-Núñez, Emilio

2015-02-05

A procedure to automatically find the transition states (TSs) of a molecular system (MS) is proposed. It has two components: high-energy chemical dynamics simulations (CDS), and an algorithm that analyzes the geometries along the trajectories to find reactive pathways. Two levels of electronic structure calculations are involved: a low level (LL) is used to integrate the trajectories and also to optimize the TSs, and a higher level (HL) is used to reoptimize the structures. The method has been tested in three MSs: formaldehyde, formic acid (FA), and vinyl cyanide (VC), using MOPAC2012 and Gaussian09 to run the LL and HL calculations, respectively. Both the efficacy and efficiency of the method are very good, with around 15 TS structures optimized every 10 trajectories, which gives a total of 7, 12, and 83 TSs for formaldehyde, FA, and VC, respectively. The use of CDS makes it a powerful tool to unveil possible nonstatistical behavior of the system under study. © 2014 Wiley Periodicals, Inc.

Improved Propulsion Modeling for Low-Thrust Trajectory Optimization

NASA Technical Reports Server (NTRS)

Knittel, Jeremy M.; Englander, Jacob A.; Ozimek, Martin T.; Atchison, Justin A.; Gould, Julian J.

2017-01-01

Low-thrust trajectory design is tightly coupled with spacecraft systems design. In particular, the propulsion and power characteristics of a low-thrust spacecraft are major drivers in the design of the optimal trajectory. Accurate modeling of the power and propulsion behavior is essential for meaningful low-thrust trajectory optimization. In this work, we discuss new techniques to improve the accuracy of propulsion modeling in low-thrust trajectory optimization while maintaining the smooth derivatives that are necessary for a gradient-based optimizer. The resulting model is significantly more realistic than the industry standard and performs well inside an optimizer. A variety of deep-space trajectory examples are presented.

Optimal short-range trajectories for helicopters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slater, G.L.; Erzberger, H.

1982-12-01

An optimal flight path algorithm using a simplified altitude state model and a priori climb cruise descent flight profile was developed and applied to determine minimum fuel and minimum cost trajectories for a helicopter flying a fixed range trajectory. In addition, a method was developed for obtaining a performance model in simplified form which is based on standard flight manual data and which is applicable to the computation of optimal trajectories. The entire performance optimization algorithm is simple enough that on line trajectory optimization is feasible with a relatively small computer. The helicopter model used is the Silorsky S-61N. Themore » results show that for this vehicle the optimal flight path and optimal cruise altitude can represent a 10% fuel saving on a minimum fuel trajectory. The optimal trajectories show considerable variability because of helicopter weight, ambient winds, and the relative cost trade off between time and fuel. In general, reasonable variations from the optimal velocities and cruise altitudes do not significantly degrade the optimal cost. For fuel optimal trajectories, the optimum cruise altitude varies from the maximum (12,000 ft) to the minimum (0 ft) depending on helicopter weight.« less

Near-Earth object intercept trajectory design for planetary defense

NASA Astrophysics Data System (ADS)

Vardaxis, George; Wie, Bong

2014-08-01

Tracking the orbit of asteroids and planning for asteroid missions have ceased to be a simple exercise, and become more of a necessity, as the number of identified potentially hazardous near-Earth asteroids increases. Several software tools such as Mystic, MALTO, Copernicus, SNAP, OTIS, and GMAT have been developed by NASA for spacecraft trajectory optimization and mission design. However, this paper further expands upon the development and validation of an Asteroid Mission Design Software Tool (AMiDST), through the use of approach and post-encounter orbital variations and analytic keyhole theory. Combining these new capabilities with that of a high-precision orbit propagator, this paper describes fictional mission trajectory design examples of using AMiDST as applied to a fictitious asteroid 2013 PDC-E. During the 2013 IAA Planetary Defense Conference, the asteroid 2013 PDC-E was used for an exercise where participants simulated the decision-making process for developing deflection and civil defense responses to a hypothetical asteroid threat.

MIDAS - Mission design and analysis software for the optimization of ballistic interplanetary trajectories

NASA Technical Reports Server (NTRS)

Sauer, Carl G., Jr.

1989-01-01

A patched conic trajectory optimization program MIDAS is described that was developed to investigate a wide variety of complex ballistic heliocentric transfer trajectories. MIDAS includes the capability of optimizing trajectory event times such as departure date, arrival date, and intermediate planetary flyby dates and is able to both add and delete deep space maneuvers when dictated by the optimization process. Both powered and unpowered flyby or gravity assist trajectories of intermediate bodies can be handled and capability is included to optimize trajectories having a rendezvous with an intermediate body such as for a sample return mission. Capability is included in the optimization process to constrain launch energy and launch vehicle parking orbit parameters.

Fast optimization of glide vehicle reentry trajectory based on genetic algorithm

NASA Astrophysics Data System (ADS)

Jia, Jun; Dong, Ruixing; Yuan, Xuejun; Wang, Chuangwei

2018-02-01

An optimization method of reentry trajectory based on genetic algorithm is presented to meet the need of reentry trajectory optimization for glide vehicle. The dynamic model for the glide vehicle during reentry period is established. Considering the constraints of heat flux, dynamic pressure, overload etc., the optimization of reentry trajectory is investigated by utilizing genetic algorithm. The simulation shows that the method presented by this paper is effective for the optimization of reentry trajectory of glide vehicle. The efficiency and speed of this method is comparative with the references. Optimization results meet all constraints, and the on-line fast optimization is potential by pre-processing the offline samples.

Survey of optimization techniques for nonlinear spacecraft trajectory searches

NASA Technical Reports Server (NTRS)

Wang, Tseng-Chan; Stanford, Richard H.; Sunseri, Richard F.; Breckheimer, Peter J.

1988-01-01

Mathematical analysis of the optimal search of a nonlinear spacecraft trajectory to arrive at a set of desired targets is presented. A high precision integrated trajectory program and several optimization software libraries are used to search for a converged nonlinear spacecraft trajectory. Several examples for the Galileo Jupiter Orbiter and the Ocean Topography Experiment (TOPEX) are presented that illustrate a variety of the optimization methods used in nonlinear spacecraft trajectory searches.

Preparing GMAT for Operational Maneuver Planning of the Advanced Composition Explorer (ACE)

NASA Technical Reports Server (NTRS)

Qureshi, Rizwan Hamid; Hughes, Steven P.

2014-01-01

The General Mission Analysis Tool (GMAT) is an open-source space mission design, analysis and trajectory optimization tool. GMAT is developed by a team of NASA, private industry, public and private contributors. GMAT is designed to model, optimize and estimate spacecraft trajectories in flight regimes ranging from low Earth orbit to lunar applications, interplanetary trajectories and other deep space missions. GMAT has also been flight qualified to support operational maneuver planning for the Advanced Composition Explorer (ACE) mission. ACE was launched in August, 1997 and is orbiting the Sun-Earth L1 libration point. The primary science objective of ACE is to study the composition of both the solar wind and the galactic cosmic rays. Operational orbit determination, maneuver operations and product generation for ACE are conducted by NASA Goddard Space Flight Center (GSFC) Flight Dynamics Facility (FDF). This paper discusses the entire engineering lifecycle and major operational certification milestones that GMAT successfully completed to obtain operational certification for the ACE mission. Operational certification milestones such as gathering of the requirements for ACE operational maneuver planning, gap analysis, test plans and procedures development, system design, pre-shadow operations, training to FDF ACE maneuver planners, shadow operations, Test Readiness Review (TRR) and finally Operational Readiness Review (ORR) are discussed. These efforts have demonstrated that GMAT is flight quality software ready to support ACE mission operations in the FDF.

Preliminary Analysis of Low-Thrust Gravity Assist Trajectories by An Inverse Method and a Global Optimization Technique.

NASA Astrophysics Data System (ADS)

de Pascale, P.; Vasile, M.; Casotto, S.

The design of interplanetary trajectories requires the solution of an optimization problem, which has been traditionally solved by resorting to various local optimization techniques. All such approaches, apart from the specific method employed (direct or indirect), require an initial guess, which deeply influences the convergence to the optimal solution. The recent developments in low-thrust propulsion have widened the perspectives of exploration of the Solar System, while they have at the same time increased the difficulty related to the trajectory design process. Continuous thrust transfers, typically characterized by multiple spiraling arcs, have a broad number of design parameters and thanks to the flexibility offered by such engines, they typically turn out to be characterized by a multi-modal domain, with a consequent larger number of optimal solutions. Thus the definition of the first guesses is even more challenging, particularly for a broad search over the design parameters, and it requires an extensive investigation of the domain in order to locate the largest number of optimal candidate solutions and possibly the global optimal one. In this paper a tool for the preliminary definition of interplanetary transfers with coast-thrust arcs and multiple swing-bys is presented. Such goal is achieved combining a novel methodology for the description of low-thrust arcs, with a global optimization algorithm based on a hybridization of an evolutionary step and a deterministic step. Low thrust arcs are described in a 3D model in order to account the beneficial effects of low-thrust propulsion for a change of inclination, resorting to a new methodology based on an inverse method. The two-point boundary values problem (TPBVP) associated with a thrust arc is solved by imposing a proper parameterized evolution of the orbital parameters, by which, the acceleration required to follow the given trajectory with respect to the constraints set is obtained simply through algebraic computation. By this method a low-thrust transfer satisfying the boundary conditions on position and velocity can be quickly assessed, with low computational effort since no numerical propagation is required. The hybrid global optimization algorithm is made of a double step. Through the evolutionary search a large number of optima, and eventually the global one, are located, while the deterministic step consists of a branching process that exhaustively partitions the domain in order to have an extensive characterization of such a complex space of solutions. Furthermore, the approach implements a novel direct constraint-handling technique allowing the treatment of mixed-integer nonlinear programming problems (MINLP) typical of multiple swingby trajectories. A low-thrust transfer to Mars is studied as a test bed for the low-thrust model, thus presenting the main characteristics of the different shapes proposed and the features of the possible sub-arcs segmentations between two planets with respect to different objective functions: minimum time and minimum fuel consumption transfers. Other various test cases are also shown and further optimized, proving the effective capability of the proposed tool.

Finite burn maneuver modeling for a generalized spacecraft trajectory design and optimization system.

PubMed

Ocampo, Cesar

2004-05-01

The modeling, design, and optimization of finite burn maneuvers for a generalized trajectory design and optimization system is presented. A generalized trajectory design and optimization system is a system that uses a single unified framework that facilitates the modeling and optimization of complex spacecraft trajectories that may operate in complex gravitational force fields, use multiple propulsion systems, and involve multiple spacecraft. The modeling and optimization issues associated with the use of controlled engine burn maneuvers of finite thrust magnitude and duration are presented in the context of designing and optimizing a wide class of finite thrust trajectories. Optimal control theory is used examine the optimization of these maneuvers in arbitrary force fields that are generally position, velocity, mass, and are time dependent. The associated numerical methods used to obtain these solutions involve either, the solution to a system of nonlinear equations, an explicit parameter optimization method, or a hybrid parameter optimization that combines certain aspects of both. The theoretical and numerical methods presented here have been implemented in copernicus, a prototype trajectory design and optimization system under development at the University of Texas at Austin.

Analysis of Video-Based Microscopic Particle Trajectories Using Kalman Filtering

PubMed Central

Wu, Pei-Hsun; Agarwal, Ashutosh; Hess, Henry; Khargonekar, Pramod P.; Tseng, Yiider

2010-01-01

Abstract The fidelity of the trajectories obtained from video-based particle tracking determines the success of a variety of biophysical techniques, including in situ single cell particle tracking and in vitro motility assays. However, the image acquisition process is complicated by system noise, which causes positioning error in the trajectories derived from image analysis. Here, we explore the possibility of reducing the positioning error by the application of a Kalman filter, a powerful algorithm to estimate the state of a linear dynamic system from noisy measurements. We show that the optimal Kalman filter parameters can be determined in an appropriate experimental setting, and that the Kalman filter can markedly reduce the positioning error while retaining the intrinsic fluctuations of the dynamic process. We believe the Kalman filter can potentially serve as a powerful tool to infer a trajectory of ultra-high fidelity from noisy images, revealing the details of dynamic cellular processes. PMID:20550894

Performance Analysis and Design Synthesis (PADS) computer program. Volume 1: Formulation

NASA Technical Reports Server (NTRS)

1972-01-01

The program formulation for PADS computer program is presented. It can size launch vehicles in conjunction with calculus-of-variations optimal trajectories and can also be used as a general-purpose branched trajectory optimization program. In the former use, it has the Space Shuttle Synthesis Program as well as a simplified stage weight module for optimally sizing manned recoverable launch vehicles. For trajectory optimization alone or with sizing, PADS has two trajectory modules. The first trajectory module uses the method of steepest descent; the second employs the method of quasilinearization, which requires a starting solution from the first trajectory module.

Low-Thrust Trajectory Optimization with Simplified SQP Algorithm

NASA Technical Reports Server (NTRS)

Parrish, Nathan L.; Scheeres, Daniel J.

2017-01-01

The problem of low-thrust trajectory optimization in highly perturbed dynamics is a stressing case for many optimization tools. Highly nonlinear dynamics and continuous thrust are each, separately, non-trivial problems in the field of optimal control, and when combined, the problem is even more difficult. This paper de-scribes a fast, robust method to design a trajectory in the CRTBP (circular restricted three body problem), beginning with no or very little knowledge of the system. The approach is inspired by the SQP (sequential quadratic programming) algorithm, in which a general nonlinear programming problem is solved via a sequence of quadratic problems. A few key simplifications make the algorithm presented fast and robust to initial guess: a quadratic cost function, neglecting the line search step when the solution is known to be far away, judicious use of end-point constraints, and mesh refinement on multiple shooting with fixed-step integration.In comparison to the traditional approach of plugging the problem into a “black-box” NLP solver, the methods shown converge even when given no knowledge of the solution at all. It was found that the only piece of information that the user needs to provide is a rough guess for the time of flight, as the transfer time guess will dictate which set of local solutions the algorithm could converge on. This robustness to initial guess is a compelling feature, as three-body orbit transfers are challenging to design with intuition alone. Of course, if a high-quality initial guess is available, the methods shown are still valid.We have shown that endpoints can be efficiently constrained to lie on 3-body repeating orbits, and that time of flight can be optimized as well. When optimizing the endpoints, we must make a trade between converging quickly on sub-optimal endpoints or converging more slowly on end-points that are arbitrarily close to optimal. It is easy for the mission design engineer to adjust this trade based on the problem at hand.The biggest limitation to the algorithm at this point is that multi-revolution transfers (greater than 2 revolutions) do not work nearly as well. This restriction comes in because the relationship between node 1 and node N becomes increasingly nonlinear as the angular distance grows. Trans-fers with more than about 1.5 complete revolutions generally require the line search to improve convergence. Future work includes: Comparison of this algorithm with other established tools; improvements to how multiple-revolution transfers are handled; parallelization of the Jacobian computation; in-creased efficiency for the line search; and optimization of many more trajectories between a variety of 3-body orbits.

Strategies and trajectories of coral reef fish larvae optimizing self-recruitment.

PubMed

Irisson, Jean-Olivier; LeVan, Anselme; De Lara, Michel; Planes, Serge

2004-03-21

Like many marine organisms, most coral reef fishes have a dispersive larval phase. The fate of this phase is of great concern for their ecology as it may determine population demography and connectivity. As direct study of the larval phase is difficult, we tackle the question of dispersion from an opposite point of view and study self-recruitment. In this paper, we propose a mathematical model of the pelagic phase, parameterized by a limited number of factors (currents, predator and prey distributions, energy budgets) and which focuses on the behavioral response of the larvae to these factors. We evaluate optimal behavioral strategies of the larvae (i.e. strategies that maximize the probability of return to the natal reef) and examine the trajectories of dispersal that they induce. Mathematically, larval behavior is described by a controlled Markov process. A strategy induces a sequence, indexed by time steps, of "decisions" (e.g. looking for food, swimming in a given direction). Biological, physical and topographic constraints are captured through the transition probabilities and the sets of possible decisions. Optimal strategies are found by means of the so-called stochastic dynamic programming equation. A computer program is developed and optimal decisions and trajectories are numerically derived. We conclude that this technique can be considered as a good tool to represent plausible larval behaviors and that it has great potential in terms of theoretical investigations and also for field applications.

Parametric Study of Biconic Re-Entry Vehicles

NASA Technical Reports Server (NTRS)

Steele, Bryan; Banks, Daniel W.; Whitmore, Stephen A.

2007-01-01

An optimization based on hypersonic aerodynamic performance and volumetric efficiency was accomplished for a range of biconic configurations. Both axisymmetric and quasi-axisymmetric geometries (bent and flattened) were analyzed. The aerodynamic optimization wag based on hypersonic simple Incidence angle analysis tools. The range of configurations included those suitable for r lunar return trajectory with a lifting aerocapture at Earth and an overall volume that could support a nominal crew. The results yielded five configurations that had acceptable aerodynamic performance and met overall geometry and size limitations

Four-body trajectory optimization

NASA Technical Reports Server (NTRS)

Pu, C. L.; Edelbaum, T. N.

1974-01-01

A comprehensive optimization program has been developed for computing fuel-optimal trajectories between the earth and a point in the sun-earth-moon system. It presents methods for generating fuel optimal two-impulse trajectories which may originate at the earth or a point in space and fuel optimal three-impulse trajectories between two points in space. The extrapolation of the state vector and the computation of the state transition matrix are accomplished by the Stumpff-Weiss method. The cost and constraint gradients are computed analytically in terms of the terminal state and the state transition matrix. The 4-body Lambert problem is solved by using the Newton-Raphson method. An accelerated gradient projection method is used to optimize a 2-impulse trajectory with terminal constraint. The Davidon's Variance Method is used both in the accelerated gradient projection method and the outer loop of a 3-impulse trajectory optimization problem.

Development of Complexity Science and Technology Tools for NextGen Airspace Research and Applications

NASA Technical Reports Server (NTRS)

Holmes, Bruce J.; Sawhill, Bruce K.; Herriot, James; Seehart, Ken; Zellweger, Dres; Shay, Rick

2012-01-01

The objective of this research by NextGen AeroSciences, LLC is twofold: 1) to deliver an initial "toolbox" of algorithms, agent-based structures, and method descriptions for introducing trajectory agency as a methodology for simulating and analyzing airspace states, including bulk properties of large numbers of heterogeneous 4D aircraft trajectories in a test airspace -- while maintaining or increasing system safety; and 2) to use these tools in a test airspace to identify possible phase transition structure to predict when an airspace will approach the limits of its capacity. These 4D trajectories continuously replan their paths in the presence of noise and uncertainty while optimizing performance measures and performing conflict detection and resolution. In this approach, trajectories are represented as extended objects endowed with pseudopotential, maintaining time and fuel-efficient paths by bending just enough to accommodate separation while remaining inside of performance envelopes. This trajectory-centric approach differs from previous aircraft-centric distributed approaches to deconfliction. The results of this project are the following: 1) we delivered a toolbox of algorithms, agent-based structures and method descriptions as pseudocode; and 2) we corroborated the existence of phase transition structure in simulation with the addition of "early warning" detected prior to "full" airspace. This research suggests that airspace "fullness" can be anticipated and remedied before the airspace becomes unsafe.

An Expert System-Driven Method for Parametric Trajectory Optimization During Conceptual Design

NASA Technical Reports Server (NTRS)

Dees, Patrick D.; Zwack, Mathew R.; Steffens, Michael; Edwards, Stephen; Diaz, Manuel J.; Holt, James B.

2015-01-01

During the early phases of engineering design, the costs committed are high, costs incurred are low, and the design freedom is high. It is well documented that decisions made in these early design phases drive the entire design's life cycle cost. In a traditional paradigm, key design decisions are made when little is known about the design. As the design matures, design changes become more difficult in both cost and schedule to enact. The current capability-based paradigm, which has emerged because of the constrained economic environment, calls for the infusion of knowledge usually acquired during later design phases into earlier design phases, i.e. bringing knowledge acquired during preliminary and detailed design into pre-conceptual and conceptual design. An area of critical importance to launch vehicle design is the optimization of its ascent trajectory, as the optimal trajectory will be able to take full advantage of the launch vehicle's capability to deliver a maximum amount of payload into orbit. Hence, the optimal ascent trajectory plays an important role in the vehicle's affordability posture yet little of the information required to successfully optimize a trajectory is known early in the design phase. Thus, the current paradigm of optimizing ascent trajectories involves generating point solutions for every change in a vehicle's design parameters. This is often a very tedious, manual, and time-consuming task for the analysts. Moreover, the trajectory design space is highly non-linear and multi-modal due to the interaction of various constraints. When these obstacles are coupled with the Program to Optimize Simulated Trajectories (POST), an industry standard program to optimize ascent trajectories that is difficult to use, expert trajectory analysts are required to effectively optimize a vehicle's ascent trajectory. Over the course of this paper, the authors discuss a methodology developed at NASA Marshall's Advanced Concepts Office to address these issues. The methodology is two-fold: first, capture the heuristics developed by human analysts over their many years of experience; and secondly, leverage the power of modern computing to evaluate multiple trajectories simultaneously and therefore enable the exploration of the trajectory's design space early during the pre- conceptual and conceptual phases of design. This methodology is coupled with design of experiments in order to train surrogate models, which enables trajectory design space visualization and parametric optimal ascent trajectory information to be available when early design decisions are being made.

Optimal trajectories for the aeroassisted flight experiment, 1988-89

NASA Technical Reports Server (NTRS)

Miele, A.

1989-01-01

Research is summarized on optimal trajectories for the aeroassisted flight experiment, performed by the Aero-Astronautics Group of Rice University during the period 1988 through 1989. This research includes the following topics: (1) equations of motion in an Earth-fixed system; (2) equations of motion in an inertial system; (3) formultion of the optimal trajectory problem; (4) results on the optimal trajectory problem; and (5) guidance implications.

Automatic design of fiber-reinforced soft actuators for trajectory matching

NASA Astrophysics Data System (ADS)

Connolly, Fionnuala; Walsh, Conor J.; Bertoldi, Katia

2017-01-01

Soft actuators are the components responsible for producing motion in soft robots. Although soft actuators have allowed for a variety of innovative applications, there is a need for design tools that can help to efficiently and systematically design actuators for particular functions. Mathematical modeling of soft actuators is an area that is still in its infancy but has the potential to provide quantitative insights into the response of the actuators. These insights can be used to guide actuator design, thus accelerating the design process. Here, we study fluid-powered fiber-reinforced actuators, because these have previously been shown to be capable of producing a wide range of motions. We present a design strategy that takes a kinematic trajectory as its input and uses analytical modeling based on nonlinear elasticity and optimization to identify the optimal design parameters for an actuator that will follow this trajectory upon pressurization. We experimentally verify our modeling approach, and finally we demonstrate how the strategy works, by designing actuators that replicate the motion of the index finger and thumb.

Automatic design of fiber-reinforced soft actuators for trajectory matching

PubMed Central

Connolly, Fionnuala; Walsh, Conor J.; Bertoldi, Katia

2017-01-01

Soft actuators are the components responsible for producing motion in soft robots. Although soft actuators have allowed for a variety of innovative applications, there is a need for design tools that can help to efficiently and systematically design actuators for particular functions. Mathematical modeling of soft actuators is an area that is still in its infancy but has the potential to provide quantitative insights into the response of the actuators. These insights can be used to guide actuator design, thus accelerating the design process. Here, we study fluid-powered fiber-reinforced actuators, because these have previously been shown to be capable of producing a wide range of motions. We present a design strategy that takes a kinematic trajectory as its input and uses analytical modeling based on nonlinear elasticity and optimization to identify the optimal design parameters for an actuator that will follow this trajectory upon pressurization. We experimentally verify our modeling approach, and finally we demonstrate how the strategy works, by designing actuators that replicate the motion of the index finger and thumb. PMID:27994133

Automatic design of fiber-reinforced soft actuators for trajectory matching.

PubMed

Connolly, Fionnuala; Walsh, Conor J; Bertoldi, Katia

2017-01-03

Soft actuators are the components responsible for producing motion in soft robots. Although soft actuators have allowed for a variety of innovative applications, there is a need for design tools that can help to efficiently and systematically design actuators for particular functions. Mathematical modeling of soft actuators is an area that is still in its infancy but has the potential to provide quantitative insights into the response of the actuators. These insights can be used to guide actuator design, thus accelerating the design process. Here, we study fluid-powered fiber-reinforced actuators, because these have previously been shown to be capable of producing a wide range of motions. We present a design strategy that takes a kinematic trajectory as its input and uses analytical modeling based on nonlinear elasticity and optimization to identify the optimal design parameters for an actuator that will follow this trajectory upon pressurization. We experimentally verify our modeling approach, and finally we demonstrate how the strategy works, by designing actuators that replicate the motion of the index finger and thumb.

An Energy-Aware Trajectory Optimization Layer for sUAS

NASA Astrophysics Data System (ADS)

Silva, William A.

The focus of this work is the implementation of an energy-aware trajectory optimization algorithm that enables small unmanned aircraft systems (sUAS) to operate in unknown, dynamic severe weather environments. The software is designed as a component of an Energy-Aware Dynamic Data Driven Application System (EA-DDDAS) for sUAS. This work addresses the challenges of integrating and executing an online trajectory optimization algorithm during mission operations in the field. Using simplified aircraft kinematics, the energy-aware algorithm enables extraction of kinetic energy from measured winds to optimize thrust use and endurance during flight. The optimization layer, based upon a nonlinear program formulation, extracts energy by exploiting strong wind velocity gradients in the wind field, a process known as dynamic soaring. The trajectory optimization layer extends the energy-aware path planner developed by Wenceslao Shaw-Cortez te{Shaw-cortez2013} to include additional mission configurations, simulations with a 6-DOF model, and validation of the system with flight testing in June 2015 in Lubbock, Texas. The trajectory optimization layer interfaces with several components within the EA-DDDAS to provide an sUAS with optimal flight trajectories in real-time during severe weather. As a result, execution timing, data transfer, and scalability are considered in the design of the software. Severe weather also poses a measure of unpredictability to the system with respect to communication between systems and available data resources during mission operations. A heuristic mission tree with different cost functions and constraints is implemented to provide a level of adaptability to the optimization layer. Simulations and flight experiments are performed to assess the efficacy of the trajectory optimization layer. The results are used to assess the feasibility of flying dynamic soaring trajectories with existing controllers as well as to verify the interconnections between EA-DDDAS components. Results also demonstrate the usage of the trajectory optimization layer in conjunction with a lattice-based path planner as a method of guiding the optimization layer and stitching together subsequent trajectories.

Optimal control and optimal trajectories of regional macroeconomic dynamics based on the Pontryagin maximum principle

NASA Astrophysics Data System (ADS)

Bulgakov, V. K.; Strigunov, V. V.

2009-05-01

The Pontryagin maximum principle is used to prove a theorem concerning optimal control in regional macroeconomics. A boundary value problem for optimal trajectories of the state and adjoint variables is formulated, and optimal curves are analyzed. An algorithm is proposed for solving the boundary value problem of optimal control. The performance of the algorithm is demonstrated by computing an optimal control and the corresponding optimal trajectories.

Four-body trajectory optimization

NASA Technical Reports Server (NTRS)

Pu, C. L.; Edelbaum, T. N.

1973-01-01

A collection of typical three-body trajectories from the L1 libration point on the sun-earth line to the earth is presented. These trajectories in the sun-earth system are grouped into four distinct families which differ in transfer time and delta V requirements. Curves showing the variations of delta V with respect to transfer time, and typical two and three-impulse primer vector histories, are included. The development of a four-body trajectory optimization program to compute fuel optimal trajectories between the earth and a point in the sun-earth-moon system are also discussed. Methods for generating fuel optimal two-impulse trajectories which originate at the earth or a point in space, and fuel optimal three-impulse trajectories between two points in space, are presented. A brief qualitative comparison of these methods is given. An example of a four-body two-impulse transfer from the Li libration point to the earth is included.

A Robot Trajectory Optimization Approach for Thermal Barrier Coatings Used for Free-Form Components

NASA Astrophysics Data System (ADS)

Cai, Zhenhua; Qi, Beichun; Tao, Chongyuan; Luo, Jie; Chen, Yuepeng; Xie, Changjun

2017-10-01

This paper is concerned with a robot trajectory optimization approach for thermal barrier coatings. As the requirements of high reproducibility of complex workpieces increase, an optimal thermal spraying trajectory should not only guarantee an accurate control of spray parameters defined by users (e.g., scanning speed, spray distance, scanning step, etc.) to achieve coating thickness homogeneity but also help to homogenize the heat transfer distribution on the coating surface. A mesh-based trajectory generation approach is introduced in this work to generate path curves on a free-form component. Then, two types of meander trajectories are generated by performing a different connection method. Additionally, this paper presents a research approach for introducing the heat transfer analysis into the trajectory planning process. Combining heat transfer analysis with trajectory planning overcomes the defects of traditional trajectory planning methods (e.g., local over-heating), which helps form the uniform temperature field by optimizing the time sequence of path curves. The influence of two different robot trajectories on the process of heat transfer is estimated by coupled FEM models which demonstrates the effectiveness of the presented optimization approach.

Optimal solar sail planetocentric trajectories

NASA Technical Reports Server (NTRS)

Sackett, L. L.

1977-01-01

The analysis of solar sail planetocentric optimal trajectory problem is described. A computer program was produced to calculate optimal trajectories for a limited performance analysis. A square sail model is included and some consideration is given to a heliogyro sail model. Orbit to a subescape point and orbit to orbit transfer are considered. Trajectories about the four inner planets can be calculated and shadowing, oblateness, and solar motion may be included. Equinoctial orbital elements are used to avoid the classical singularities, and the method of averaging is applied to increase computational speed. Solution of the two-point boundary value problem which arises from the application of optimization theory is accomplished with a Newton procedure. Time optimal trajectories are emphasized, but a penalty function has been considered to prevent trajectories which intersect a planet's surface.

An adaptive reentry guidance method considering the influence of blackout zone

NASA Astrophysics Data System (ADS)

Wu, Yu; Yao, Jianyao; Qu, Xiangju

2018-01-01

Reentry guidance has been researched as a popular topic because it is critical for a successful flight. In view that the existing guidance methods do not take into account the accumulated navigation error of Inertial Navigation System (INS) in the blackout zone, in this paper, an adaptive reentry guidance method is proposed to obtain the optimal reentry trajectory quickly with the target of minimum aerodynamic heating rate. The terminal error in position and attitude can be also reduced with the proposed method. In this method, the whole reentry guidance task is divided into two phases, i.e., the trajectory updating phase and the trajectory planning phase. In the first phase, the idea of model predictive control (MPC) is used, and the receding optimization procedure ensures the optimal trajectory in the next few seconds. In the trajectory planning phase, after the vehicle has flown out of the blackout zone, the optimal reentry trajectory is obtained by online planning to adapt to the navigation information. An effective swarm intelligence algorithm, i.e. pigeon inspired optimization (PIO) algorithm, is applied to obtain the optimal reentry trajectory in both of the two phases. Compared to the trajectory updating method, the proposed method can reduce the terminal error by about 30% considering both the position and attitude, especially, the terminal error of height has almost been eliminated. Besides, the PIO algorithm performs better than the particle swarm optimization (PSO) algorithm both in the trajectory updating phase and the trajectory planning phases.

Performance Analysis and Design Synthesis (PADS) computer program. Volume 2: Program description, part 1

NASA Technical Reports Server (NTRS)

1972-01-01

The Performance Analysis and Design Synthesis (PADS) computer program has a two-fold purpose. It can size launch vehicles in conjunction with calculus-of-variations optimal trajectories and can also be used as a general-purpose branched trajectory optimization program. In the former use, it has the Space Shuttle Synthesis Program as well as a simplified stage weight module for optimally sizing manned recoverable launch vehicles. For trajectory optimization alone or with sizing, PADS has two trajectory modules. The first trajectory module uses the method of steepest descent; the second employs the method of quasilinearization, which requires a starting solution from the first trajectory module. For Volume 1 see N73-13199.

Performance Analysis and Design Synthesis (PADS) computer program. Volume 3: User manual

NASA Technical Reports Server (NTRS)

1972-01-01

The two-fold purpose of the Performance Analysis and Design Synthesis (PADS) computer program is discussed. The program can size launch vehicles in conjunction with calculus-of-variations optimal trajectories and can also be used as a general purpose branched trajectory optimization program. For trajectory optimization alone or with sizing, PADS has two trajectory modules. The first trajectory module uses the method of steepest descent. The second module uses the method of quasi-linearization, which requires a starting solution from the first trajectory module.

Trajectory Optimization for Missions to Small Bodies with a Focus on Scientific Merit.

PubMed

Englander, Jacob A; Vavrina, Matthew A; Lim, Lucy F; McFadden, Lucy A; Rhoden, Alyssa R; Noll, Keith S

2017-01-01

Trajectory design for missions to small bodies is tightly coupled both with the selection of targets for a mission and with the choice of spacecraft power, propulsion, and other hardware. Traditional methods of trajectory optimization have focused on finding the optimal trajectory for an a priori selection of destinations and spacecraft parameters. Recent research has expanded the field of trajectory optimization to multidisciplinary systems optimization that includes spacecraft parameters. The logical next step is to extend the optimization process to include target selection based not only on engineering figures of merit but also scientific value. This paper presents a new technique to solve the multidisciplinary mission optimization problem for small-bodies missions, including classical trajectory design, the choice of spacecraft power and propulsion systems, and also the scientific value of the targets. This technique, when combined with modern parallel computers, enables a holistic view of the small body mission design process that previously required iteration among several different design processes.

Trajectory optimization for lunar rover performing vertical takeoff vertical landing maneuvers in the presence of terrain

NASA Astrophysics Data System (ADS)

Ma, Lin; Wang, Kexin; Xu, Zuhua; Shao, Zhijiang; Song, Zhengyu; Biegler, Lorenz T.

2018-05-01

This study presents a trajectory optimization framework for lunar rover performing vertical takeoff vertical landing (VTVL) maneuvers in the presence of terrain using variable-thrust propulsion. First, a VTVL trajectory optimization problem with three-dimensional kinematics and dynamics model, boundary conditions, and path constraints is formulated. Then, a finite-element approach transcribes the formulated trajectory optimization problem into a nonlinear programming (NLP) problem solved by a highly efficient NLP solver. A homotopy-based backtracking strategy is applied to enhance the convergence in solving the formulated VTVL trajectory optimization problem. The optimal thrust solution typically has a "bang-bang" profile considering that bounds are imposed on the magnitude of engine thrust. An adaptive mesh refinement strategy based on a constant Hamiltonian profile is designed to address the difficulty in locating the breakpoints in the thrust profile. Four scenarios are simulated. Simulation results indicate that the proposed trajectory optimization framework has sufficient adaptability to handle VTVL missions efficiently.

Trajectory optimization for an asymmetric launch vehicle. M.S. Thesis - MIT

NASA Technical Reports Server (NTRS)

Sullivan, Jeanne Marie

1990-01-01

A numerical optimization technique is used to fully automate the trajectory design process for an symmetric configuration of the proposed Advanced Launch System (ALS). The objective of the ALS trajectory design process is the maximization of the vehicle mass when it reaches the desired orbit. The trajectories used were based on a simple shape that could be described by a small set of parameters. The use of a simple trajectory model can significantly reduce the computation time required for trajectory optimization. A predictive simulation was developed to determine the on-orbit mass given an initial vehicle state, wind information, and a set of trajectory parameters. This simulation utilizes an idealized control system to speed computation by increasing the integration time step. The conjugate gradient method is used for the numerical optimization of on-orbit mass. The method requires only the evaluation of the on-orbit mass function using the predictive simulation, and the gradient of the on-orbit mass function with respect to the trajectory parameters. The gradient is approximated with finite differencing. Prelaunch trajectory designs were carried out using the optimization procedure. The predictive simulation is used in flight to redesign the trajectory to account for trajectory deviations produced by off-nominal conditions, e.g., stronger than expected head winds.

Coupled Low-thrust Trajectory and System Optimization via Multi-Objective Hybrid Optimal Control

NASA Technical Reports Server (NTRS)

Vavrina, Matthew A.; Englander, Jacob Aldo; Ghosh, Alexander R.

2015-01-01

The optimization of low-thrust trajectories is tightly coupled with the spacecraft hardware. Trading trajectory characteristics with system parameters ton identify viable solutions and determine mission sensitivities across discrete hardware configurations is labor intensive. Local independent optimization runs can sample the design space, but a global exploration that resolves the relationships between the system variables across multiple objectives enables a full mapping of the optimal solution space. A multi-objective, hybrid optimal control algorithm is formulated using a multi-objective genetic algorithm as an outer loop systems optimizer around a global trajectory optimizer. The coupled problem is solved simultaneously to generate Pareto-optimal solutions in a single execution. The automated approach is demonstrated on two boulder return missions.

Advanced Free Flight Planner and Dispatcher's Workstation: Preliminary Design Specification

NASA Technical Reports Server (NTRS)

Wilson, J.; Wright, C.; Couluris, G. J.

1997-01-01

The National Aeronautics and Space Administration (NASA) has implemented the Advanced Air Transportation Technology (AATT) program to investigate future improvements to the national and international air traffic management systems. This research, as part of the AATT program, developed preliminary design requirements for an advanced Airline Operations Control (AOC) dispatcher's workstation, with emphasis on flight planning. This design will support the implementation of an experimental workstation in NASA laboratories that would emulate AOC dispatch operations. The work developed an airline flight plan data base and specified requirements for: a computer tool for generation and evaluation of free flight, user preferred trajectories (UPT); the kernel of an advanced flight planning system to be incorporated into the UPT-generation tool; and an AOC workstation to house the UPT-generation tool and to provide a real-time testing environment. A prototype for the advanced flight plan optimization kernel was developed and demonstrated. The flight planner uses dynamic programming to search a four-dimensional wind and temperature grid to identify the optimal route, altitude and speed for successive segments of a flight. An iterative process is employed in which a series of trajectories are successively refined until the LTPT is identified. The flight planner is designed to function in the current operational environment as well as in free flight. The free flight environment would enable greater flexibility in UPT selection based on alleviation of current procedural constraints. The prototype also takes advantage of advanced computer processing capabilities to implement more powerful optimization routines than would be possible with older computer systems.

On making things the best - Aeronautical uses of optimization /Wright Bros. lecture/

NASA Technical Reports Server (NTRS)

Ashley, H.

1981-01-01

The paper's purpose is to summarize and evaluate the results of an investigation into the degree to which formal optimization methods have contributed practically to the design and operation of atmospheric flight vehicles. The nature of this technology is reviewed and illustrated with simple structural examples. A series of published successful applications is described, from the fields of aerodynamics, structures, guidance and control, optimal trajectories and vehicle configuration optimization. The corresponding improvements over conventional analysis are assessed. Speculations are offered as to why these tools have made such little headway toward acceptance by designers. The growing need for their use in the future is explained; they hold out an unparalleled opportunity for improved efficiencies.

The Future of Air Traffic Management

NASA Technical Reports Server (NTRS)

Denery, Dallas G.; Erzberger, Heinz; Edwards, Thomas A. (Technical Monitor)

1998-01-01

A system for the control of terminal area traffic to improve productivity, referred to as the Center-TRACON Automation System (CTAS), is being developed at NASA's Ames Research Center under a joint program with the FAA. CTAS consists of a set of integrated tools that provide computer-generated advisories for en-route and terminal area controllers. The premise behind the design of CTAS has been that successful planning of traffic requires accurate trajectory prediction. Data bases consisting of representative aircraft performance models, airline preferred operational procedures and a three dimensional wind model support the trajectory prediction. The research effort has been the design of a set of automation tools that make use of this trajectory prediction capability to assist controllers in overall management of traffic. The first tool, the Traffic Management Advisor (TMA), provides the overall flow management between the en route and terminal areas. A second tool, the Final Approach Spacing Tool (FAST) provides terminal area controllers with sequence and runway advisories to allow optimal use of the runways. The TMA and FAST are now being used in daily operations at Dallas/Ft. Worth airport. Additional activities include the development of several other tools. These include: 1) the En Route Descent Advisor that assist the en route controller in issuing conflict free descents and ascents; 2) the extension of FAST to include speed and heading advisories and the Expedite Departure Path (EDP) that assists the terminal controller in management of departures; and 3) the Collaborative Arrival Planner (CAP) that will assist the airlines in operational decision making. The purpose of this presentation is to review the CTAS concept and to present the results of recent field tests. The paper will first discuss the overall concept and then discuss the status of the individual tools.

Optimal helicopter trajectory planning for terrain following flight

NASA Technical Reports Server (NTRS)

Menon, P. K. A.

1990-01-01

Helicopters operating in high threat areas have to fly close to the earth surface to minimize the risk of being detected by the adversaries. Techniques are presented for low altitude helicopter trajectory planning. These methods are based on optimal control theory and appear to be implementable onboard in realtime. Second order necessary conditions are obtained to provide a criterion for finding the optimal trajectory when more than one extremal passes through a given point. A second trajectory planning method incorporating a quadratic performance index is also discussed. Trajectory planning problem is formulated as a differential game. The objective is to synthesize optimal trajectories in the presence of an actively maneuvering adversary. Numerical methods for obtaining solutions to these problems are outlined. As an alternative to numerical method, feedback linearizing transformations are combined with the linear quadratic game results to synthesize explicit nonlinear feedback strategies for helicopter pursuit-evasion. Some of the trajectories generated from this research are evaluated on a six-degree-of-freedom helicopter simulation incorporating an advanced autopilot. The optimal trajectory planning methods presented are also useful for autonomous land vehicle guidance.

Program to Optimize Simulated Trajectories (POST). Volume 2: Utilization manual

NASA Technical Reports Server (NTRS)

Bauer, G. L.; Cornick, D. E.; Habeger, A. R.; Petersen, F. M.; Stevenson, R.

1975-01-01

Information pertinent to users of the program to optimize simulated trajectories (POST) is presented. The input required and output available is described for each of the trajectory and targeting/optimization options. A sample input listing and resulting output are given.

An inverse dynamics approach to trajectory optimization for an aerospace plane

NASA Technical Reports Server (NTRS)

Lu, Ping

1992-01-01

An inverse dynamics approach for trajectory optimization is proposed. This technique can be useful in many difficult trajectory optimization and control problems. The application of the approach is exemplified by ascent trajectory optimization for an aerospace plane. Both minimum-fuel and minimax types of performance indices are considered. When rocket augmentation is available for ascent, it is shown that accurate orbital insertion can be achieved through the inverse control of the rocket in the presence of disturbances.

Efficient Optimization of Low-Thrust Spacecraft Trajectories

NASA Technical Reports Server (NTRS)

Lee, Seungwon; Fink, Wolfgang; Russell, Ryan; Terrile, Richard; Petropoulos, Anastassios; vonAllmen, Paul

2007-01-01

A paper describes a computationally efficient method of optimizing trajectories of spacecraft driven by propulsion systems that generate low thrusts and, hence, must be operated for long times. A common goal in trajectory-optimization problems is to find minimum-time, minimum-fuel, or Pareto-optimal trajectories (here, Pareto-optimality signifies that no other solutions are superior with respect to both flight time and fuel consumption). The present method utilizes genetic and simulated-annealing algorithms to search for globally Pareto-optimal solutions. These algorithms are implemented in parallel form to reduce computation time. These algorithms are coupled with either of two traditional trajectory- design approaches called "direct" and "indirect." In the direct approach, thrust control is discretized in either arc time or arc length, and the resulting discrete thrust vectors are optimized. The indirect approach involves the primer-vector theory (introduced in 1963), in which the thrust control problem is transformed into a co-state control problem and the initial values of the co-state vector are optimized. In application to two example orbit-transfer problems, this method was found to generate solutions comparable to those of other state-of-the-art trajectory-optimization methods while requiring much less computation time.

Two-year trajectory of fall risk in people with Parkinson’s disease: a latent class analysis

PubMed Central

Paul, Serene S; Thackeray, Anne; Duncan, Ryan P; Cavanaugh, James T; Ellis, Theresa D; Earhart, Gammon M; Ford, Matthew P; Foreman, K Bo; Dibble, Leland E

2015-01-01

Objective To examine fall risk trajectories occurring naturally in a sample of individuals with early to middle stage Parkinson’s disease (PD). Design Latent class analysis, specifically growth mixture modeling (GMM) of longitudinal fall risk trajectories. Setting Not applicable. Participants 230 community-dwelling PD participants of a longitudinal cohort study who attended at least two of five assessments over a two year period. Interventions Not applicable. Main Outcome Measures Fall risk trajectory (low, medium or high risk) and stability of fall risk trajectory (stable or fluctuating). Fall risk was determined at 6-monthly intervals using a simple clinical tool based on fall history, freezing of gait, and gait speed. Results The GMM optimally grouped participants into three fall risk trajectories that closely mirrored baseline fall risk status (p=.001). The high fall risk trajectory was most common (42.6%) and included participants with longer and more severe disease and with higher postural instability and gait disability (PIGD) scores than the low and medium risk trajectories (p<.001). Fluctuating fall risk (posterior probability <0.8 of belonging to any trajectory) was found in only 22.6% of the sample, most commonly among individuals who were transitioning to PIGD predominance. Conclusions Regardless of their baseline characteristics, most participants had clear and stable fall risk trajectories over two years. Further investigation is required to determine whether interventions to improve gait and balance may improve fall risk trajectories in people with PD. PMID:26606871

A Method of Trajectory Design for Manned Asteroids Exploration

NASA Astrophysics Data System (ADS)

Gan, Q. B.; Zhang, Y.; Zhu, Z. F.; Han, W. H.; Dong, X.

2014-11-01

A trajectory optimization method of the nuclear propulsion manned asteroids exploration is presented. In the case of launching between 2035 and 2065, based on the Lambert transfer orbit, the phases of departure from and return to the Earth are searched at first. Then the optimal flight trajectory in the feasible regions is selected by pruning the flight sequences. Setting the nuclear propulsion flight plan as propel-coast-propel, and taking the minimal mass of aircraft departure as the index, the nuclear propulsion flight trajectory is separately optimized using a hybrid method. With the initial value of the optimized local parameters of each three phases, the global parameters are jointedly optimized. At last, the minimal departure mass trajectory design result is given.

Numerical Flight Mechanics Analysis Of The SHEFEX I Ascent And Re-Entry Phases

NASA Astrophysics Data System (ADS)

Bartolome Calvo, Javier; Eggers, Thino

2011-08-01

The SHarp Edge Flight EXperiment (SHEFEX) I provides a huge amount of scientific data to validate numerical tools in hypersonic flows. These data allow the direct comparison of flight measurements with the current numerical tools available at DLR. Therefore, this paper is devoted to apply a recently developed direct coupling between aerodynamics and flight dynamics to the SHEFEX I flight. In a first step, mission analyses are carried out using the trajectory optimization program REENT 6D coupled to missile DATCOM. In a second step, the direct coupling between the trajectory program and the DLR TAU code, in which the unsteady Euler equations including rigid body motion are solved, is applied to analyze some interesting parts of ascent and re-entry phases of the flight experiment. The agreement of the numerical predictions with the obtained flight data is satisfactory assuming a variable fin deflection angle.

Deconflicting Wind-Optimal Aircraft Trajectories in North Atlantic Oceanic Airspace

NASA Technical Reports Server (NTRS)

Rodionova, Olga; Delahaye, Daniel; Sridhar, Banavar; Ng, Hok K.

2016-01-01

North Atlantic oceanic airspace accommodates more than 1000 flights daily, and is subjected to very strong winds. Flying wind-optimal trajectories yields time and fuel savings for each individual flight. However, when taken together, these trajectories induce a large amount of potential en-route conflicts. This paper analyses the detected conflicts, figuring out conflict distribution in time and space. It further describes an optimization algorithm aimed at reducing the number of conflicts for a daily set of flights on strategic level. Several trajectory modification strategies are discussed, followed with simulation results. Finally, an algorithm improvement is presented aiming at better preserving the trajectory optimality.

Sensitivity Analysis and Mitigation with Applications to Ballistic and Low-thrust Trajectory Design

NASA Astrophysics Data System (ADS)

Alizadeh, Iman

The ever increasing desire to expand space mission capabilities within the limited budgets of space industries requires new approaches to the old problem of spacecraft trajectory design. For example, recent initiatives for space exploration involve developing new tools to design low-cost, fail-safe trajectories to visit several potential destinations beyond our celestial neighborhood such as Jupiter's moons, asteroids, etc. Designing and navigating spacecraft trajectories to reach these destinations safely are complex and challenging. In particular, fundamental questions of orbital stability imposed by planetary protection requirements are not easily taken into account by standard optimal control schemes. The event of temporary engine loss or an unexpected missed thrust can indeed quickly lead to impact with planetary bodies or other unrecoverable trajectories. While electric propulsion technology provides superior efficiency compared to chemical engines, the very low-control authority and engine performance degradation can impose higher risk to the mission in strongly perturbed orbital environments. The risk is due to the complex gravitational field and its associated chaotic dynamics which causes large navigation dispersions in a short time if left un-controlled. Moreover, in these situations it can be outside the low-thrust propulsion system capability to correct the spacecraft trajectory in a reasonable time frame. These concerns can lead to complete or partial mission failure or even an infeasible mission concept at the early design stage. The goal of this research is to assess and increase orbital stability of ballistic and low-thrust transfer trajectories in multi-body systems. In particular, novel techniques are presented to characterize sensitivity and improve recovery characteristics of ballistic and low-thrust trajectories in unstable orbital environments. The techniques developed are based on perturbation analysis around ballistic trajectories to determine analytically the maximum divergence directions and also optimal control theory with nonstandard cost functions along with inverse dynamics applied to low-thrust trajectories. Several mission scenarios are shown to demonstrate the applicability of the techniques in the Earth-Moon and the Jupiter-Europa system. In addition, the results provide fundamental insight into design, stability analysis and guidance, navigation and control of low-thrust trajectories to meet challenging mission requirements in support of NASA's vision for space exploration.

New trends in astrodynamics and applications: optimal trajectories for space guidance.

PubMed

Azimov, Dilmurat; Bishop, Robert

2005-12-01

This paper represents recent results on the development of optimal analytic solutions to the variation problem of trajectory optimization and their application in the construction of on-board guidance laws. The importance of employing the analytically integrated trajectories in a mission design is discussed. It is assumed that the spacecraft is equipped with a power-limited propulsion and moving in a central Newtonian field. Satisfaction of the necessary and sufficient conditions for optimality of trajectories is analyzed. All possible thrust arcs and corresponding classes of the analytical solutions are classified based on the propulsion system parameters and performance index of the problem. The solutions are presented in a form convenient for applications in escape, capture, and interorbital transfer problems. Optimal guidance and neighboring optimal guidance problems are considered. It is shown that the analytic solutions can be used as reference trajectories in constructing the guidance algorithms for the maneuver problems mentioned above. An illustrative example of a spiral trajectory that terminates on a given elliptical parking orbit is discussed.

The design of electron and ion guns, beams, and collectors

NASA Astrophysics Data System (ADS)

Becker, Reinard; Herrmannsfeldt, William B.

2004-01-01

The well known `SLAC Electron Trajectory Program' (EGUN) has been ported to PCs and has been developed into a family of programs for the design and the optimization of particle optics devices including electron and ion guns, beam transport sections and collectors. We will discuss the application of these tools for the design and the optimization of the essential parts of EBIS/T devices. The discussion will include conditions in which restrictions in the reliability of simulations may occur due to the mathematical modeling and how to overcome them.

Operator-assisted planning and execution of proximity operations subject to operational constraints

NASA Technical Reports Server (NTRS)

Grunwald, Arthur J.; Ellis, Stephen R.

1991-01-01

Future multi-vehicle operations will involve multiple scenarios that will require a planning tool for the rapid, interactive creation of fuel-efficient trajectories. The planning process must deal with higher-order, non-linear processes involving dynamics that are often counter-intuitive. The optimization of resulting trajectories can be difficult to envision. An interaction proximity operations planning system is being developed to provide the operator with easily interpreted visual feedback of trajectories and constraints. This system is hosted on an IRIS 4D graphics platform and utilizes the Clohessy-Wiltshire equations. An inverse dynamics algorithm is used to remove non-linearities while the trajectory maneuvers are decoupled and separated in a geometric spreadsheet. The operator has direct control of the position and time of trajectory waypoints to achieve the desired end conditions. Graphics provide the operator with visualization of satisfying operational constraints such as structural clearance, plume impingement, approach velocity limits, and arrival or departure corridors. Primer vector theory is combined with graphical presentation to improve operator understanding of suggested automated system solutions and to allow the operator to review, edit, or provide corrective action to the trajectory plan.

Automated trajectory planning for multiple-flyby interplanetary missions

NASA Astrophysics Data System (ADS)

Englander, Jacob

Many space mission planning problems may be formulated as hybrid optimal control problems (HOCP), i.e. problems that include both real-valued variables and categorical variables. In interplanetary trajectory design problems the categorical variables will typically specify the sequence of planets at which to perform flybys, and the real-valued variables will represent the launch date, ight times between planets, magnitudes and directions of thrust, flyby altitudes, etc. The contribution of this work is a framework for the autonomous optimization of multiple-flyby interplanetary trajectories. The trajectory design problem is converted into a HOCP with two nested loops: an "outer-loop" that finds the sequence of flybys and an "inner-loop" that optimizes the trajectory for each candidate yby sequence. The problem of choosing a sequence of flybys is posed as an integer programming problem and solved using a genetic algorithm (GA). This is an especially difficult problem to solve because GAs normally operate on a fixed-length set of decision variables. Since in interplanetary trajectory design the number of flyby maneuvers is not known a priori, it was necessary to devise a method of parameterizing the problem such that the GA can evolve a variable-length sequence of flybys. A novel "null gene" transcription was developed to meet this need. Then, for each candidate sequence of flybys, a trajectory must be found that visits each of the flyby targets and arrives at the final destination while optimizing some cost metric, such as minimizing ▵v or maximizing the final mass of the spacecraft. Three different classes of trajectory are described in this work, each of which requireda different physical model and optimization method. The choice of a trajectory model and optimization method is especially challenging because of the nature of the hybrid optimal control problem. Because the trajectory optimization problem is generated in real time by the outer-loop, the inner-loop optimization algorithm cannot require any a priori information and must always return a solution. In addition, the upper and lower bounds on each decision variable cannot be chosen a priori by the user because the user has no way to know what problem will be solved. Instead a method of choosing upper and lower bounds via a set of simple rules was developed and used for all three types of trajectory optimization problem. Many optimization algorithms were tested and discarded until suitable algorithms were found for each type of trajectory. The first class of trajectories use chemical propulsion and may only apply a ▵v at the periapse of each flyby. These Multiple Gravity Assist (MGA) trajectories are optimized using a cooperative algorithm of Differential Evolution (DE) and Particle Swarm Optimization (PSO). The second class of trajectories, known as Multiple Gravity Assist with one Deep Space Maneuver (MGA-DSM), also use chemical propulsion but instead of maneuvering at the periapse of each flyby as in the MGA case a maneuver is applied at a free point along each planet-to-planet arc, i.e. there is one maneuver for each pair of flybys. MGA-DSM trajectories are parameterized by more variables than MGA trajectories, and so the cooperative algorithm of DE and PSO that was used to optimize MGA trajectories was found to be less effective when applied to MGA-DSM. Instead, either PSO or DE alone were found to be more effective. The third class of trajectories addressed in this work are those using continuousthrust propulsion. Continuous-thrust trajectory optimization problems are more challenging than impulsive-thrust problems because the control variables are a continuous time series rather than a small set of parameters and because the spacecraft does not follow a conic section trajectory, leading to a large number of nonlinear constraints that must be satisfied to ensure that the spacecraft obeys the equations of motion. Many models and optimization algorithms were applied including direct transcription with nonlinear programming (DTNLP), the inverse-polynomial shapebased method, and feasible region analysis. However the only physical model and optimization method that proved reliable enough were the Sims-Flanagan transcription coupled with a nonlinear programming solver and the monotonic basin hopping (MBH) global search heuristic. The methods developed here are demonstrated to optimize a set of example trajectories, including a recreation of the Cassini mission, a Galileo-like mission, and conceptual continuous-thrust missions to Jupiter, Mercury, and Uranus.

Trajectory Design Considerations for Exploration Mission 1

NASA Technical Reports Server (NTRS)

Dawn, Timothy F.; Gutkowski, Jeffrey P.; Batcha, Amelia L.; Williams, Jacob; Pedrotty, Samuel M.

2018-01-01

Exploration Mission 1 (EM-1) will be the first mission to send an uncrewed Orion Multi-Purpose Crew Vehicle (MPCV) to cislunar space in the fall of 2019. EM-1 was originally conceived as a lunar free-return mission, but was later changed to a Distant Retrograde Orbit (DRO) mission as a precursor to the Asteroid Redirect Mission. To understand the required mission performance (i.e., propellant requirement), a series of trajectory optimization runs was conducted using JSC's Copernicus spacecraft trajectory optimization tool. In order for the runs to be done in a timely manner, it was necessary to employ a parallelization approach on a computing cluster using a new trajectory scan tool written in Python. Details of the scan tool are provided and how it is used to perform the scans and post-process the results. Initially, a scan of daily due east launched EM-1 DRO missions in 2018 was made. Valid mission opportunities are ones that do not exceed the useable propellant available to perform the required burns. The initial scan data showed the propellant and delta-V performance patterns for each launch period. As questions were raised from different subsystems (e.g., power, thermal, communications, flight operations, etc.), the mission parameters or data that were of interest to them were added to the scan output data file. The additional data includes: (1) local launch and landing times in relation to sunrise and sunset, (2) length of eclipse periods during the in-space portion of the mission, (3) Earth line of sight from cislunar space, (4) Deep Space Network field of view looking towards cislunar space, and (5) variation of the downrange distance from Earth entry interface to splashdown. Mission design trades can also be performed based on the information that the additional data shows. For example, if the landing is in darkness, but the recovery operations team desires a landing in daylight, then an analysis is performed to determine how to change the mission design to meet this request. Also, subsystems request feasibility of alternate or contingency mission designs, such as adding an Orion main engine checkout burn or Orion completing all of its burns using only its auxiliary thrusters. This paper examines and presents the evolving trade studies that incorporate subsystem feedback and demonstrate the feasibility of these constrained mission trajectory designs and contingencies.

Near-Optimal Re-Entry Trajectories for Reusable Launch Vehicles

NASA Technical Reports Server (NTRS)

Chou, H.-C.; Ardema, M. D.; Bowles, J. V.

1997-01-01

A near-optimal guidance law for the descent trajectory for earth orbit re-entry of a fully reusable single-stage-to-orbit pure rocket launch vehicle is derived. A methodology is developed to investigate using both bank angle and altitude as control variables and selecting parameters that maximize various performance functions. The method is based on the energy-state model of the aircraft equations of motion. The major task of this paper is to obtain optimal re-entry trajectories under a variety of performance goals: minimum time, minimum surface temperature, minimum heating, and maximum heading change; four classes of trajectories were investigated: no banking, optimal left turn banking, optimal right turn banking, and optimal bank chattering. The cost function is in general a weighted sum of all performance goals. In particular, the trade-off between minimizing heat load into the vehicle and maximizing cross range distance is investigated. The results show that the optimization methodology can be used to derive a wide variety of near-optimal trajectories.

Rapid design and optimization of low-thrust rendezvous/interception trajectory for asteroid deflection missions

NASA Astrophysics Data System (ADS)

Li, Shuang; Zhu, Yongsheng; Wang, Yukai

2014-02-01

Asteroid deflection techniques are essential in order to protect the Earth from catastrophic impacts by hazardous asteroids. Rapid design and optimization of low-thrust rendezvous/interception trajectories is considered as one of the key technologies to successfully deflect potentially hazardous asteroids. In this paper, we address a general framework for the rapid design and optimization of low-thrust rendezvous/interception trajectories for future asteroid deflection missions. The design and optimization process includes three closely associated steps. Firstly, shape-based approaches and genetic algorithm (GA) are adopted to perform preliminary design, which provides a reasonable initial guess for subsequent accurate optimization. Secondly, Radau pseudospectral method is utilized to transcribe the low-thrust trajectory optimization problem into a discrete nonlinear programming (NLP) problem. Finally, sequential quadratic programming (SQP) is used to efficiently solve the nonlinear programming problem and obtain the optimal low-thrust rendezvous/interception trajectories. The rapid design and optimization algorithms developed in this paper are validated by three simulation cases with different performance indexes and boundary constraints.

Program to Optimize Simulated Trajectories (POST). Volume 1: Formulation manual

NASA Technical Reports Server (NTRS)

Brauer, G. L.; Cornick, D. E.; Habeger, A. R.; Petersen, F. M.; Stevenson, R.

1975-01-01

A general purpose FORTRAN program for simulating and optimizing point mass trajectories (POST) of aerospace vehicles is described. The equations and the numerical techniques used in the program are documented. Topics discussed include: coordinate systems, planet model, trajectory simulation, auxiliary calculations, and targeting and optimization.

Theoretical Foundation of Copernicus: A Unified System for Trajectory Design and Optimization

NASA Technical Reports Server (NTRS)

Ocampo, Cesar; Senent, Juan S.; Williams, Jacob

2010-01-01

The fundamental methods are described for the general spacecraft trajectory design and optimization software system called Copernicus. The methods rely on a unified framework that is used to model, design, and optimize spacecraft trajectories that may operate in complex gravitational force fields, use multiple propulsion systems, and involve multiple spacecraft. The trajectory model, with its associated equations of motion and maneuver models, are discussed.

Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

NASA Technical Reports Server (NTRS)

Pinson, Robin M.; Lu, Ping

2016-01-01

Mission proposals that land on asteroids are becoming popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site. The problem under investigation is how to design a fuel-optimal powered descent trajectory that can be quickly computed on- board the spacecraft, without interaction from ground control. An optimal trajectory designed immediately prior to the descent burn has many advantages. These advantages include the ability to use the actual vehicle starting state as the initial condition in the trajectory design and the ease of updating the landing target site if the original landing site is no longer viable. For long trajectories, the trajectory can be updated periodically by a redesign of the optimal trajectory based on current vehicle conditions to improve the guidance performance. One of the key drivers for being completely autonomous is the infrequent and delayed communication between ground control and the vehicle. Challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies and low thrust vehicles. There are two previous studies that form the background to the current investigation. The first set looked in-depth at applying convex optimization to a powered descent trajectory on Mars with promising results.1, 2 This showed that the powered descent equations of motion can be relaxed and formed into a convex optimization problem and that the optimal solution of the relaxed problem is indeed a feasible solution to the original problem. This analysis used a constant gravity field. The second area applied a successive solution process to formulate a second order cone program that designs rendezvous and proximity operations trajectories.3, 4 These trajectories included a Newtonian gravity model. The equivalence of the solutions between the relaxed and the original problem is theoretically established. The proposed solution for designing the asteroid powered descent trajectory is to use convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process to design the fuel optimal trajectory. The solution to the convex optimization problem is the thrust profile, magnitude and direction, that will yield the minimum fuel trajectory for a soft landing at the target site, subject to various mission and operational constraints. The equations of motion are formulated in a rotating coordinate system and includes a high fidelity gravity model. The vehicle's thrust magnitude can vary between maximum and minimum bounds during the burn. Also, constraints are included to ensure that the vehicle does not run out of propellant, or go below the asteroid's surface, and any vehicle pointing requirements. The equations of motion are discretized and propagated with the trapezoidal rule in order to produce equality constraints for the optimization problem. These equality constraints allow the optimization algorithm to solve the entire problem, without including a propagator inside the optimization algorithm.

Simulation of the Simbol-X telescope: imaging performance of a deformable x-ray telescope

NASA Astrophysics Data System (ADS)

Chauvin, Maxime; Roques, Jean-Pierre

2009-08-01

We have developed a simulation tool for a Wolter I telescope subject to deformations. The aim is to understand and predict the behavior of Simbol-X and other future missions (NuSTAR, Astro-H, IXO, ...). Our code, based on Monte-Carlo ray-tracing, computes the full photon trajectories up to the detector plane, along with the deformations. The degradation of the imaging system is corrected using metrology. This tool allows to perform many analyzes in order to optimize the configuration of any of these telescopes.

Optimal lifting ascent trajectories for the space shuttle

NASA Technical Reports Server (NTRS)

Rau, T. R.; Elliott, J. R.

1972-01-01

The performance gains which are possible through the use of optimal trajectories for a particular space shuttle configuration are discussed. The spacecraft configurations and aerodynamic characteristics are described. Shuttle mission payload capability is examined with respect to the optimal orbit inclination for unconstrained, constrained, and nonlifting conditions. The effects of velocity loss and heating rate on the optimal ascent trajectory are investigated.

Trajectory Browser: An Online Tool for Interplanetary Trajectory Analysis and Visualization

NASA Technical Reports Server (NTRS)

Foster, Cyrus James

2013-01-01

The trajectory browser is a web-based tool developed at the NASA Ames Research Center for finding preliminary trajectories to planetary bodies and for providing relevant launch date, time-of-flight and (Delta)V requirements. The site hosts a database of transfer trajectories from Earth to planets and small-bodies for various types of missions such as rendezvous, sample return or flybys. A search engine allows the user to find trajectories meeting desired constraints on the launch window, mission duration and (Delta)V capability, while a trajectory viewer tool allows the visualization of the heliocentric trajectory and the detailed mission itinerary. The anticipated user base of this tool consists primarily of scientists and engineers designing interplanetary missions in the context of pre-phase A studies, particularly for performing accessibility surveys to large populations of small-bodies.

Genetic Algorithm Optimizes Q-LAW Control Parameters

NASA Technical Reports Server (NTRS)

Lee, Seungwon; von Allmen, Paul; Petropoulos, Anastassios; Terrile, Richard

2008-01-01

A document discusses a multi-objective, genetic algorithm designed to optimize Lyapunov feedback control law (Q-law) parameters in order to efficiently find Pareto-optimal solutions for low-thrust trajectories for electronic propulsion systems. These would be propellant-optimal solutions for a given flight time, or flight time optimal solutions for a given propellant requirement. The approximate solutions are used as good initial solutions for high-fidelity optimization tools. When the good initial solutions are used, the high-fidelity optimization tools quickly converge to a locally optimal solution near the initial solution. Q-law control parameters are represented as real-valued genes in the genetic algorithm. The performances of the Q-law control parameters are evaluated in the multi-objective space (flight time vs. propellant mass) and sorted by the non-dominated sorting method that assigns a better fitness value to the solutions that are dominated by a fewer number of other solutions. With the ranking result, the genetic algorithm encourages the solutions with higher fitness values to participate in the reproduction process, improving the solutions in the evolution process. The population of solutions converges to the Pareto front that is permitted within the Q-law control parameter space.

Comparison of kinematic and dynamic leg trajectory optimization techniques for biped robot locomotion

NASA Astrophysics Data System (ADS)

Khusainov, R.; Klimchik, A.; Magid, E.

2017-01-01

The paper presents comparison analysis of two approaches in defining leg trajectories for biped locomotion. The first one operates only with kinematic limitations of leg joints and finds the maximum possible locomotion speed for given limits. The second approach defines leg trajectories from the dynamic stability point of view and utilizes ZMP criteria. We show that two methods give different trajectories and demonstrate that trajectories based on pure dynamic optimization cannot be realized due to joint limits. Kinematic optimization provides unstable solution which can be balanced by upper body movement.

Optimization and guidance of flight trajectories for the national aerospace plane

NASA Technical Reports Server (NTRS)

Miele, Angelo

1990-01-01

The research on optimal trajectories for the National Aerospace Plane (NASP) performed by the Aero-Astronautics Group of Rice University from June 22, 1989 to December 31, 1990 is summarized. The aerospace plane is assumed to be controlled via the angle of attack and the power setting. The time history of the controls is optimized simultaneously with the switch times from one powerplant to another and the final time. The intent is to arrive at NASP guidance trajectories exhibiting many of the desirable characteristics of NASP optimal trajectories.

Interplanetary Program to Optimize Simulated Trajectories (IPOST). Volume 2: Analytic manual

NASA Technical Reports Server (NTRS)

Hong, P. E.; Kent, P. D.; Olson, D. W.; Vallado, C. A.

1992-01-01

The Interplanetary Program to Optimize Space Trajectories (IPOST) is intended to support many analysis phases, from early interplanetary feasibility studies through spacecraft development and operations. The IPOST output provides information for sizing and understanding mission impacts related to propulsion, guidance, communications, sensor/actuators, payload, and other dynamic and geometric environments. IPOST models three degree of freedom trajectory events, such as launch/ascent, orbital coast, propulsive maneuvering (impulsive and finite burn), gravity assist, and atmospheric entry. Trajectory propagation is performed using a choice of Cowell, Encke, Multiconic, Onestep, or Conic methods. The user identifies a desired sequence of trajectory events, and selects which parameters are independent (controls) and dependent (targets), as well as other constraints and the cost function. Targeting and optimization is performed using the Stanford NPSOL algorithm. IPOST structure allows subproblems within a master optimization problem to aid in the general constrained parameter optimization solution. An alternate optimization method uses implicit simulation and collocation techniques.

Improvement of Automated POST Case Success Rate Using Support Vector Machines

NASA Technical Reports Server (NTRS)

Zwack, Mathew R.; Dees, Patrick D.

2017-01-01

During early conceptual design of complex systems, concept down selection can have a large impact upon program life-cycle cost. Therefore, any concepts selected during early design will inherently commit program costs and affect the overall probability of program success. For this reason it is important to consider as large a design space as possible in order to better inform the down selection process. For conceptual design of launch vehicles, trajectory analysis and optimization often presents the largest obstacle to evaluating large trade spaces. This is due to the sensitivity of the trajectory discipline to changes in all other aspects of the vehicle design. Small deltas in the performance of other subsystems can result in relatively large fluctuations in the ascent trajectory because the solution space is non-linear and multi-modal. In order to help capture large design spaces for new launch vehicles, the authors have performed previous work seeking to automate the execution of the industry standard tool, Program to Optimize Simulated Trajectories (POST). This work initially focused on implementation of analyst heuristics to enable closure of cases in an automated fashion, with the goal of applying the concepts of design of experiments (DOE) and surrogate modeling to enable near instantaneous throughput of vehicle cases.3 As noted in [4] work was then completed to improve the DOE process by utilizing a graph theory based approach to connect similar design points.

Task driven optimal leg trajectories in insect-scale legged microrobots

NASA Astrophysics Data System (ADS)

Doshi, Neel; Goldberg, Benjamin; Jayaram, Kaushik; Wood, Robert

Origami inspired layered manufacturing techniques and 3D-printing have enabled the development of highly articulated legged robots at the insect-scale, including the 1.43g Harvard Ambulatory MicroRobot (HAMR). Research on these platforms has expanded its focus from manufacturing aspects to include design optimization and control for application-driven tasks. Consequently, the choice of gait selection, body morphology, leg trajectory, foot design, etc. have become areas of active research. HAMR has two controlled degrees-of-freedom per leg, making it an ideal candidate for exploring leg trajectory. We will discuss our work towards optimizing HAMR's leg trajectories for two different tasks: climbing using electroadhesives and level ground running (5-10 BL/s). These tasks demonstrate the ability of single platform to adapt to vastly different locomotive scenarios: quasi-static climbing with controlled ground contact, and dynamic running with un-controlled ground contact. We will utilize trajectory optimization methods informed by existing models and experimental studies to determine leg trajectories for each task. We also plan to discuss how task specifications and choice of objective function have contributed to the shape of these optimal leg trajectories.

Optimal heliocentric trajectories for solar sail with minimum area

NASA Astrophysics Data System (ADS)

Petukhov, Vyacheslav G.

2018-05-01

The fixed-time heliocentric trajectory optimization problem is considered for planar solar sail with minimum area. Necessary optimality conditions are derived, a numerical method for solving the problem is developed, and numerical examples of optimal trajectories to Mars, Venus and Mercury are presented. The dependences of the minimum area of the solar sail from the date of departure from the Earth, the time of flight and the departing hyperbolic excess of velocity are analyzed. In particular, for the rendezvous problem (approaching a target planet with zero relative velocity) with zero departing hyperbolic excess of velocity for a flight duration of 1200 days it was found that the minimum area-to-mass ratio should be about 12 m2/kg for trajectory to Venus, 23.5 m2/kg for the trajectory to Mercury and 25 m2/kg for trajectory to Mars.

Design Tool Using a New Optimization Method Based on a Stochastic Process

NASA Astrophysics Data System (ADS)

Yoshida, Hiroaki; Yamaguchi, Katsuhito; Ishikawa, Yoshio

Conventional optimization methods are based on a deterministic approach since their purpose is to find out an exact solution. However, such methods have initial condition dependence and the risk of falling into local solution. In this paper, we propose a new optimization method based on the concept of path integrals used in quantum mechanics. The method obtains a solution as an expected value (stochastic average) using a stochastic process. The advantages of this method are that it is not affected by initial conditions and does not require techniques based on experiences. We applied the new optimization method to a hang glider design. In this problem, both the hang glider design and its flight trajectory were optimized. The numerical calculation results prove that performance of the method is sufficient for practical use.

Fast Optimization for Aircraft Descent and Approach Trajectory

NASA Technical Reports Server (NTRS)

Luchinsky, Dmitry G.; Schuet, Stefan; Brenton, J.; Timucin, Dogan; Smith, David; Kaneshige, John

2017-01-01

We address problem of on-line scheduling of the aircraft descent and approach trajectory. We formulate a general multiphase optimal control problem for optimization of the descent trajectory and review available methods of its solution. We develop a fast algorithm for solution of this problem using two key components: (i) fast inference of the dynamical and control variables of the descending trajectory from the low dimensional flight profile data and (ii) efficient local search for the resulting reduced dimensionality non-linear optimization problem. We compare the performance of the proposed algorithm with numerical solution obtained using optimal control toolbox General Pseudospectral Optimal Control Software. We present results of the solution of the scheduling problem for aircraft descent using novel fast algorithm and discuss its future applications.

Properties of the optimal trajectories for coplanar, aeroassisted orbital transfer

NASA Technical Reports Server (NTRS)

Miele, A.; Wang, T.; Deaton, A. W.

1990-01-01

The optimization of trajectories for coplaner, aeroassisted orbital transfer (AOT) from a high Earth orbit (HEO) to a low Earth orbit (LEO) is examined. In particular, HEO can be a geosynchronous Earth orbit (GEO). It is assumed that the initial and final orbits are circular, that the gravitational field is central and is governed by the inverse square law, and that two impulses are employed, one at HEO exit and one at LEO entry. During the atmospheric pass, the trajectory is controlled via the lift coefficient in such a way that the total characteristic velocity is minimized. First, an ideal optimal trajectory is determined analytically for lift coefficient unbounded. This trajectory is called grazing trajectory, because the atmospheric pass is made by flying at constant altitude along the edge of the atmosphere until the excess velocity is depleted. For the grazing trajectory, the lift coefficient varies in such a way that the lift, the centrifugal force due to the Earth's curvature, the weight, and the Coriolis force due to the Earth's rotation are in static balance. Also, the grazing trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, dynamic pressure, and heating rate. Next, starting from the grazing trajectory results, a real optimal trajectory is determined numerically for the lift coefficient bounded from both below and above. This trajectory is characterized by atmospheric penetration with the smallest possible entry angle, followed by flight at the lift coefficient lower bound. Consistently with the grazing trajectory behavior, the real optimal trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, the dynamic pressure, and the heating rate.

Mission Design and Optimal Asteroid Deflection for Planetary Defense

NASA Technical Reports Server (NTRS)

Sarli, Bruno V.; Knittel, Jeremy M.; Englander, Jacob A.; Barbee, Brent W.

2017-01-01

Planetary defense is a topic of increasing interest for many reasons, which has been mentioned in "Vision and Voyages for Planetary Science in the Decade 2013-2022''. However, perhaps one of the most significant rationales for asteroid studies is the number of close approaches that have been documented recently. A space mission with a planetary defense objective aims to deflect the threatening body as far as possible from Earth. The design of a mission that optimally deflects an asteroid has different challenges: speed, precision, and system trade-off. This work addresses such issues and develops a fast transcription of the problem that can be implemented into an optimization tool, which allows for a broader trade study of different mission concepts with a medium fidelity. Such work is suitable for a mission?s preliminary study. It is shown, using the fictitious asteroid impact scenario 2017 PDC, that the complete tool is able to account for the orbit sensitivity to small perturbations and quickly optimize a deflection trajectory. The speed in which the tool operates allows for a trade study between the available hardware. As a result, key deflection dates and mission strategies are identified for the 2017 PDC.

Mission Design and Optimal Asteroid Deflection for Planetary Defense

NASA Technical Reports Server (NTRS)

Sarli, Bruno V.; Knittel, Jeremy M.; Englander, Jacob A.; Barbee, Brent W.

2017-01-01

Planetary defense is a topic of increasing interest for many reasons, which has been mentioned in "Vision and Voyages for Planetary Science in the Decade 2013-2022". However, perhaps one of the most significant rationales for asteroid studies is the number of close approaches that have been documented recently. A space mission with a planetary defense objective aims to deflect the threatening body as far as possible from Earth. The design of a mission that optimally deflects an asteroid has different challenges: speed, precision, and system trade-off. This work addresses such issues and develops a fast transcription of the problem that can be implemented into an optimization tool, which allows for a broader trade study of different mission concepts with a medium fidelity. Such work is suitable for a mission's preliminary study. It is shown, using the fictitious asteroid impact scenario 2017 PDC, that the complete tool is able to account for the orbit sensitivity to small perturbations and quickly optimize a deflection trajectory. The speed in which the tool operates allows for a trade study between the available hardware. As a result, key deflection dates and mission strategies are identified for the 2017 PDC.

A System Trade Study of Remote Infrared Imaging for Space Shuttle Reentry

NASA Technical Reports Server (NTRS)

Schwartz, Richard J.; Ross, Martin N.; Baize, Rosemary; Horvath, Thomas J.; Berry, Scott A.; Krasa, Paul W.

2008-01-01

A trade study reviewing the primary operational parameters concerning the deployment of imaging assets in support of the Hypersonic Thermodynamic Infrared Measurements (HYTHIRM) project was undertaken. The objective was to determine key variables and constraints for obtaining thermal images of the Space Shuttle orbiter during reentry. The trade study investigated the performance characteristics and operating environment of optical instrumentation that may be deployed during a HYTHIRM data collection mission, and specified contributions to the Point Spread Function. It also investigated the constraints that have to be considered in order to optimize deployment through the use of mission planning tools. These tools simulate the radiance modeling of the vehicle as well as the expected spatial resolution based on the Orbiter trajectory and placement of land based or airborne optical sensors for given Mach numbers. Lastly, this report focused on the tools and methodology that have to be in place for real-time mission planning in order to handle the myriad of variables such as trajectory ground track, weather, and instrumentation availability that may only be known in the hours prior to landing.

Constrained Multi-Level Algorithm for Trajectory Optimization

NASA Astrophysics Data System (ADS)

Adimurthy, V.; Tandon, S. R.; Jessy, Antony; Kumar, C. Ravi

The emphasis on low cost access to space inspired many recent developments in the methodology of trajectory optimization. Ref.1 uses a spectral patching method for optimization, where global orthogonal polynomials are used to describe the dynamical constraints. A two-tier approach of optimization is used in Ref.2 for a missile mid-course trajectory optimization. A hybrid analytical/numerical approach is described in Ref.3, where an initial analytical vacuum solution is taken and gradually atmospheric effects are introduced. Ref.4 emphasizes the fact that the nonlinear constraints which occur in the initial and middle portions of the trajectory behave very nonlinearly with respect the variables making the optimization very difficult to solve in the direct and indirect shooting methods. The problem is further made complex when different phases of the trajectory have different objectives of optimization and also have different path constraints. Such problems can be effectively addressed by multi-level optimization. In the multi-level methods reported so far, optimization is first done in identified sub-level problems, where some coordination variables are kept fixed for global iteration. After all the sub optimizations are completed, higher-level optimization iteration with all the coordination and main variables is done. This is followed by further sub system optimizations with new coordination variables. This process is continued until convergence. In this paper we use a multi-level constrained optimization algorithm which avoids the repeated local sub system optimizations and which also removes the problem of non-linear sensitivity inherent in the single step approaches. Fall-zone constraints, structural load constraints and thermal constraints are considered. In this algorithm, there is only a single multi-level sequence of state and multiplier updates in a framework of an augmented Lagrangian. Han Tapia multiplier updates are used in view of their special role in diagonalised methods, being the only single update with quadratic convergence. For a single level, the diagonalised multiplier method (DMM) is described in Ref.5. The main advantage of the two-level analogue of the DMM approach is that it avoids the inner loop optimizations required in the other methods. The scheme also introduces a gradient change measure to reduce the computational time needed to calculate the gradients. It is demonstrated that the new multi-level scheme leads to a robust procedure to handle the sensitivity of the constraints, and the multiple objectives of different trajectory phases. Ref. 1. Fahroo, F and Ross, M., " A Spectral Patching Method for Direct Trajectory Optimization" The Journal of the Astronautical Sciences, Vol.48, 2000, pp.269-286 Ref. 2. Phililps, C.A. and Drake, J.C., "Trajectory Optimization for a Missile using a Multitier Approach" Journal of Spacecraft and Rockets, Vol.37, 2000, pp.663-669 Ref. 3. Gath, P.F., and Calise, A.J., " Optimization of Launch Vehicle Ascent Trajectories with Path Constraints and Coast Arcs", Journal of Guidance, Control, and Dynamics, Vol. 24, 2001, pp.296-304 Ref. 4. Betts, J.T., " Survey of Numerical Methods for Trajectory Optimization", Journal of Guidance, Control, and Dynamics, Vol.21, 1998, pp. 193-207 Ref. 5. Adimurthy, V., " Launch Vehicle Trajectory Optimization", Acta Astronautica, Vol.15, 1987, pp.845-850.

Visual display aid for orbital maneuvering - Design considerations

NASA Technical Reports Server (NTRS)

Grunwald, Arthur J.; Ellis, Stephen R.

1993-01-01

This paper describes the development of an interactive proximity operations planning system that allows on-site planning of fuel-efficient multiburn maneuvers in a potential multispacecraft environment. Although this display system most directly assists planning by providing visual feedback to aid visualization of the trajectories and constraints, its most significant features include: (1) the use of an 'inverse dynamics' algorithm that removes control nonlinearities facing the operator, and (2) a trajectory planning technique that separates, through a 'geometric spreadsheet', the normally coupled complex problems of planning orbital maneuvers and allows solution by an iterative sequence of simple independent actions. The visual feedback of trajectory shapes and operational constraints, provided by user-transparent and continuously active background computations, allows the operator to make fast, iterative design changes that rapidly converge to fuel-efficient solutions. The planning tool provides an example of operator-assisted optimization of nonlinear cost functions.

Two-Year Trajectory of Fall Risk in People With Parkinson Disease: A Latent Class Analysis.

PubMed

Paul, Serene S; Thackeray, Anne; Duncan, Ryan P; Cavanaugh, James T; Ellis, Theresa D; Earhart, Gammon M; Ford, Matthew P; Foreman, K Bo; Dibble, Leland E

2016-03-01

To examine fall risk trajectories occurring naturally in a sample of individuals with early to middle stage Parkinson disease (PD). Latent class analysis, specifically growth mixture modeling (GMM), of longitudinal fall risk trajectories. Assessments were conducted at 1 of 4 universities. Community-dwelling participants with PD of a longitudinal cohort study who attended at least 2 of 5 assessments over a 2-year follow-up period (N=230). Not applicable. Fall risk trajectory (low, medium, or high risk) and stability of fall risk trajectory (stable or fluctuating). Fall risk was determined at 6 monthly intervals using a simple clinical tool based on fall history, freezing of gait, and gait speed. The GMM optimally grouped participants into 3 fall risk trajectories that closely mirrored baseline fall risk status (P=.001). The high fall risk trajectory was most common (42.6%) and included participants with longer and more severe disease and with higher postural instability and gait disability (PIGD) scores than the low and medium fall risk trajectories (P<.001). Fluctuating fall risk (posterior probability <0.8 of belonging to any trajectory) was found in only 22.6% of the sample, most commonly among individuals who were transitioning to PIGD predominance. Regardless of their baseline characteristics, most participants had clear and stable fall risk trajectories over 2 years. Further investigation is required to determine whether interventions to improve gait and balance may improve fall risk trajectories in people with PD. Copyright © 2016 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

Adaptive surrogate model based multi-objective transfer trajectory optimization between different libration points

NASA Astrophysics Data System (ADS)

Peng, Haijun; Wang, Wei

2016-10-01

An adaptive surrogate model-based multi-objective optimization strategy that combines the benefits of invariant manifolds and low-thrust control toward developing a low-computational-cost transfer trajectory between libration orbits around the L1 and L2 libration points in the Sun-Earth system has been proposed in this paper. A new structure for a multi-objective transfer trajectory optimization model that divides the transfer trajectory into several segments and gives the dominations for invariant manifolds and low-thrust control in different segments has been established. To reduce the computational cost of multi-objective transfer trajectory optimization, a mixed sampling strategy-based adaptive surrogate model has been proposed. Numerical simulations show that the results obtained from the adaptive surrogate-based multi-objective optimization are in agreement with the results obtained using direct multi-objective optimization methods, and the computational workload of the adaptive surrogate-based multi-objective optimization is only approximately 10% of that of direct multi-objective optimization. Furthermore, the generating efficiency of the Pareto points of the adaptive surrogate-based multi-objective optimization is approximately 8 times that of the direct multi-objective optimization. Therefore, the proposed adaptive surrogate-based multi-objective optimization provides obvious advantages over direct multi-objective optimization methods.

Advanced launch system trajectory optimization using suboptimal control

NASA Technical Reports Server (NTRS)

Shaver, Douglas A.; Hull, David G.

1993-01-01

The maximum-final mass trajectory of a proposed configuration of the Advanced Launch System is presented. A model for the two-stage rocket is given; the optimal control problem is formulated as a parameter optimization problem; and the optimal trajectory is computed using a nonlinear programming code called VF02AD. Numerical results are presented for the controls (angle of attack and velocity roll angle) and the states. After the initial rotation, the angle of attack goes to a positive value to keep the trajectory as high as possible, returns to near zero to pass through the transonic regime and satisfy the dynamic pressure constraint, returns to a positive value to keep the trajectory high and to take advantage of minimum drag at positive angle of attack due to aerodynamic shading of the booster, and then rolls off to negative values to satisfy the constraints. Because the engines cannot be throttled, the maximum dynamic pressure occurs at a single point; there is no maximum dynamic pressure subarc. To test approximations for obtaining analytical solutions for guidance, two additional optimal trajectories are computed: one using untrimmed aerodynamics and one using no atmospheric effects except for the dynamic pressure constraint. It is concluded that untrimmed aerodynamics has a negligible effect on the optimal trajectory and that approximate optimal controls should be able to be obtained by treating atmospheric effects as perturbations.

Overview and Software Architecture of the Copernicus Trajectory Design and Optimization System

NASA Technical Reports Server (NTRS)

Williams, Jacob; Senent, Juan S.; Ocampo, Cesar; Mathur, Ravi; Davis, Elizabeth C.

2010-01-01

The Copernicus Trajectory Design and Optimization System represents an innovative and comprehensive approach to on-orbit mission design, trajectory analysis and optimization. Copernicus integrates state of the art algorithms in optimization, interactive visualization, spacecraft state propagation, and data input-output interfaces, allowing the analyst to design spacecraft missions to all possible Solar System destinations. All of these features are incorporated within a single architecture that can be used interactively via a comprehensive GUI interface, or passively via external interfaces that execute batch processes. This paper describes the Copernicus software architecture together with the challenges associated with its implementation. Additionally, future development and planned new capabilities are discussed. Key words: Copernicus, Spacecraft Trajectory Optimization Software.

Feedback Implementation of Zermelo's Optimal Control by Sugeno Approximation

NASA Technical Reports Server (NTRS)

Clifton, C.; Homaifax, A.; Bikdash, M.

1997-01-01

This paper proposes an approach to implement optimal control laws of nonlinear systems in real time. Our methodology does not require solving two-point boundary value problems online and may not require it off-line either. The optimal control law is learned using the original Sugeno controller (OSC) from a family of optimal trajectories. We compare the trajectories generated by the OSC and the trajectories yielded by the optimal feedback control law when applied to Zermelo's ship steering problem.

Optimal Trajectories Generation in Robotic Fiber Placement Systems

NASA Astrophysics Data System (ADS)

Gao, Jiuchun; Pashkevich, Anatol; Caro, Stéphane

2017-06-01

The paper proposes a methodology for optimal trajectories generation in robotic fiber placement systems. A strategy to tune the parameters of the optimization algorithm at hand is also introduced. The presented technique transforms the original continuous problem into a discrete one where the time-optimal motions are generated by using dynamic programming. The developed strategy for the optimization algorithm tuning allows essentially reducing the computing time and obtaining trajectories satisfying industrial constraints. Feasibilities and advantages of the proposed methodology are confirmed by an application example.

Overview of the Development for a Suite of Low-Thrust Trajectory Analysis Tools

NASA Technical Reports Server (NTRS)

Kos, Larry D.; Polsgrove, Tara; Hopkins, Randall; Thomas, Dan; Sims, Jon A.

2006-01-01

A NASA intercenter team has developed a suite of low-thrust trajectory analysis tools to make a significant improvement in three major facets of low-thrust trajectory and mission analysis. These are: 1) ease of use, 2) ability to more robustly converge to solutions, and 3) higher fidelity modeling and accuracy of results. Due mostly to the short duration of the development, the team concluded that a suite of tools was preferred over having one integrated tool. This tool-suite, their characteristics, and their applicability will be described. Trajectory analysts can read this paper and determine which tool is most appropriate for their problem.

Coupled Solid Rocket Motor Ballistics and Trajectory Modeling for Higher Fidelity Launch Vehicle Design

NASA Technical Reports Server (NTRS)

Ables, Brett

2014-01-01

Multi-stage launch vehicles with solid rocket motors (SRMs) face design optimization challenges, especially when the mission scope changes frequently. Significant performance benefits can be realized if the solid rocket motors are optimized to the changing requirements. While SRMs represent a fixed performance at launch, rapid design iterations enable flexibility at design time, yielding significant performance gains. The streamlining and integration of SRM design and analysis can be achieved with improved analysis tools. While powerful and versatile, the Solid Performance Program (SPP) is not conducive to rapid design iteration. Performing a design iteration with SPP and a trajectory solver is a labor intensive process. To enable a better workflow, SPP, the Program to Optimize Simulated Trajectories (POST), and the interfaces between them have been improved and automated, and a graphical user interface (GUI) has been developed. The GUI enables real-time visual feedback of grain and nozzle design inputs, enforces parameter dependencies, removes redundancies, and simplifies manipulation of SPP and POST's numerous options. Automating the analysis also simplifies batch analyses and trade studies. Finally, the GUI provides post-processing, visualization, and comparison of results. Wrapping legacy high-fidelity analysis codes with modern software provides the improved interface necessary to enable rapid coupled SRM ballistics and vehicle trajectory analysis. Low cost trade studies demonstrate the sensitivities of flight performance metrics to propulsion characteristics. Incorporating high fidelity analysis from SPP into vehicle design reduces performance margins and improves reliability. By flying an SRM designed with the same assumptions as the rest of the vehicle, accurate comparisons can be made between competing architectures. In summary, this flexible workflow is a critical component to designing a versatile launch vehicle model that can accommodate a volatile mission scope.

Trajectory Design Tools for Libration and Cis-Lunar Environments

NASA Technical Reports Server (NTRS)

Folta, David C.; Webster, Cassandra M.; Bosanac, Natasha; Cox, Andrew; Guzzetti, Davide; Howell, Kathleen C.

2016-01-01

Innovative trajectory design tools are required to support challenging multi-body regimes with complex dynamics, uncertain perturbations, and the integration of propulsion influences. Two distinctive tools, Adaptive Trajectory Design and the General Mission Analysis Tool have been developed and certified to provide the astrodynamics community with the ability to design multi-body trajectories. In this paper we discuss the multi-body design process and the capabilities of both tools. Demonstrable applications to confirmed missions, the Lunar IceCube Cubesat lunar mission and the Wide-Field Infrared Survey Telescope (WFIRST) Sun-Earth L2 mission, are presented.

A fast inverse treatment planning strategy facilitating optimized catheter selection in image-guided high-dose-rate interstitial gynecologic brachytherapy.

PubMed

Guthier, Christian V; Damato, Antonio L; Hesser, Juergen W; Viswanathan, Akila N; Cormack, Robert A

2017-12-01

Interstitial high-dose rate (HDR) brachytherapy is an important therapeutic strategy for the treatment of locally advanced gynecologic (GYN) cancers. The outcome of this therapy is determined by the quality of dose distribution achieved. This paper focuses on a novel yet simple heuristic for catheter selection for GYN HDR brachytherapy and their comparison against state of the art optimization strategies. The proposed technique is intended to act as a decision-supporting tool to select a favorable needle configuration. The presented heuristic for catheter optimization is based on a shrinkage-type algorithm (SACO). It is compared against state of the art planning in a retrospective study of 20 patients who previously received image-guided interstitial HDR brachytherapy using a Syed Neblett template. From those plans, template orientation and position are estimated via a rigid registration of the template with the actual catheter trajectories. All potential straight trajectories intersecting the contoured clinical target volume (CTV) are considered for catheter optimization. Retrospectively generated plans and clinical plans are compared with respect to dosimetric performance and optimization time. All plans were generated with one single run of the optimizer lasting 0.6-97.4 s. Compared to manual optimization, SACO yields a statistically significant (P ≤ 0.05) improved target coverage while at the same time fulfilling all dosimetric constraints for organs at risk (OARs). Comparing inverse planning strategies, dosimetric evaluation for SACO and "hybrid inverse planning and optimization" (HIPO), as gold standard, shows no statistically significant difference (P > 0.05). However, SACO provides the potential to reduce the number of used catheters without compromising plan quality. The proposed heuristic for needle selection provides fast catheter selection with optimization times suited for intraoperative treatment planning. Compared to manual optimization, the proposed methodology results in fewer catheters without a clinically significant loss in plan quality. The proposed approach can be used as a decision support tool that guides the user to find the ideal number and configuration of catheters. © 2017 American Association of Physicists in Medicine.

Interplanetary program to optimize simulated trajectories (IPOST). Volume 4: Sample cases

NASA Technical Reports Server (NTRS)

Hong, P. E.; Kent, P. D; Olson, D. W.; Vallado, C. A.

1992-01-01

The Interplanetary Program to Optimize Simulated Trajectories (IPOST) is intended to support many analysis phases, from early interplanetary feasibility studies through spacecraft development and operations. The IPOST output provides information for sizing and understanding mission impacts related to propulsion, guidance, communications, sensor/actuators, payload, and other dynamic and geometric environments. IPOST models three degree of freedom trajectory events, such as launch/ascent, orbital coast, propulsive maneuvering (impulsive and finite burn), gravity assist, and atmospheric entry. Trajectory propagation is performed using a choice of Cowell, Encke, Multiconic, Onestep, or Conic methods. The user identifies a desired sequence of trajectory events, and selects which parameters are independent (controls) and dependent (targets), as well as other constraints and the cost function. Targeting and optimization are performed using the Standard NPSOL algorithm. The IPOST structure allows sub-problems within a master optimization problem to aid in the general constrained parameter optimization solution. An alternate optimization method uses implicit simulation and collocation techniques.

The effect of parking orbit constraints on the optimization of ballistic planetary trajectories

NASA Technical Reports Server (NTRS)

Sauer, C. G., Jr.

1984-01-01

The optimization of ballistic planetary trajectories is developed which includes constraints on departure parking orbit inclination and node. This problem is formulated to result in a minimum total Delta V where the entire constrained injection Delta V is included in the optimization. An additional Delta V is also defined to allow for possible optimization of parking orbit inclination when the launch vehicle orbit capability varies as a function of parking orbit inclination. The optimization problem is formulated using primer vector theory to derive partial derivatives of total Delta V with respect to possible free parameters. Minimization of total Delta V is accomplished using a quasi-Newton gradient search routine. The analysis is applied to an Eros rendezvous mission whose transfer trajectories are characterized by high values of launch asymptote declination during particular launch opportunities. Comparisons in performance are made between trajectories where parking orbit constraints are included in the optimization and trajectories where the constraints are not included.

An Automated Method to Compute Orbital Re-entry Trajectories with Heating Constraints

NASA Technical Reports Server (NTRS)

Zimmerman, Curtis; Dukeman, Greg; Hanson, John; Fogle, Frank R. (Technical Monitor)

2002-01-01

Determining how to properly manipulate the controls of a re-entering re-usable launch vehicle (RLV) so that it is able to safely return to Earth and land involves the solution of a two-point boundary value problem (TPBVP). This problem, which can be quite difficult, is traditionally solved on the ground prior to flight. If necessary, a nearly unlimited amount of time is available to find the 'best' solution using a variety of trajectory design and optimization tools. The role of entry guidance during flight is to follow the pre- determined reference solution while correcting for any errors encountered along the way. This guidance method is both highly reliable and very efficient in terms of onboard computer resources. There is a growing interest in a style of entry guidance that places the responsibility of solving the TPBVP in the actual entry guidance flight software. Here there is very limited computer time. The powerful, but finicky, mathematical tools used by trajectory designers on the ground cannot in general be converted to do the job. Non-convergence or slow convergence can result in disaster. The challenges of designing such an algorithm are numerous and difficult. Yet the payoff (in the form of decreased operational costs and increased safety) can be substantiaL This paper presents an algorithm that incorporates features of both types of guidance strategies. It takes an initial RLV orbital re-entry state and finds a trajectory that will safely transport the vehicle to Earth. During actual flight, the computed trajectory is used as the reference to be flown by a more traditional guidance method.

Design and Analysis of Optimal Ascent Trajectories for Stratospheric Airships

NASA Astrophysics Data System (ADS)

Mueller, Joseph Bernard

Stratospheric airships are lighter-than-air vehicles that have the potential to provide a long-duration airborne presence at altitudes of 18-22 km. Designed to operate on solar power in the calm portion of the lower stratosphere and above all regulated air traffic and cloud cover, these vehicles represent an emerging platform that resides between conventional aircraft and satellites. A particular challenge for airship operation is the planning of ascent trajectories, as the slow moving vehicle must traverse the high wind region of the jet stream. Due to large changes in wind speed and direction across altitude and the susceptibility of airship motion to wind, the trajectory must be carefully planned, preferably optimized, in order to ensure that the desired station be reached within acceptable performance bounds of flight time and energy consumption. This thesis develops optimal ascent trajectories for stratospheric airships, examines the structure and sensitivity of these solutions, and presents a strategy for onboard guidance. Optimal ascent trajectories are developed that utilize wind energy to achieve minimum-time and minimum-energy flights. The airship is represented by a three-dimensional point mass model, and the equations of motion include aerodynamic lift and drag, vectored thrust, added mass effects, and accelerations due to mass flow rate, wind rates, and Earth rotation. A representative wind profile is developed based on historical meteorological data and measurements. Trajectory optimization is performed by first defining an optimal control problem with both terminal and path constraints, then using direct transcription to develop an approximate nonlinear parameter optimization problem of finite dimension. Optimal ascent trajectories are determined using SNOPT for a variety of upwind, downwind, and crosswind launch locations. Results of extensive optimization solutions illustrate definitive patterns in the ascent path for minimum time flights across varying launch locations, and show that significant energy savings can be realized with minimum-energy flights, compared to minimum-time time flights, given small increases in flight time. The performance of the optimal trajectories are then studied with respect to solar energy production during ascent, as well as sensitivity of the solutions to small changes in drag coefficient and wind model parameters. Results of solar power model simulations indicate that solar energy is sufficient to power ascent flights, but that significant energy loss can occur for certain types of trajectories. Sensitivity to the drag and wind model is approximated through numerical simulations, showing that optimal solutions change gradually with respect to changing wind and drag parameters and providing deeper insight into the characteristics of optimal airship flights. Finally, alternative methods are developed to generate near-optimal ascent trajectories in a manner suitable for onboard implementation. The structures and characteristics of previously developed minimum-time and minimum-energy ascent trajectories are used to construct simplified trajectory models, which are efficiently solved in a smaller numerical optimization problem. Comparison of these alternative solutions to the original SNOPT solutions show excellent agreement, suggesting the alternate formulations are an effective means to develop near-optimal solutions in an onboard setting.

Simulation and Application of GPOPS for a Trajectory Optimization and Mission Planning Tool

DTIC Science & Technology

2010-03-01

12,000lbf) vaccum Specific Impulse 269 s 455 s 316 s Burn Time 124 s 480 s 1250s Fuel Solid LOX/ LH2 MMH/N2O4 Height 184 ft Diameter 28.5 ft...285,000 lb Engine 2 J-2S Linear Aerospikes Thrust 410,000 lbf Fuel LOX/ LH2 20 Figure 9: Minuteman Launch [29] Currently the main missile

Minimum Hamiltonian Ascent Trajectory Evaluation (MASTRE) program (update to automatic flight trajectory design, performance prediction, and vehicle sizing for support of Shuttle and Shuttle derived vehicles) engineering manual

NASA Technical Reports Server (NTRS)

Lyons, J. T.

1993-01-01

The Minimum Hamiltonian Ascent Trajectory Evaluation (MASTRE) program and its predecessors, the ROBOT and the RAGMOP programs, have had a long history of supporting MSFC in the simulation of space boosters for the purpose of performance evaluation. The ROBOT program was used in the simulation of the Saturn 1B and Saturn 5 vehicles in the 1960's and provided the first utilization of the minimum Hamiltonian (or min-H) methodology and the steepest ascent technique to solve the optimum trajectory problem. The advent of the Space Shuttle in the 1970's and its complex airplane design required a redesign of the trajectory simulation code since aerodynamic flight and controllability were required for proper simulation. The RAGMOP program was the first attempt to incorporate the complex equations of the Space Shuttle into an optimization tool by using an optimization method based on steepest ascent techniques (but without the min-H methodology). Development of the complex partial derivatives associated with the Space Shuttle configuration and using techniques from the RAGMOP program, the ROBOT program was redesigned to incorporate these additional complexities. This redesign created the MASTRE program, which was referred to as the Minimum Hamiltonian Ascent Shuttle TRajectory Evaluation program at that time. Unique to this program were first-stage (or booster) nonlinear aerodynamics, upper-stage linear aerodynamics, engine control via moment balance, liquid and solid thrust forces, variable liquid throttling to maintain constant acceleration limits, and a total upgrade of the equations used in the forward and backward integration segments of the program. This modification of the MASTRE code has been used to simulate the new space vehicles associated with the National Launch Systems (NLS). Although not as complicated as the Space Shuttle, the simulation and analysis of the NLS vehicles required additional modifications to the MASTRE program in the areas of providing additional flexibility in the use of the program, allowing additional optimization options, and providing special options for the NLS configuration.

Thermally-Constrained Fuel-Optimal ISS Maneuvers

NASA Technical Reports Server (NTRS)

Bhatt, Sagar; Svecz, Andrew; Alaniz, Abran; Jang, Jiann-Woei; Nguyen, Louis; Spanos, Pol

2015-01-01

Optimal Propellant Maneuvers (OPMs) are now being used to rotate the International Space Station (ISS) and have saved hundreds of kilograms of propellant over the last two years. The savings are achieved by commanding the ISS to follow a pre-planned attitude trajectory optimized to take advantage of environmental torques. The trajectory is obtained by solving an optimal control problem. Prior to use on orbit, OPM trajectories are screened to ensure a static sun vector (SSV) does not occur during the maneuver. The SSV is an indicator that the ISS hardware temperatures may exceed thermal limits, causing damage to the components. In this paper, thermally-constrained fuel-optimal trajectories are presented that avoid an SSV and can be used throughout the year while still reducing propellant consumption significantly.

Mission Analysis, Operations, and Navigation Toolkit Environment (Monte) Version 040

NASA Technical Reports Server (NTRS)

Sunseri, Richard F.; Wu, Hsi-Cheng; Evans, Scott E.; Evans, James R.; Drain, Theodore R.; Guevara, Michelle M.

2012-01-01

Monte is a software set designed for use in mission design and spacecraft navigation operations. The system can process measurement data, design optimal trajectories and maneuvers, and do orbit determination, all in one application. For the first time, a single software set can be used for mission design and navigation operations. This eliminates problems due to different models and fidelities used in legacy mission design and navigation software. The unique features of Monte 040 include a blowdown thruster model for GRAIL (Gravity Recovery and Interior Laboratory) with associated pressure models, as well as an updated, optimalsearch capability (COSMIC) that facilitated mission design for ARTEMIS. Existing legacy software lacked the capabilities necessary for these two missions. There is also a mean orbital element propagator and an osculating to mean element converter that allows long-term orbital stability analysis for the first time in compiled code. The optimized trajectory search tool COSMIC allows users to place constraints and controls on their searches without any restrictions. Constraints may be user-defined and depend on trajectory information either forward or backwards in time. In addition, a long-term orbit stability analysis tool (morbiter) existed previously as a set of scripts on top of Monte. Monte is becoming the primary tool for navigation operations, a core competency at JPL. The mission design capabilities in Monte are becoming mature enough for use in project proposals as well as post-phase A mission design. Monte has three distinct advantages over existing software. First, it is being developed in a modern paradigm: object- oriented C++ and Python. Second, the software has been developed as a toolkit, which allows users to customize their own applications and allows the development team to implement requirements quickly, efficiently, and with minimal bugs. Finally, the software is managed in accordance with the CMMI (Capability Maturity Model Integration), where it has been ap praised at maturity level 3.

Launch vehicle design and GNC sizing with ASTOS

NASA Astrophysics Data System (ADS)

Cremaschi, Francesco; Winter, Sebastian; Rossi, Valerio; Wiegand, Andreas

2018-03-01

The European Space Agency (ESA) is currently involved in several activities related to launch vehicle designs (Future Launcher Preparatory Program, Ariane 6, VEGA evolutions, etc.). Within these activities, ESA has identified the importance of developing a simulation infrastructure capable of supporting the multi-disciplinary design and preliminary guidance navigation and control (GNC) design of different launch vehicle configurations. Astos Solutions has developed the multi-disciplinary optimization and launcher GNC simulation and sizing tool (LGSST) under ESA contract. The functionality is integrated in the Analysis, Simulation and Trajectory Optimization Software for space applications (ASTOS) and is intended to be used from the early design phases up to phase B1 activities. ASTOS shall enable the user to perform detailed vehicle design tasks and assessment of GNC systems, covering all aspects of rapid configuration and scenario management, sizing of stages, trajectory-dependent estimation of structural masses, rigid and flexible body dynamics, navigation, guidance and control, worst case analysis, launch safety analysis, performance analysis, and reporting.

The Tool for Designing Engineering Systems Using a New Optimization Method Based on a Stochastic Process

NASA Astrophysics Data System (ADS)

Yoshida, Hiroaki; Yamaguchi, Katsuhito; Ishikawa, Yoshio

The conventional optimization methods were based on a deterministic approach, since their purpose is to find out an exact solution. However, these methods have initial condition dependence and risk of falling into local solution. In this paper, we propose a new optimization method based on a concept of path integral method used in quantum mechanics. The method obtains a solutions as an expected value (stochastic average) using a stochastic process. The advantages of this method are not to be affected by initial conditions and not to need techniques based on experiences. We applied the new optimization method to a design of the hang glider. In this problem, not only the hang glider design but also its flight trajectory were optimized. The numerical calculation results showed that the method has a sufficient performance.

Optimization of interplanetary trajectories with unpowered planetary swingbys

NASA Technical Reports Server (NTRS)

Sauer, Carl G., Jr.

1988-01-01

A method is presented for calculating and optimizing unpowered planetary swingby trajectories using a patched conic trajectory generator. Examples of unpowered swingby trajectories are given to demonstrate the method. The method, which uses primer vector theory, is not highly accurate, but provides projections for preliminary mission definition studies. Advantages to using a patched conic trajectory simulation for preliminary studies which examine many different and complex missions include calculation speed and adaptability to changes or additions to the formulation.

Rapid indirect trajectory optimization on highly parallel computing architectures

NASA Astrophysics Data System (ADS)

Antony, Thomas

Trajectory optimization is a field which can benefit greatly from the advantages offered by parallel computing. The current state-of-the-art in trajectory optimization focuses on the use of direct optimization methods, such as the pseudo-spectral method. These methods are favored due to their ease of implementation and large convergence regions while indirect methods have largely been ignored in the literature in the past decade except for specific applications in astrodynamics. It has been shown that the shortcomings conventionally associated with indirect methods can be overcome by the use of a continuation method in which complex trajectory solutions are obtained by solving a sequence of progressively difficult optimization problems. High performance computing hardware is trending towards more parallel architectures as opposed to powerful single-core processors. Graphics Processing Units (GPU), which were originally developed for 3D graphics rendering have gained popularity in the past decade as high-performance, programmable parallel processors. The Compute Unified Device Architecture (CUDA) framework, a parallel computing architecture and programming model developed by NVIDIA, is one of the most widely used platforms in GPU computing. GPUs have been applied to a wide range of fields that require the solution of complex, computationally demanding problems. A GPU-accelerated indirect trajectory optimization methodology which uses the multiple shooting method and continuation is developed using the CUDA platform. The various algorithmic optimizations used to exploit the parallelism inherent in the indirect shooting method are described. The resulting rapid optimal control framework enables the construction of high quality optimal trajectories that satisfy problem-specific constraints and fully satisfy the necessary conditions of optimality. The benefits of the framework are highlighted by construction of maximum terminal velocity trajectories for a hypothetical long range weapon system. The techniques used to construct an initial guess from an analytic near-ballistic trajectory and the methods used to formulate the necessary conditions of optimality in a manner that is transparent to the designer are discussed. Various hypothetical mission scenarios that enforce different combinations of initial, terminal, interior point and path constraints demonstrate the rapid construction of complex trajectories without requiring any a-priori insight into the structure of the solutions. Trajectory problems of this kind were previously considered impractical to solve using indirect methods. The performance of the GPU-accelerated solver is found to be 2x--4x faster than MATLAB's bvp4c, even while running on GPU hardware that is five years behind the state-of-the-art.

Optimizing Mars Airplane Trajectory with the Application Navigation System

NASA Technical Reports Server (NTRS)

Frumkin, Michael; Riley, Derek

2004-01-01

Planning complex missions requires a number of programs to be executed in concert. The Application Navigation System (ANS), developed in the NAS Division, can execute many interdependent programs in a distributed environment. We show that the ANS simplifies user effort and reduces time in optimization of the trajectory of a martian airplane. We use a software package, Cart3D, to evaluate trajectories and a shortest path algorithm to determine the optimal trajectory. ANS employs the GridScape to represent the dynamic state of the available computer resources. Then, ANS uses a scheduler to dynamically assign ready task to machine resources and the GridScape for tracking available resources and forecasting completion time of running tasks. We demonstrate system capability to schedule and run the trajectory optimization application with efficiency exceeding 60% on 64 processors.

Guidance and Control strategies for aerospace vehicles

NASA Technical Reports Server (NTRS)

Hibey, J. L.; Naidu, D. S.; Charalambous, C. D.

1989-01-01

A neighboring optimal guidance scheme was devised for a nonlinear dynamic system with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory was determined. Then, a neighboring, optimal guidance scheme was obtained for open loop and closed loop control configurations. Taking modelling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme was devised. Finally, the optimal trajectory was approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical vehicle. A fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is also addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in reference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions.

Reactive Collision Avoidance Algorithm

NASA Technical Reports Server (NTRS)

Scharf, Daniel; Acikmese, Behcet; Ploen, Scott; Hadaegh, Fred

2010-01-01

The reactive collision avoidance (RCA) algorithm allows a spacecraft to find a fuel-optimal trajectory for avoiding an arbitrary number of colliding spacecraft in real time while accounting for acceleration limits. In addition to spacecraft, the technology can be used for vehicles that can accelerate in any direction, such as helicopters and submersibles. In contrast to existing, passive algorithms that simultaneously design trajectories for a cluster of vehicles working to achieve a common goal, RCA is implemented onboard spacecraft only when an imminent collision is detected, and then plans a collision avoidance maneuver for only that host vehicle, thus preventing a collision in an off-nominal situation for which passive algorithms cannot. An example scenario for such a situation might be when a spacecraft in the cluster is approaching another one, but enters safe mode and begins to drift. Functionally, the RCA detects colliding spacecraft, plans an evasion trajectory by solving the Evasion Trajectory Problem (ETP), and then recovers after the collision is avoided. A direct optimization approach was used to develop the algorithm so it can run in real time. In this innovation, a parameterized class of avoidance trajectories is specified, and then the optimal trajectory is found by searching over the parameters. The class of trajectories is selected as bang-off-bang as motivated by optimal control theory. That is, an avoiding spacecraft first applies full acceleration in a constant direction, then coasts, and finally applies full acceleration to stop. The parameter optimization problem can be solved offline and stored as a look-up table of values. Using a look-up table allows the algorithm to run in real time. Given a colliding spacecraft, the properties of the collision geometry serve as indices of the look-up table that gives the optimal trajectory. For multiple colliding spacecraft, the set of trajectories that avoid all spacecraft is rapidly searched on-line. The optimal avoidance trajectory is implemented as a receding-horizon model predictive control law. Therefore, at each time step, the optimal avoidance trajectory is found and the first time step of its acceleration is applied. At the next time step of the control computer, the problem is re-solved and the new first time step is again applied. This continual updating allows the RCA algorithm to adapt to a colliding spacecraft that is making erratic course changes.

A Method of Trajectory Design for Manned Asteroid Explorations1,2

NASA Astrophysics Data System (ADS)

Gan, Qing-Bo; Zhang, Yang; Zhu, Zheng-Fan; Han, Wei-Hua; Dong, Xin

2015-07-01

A trajectory optimization method for the nuclear-electric propulsion manned asteroid explorations is presented. In the case of launching between 2035 and 2065, based on the two-pulse single-cycle Lambert transfer orbit, the phases of departure from and return to the Earth are searched at first. Then the optimal flight trajectory is selected by pruning the flight sequences in two feasible regions. Setting the flight strategy of propelling-taxiing-propelling, and taking the minimal fuel consumption as the performance index, the nuclear-electric propulsion flight trajectory is optimized using the hybrid method. Finally, taking the segmentally optimized parameters as the initial values, in accordance with the overall mission constraints, the globally optimized parameters are obtained. And the numerical and diagrammatical results are given at the same time.

Program manual for ASTOP, an Arbitrary space trajectory optimization program

NASA Technical Reports Server (NTRS)

Horsewood, J. L.

1974-01-01

The ASTOP program (an Arbitrary Space Trajectory Optimization Program) designed to generate optimum low-thrust trajectories in an N-body field while satisfying selected hardware and operational constraints is presented. The trajectory is divided into a number of segments or arcs over which the control is held constant. This constant control over each arc is optimized using a parameter optimization scheme based on gradient techniques. A modified Encke formulation of the equations of motion is employed. The program provides a wide range of constraint, end conditions, and performance index options. The basic approach is conducive to future expansion of features such as the incorporation of new constraints and the addition of new end conditions.

Dimensioning appropriate technical and economic parameters of elements in urban distribution power nets based on discrete fast marching method

NASA Astrophysics Data System (ADS)

Afanasyev, A. P.; Bazhenov, R. I.; Luchaninov, D. V.

2018-05-01

The main purpose of the research is to develop techniques for defining the best technical and economic trajectories of cables in urban power systems. The proposed algorithms of calculation of the routes for laying cables take into consideration topological, technical and economic features of the cabling. The discrete option of an algorithm Fast marching method is applied as a calculating tool. It has certain advantages compared to other approaches. In particular, this algorithm is cost-effective to compute, therefore, it is not iterative. Trajectories of received laying cables are considered as optimal ones from the point of view of technical and economic criteria. They correspond to the present rules of modern urban development.

Trajectory Optimization of Electric Aircraft Subject to Subsystem Thermal Constraints

NASA Technical Reports Server (NTRS)

Falck, Robert D.; Chin, Jeffrey C.; Schnulo, Sydney L.; Burt, Jonathan M.; Gray, Justin S.

2017-01-01

Electric aircraft pose a unique design challenge in that they lack a simple way to reject waste heat from the power train. While conventional aircraft reject most of their excess heat in the exhaust stream, for electric aircraft this is not an option. To examine the implications of this challenge on electric aircraft design and performance, we developed a model of the electric subsystems for the NASA X-57 electric testbed aircraft. We then coupled this model with a model of simple 2D aircraft dynamics and used a Legendre-Gauss-Lobatto collocation optimal control approach to find optimal trajectories for the aircraft with and without thermal constraints. The results show that the X-57 heat rejection systems are well designed for maximum-range and maximum-efficiency flight, without the need to deviate from an optimal trajectory. Stressing the thermal constraints by reducing the cooling capacity or requiring faster flight has a minimal impact on performance, as the trajectory optimization technique is able to find flight paths which honor the thermal constraints with relatively minor deviations from the nominal optimal trajectory.

Rapid Generation of Optimal Asteroid Powered Descent Trajectories Via Convex Optimization

NASA Technical Reports Server (NTRS)

Pinson, Robin; Lu, Ping

2015-01-01

This paper investigates a convex optimization based method that can rapidly generate the fuel optimal asteroid powered descent trajectory. The ultimate goal is to autonomously design the optimal powered descent trajectory on-board the spacecraft immediately prior to the descent burn. Compared to a planetary powered landing problem, the major difficulty is the complex gravity field near the surface of an asteroid that cannot be approximated by a constant gravity field. This paper uses relaxation techniques and a successive solution process that seeks the solution to the original nonlinear, nonconvex problem through the solutions to a sequence of convex optimal control problems.

Swing-leg trajectory of running guinea fowl suggests task-level priority of force regulation rather than disturbance rejection.

PubMed

Blum, Yvonne; Vejdani, Hamid R; Birn-Jeffery, Aleksandra V; Hubicki, Christian M; Hurst, Jonathan W; Daley, Monica A

2014-01-01

To achieve robust and stable legged locomotion in uneven terrain, animals must effectively coordinate limb swing and stance phases, which involve distinct yet coupled dynamics. Recent theoretical studies have highlighted the critical influence of swing-leg trajectory on stability, disturbance rejection, leg loading and economy of walking and running. Yet, simulations suggest that not all these factors can be simultaneously optimized. A potential trade-off arises between the optimal swing-leg trajectory for disturbance rejection (to maintain steady gait) versus regulation of leg loading (for injury avoidance and economy). Here we investigate how running guinea fowl manage this potential trade-off by comparing experimental data to predictions of hypothesis-based simulations of running over a terrain drop perturbation. We use a simple model to predict swing-leg trajectory and running dynamics. In simulations, we generate optimized swing-leg trajectories based upon specific hypotheses for task-level control priorities. We optimized swing trajectories to achieve i) constant peak force, ii) constant axial impulse, or iii) perfect disturbance rejection (steady gait) in the stance following a terrain drop. We compare simulation predictions to experimental data on guinea fowl running over a visible step down. Swing and stance dynamics of running guinea fowl closely match simulations optimized to regulate leg loading (priorities i and ii), and do not match the simulations optimized for disturbance rejection (priority iii). The simulations reinforce previous findings that swing-leg trajectory targeting disturbance rejection demands large increases in stance leg force following a terrain drop. Guinea fowl negotiate a downward step using unsteady dynamics with forward acceleration, and recover to steady gait in subsequent steps. Our results suggest that guinea fowl use swing-leg trajectory consistent with priority for load regulation, and not for steadiness of gait. Swing-leg trajectory optimized for load regulation may facilitate economy and injury avoidance in uneven terrain.

Swing-Leg Trajectory of Running Guinea Fowl Suggests Task-Level Priority of Force Regulation Rather than Disturbance Rejection

PubMed Central

Blum, Yvonne; Vejdani, Hamid R.; Birn-Jeffery, Aleksandra V.; Hubicki, Christian M.; Hurst, Jonathan W.; Daley, Monica A.

2014-01-01

To achieve robust and stable legged locomotion in uneven terrain, animals must effectively coordinate limb swing and stance phases, which involve distinct yet coupled dynamics. Recent theoretical studies have highlighted the critical influence of swing-leg trajectory on stability, disturbance rejection, leg loading and economy of walking and running. Yet, simulations suggest that not all these factors can be simultaneously optimized. A potential trade-off arises between the optimal swing-leg trajectory for disturbance rejection (to maintain steady gait) versus regulation of leg loading (for injury avoidance and economy). Here we investigate how running guinea fowl manage this potential trade-off by comparing experimental data to predictions of hypothesis-based simulations of running over a terrain drop perturbation. We use a simple model to predict swing-leg trajectory and running dynamics. In simulations, we generate optimized swing-leg trajectories based upon specific hypotheses for task-level control priorities. We optimized swing trajectories to achieve i) constant peak force, ii) constant axial impulse, or iii) perfect disturbance rejection (steady gait) in the stance following a terrain drop. We compare simulation predictions to experimental data on guinea fowl running over a visible step down. Swing and stance dynamics of running guinea fowl closely match simulations optimized to regulate leg loading (priorities i and ii), and do not match the simulations optimized for disturbance rejection (priority iii). The simulations reinforce previous findings that swing-leg trajectory targeting disturbance rejection demands large increases in stance leg force following a terrain drop. Guinea fowl negotiate a downward step using unsteady dynamics with forward acceleration, and recover to steady gait in subsequent steps. Our results suggest that guinea fowl use swing-leg trajectory consistent with priority for load regulation, and not for steadiness of gait. Swing-leg trajectory optimized for load regulation may facilitate economy and injury avoidance in uneven terrain. PMID:24979750

Mystic: Implementation of the Static Dynamic Optimal Control Algorithm for High-Fidelity, Low-Thrust Trajectory Design

NASA Technical Reports Server (NTRS)

Whiffen, Gregory J.

2006-01-01

Mystic software is designed to compute, analyze, and visualize optimal high-fidelity, low-thrust trajectories, The software can be used to analyze inter-planetary, planetocentric, and combination trajectories, Mystic also provides utilities to assist in the operation and navigation of low-thrust spacecraft. Mystic will be used to design and navigate the NASA's Dawn Discovery mission to orbit the two largest asteroids, The underlying optimization algorithm used in the Mystic software is called Static/Dynamic Optimal Control (SDC). SDC is a nonlinear optimal control method designed to optimize both 'static variables' (parameters) and dynamic variables (functions of time) simultaneously. SDC is a general nonlinear optimal control algorithm based on Bellman's principal.

Aircraft Trajectories Computation-Prediction-Control. Volume 1 (La Trajectoire de l’Avion Calcul-Prediction-Controle)

DTIC Science & Technology

1990-03-01

knowledge covering problems of this type is called calculus of variations or optimal control theory (Refs. 1-8). As stated before, appli - cations occur...to the optimality conditions and the feasibility equations of Problem (GP), respectively. Clearly, after the transformation (26) is applied , the...trajectories, the primal sequential gradient-restoration algorithm (PSGRA) is applied to compute optimal trajectories for aeroassisted orbital transfer

Ares I-X Malfunction Turn Range Safety Analysis

NASA Technical Reports Server (NTRS)

Beaty, J. R.

2011-01-01

Ares I-X was the designation given to the flight test version of the Ares I rocket which was developed by NASA (also known as the Crew Launch Vehicle (CLV) component of the Constellation Program). The Ares I-X flight test vehicle achieved a successful flight test on October 28, 2009, from Pad LC-39B at Kennedy Space Center, Florida (KSC). As part of the flight plan approval for the test vehicle, a range safety malfunction turn analysis was performed to support the risk assessment and vehicle destruct criteria development processes. Several vehicle failure scenarios were identified which could have caused the vehicle trajectory to deviate from its normal flight path. The effects of these failures were evaluated with an Ares I-X 6 degrees-of-freedom (6-DOF) digital simulation, using the Program to Optimize Simulated Trajectories Version II (POST2) simulation tool. The Ares I-X simulation analysis provided output files containing vehicle trajectory state information. These were used by other risk assessment and vehicle debris trajectory simulation tools to determine the risk to personnel and facilities in the vicinity of the launch area at KSC, and to develop the vehicle destruct criteria used by the flight test range safety officer in the event of a flight test anomaly of the vehicle. The simulation analysis approach used for this study is described, including descriptions of the failure modes which were considered and the underlying assumptions and ground rules of the study.

Fast three-dimensional inner volume excitations using parallel transmission and optimized k-space trajectories.

PubMed

Davids, Mathias; Schad, Lothar R; Wald, Lawrence L; Guérin, Bastien

2016-10-01

To design short parallel transmission (pTx) pulses for excitation of arbitrary three-dimensional (3D) magnetization patterns. We propose a joint optimization of the pTx radiofrequency (RF) and gradient waveforms for excitation of arbitrary 3D magnetization patterns. Our optimization of the gradient waveforms is based on the parameterization of k-space trajectories (3D shells, stack-of-spirals, and cross) using a small number of shape parameters that are well-suited for optimization. The resulting trajectories are smooth and sample k-space efficiently with few turns while using the gradient system at maximum performance. Within each iteration of the k-space trajectory optimization, we solve a small tip angle least-squares RF pulse design problem. Our RF pulse optimization framework was evaluated both in Bloch simulations and experiments on a 7T scanner with eight transmit channels. Using an optimized 3D cross (shells) trajectory, we were able to excite a cube shape (brain shape) with 3.4% (6.2%) normalized root-mean-square error in less than 5 ms using eight pTx channels and a clinical gradient system (Gmax  = 40 mT/m, Smax  = 150 T/m/s). This compared with 4.7% (41.2%) error for the unoptimized 3D cross (shells) trajectory. Incorporation of B0 robustness in the pulse design significantly altered the k-space trajectory solutions. Our joint gradient and RF optimization approach yields excellent excitation of 3D cube and brain shapes in less than 5 ms, which can be used for reduced field of view imaging and fat suppression in spectroscopy by excitation of the brain only. Magn Reson Med 76:1170-1182, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Exact and explicit optimal solutions for trajectory planning and control of single-link flexible-joint manipulators

NASA Technical Reports Server (NTRS)

Chen, Guanrong

1991-01-01

An optimal trajectory planning problem for a single-link, flexible joint manipulator is studied. A global feedback-linearization is first applied to formulate the nonlinear inequality-constrained optimization problem in a suitable way. Then, an exact and explicit structural formula for the optimal solution of the problem is derived and the solution is shown to be unique. It turns out that the optimal trajectory planning and control can be done off-line, so that the proposed method is applicable to both theoretical analysis and real time tele-robotics control engineering.

Low-Thrust Many-Revolution Trajectory Optimization via Differential Dynamic Programming and a Sundman Transformation

NASA Technical Reports Server (NTRS)

Aziz, Jonathan D.; Parker, Jeffrey S.; Scheeres, Daniel J.; Englander, Jacob A.

2017-01-01

Low-thrust trajectories about planetary bodies characteristically span a high count of orbital revolutions. Directing the thrust vector over many revolutions presents a challenging optimization problem for any conventional strategy. This paper demonstrates the tractability of low-thrust trajectory optimization about planetary bodies by applying a Sundman transformation to change the independent variable of the spacecraft equations of motion to the eccentric anomaly and performing the optimization with differential dynamic programming. Fuel-optimal geocentric transfers are shown in excess of 1000 revolutions while subject to Earths J2 perturbation and lunar gravity.

On the Optimization of Aerospace Plane Ascent Trajectory

NASA Astrophysics Data System (ADS)

Al-Garni, Ahmed; Kassem, Ayman Hamdy

A hybrid heuristic optimization technique based on genetic algorithms and particle swarm optimization has been developed and tested for trajectory optimization problems with multi-constraints and a multi-objective cost function. The technique is used to calculate control settings for two types for ascending trajectories (constant dynamic pressure and minimum-fuel-minimum-heat) for a two-dimensional model of an aerospace plane. A thorough statistical analysis is done on the hybrid technique to make comparisons with both basic genetic algorithms and particle swarm optimization techniques with respect to convergence and execution time. Genetic algorithm optimization showed better execution time performance while particle swarm optimization showed better convergence performance. The hybrid optimization technique, benefiting from both techniques, showed superior robust performance compromising convergence trends and execution time.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reister, D.B.; Pin, F.G.

This paper addresses the problem of time-optional motions for a mobile platform in a planar environment. The platform has two non-steerable independently driven wheels. The overall mission of the robot is expressed in terms of a sequence of via points at which the platform must be at rest in a given configuration (position and orientation). The objective is to plan time-optimal trajectories between these configurations assuming an unobstructed environment. Using Pontryagin's maximum principle (PMP), we formally demonstrate that all time optimal motions of the platform for this problem occur for bang-bang controls on the wheels (at each instant, the accelerationmore » on each wheel is either at its upper or lower limit). The PMP, however, only provides necessary conditions for time optimality. To find the time optimal robot trajectories, we first parameterize the bang-bang trajectories using the switch times on the wheels (the times at which the wheel accelerations change sign). With this parameterization, we can fully search the robot trajectory space and find the switch times that will produce particular paths to a desired final configuration of the platform. We show numerically that robot trajectories with three switch times (two on one wheel, one on the other) can reach any position, while trajectories with four switch times can reach any configuration. By numerical comparison with other trajectories involving similar or greater numbers of switch times, we then identify the sets of time-optimal trajectories. These are uniquely defined using ranges of the parameters, and consist of subsets of trajectories with three switch times for the problem when the final orientation of the robot is not specified, and four switch times when a full final configuration is specified. We conclude with a description of the use of the method for trajectory planning for one of our robots.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reister, D.B.; Pin, F.G.

This paper addresses the problem of time-optional motions for a mobile platform in a planar environment. The platform has two non-steerable independently driven wheels. The overall mission of the robot is expressed in terms of a sequence of via points at which the platform must be at rest in a given configuration (position and orientation). The objective is to plan time-optimal trajectories between these configurations assuming an unobstructed environment. Using Pontryagin`s maximum principle (PMP), we formally demonstrate that all time optimal motions of the platform for this problem occur for bang-bang controls on the wheels (at each instant, the accelerationmore » on each wheel is either at its upper or lower limit). The PMP, however, only provides necessary conditions for time optimality. To find the time optimal robot trajectories, we first parameterize the bang-bang trajectories using the switch times on the wheels (the times at which the wheel accelerations change sign). With this parameterization, we can fully search the robot trajectory space and find the switch times that will produce particular paths to a desired final configuration of the platform. We show numerically that robot trajectories with three switch times (two on one wheel, one on the other) can reach any position, while trajectories with four switch times can reach any configuration. By numerical comparison with other trajectories involving similar or greater numbers of switch times, we then identify the sets of time-optimal trajectories. These are uniquely defined using ranges of the parameters, and consist of subsets of trajectories with three switch times for the problem when the final orientation of the robot is not specified, and four switch times when a full final configuration is specified. We conclude with a description of the use of the method for trajectory planning for one of our robots.« less

Minimum fuel trajectory for the aerospace-plane

NASA Technical Reports Server (NTRS)

Breakwell, John V.; Golan, Oded; Sauvageot, Anne

1990-01-01

An overall trajectory for a single-stage-to-orbit vehicle with an initial weight of 234 tons is calculated, and four different propulsion models including turbojet, ramjet, scramjet, and rocket are considered. First, the atmospheric flight in the thicker atmosphere is discussed with emphasis on trajectory optimization, optimization problem, aerodynamic problem, propulsion model, and initial conditions. The performance of turbojet and ramjet-scramjet engines is analyzed; and then the flight to orbit is assessed from the optimization point of view. It is shown that roll modulation saves little during the trajectory, and the combined application of airbreathing propulsion and aerodynamic lift is suggested.

Optimal trajectories for the aeroassisted flight experiment. Part 4: Data, tables, and graphs

NASA Technical Reports Server (NTRS)

Miele, A.; Wang, T.; Lee, W. Y.; Wang, H.; Wu, G. D.

1989-01-01

The determination of optimal trajectories for the aeroassisted flight experiment (AFE) is discussed. Data, tables, and graphs relative to the following transfers are presented: (IA) indirect ascent to a 178 NM perigee via a 197 NM apogee; and (DA) direct ascent to a 178 NM apogee. For both transfers, two cases are investigated: (1) the bank angle is continuously variable; and (2) the trajectory is divided into segments along which the bank angle is constant. For case (2), the following subcases are studied: two segments, three segments, four segments, and five segments; because the time duration of each segment is optimized, the above subcases involve four, six, eight, and ten parameters, respectively. Presented here are systematic data on a total of ten optimal trajectories (OT), five for Transfer IA and five for Transfer DA. For comparison purposes and only for Transfer IA, a five-segment reference trajectory RT is also considered.

Trajectory Design for the Transiting Exoplanet Survey Satellite (TESS)

NASA Technical Reports Server (NTRS)

Dichmann, Donald J.; Parker, Joel; Williams, Trevor; Mendelsohn, Chad

2014-01-01

The Transiting Exoplanet Survey Satellite (TESS) is a National Aeronautics and Space Administration (NASA) mission launching in 2017. TESS will travel in a highly eccentric orbit around Earth, with initial perigee radius near 17 Earth radii (Re) and apogee radius near 59 Re. The orbit period is near 2:1 resonance with the Moon, with apogee nearly 90 degrees out-of-phase with the Moon, in a configuration that has been shown to be operationally stable. TESS will execute phasing loops followed by a lunar flyby, with a final maneuver to achieve 2:1 resonance with the Moon. The goals of a resonant orbit with long-term stability, short eclipses and limited oscillations of perigee present significant challenges to the trajectory design. To rapidly assess launch opportunities, we adapted the SWM76 launch window tool to assess the TESS mission constraints. To understand the long-term dynamics of such a resonant orbit in the Earth-Moon system we employed Dynamical Systems Theory in the Circular Restricted 3-Body Problem (CR3BP). For precise trajectory analysis we use a high-fidelity model and multiple shooting in the General Mission Analysis Tool (GMAT) to optimize the maneuver delta-V and meet mission constraints. Finally we describe how the techniques we have developed can be applied to missions with similar requirements.

Numerical optimization of actuator trajectories for ITER hybrid scenario profile evolution

NASA Astrophysics Data System (ADS)

van Dongen, J.; Felici, F.; Hogeweij, G. M. D.; Geelen, P.; Maljaars, E.

2014-12-01

Optimal actuator trajectories for an ITER hybrid scenario ramp-up are computed using a numerical optimization method. For both L-mode and H-mode scenarios, the time trajectory of plasma current, EC heating and current drive distribution is determined that minimizes a chosen cost function, while satisfying constraints. The cost function is formulated to reflect two desired properties of the plasma q profile at the end of the ramp-up. The first objective is to maximize the ITG turbulence threshold by maximizing the volume-averaged s/q ratio. The second objective is to achieve a stationary q profile by having a flat loop voltage profile. Actuator and physics-derived constraints are included, imposing limits on plasma current, ramp rates, internal inductance and q profile. This numerical method uses the fast control-oriented plasma profile evolution code RAPTOR, which is successfully benchmarked against more complete CRONOS simulations for L-mode and H-mode mode ITER hybrid scenarios. It is shown that the optimized trajectories computed using RAPTOR also result in an improved ramp-up scenario for CRONOS simulations using the same input trajectories. Furthermore, the optimal trajectories are shown to vary depending on the precise timing of the L-H transition.

A comparison of time-optimal interception trajectories for the F-8 and F-15

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Pettengill, James B.

1990-01-01

The simulation results of a real time control algorithm for onboard computation of time-optimal intercept trajectories for the F-8 and F-15 aircraft are given. Due to the inherent aerodynamic and propulsion differences in the aircraft, there are major differences in their optimal trajectories. The significant difference in the two aircrafts are their flight envelopes. The F-8's optimal cruise velocity is thrust limited, while the F-15's optimal cruise velocity is at the intersection of the Mach and dynamic pressure constraint boundaries. This inherent difference necessitated the development of a proportional thrust controller for use as the F-15 approaches it's optimal cruise energy. Documented here is the application of singular perturbation theory to the trajectory optimization problem, along with a summary of the control algorithms. Numerical results for the two aircraft are compared to illustrate the performance of the minimum time algorithm, and to compute the resulting flight paths.

Design of Quiet Rotorcraft Approach Trajectories: Verification Phase

NASA Technical Reports Server (NTRS)

Padula, Sharon L.

2010-01-01

Flight testing that is planned for October 2010 will provide an opportunity to evaluate rotorcraft trajectory optimization techniques. The flight test will involve a fully instrumented MD-902 helicopter, which will be flown over an array of microphones. In this work, the helicopter approach trajectory is optimized via a multiobjective genetic algorithm to improve community noise, passenger comfort, and pilot acceptance. Previously developed optimization strategies are modified to accommodate new helicopter data and to increase pilot acceptance. This paper describes the MD-902 trajectory optimization plus general optimization strategies and modifications that are needed to reduce the uncertainty in noise predictions. The constraints that are imposed by the flight test conditions and characteristics of the MD-902 helicopter limit the testing possibilities. However, the insights that will be gained through this research will prove highly valuable.

An Automated Method to Compute Orbital Re-Entry Trajectories with Heating Constraints

NASA Technical Reports Server (NTRS)

Zimmerman, Curtis; Dukeman, Greg; Hanson, John; Fogle, Frank R. (Technical Monitor)

2002-01-01

Determining how to properly manipulate the controls of a re-entering re-usable launch vehicle (RLV) so that it is able to safely return to Earth and land involves the solution of a two-point boundary value problem (TPBVP). This problem, which can be quite difficult, is traditionally solved on the ground prior to flight. If necessary, a nearly unlimited amount of time is available to find the "best" solution using a variety of trajectory design and optimization tools. The role of entry guidance during flight is to follow the pre-determined reference solution while correcting for any errors encountered along the way. This guidance method is both highly reliable and very efficient in terms of onboard computer resources. There is a growing interest in a style of entry guidance that places the responsibility of solving the TPBVP in the actual entry guidance flight software. Here there is very limited computer time. The powerful, but finicky, mathematical tools used by trajectory designers on the ground cannot in general be made to do the job. Nonconvergence or slow convergence can result in disaster. The challenges of designing such an algorithm are numerous and difficult. Yet the payoff (in the form of decreased operational costs and increased safety) can be substantial. This paper presents an algorithm that incorporates features of both types of guidance strategies. It takes an initial RLV orbital re-entry state and finds a trajectory that will safely transport the vehicle to a Terminal Area Energy Management (TAEM) region. During actual flight, the computed trajectory is used as the reference to be flown by a more traditional guidance method.

Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems

NASA Astrophysics Data System (ADS)

Tobasco, Ian; Goluskin, David; Doering, Charles R.

2018-02-01

For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper bounds on time averages can be proved a priori using auxiliary functions, the optimal choice of which is a convex optimization problem. We prove that the problems of finding maximal trajectories and minimal auxiliary functions are strongly dual. Thus, auxiliary functions provide arbitrarily sharp upper bounds on time averages. Moreover, any nearly minimal auxiliary function provides phase space volumes in which all nearly maximal trajectories are guaranteed to lie. For polynomial equations, auxiliary functions can be constructed by semidefinite programming, which we illustrate using the Lorenz system.

Safe-trajectory optimization and tracking control in ultra-close proximity to a failed satellite

NASA Astrophysics Data System (ADS)

Zhang, Jingrui; Chu, Xiaoyu; Zhang, Yao; Hu, Quan; Zhai, Guang; Li, Yanyan

2018-03-01

This paper presents a trajectory-optimization method for a chaser spacecraft operating in ultra-close proximity to a failed satellite. Based on the combination of active and passive trajectory protection, the constraints in the optimization framework are formulated for collision avoidance and successful docking in the presence of any thruster failure. The constraints are then handled by an adaptive Gauss pseudospectral method, in which the dynamic residuals are used as the metric to determine the distribution of collocation points. A finite-time feedback control is further employed in tracking the optimized trajectory. In particular, the stability and convergence of the controller are proved. Numerical results are given to demonstrate the effectiveness of the proposed methods.

Optimal Output Trajectory Redesign for Invertible Systems

NASA Technical Reports Server (NTRS)

Devasia, S.

1996-01-01

Given a desired output trajectory, inversion-based techniques find input-state trajectories required to exactly track the output. These inversion-based techniques have been successfully applied to the endpoint tracking control of multijoint flexible manipulators and to aircraft control. The specified output trajectory uniquely determines the required input and state trajectories that are found through inversion. These input-state trajectories exactly track the desired output; however, they might not meet acceptable performance requirements. For example, during slewing maneuvers of flexible structures, the structural deformations, which depend on the required state trajectories, may be unacceptably large. Further, the required inputs might cause actuator saturation during an exact tracking maneuver, for example, in the flight control of conventional takeoff and landing aircraft. In such situations, a compromise is desired between the tracking requirement and other goals such as reduction of internal vibrations and prevention of actuator saturation; the desired output trajectory needs to redesigned. Here, we pose the trajectory redesign problem as an optimization of a general quadratic cost function and solve it in the context of linear systems. The solution is obtained as an off-line prefilter of the desired output trajectory. An advantage of our technique is that the prefilter is independent of the particular trajectory. The prefilter can therefore be precomputed, which is a major advantage over other optimization approaches. Previous works have addressed the issue of preshaping inputs to minimize residual and in-maneuver vibrations for flexible structures; Since the command preshaping is computed off-line. Further minimization of optimal quadratic cost functions has also been previously use to preshape command inputs for disturbance rejection. All of these approaches are applicable when the inputs to the system are known a priori. Typically, outputs (not inputs) are specified in tracking problems, and hence the input trajectories have to be computed. The inputs to the system are however, difficult to determine for non-minimum phase systems like flexible structures. One approach to solve this problem is to (1) choose a tracking controller (the desired output trajectory is now an input to the closed-loop system and (2) redesign this input to the closed-loop system. Thus we effectively perform output redesign. These redesigns are however, dependent on the choice of the tracking controllers. Thus the controller optimization and trajectory redesign problems become coupled; this coupled optimization is still an open problem. In contrast, we decouple the trajectory redesign problem from the choice of feedback-based tracking controller. It is noted that our approach remains valid when a particular tracking controller is chosen. In addition, the formulation of our problem not only allows for the minimization of residual vibration as in available techniques but also allows for the optimal reduction fo vibrations during the maneuver, e.g., the altitude control of flexible spacecraft. We begin by formulating the optimal output trajectory redesign problem and then solve it in the context of general linear systems. This theory is then applied to an example flexible structure, and simulation results are provided.

Exploring the complexity of quantum control optimization trajectories.

PubMed

Nanduri, Arun; Shir, Ofer M; Donovan, Ashley; Ho, Tak-San; Rabitz, Herschel

2015-01-07

The control of quantum system dynamics is generally performed by seeking a suitable applied field. The physical objective as a functional of the field forms the quantum control landscape, whose topology, under certain conditions, has been shown to contain no critical point suboptimal traps, thereby enabling effective searches for fields that give the global maximum of the objective. This paper addresses the structure of the landscape as a complement to topological critical point features. Recent work showed that landscape structure is highly favorable for optimization of state-to-state transition probabilities, in that gradient-based control trajectories to the global maximum value are nearly straight paths. The landscape structure is codified in the metric R ≥ 1.0, defined as the ratio of the length of the control trajectory to the Euclidean distance between the initial and optimal controls. A value of R = 1 would indicate an exactly straight trajectory to the optimal observable value. This paper extends the state-to-state transition probability results to the quantum ensemble and unitary transformation control landscapes. Again, nearly straight trajectories predominate, and we demonstrate that R can take values approaching 1.0 with high precision. However, the interplay of optimization trajectories with critical saddle submanifolds is found to influence landscape structure. A fundamental relationship necessary for perfectly straight gradient-based control trajectories is derived, wherein the gradient on the quantum control landscape must be an eigenfunction of the Hessian. This relation is an indicator of landscape structure and may provide a means to identify physical conditions when control trajectories can achieve perfect linearity. The collective favorable landscape topology and structure provide a foundation to understand why optimal quantum control can be readily achieved.

Suborbital spaceplane optimization using non-stationary Gaussian processes

NASA Astrophysics Data System (ADS)

Dufour, Robin; de Muelenaere, Julien; Elham, Ali

2014-10-01

This paper presents multidisciplinary design optimization of a sub-orbital spaceplane. The optimization includes three disciplines: the aerodynamics, the structure and the trajectory. An Adjoint Euler code is used to calculate the aerodynamic lift and drag of the vehicle as well as their derivatives with respect to the design variables. A new surrogate model has been developed based on a non-stationary Gaussian process. That model was used to estimate the aerodynamic characteristics of the vehicle during the trajectory optimization. The trajectory of thevehicle has been optimized together with its geometry in order to maximize the amount of payload that can be carried by the spaceplane.

Singular-Arc Time-Optimal Trajectory of Aircraft in Two-Dimensional Wind Field

NASA Technical Reports Server (NTRS)

Nguyen, Nhan

2006-01-01

This paper presents a study of a minimum time-to-climb trajectory analysis for aircraft flying in a two-dimensional altitude dependent wind field. The time optimal control problem possesses a singular control structure when the lift coefficient is taken as a control variable. A singular arc analysis is performed to obtain an optimal control solution on the singular arc. Using a time-scale separation with the flight path angle treated as a fast state, the dimensionality of the optimal control solution is reduced by eliminating the lift coefficient control. A further singular arc analysis is used to decompose the original optimal control solution into the flight path angle solution and a trajectory solution as a function of the airspeed and altitude. The optimal control solutions for the initial and final climb segments are computed using a shooting method with known starting values on the singular arc The numerical results of the shooting method show that the optimal flight path angle on the initial and final climb segments are constant. The analytical approach provides a rapid means for analyzing a time optimal trajectory for aircraft performance.

Optimization of Insertion Cost for Transfer Trajectories to Libration Point Orbits

NASA Technical Reports Server (NTRS)

Howell, K. C.; Wilson, R. S.; Lo, M. W.

1999-01-01

The objective of this work is the development of efficient techniques to optimize the cost associated with transfer trajectories to libration point orbits in the Sun-Earth-Moon four body problem, that may include lunar gravity assists. Initially, dynamical systems theory is used to determine invariant manifolds associated with the desired libration point orbit. These manifolds are employed to produce an initial approximation to the transfer trajectory. Specific trajectory requirements such as, transfer injection constraints, inclusion of phasing loops, and targeting of a specified state on the manifold are then incorporated into the design of the transfer trajectory. A two level differential corrections process is used to produce a fully continuous trajectory that satisfies the design constraints, and includes appropriate lunar and solar gravitational models. Based on this methodology, and using the manifold structure from dynamical systems theory, a technique is presented to optimize the cost associated with insertion onto a specified libration point orbit.

Reliability-based trajectory optimization using nonintrusive polynomial chaos for Mars entry mission

NASA Astrophysics Data System (ADS)

Huang, Yuechen; Li, Haiyang

2018-06-01

This paper presents the reliability-based sequential optimization (RBSO) method to settle the trajectory optimization problem with parametric uncertainties in entry dynamics for Mars entry mission. First, the deterministic entry trajectory optimization model is reviewed, and then the reliability-based optimization model is formulated. In addition, the modified sequential optimization method, in which the nonintrusive polynomial chaos expansion (PCE) method and the most probable point (MPP) searching method are employed, is proposed to solve the reliability-based optimization problem efficiently. The nonintrusive PCE method contributes to the transformation between the stochastic optimization (SO) and the deterministic optimization (DO) and to the approximation of trajectory solution efficiently. The MPP method, which is used for assessing the reliability of constraints satisfaction only up to the necessary level, is employed to further improve the computational efficiency. The cycle including SO, reliability assessment and constraints update is repeated in the RBSO until the reliability requirements of constraints satisfaction are satisfied. Finally, the RBSO is compared with the traditional DO and the traditional sequential optimization based on Monte Carlo (MC) simulation in a specific Mars entry mission to demonstrate the effectiveness and the efficiency of the proposed method.

The design of transfer trajectory for Ivar asteroid exploration mission

NASA Astrophysics Data System (ADS)

Qiao, Dong; Cui, Hutao; Cui, Pingyuan

2009-12-01

An impending demand for exploring the small bodies, such as the comets and the asteroids, envisioned the Chinese Deep Space exploration mission to the Near Earth asteroid Ivar. A design and optimal method of transfer trajectory for asteroid Ivar is discussed in this paper. The transfer trajectory for rendezvous with asteroid Ivar is designed by means of Earth gravity assist with deep space maneuver (Delta-VEGA) technology. A Delta-VEGA transfer trajectory is realized by several trajectory segments, which connect the deep space maneuver and swingby point. Each trajectory segment is found by solving Lambert problem. Through adjusting deep maneuver and arrival time, the match condition of swingby is satisfied. To reduce the total mission velocity increments further, a procedure is developed which minimizes total velocity increments for this scheme of transfer trajectory for asteroid Ivar. The trajectory optimization problem is solved with a quasi-Newton algorithm utilizing analytic first derivatives, which are derived from the transversality conditions associated with the optimization formulation and primer vector theory. The simulation results show the scheme for transfer trajectory causes C3 and total velocity increments decrease of 48.80% and 13.20%, respectively.

General Mission Analysis Tool (GMAT): Mission, Vision, and Business Case

NASA Technical Reports Server (NTRS)

Hughes, Steven P.

2007-01-01

The Goal of the GMAT project is to develop new space trajectory optimization and mission design technology by working inclusively with ordinary people, universities businesses and other government organizations; and to share that technology in an open and unhindered way. GMAT's a free and open source software system; free for anyone to use in development of new mission concepts or to improve current missions, freely available in source code form for enhancement or future technology development.

Interplanetary Program to Optimize Simulated Trajectories (IPOST). Volume 1: User's guide

NASA Technical Reports Server (NTRS)

Hong, P. E.; Kent, P. D.; Olson, D. W.; Vallado, C. A.

1992-01-01

IPOST is intended to support many analysis phases, from early interplanetary feasibility studies through spacecraft development and operations. The IPOST output provides information for sizing and understanding mission impacts related to propulsion, guidance, communications, sensor/actuators, payload, and other dynamic and geometric environments. IPOST models three degree of freedom trajectory events, such as launch/ascent, orbital coast, propulsive maneuvering (impulsive and finite burn), gravity assist, and atmospheric entry. Trajectory propagation is performed using a choice of Cowell, Encke, Multiconic, Onestep, or Conic methods. The user identifies a desired sequence fo trajectory events, and selects which parameters are independent (controls) and dependent (targets), as well as other constraints and the coat function. Targeting and optimization is performed using the Stanford NPSOL algorithm. IPOST structure allows sub-problems within a master optimization problem to aid in the general constrained parameter optimization solution. An alternate optimization method uses implicit simulation and collocation techniques.

Autonomous optimal trajectory design employing convex optimization for powered descent on an asteroid

NASA Astrophysics Data System (ADS)

Pinson, Robin Marie

Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant (fuel) optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from ground control. The goal is to autonomously design the optimal powered descent trajectory onboard the spacecraft immediately prior to the descent burn for use during the burn. Compared to a planetary powered landing problem, the challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies, and low thrust vehicles. The nonlinear gravity fields cannot be represented by a constant gravity model nor a Newtonian model. The trajectory design algorithm needs to be robust and efficient to guarantee a designed trajectory and complete the calculations in a reasonable time frame. This research investigates the following questions: Can convex optimization be used to design the minimum propellant powered descent trajectory for a soft landing on an asteroid? Is this method robust and reliable to allow autonomy onboard the spacecraft without interaction from ground control? This research designed a convex optimization based method that rapidly generates the propellant optimal asteroid powered descent trajectory. The solution to the convex optimization problem is the thrust magnitude and direction, which designs and determines the trajectory. The propellant optimal problem was formulated as a second order cone program, a subset of convex optimization, through relaxation techniques by including a slack variable, change of variables, and incorporation of the successive solution method. Convex optimization solvers, especially second order cone programs, are robust, reliable, and are guaranteed to find the global minimum provided one exists. In addition, an outer optimization loop using Brent's method determines the optimal flight time corresponding to the minimum propellant usage over all flight times. Inclusion of additional trajectory constraints, solely vertical motion near the landing site and glide slope, were evaluated. Through a theoretical proof involving the Minimum Principle from Optimal Control Theory and the Karush-Kuhn-Tucker conditions it was shown that the relaxed problem is identical to the original problem at the minimum point. Therefore, the optimal solution of the relaxed problem is an optimal solution of the original problem, referred to as lossless convexification. A key finding is that this holds for all levels of gravity model fidelity. The designed thrust magnitude profiles were the bang-bang predicted by Optimal Control Theory. The first high fidelity gravity model employed was the 2x2 spherical harmonics model assuming a perfect triaxial ellipsoid and placement of the coordinate frame at the asteroid's center of mass and aligned with the semi-major axes. The spherical harmonics model is not valid inside the Brillouin sphere and this becomes relevant for irregularly shaped asteroids. Then, a higher fidelity model was implemented combining the 4x4 spherical harmonics gravity model with the interior spherical Bessel gravity model. All gravitational terms in the equations of motion are evaluated with the position vector from the previous iteration, creating the successive solution method. Methodology success was shown by applying the algorithm to three triaxial ellipsoidal asteroids with four different rotation speeds using the 2x2 gravity model. Finally, the algorithm was tested using the irregularly shaped asteroid, Castalia.

Global Optimization of Low-Thrust Interplanetary Trajectories Subject to Operational Constraints

NASA Technical Reports Server (NTRS)

Englander, Jacob A.; Vavrina, Matthew A.; Hinckley, David

2016-01-01

Low-thrust interplanetary space missions are highly complex and there can be many locally optimal solutions. While several techniques exist to search for globally optimal solutions to low-thrust trajectory design problems, they are typically limited to unconstrained trajectories. The operational design community in turn has largely avoided using such techniques and has primarily focused on accurate constrained local optimization combined with grid searches and intuitive design processes at the expense of efficient exploration of the global design space. This work is an attempt to bridge the gap between the global optimization and operational design communities by presenting a mathematical framework for global optimization of low-thrust trajectories subject to complex constraints including the targeting of planetary landing sites, a solar range constraint to simplify the thermal design of the spacecraft, and a real-world multi-thruster electric propulsion system that must switch thrusters on and off as available power changes over the course of a mission.

Multiobjective Optimization of Low-Energy Trajectories Using Optimal Control on Dynamical Channels

NASA Technical Reports Server (NTRS)

Coffee, Thomas M.; Anderson, Rodney L.; Lo, Martin W.

2011-01-01

We introduce a computational method to design efficient low-energy trajectories by extracting initial solutions from dynamical channels formed by invariant manifolds, and improving these solutions through variational optimal control. We consider trajectories connecting two unstable periodic orbits in the circular restricted 3-body problem (CR3BP). Our method leverages dynamical channels to generate a range of solutions, and approximates the areto front for impulse and time of flight through a multiobjective optimization of these solutions based on primer vector theory. We demonstrate the application of our method to a libration orbit transfer in the Earth-Moon system.

Spacecraft formation flying for Earth-crossing object deflections using a power limited laser ablating

NASA Astrophysics Data System (ADS)

Yoo, Sung-Moon; Song, Young-Joo; Park, Sang-Young; Choi, Kyu-Hong

2009-06-01

A formation flying strategy with an Earth-crossing object (ECO) is proposed to avoid the Earth collision. Assuming that a future conceptual spacecraft equipped with a powerful laser ablation tool already rendezvoused with a fictitious Earth collision object, the optimal required laser operating duration and direction histories are accurately derived to miss the Earth. Based on these results, the concept of formation flying between the object and the spacecraft is applied and analyzed as to establish the spacecraft's orbital motion design strategy. A fictitious "Apophis"-like object is established to impact with the Earth and two major deflection scenarios are designed and analyzed. These scenarios include the cases for the both short and long laser operating duration to avoid the Earth impact. Also, requirement of onboard laser tool's for both cases are discussed. As a result, the optimal initial conditions for the spacecraft to maintain its relative trajectory to the object are discovered. Additionally, the discovered optimal initial conditions also satisfied the optimal required laser operating conditions with no additional spacecraft's own fuel expenditure to achieve the spacecraft formation flying with the ECO. The initial conditions founded in the current research can be used as a spacecraft's initial rendezvous points with the ECO when designing the future deflection missions with laser ablation tools. The results with proposed strategy are expected to make more advances in the fields of the conceptual studies, especially for the future deflection missions using powerful laser ablation tools.

Designing train-speed trajectory with energy efficiency and service quality

NASA Astrophysics Data System (ADS)

Jia, Jiannan; Yang, Kai; Yang, Lixing; Gao, Yuan; Li, Shukai

2018-05-01

With the development of automatic train operations, optimal trajectory design is significant to the performance of train operations in railway transportation systems. Considering energy efficiency and service quality, this article formulates a bi-objective train-speed trajectory optimization model to minimize simultaneously the energy consumption and travel time in an inter-station section. This article is distinct from previous studies in that more sophisticated train driving strategies characterized by the acceleration/deceleration gear, the cruising speed, and the speed-shift site are specifically considered. For obtaining an optimal train-speed trajectory which has equal satisfactory degree on both objectives, a fuzzy linear programming approach is applied to reformulate the objectives. In addition, a genetic algorithm is developed to solve the proposed train-speed trajectory optimization problem. Finally, a series of numerical experiments based on a real-world instance of Beijing-Tianjin Intercity Railway are implemented to illustrate the practicability of the proposed model as well as the effectiveness of the solution methodology.

Optimal bounds and extremal trajectories for time averages in dynamical systems

NASA Astrophysics Data System (ADS)

Tobasco, Ian; Goluskin, David; Doering, Charles

2017-11-01

For systems governed by differential equations it is natural to seek extremal solution trajectories, maximizing or minimizing the long-time average of a given quantity of interest. A priori bounds on optima can be proved by constructing auxiliary functions satisfying certain point-wise inequalities, the verification of which does not require solving the underlying equations. We prove that for any bounded autonomous ODE, the problems of finding extremal trajectories on the one hand and optimal auxiliary functions on the other are strongly dual in the sense of convex duality. As a result, auxiliary functions provide arbitrarily sharp bounds on optimal time averages. Furthermore, nearly optimal auxiliary functions provide volumes in phase space where maximal and nearly maximal trajectories must lie. For polynomial systems, such functions can be constructed by semidefinite programming. We illustrate these ideas using the Lorenz system, producing explicit volumes in phase space where extremal trajectories are guaranteed to reside. Supported by NSF Award DMS-1515161, Van Loo Postdoctoral Fellowships, and the John Simon Guggenheim Foundation.

A modular approach to intensity-modulated arc therapy optimization with noncoplanar trajectories

NASA Astrophysics Data System (ADS)

Papp, Dávid; Bortfeld, Thomas; Unkelbach, Jan

2015-07-01

Utilizing noncoplanar beam angles in volumetric modulated arc therapy (VMAT) has the potential to combine the benefits of arc therapy, such as short treatment times, with the benefits of noncoplanar intensity modulated radiotherapy (IMRT) plans, such as improved organ sparing. Recently, vendors introduced treatment machines that allow for simultaneous couch and gantry motion during beam delivery to make noncoplanar VMAT treatments possible. Our aim is to provide a reliable optimization method for noncoplanar isocentric arc therapy plan optimization. The proposed solution is modular in the sense that it can incorporate different existing beam angle selection and coplanar arc therapy optimization methods. Treatment planning is performed in three steps. First, a number of promising noncoplanar beam directions are selected using an iterative beam selection heuristic; these beams serve as anchor points of the arc therapy trajectory. In the second step, continuous gantry/couch angle trajectories are optimized using a simple combinatorial optimization model to define a beam trajectory that efficiently visits each of the anchor points. Treatment time is controlled by limiting the time the beam needs to trace the prescribed trajectory. In the third and final step, an optimal arc therapy plan is found along the prescribed beam trajectory. In principle any existing arc therapy optimization method could be incorporated into this step; for this work we use a sliding window VMAT algorithm. The approach is demonstrated using two particularly challenging cases. The first one is a lung SBRT patient whose planning goals could not be satisfied with fewer than nine noncoplanar IMRT fields when the patient was treated in the clinic. The second one is a brain tumor patient, where the target volume overlaps with the optic nerves and the chiasm and it is directly adjacent to the brainstem. Both cases illustrate that the large number of angles utilized by isocentric noncoplanar VMAT plans can help improve dose conformity, homogeneity, and organ sparing simultaneously using the same beam trajectory length and delivery time as a coplanar VMAT plan.

Method of interplanetary trajectory optimization for the spacecraft with low thrust and swing-bys

NASA Astrophysics Data System (ADS)

Konstantinov, M. S.; Thein, M.

2017-07-01

The method developed to avoid the complexity of solving the multipoint boundary value problem while optimizing interplanetary trajectories of the spacecraft with electric propulsion and a sequence of swing-bys is presented in the paper. This method is based on the use of the preliminary problem solutions for the impulsive trajectories. The preliminary problem analyzed at the first stage of the study is formulated so that the analysis and optimization of a particular flight path is considered as the unconstrained minimum in the space of the selectable parameters. The existing methods can effectively solve this problem and make it possible to identify rational flight paths (the sequence of swing-bys) to receive the initial approximation for the main characteristics of the flight path (dates, values of the hyperbolic excess velocity, etc.). These characteristics can be used to optimize the trajectory of the spacecraft with electric propulsion. The special feature of the work is the introduction of the second (intermediate) stage of the research. At this stage some characteristics of the analyzed flight path (e.g. dates of swing-bys) are fixed and the problem is formulated so that the trajectory of the spacecraft with electric propulsion is optimized on selected sites of the flight path. The end-to-end optimization is carried out at the third (final) stage of the research. The distinctive feature of this stage is the analysis of the full set of optimal conditions for the considered flight path. The analysis of the characteristics of the optimal flight trajectories to Jupiter with Earth, Venus and Mars swing-bys for the spacecraft with electric propulsion are presented. The paper shows that the spacecraft weighing more than 7150 kg can be delivered into the vicinity of Jupiter along the trajectory with two Earth swing-bys by use of the space transportation system based on the "Angara A5" rocket launcher, the chemical upper stage "KVTK" and the electric propulsion system with input electrical power of 100 kW.

Visiting Vehicle Ground Trajectory Tool

NASA Technical Reports Server (NTRS)

Hamm, Dustin

2013-01-01

The International Space Station (ISS) Visiting Vehicle Group needed a targeting tool for vehicles that rendezvous with the ISS. The Visiting Vehicle Ground Trajectory targeting tool provides the ability to perform both realtime and planning operations for the Visiting Vehicle Group. This tool provides a highly reconfigurable base, which allows the Visiting Vehicle Group to perform their work. The application is composed of a telemetry processing function, a relative motion function, a targeting function, a vector view, and 2D/3D world map type graphics. The software tool provides the ability to plan a rendezvous trajectory for vehicles that visit the ISS. It models these relative trajectories using planned and realtime data from the vehicle. The tool monitors ongoing rendezvous trajectory relative motion, and ensures visiting vehicles stay within agreed corridors. The software provides the ability to update or re-plan a rendezvous to support contingency operations. Adding new parameters and incorporating them into the system was previously not available on-the-fly. If an unanticipated capability wasn't discovered until the vehicle was flying, there was no way to update things.

A New Computational Technique for the Generation of Optimised Aircraft Trajectories

NASA Astrophysics Data System (ADS)

Chircop, Kenneth; Gardi, Alessandro; Zammit-Mangion, David; Sabatini, Roberto

2017-12-01

A new computational technique based on Pseudospectral Discretisation (PSD) and adaptive bisection ɛ-constraint methods is proposed to solve multi-objective aircraft trajectory optimisation problems formulated as nonlinear optimal control problems. This technique is applicable to a variety of next-generation avionics and Air Traffic Management (ATM) Decision Support Systems (DSS) for strategic and tactical replanning operations. These include the future Flight Management Systems (FMS) and the 4-Dimensional Trajectory (4DT) planning and intent negotiation/validation tools envisaged by SESAR and NextGen for a global implementation. In particular, after describing the PSD method, the adaptive bisection ɛ-constraint method is presented to allow an efficient solution of problems in which two or multiple performance indices are to be minimized simultaneously. Initial simulation case studies were performed adopting suitable aircraft dynamics models and addressing a classical vertical trajectory optimisation problem with two objectives simultaneously. Subsequently, a more advanced 4DT simulation case study is presented with a focus on representative ATM optimisation objectives in the Terminal Manoeuvring Area (TMA). The simulation results are analysed in-depth and corroborated by flight performance analysis, supporting the validity of the proposed computational techniques.

Techniques for shuttle trajectory optimization

NASA Technical Reports Server (NTRS)

Edge, E. R.; Shieh, C. J.; Powers, W. F.

1973-01-01

The application of recently developed function-space Davidon-type techniques to the shuttle ascent trajectory optimization problem is discussed along with an investigation of the recently developed PRAXIS algorithm for parameter optimization. At the outset of this analysis, the major deficiency of the function-space algorithms was their potential storage problems. Since most previous analyses of the methods were with relatively low-dimension problems, no storage problems were encountered. However, in shuttle trajectory optimization, storage is a problem, and this problem was handled efficiently. Topics discussed include: the shuttle ascent model and the development of the particular optimization equations; the function-space algorithms; the operation of the algorithm and typical simulations; variable final-time problem considerations; and a modification of Powell's algorithm.

Low-Thrust Many-Revolution Trajectory Optimization via Differential Dynamic Programming and a Sundman Transformation

NASA Astrophysics Data System (ADS)

Aziz, Jonathan D.; Parker, Jeffrey S.; Scheeres, Daniel J.; Englander, Jacob A.

2018-01-01

Low-thrust trajectories about planetary bodies characteristically span a high count of orbital revolutions. Directing the thrust vector over many revolutions presents a challenging optimization problem for any conventional strategy. This paper demonstrates the tractability of low-thrust trajectory optimization about planetary bodies by applying a Sundman transformation to change the independent variable of the spacecraft equations of motion to an orbit angle and performing the optimization with differential dynamic programming. Fuel-optimal geocentric transfers are computed with the transfer duration extended up to 2000 revolutions. The flexibility of the approach to higher fidelity dynamics is shown with Earth's J 2 perturbation and lunar gravity included for a 500 revolution transfer.

Low-Thrust Many-Revolution Trajectory Optimization via Differential Dynamic Programming and a Sundman Transformation

NASA Astrophysics Data System (ADS)

Aziz, Jonathan D.; Parker, Jeffrey S.; Scheeres, Daniel J.; Englander, Jacob A.

2018-06-01

Low-thrust trajectories about planetary bodies characteristically span a high count of orbital revolutions. Directing the thrust vector over many revolutions presents a challenging optimization problem for any conventional strategy. This paper demonstrates the tractability of low-thrust trajectory optimization about planetary bodies by applying a Sundman transformation to change the independent variable of the spacecraft equations of motion to an orbit angle and performing the optimization with differential dynamic programming. Fuel-optimal geocentric transfers are computed with the transfer duration extended up to 2000 revolutions. The flexibility of the approach to higher fidelity dynamics is shown with Earth's J 2 perturbation and lunar gravity included for a 500 revolution transfer.

Numerical study and ex vivo assessment of HIFU treatment time reduction through optimization of focal point trajectory

NASA Astrophysics Data System (ADS)

Grisey, A.; Yon, S.; Pechoux, T.; Letort, V.; Lafitte, P.

2017-03-01

Treatment time reduction is a key issue to expand the use of high intensity focused ultrasound (HIFU) surgery, especially for benign pathologies. This study aims at quantitatively assessing the potential reduction of the treatment time arising from moving the focal point during long pulses. In this context, the optimization of the focal point trajectory is crucial to achieve a uniform thermal dose repartition and avoid boiling. At first, a numerical optimization algorithm was used to generate efficient trajectories. Thermal conduction was simulated in 3D with a finite difference code and damages to the tissue were modeled using the thermal dose formula. Given an initial trajectory, the thermal dose field was first computed, then, making use of Pontryagin's maximum principle, the trajectory was iteratively refined. Several initial trajectories were tested. Then, an ex vivo study was conducted in order to validate the efficicency of the resulting optimized strategies. Single pulses were performed at 3MHz on fresh veal liver samples with an Echopulse and the size of each unitary lesion was assessed by cutting each sample along three orthogonal planes and measuring the dimension of the whitened area based on photographs. We propose a promising approach to significantly shorten HIFU treatment time: the numerical optimization algorithm was shown to provide a reliable insight on trajectories that can improve treatment strategies. The model must now be improved in order to take in vivo conditions into account and extensively validated.

Design and optimization of interplanetary spacecraft trajectories

NASA Astrophysics Data System (ADS)

McConaghy, Thomas Troy

Scientists involved in space exploration are always looking for ways to accomplish more with their limited budgets. Mission designers can decrease operational costs by crafting trajectories with low launch costs, short time-of-flight, or low propellant requirements. Gravity-assist maneuvers and low-thrust, high-efficiency ion propulsion can be of great help. This dissertation describes advances in methods to design and optimize interplanetary spacecraft trajectories. particularly for missions using gravity-assist maneuvers or low-thrust engines (or both). The first part of this dissertation describes a new, efficient, two-step methodology to design and optimize low-thrust gravity-assist trajectories. Models for the launch vehicle, solar arrays, and engines are introduced and several examples of optimized trajectories are presented. For example, a 3.7-year Earth-Venus-Earth-Mars-Jupiter flyby trajectory with maximized final mass is described. The way that the parameterization of the optimization problem affects convergence speed and reliability is also investigated. The choice of coordinate system is shown to make a significant difference. The second part of this dissertation describes a way to construct Earth-Mars cycler trajectories---periodic orbits that repeatedly encounter Earth and Mars, yet require little or no propellant. We find that well-known cyclers, such as the Aldrin cycler, are special cases of a much larger family of cyclers. In fact, so many new cyclers are found that a comprehensive naming system (nomenclature) is proposed. One particularly promising new cycler, the "ballistic S1L1 cycler" is analyzed in greater detail.

Validation of Multibody Program to Optimize Simulated Trajectories II Parachute Simulation with Interacting Forces

NASA Technical Reports Server (NTRS)

Raiszadeh, Behzad; Queen, Eric M.; Hotchko, Nathaniel J.

2009-01-01

A capability to simulate trajectories of multiple interacting rigid bodies has been developed, tested and validated. This capability uses the Program to Optimize Simulated Trajectories II (POST 2). The standard version of POST 2 allows trajectory simulation of multiple bodies without force interaction. In the current implementation, the force interaction between the parachute and the suspended bodies has been modeled using flexible lines, allowing accurate trajectory simulation of the individual bodies in flight. The POST 2 multibody capability is intended to be general purpose and applicable to any parachute entry trajectory simulation. This research paper explains the motivation for multibody parachute simulation, discusses implementation methods, and presents validation of this capability.

Trajectory optimization for the national aerospace plane

NASA Technical Reports Server (NTRS)

Lu, Ping

1993-01-01

During the past six months the research objectives outlined in the last semi-annual report were accomplished. Specifically, these are: three-dimensional (3-D) fuel-optimal ascent trajectory of the aerospace plane and the effects of thrust vectoring control (TVC) on the fuel consumption and trajectory shaping were investigated; the maximum abort landing area (footprint) was studied; preliminary assessment of simultaneous design of the ascent trajectory and the vehicle configuration for the aerospace plane was also conducted. The work accomplished in the reporting period is summarized.

An Optimized Trajectory Planning for Welding Robot

NASA Astrophysics Data System (ADS)

Chen, Zhilong; Wang, Jun; Li, Shuting; Ren, Jun; Wang, Quan; Cheng, Qunchao; Li, Wentao

2018-03-01

In order to improve the welding efficiency and quality, this paper studies the combined planning between welding parameters and space trajectory for welding robot and proposes a trajectory planning method with high real-time performance, strong controllability and small welding error. By adding the virtual joint at the end-effector, the appropriate virtual joint model is established and the welding process parameters are represented by the virtual joint variables. The trajectory planning is carried out in the robot joint space, which makes the control of the welding process parameters more intuitive and convenient. By using the virtual joint model combined with the B-spline curve affine invariant, the welding process parameters are indirectly controlled by controlling the motion curve of the real joint. To solve the optimal time solution as the goal, the welding process parameters and joint space trajectory joint planning are optimized.

Challenges in Achieving Trajectory-Based Operations

NASA Technical Reports Server (NTRS)

Cate, Karen Tung

2012-01-01

In the past few years much of the global ATM research community has proposed advanced systems based on Trajectory-Based Operations (TBO). The concept of TBO uses four-dimensional aircraft trajectories as the base information for managing safety and capacity. Both the US and European advanced ATM programs call for the sharing of trajectory data across different decision support tools for successful operations. However, the actual integration of TBO systems presents many challenges. Trajectory predictors are built to meet the specific needs of a particular system and are not always compatible with others. Two case studies are presented which examine the challenges of introducing a new concept into two legacy systems in regards to their trajectory prediction software. The first case describes the issues with integrating a new decision support tool with a legacy operational system which overlap in domain space. These tools perform similar functions but are driven by different requirements. The difference in the resulting trajectories can lead to conflicting advisories. The second case looks at integrating this same new tool with a legacy system originally developed as an integrated system, but diverged many years ago. Both cases illustrate how the lack of common architecture concepts for the trajectory predictors added cost and complexity to the integration efforts.

Optimal low-thrust trajectories for nuclear and solar electric propulsion

NASA Astrophysics Data System (ADS)

Genta, G.; Maffione, P. F.

2016-01-01

The optimization of the trajectory and of the thrust profile of a low-thrust interplanetary transfer is usually solved under the assumption that the specific mass of the power generator is constant. While this is reasonable in the case of nuclear electric propulsion, if solar electric propulsion is used the specific mass depends on the distance of the spacecraft from the Sun. In the present paper the optimization of the trajectory of the spacecraft and of the thrust profile is solved under the latter assumption, to obtain optimized interplanetary trajectories for solar electric spacecraft, also taking into account all phases of the journey, from low orbit about the starting planet to low orbit about the destination one. General plots linking together the travel time, the specific mass of the generator and the propellant consumption are obtained.

Guidance control of small UAV with energy and maneuverability limitations for a search and coverage mission

NASA Astrophysics Data System (ADS)

Gramajo, German G.

This thesis presents an algorithm for a search and coverage mission that has increased autonomy in generating an ideal trajectory while explicitly considering the available energy in the optimization. Further, current algorithms used to generate trajectories depend on the operator providing a discrete set of turning rate requirements to obtain an optimal solution. This work proposes an additional modification to the algorithm so that it optimizes the trajectory for a range of turning rates instead of a discrete set of turning rates. This thesis conducts an evaluation of the algorithm with variation in turn duration, entry-heading angle, and entry point. Comparative studies of the algorithm with existing method indicates improved autonomy in choosing the optimization parameters while producing trajectories with better coverage area and closer final distance to the desired terminal point.

Model-Free Primitive-Based Iterative Learning Control Approach to Trajectory Tracking of MIMO Systems With Experimental Validation.

PubMed

Radac, Mircea-Bogdan; Precup, Radu-Emil; Petriu, Emil M

2015-11-01

This paper proposes a novel model-free trajectory tracking of multiple-input multiple-output (MIMO) systems by the combination of iterative learning control (ILC) and primitives. The optimal trajectory tracking solution is obtained in terms of previously learned solutions to simple tasks called primitives. The library of primitives that are stored in memory consists of pairs of reference input/controlled output signals. The reference input primitives are optimized in a model-free ILC framework without using knowledge of the controlled process. The guaranteed convergence of the learning scheme is built upon a model-free virtual reference feedback tuning design of the feedback decoupling controller. Each new complex trajectory to be tracked is decomposed into the output primitives regarded as basis functions. The optimal reference input for the control system to track the desired trajectory is next recomposed from the reference input primitives. This is advantageous because the optimal reference input is computed straightforward without the need to learn from repeated executions of the tracking task. In addition, the optimization problem specific to trajectory tracking of square MIMO systems is decomposed in a set of optimization problems assigned to each separate single-input single-output control channel that ensures a convenient model-free decoupling. The new model-free primitive-based ILC approach is capable of planning, reasoning, and learning. A case study dealing with the model-free control tuning for a nonlinear aerodynamic system is included to validate the new approach. The experimental results are given.

Optimization design and dynamic analysis on the drive mechanisms of flapping-wing air vehicles based on flapping trajectories

NASA Astrophysics Data System (ADS)

Xie, Lingwang; Zhang, Xingwei; Luo, Pan; Huang, Panpan

2017-10-01

The optimization designs and dynamic analysis on the driving mechanism of flapping-wing air vehicles on base of flapping trajectory patterns is carried out in this study. Three different driving mechanisms which are spatial double crank-rocker, plane five-bar and gear-double slider, are systematically optimized and analysed by using the Mat lab and Adams software. After a series debugging on the parameter, the comparatively ideal flapping trajectories are obtained by the simulation of Adams. Present results indicate that different drive mechanisms output different flapping trajectories and have their unique characteristic. The spatial double crank-rocker mechanism can only output the arc flapping trajectory and it has the advantages of small volume, high flexibility and efficient space utilization. Both planar five-bar mechanism and gear-double slider mechanism can output the oval, figure of eight and double eight flapping trajectories. Nevertheless, the gear-double slider mechanism has the advantage of convenient parameter setting and better performance in output double eight flapping trajectory. This study can provide theoretical basis and helpful reference for the design of the drive mechanisms of flapping-wing air vehicles with different output flapping trajectories.

Aircraft Trajectory Optimization and Contrails Avoidance in the Presence of Winds

NASA Technical Reports Server (NTRS)

Ng, Hok K.; Chen, Neil Y.

2010-01-01

There are indications that persistent contrails can lead to adverse climate change, although the complete effect on climate forcing is still uncertain. A flight trajectory optimization algorithm with fuel and contrails models, which develops alternative flight paths, provides policy makers the necessary data to make tradeoffs between persistent contrails mitigation and aircraft fuel consumption. This study develops an algorithm that calculates wind-optimal trajectories for cruising aircraft while avoiding the regions of airspace prone to persistent contrails formation. The optimal trajectories are developed by solving a non-linear optimal control problem with path constraints. The regions of airspace favorable to persistent contrails formation are modeled as penalty areas that aircraft should avoid and are adjustable. The tradeoff between persistent contrails formation and additional fuel consumption is investigated, with and without altitude optimization, for 12 city-pairs in the continental United States. Without altitude optimization, the reduction in contrail travel times is gradual with increase in total fuel consumption. When altitude is optimized, a two percent increase in total fuel consumption can reduce the total travel times through contrail regions by more than six times. Allowing further increase in fuel consumption does not seem to result in proportionate decrease in contrail travel times.

Co-state initialization for the minimum-time low-thrust trajectory optimization

NASA Astrophysics Data System (ADS)

Taheri, Ehsan; Li, Nan I.; Kolmanovsky, Ilya

2017-05-01

This paper presents an approach for co-state initialization which is a critical step in solving minimum-time low-thrust trajectory optimization problems using indirect optimal control numerical methods. Indirect methods used in determining the optimal space trajectories typically result in two-point boundary-value problems and are solved by single- or multiple-shooting numerical methods. Accurate initialization of the co-state variables facilitates the numerical convergence of iterative boundary value problem solvers. In this paper, we propose a method which exploits the trajectory generated by the so-called pseudo-equinoctial and three-dimensional finite Fourier series shape-based methods to estimate the initial values of the co-states. The performance of the approach for two interplanetary rendezvous missions from Earth to Mars and from Earth to asteroid Dionysus is compared against three other approaches which, respectively, exploit random initialization of co-states, adjoint-control transformation and a standard genetic algorithm. The results indicate that by using our proposed approach the percent of the converged cases is higher for trajectories with higher number of revolutions while the computation time is lower. These features are advantageous for broad trajectory search in the preliminary phase of mission designs.

Development of a Mars Airplane Entry, Descent, and Flight Trajectory

NASA Technical Reports Server (NTRS)

Murray, James E.; Tartabini, Paul V.

2001-01-01

An entry, descent, and flight (EDF) trajectory profile for a Mars airplane mission is defined as consisting of the following elements: ballistic entry of an aeroshell; supersonic deployment of a decelerator parachute; subsonic release of a heat shield; release, unfolding, and orientation of an airplane to flight attitude; and execution of a pull up maneuver to achieve trimmed, horizontal flight. Using the Program to Optimize Simulated Trajectories (POST) a trajectory optimization problem was formulated. Model data representative of a specific Mars airplane configuration, current models of the Mars surface topography and atmosphere, and current estimates of the interplanetary trajectory, were incorporated into the analysis. The goal is to develop an EDF trajectory to maximize the surface-relative altitude of the airplane at the end of a pull up maneuver, while subject to the mission design constraints. The trajectory performance was evaluated for three potential mission sites and was found to be site-sensitive. The trajectory performance, examined for sensitivity to a number of design and constraint variables, was found to be most sensitive to airplane mass, aerodynamic performance characteristics, and the pull up Mach constraint. Based on the results of this sensitivity study, an airplane-drag optimized trajectory was developed that showed a significant performance improvement.

An Earth-Moon Transfer Trajectory Design and Analysis Considering Spacecraft's Visibility from Daejeon Ground Station at TLI and LOI Maneuvers

NASA Astrophysics Data System (ADS)

Woo, Jin; Song, Young-Joo; Park, Sang-Young; Kim, Hae-Dong; Sim, Eun-Sup

2010-09-01

The optimal Earth-Moon transfer trajectory considering spacecraft's visibility from the Daejeon ground station visibility at both the trans lunar injection (TLI) and lunar orbit insertion (LOI) maneuvers is designed. Both the TLI and LOI maneuvers are assumed to be impulsive thrust. As the successful execution of the TLI and LOI maneuvers are crucial factors among the various lunar mission parameters, it is necessary to design an optimal lunar transfer trajectory which guarantees the visibility from a specified ground station while executing these maneuvers. The optimal Earth-Moon transfer trajectory is simulated by modifying the Korean Lunar Mission Design Software using Impulsive high Thrust Engine (KLMDS-ITE) which is developed in previous studies. Four different mission scenarios are established and simulated to analyze the effects of the spacecraft's visibility considerations at the TLI and LOI maneuvers. As a result, it is found that the optimal Earth-Moon transfer trajectory, guaranteeing the spacecraft's visibility from Daejeon ground station at both the TLI and LOI maneuvers, can be designed with slight changes in total amount of delta-Vs. About 1% difference is observed with the optimal trajectory when none of the visibility condition is guaranteed, and about 0.04% with the visibility condition is only guaranteed at the time of TLI maneuver. The spacecraft's mass which can delivered to the Moon, when both visibility conditions are secured is shown to be about 534 kg with assumptions of KSLV-2's on-orbit mass about 2.6 tons. To minimize total mission delta-Vs, it is strongly recommended that visibility conditions at both the TLI and LOI maneuvers should be simultaneously implemented to the trajectory optimization algorithm.

Spacecraft Station-Keeping Trajectory and Mission Design Tools

NASA Technical Reports Server (NTRS)

Chung, Min-Kun J.

2009-01-01

Two tools were developed for designing station-keeping trajectories and estimating delta-v requirements for designing missions to a small body such as a comet or asteroid. This innovation uses NPOPT, a non-sparse, general-purpose sequential quadratic programming (SQP) optimizer and the Two-Level Differential Corrector (T-LDC) in LTool (Libration point mission design Tool) to design three kinds of station-keeping scripts: vertical hovering, horizontal hovering, and orbiting. The T-LDC is used to differentially correct several trajectory legs that join hovering points. In a vertical hovering, the maximum and minimum range points must be connected smoothly while maintaining the spacecrafts range from a small body, all within the law of gravity and the solar radiation pressure. The same is true for a horizontal hover. A PatchPoint is an LTool class that denotes a space-time event with some extra information for differential correction, including a set of constraints to be satisfied by T-LDC. Given a set of PatchPoints, each with its own constraint, the T-LDC differentially corrects the entire trajectory by connecting each trajectory leg joined by PatchPoints while satisfying all specified constraints at the same time. Vertical and horizontal hover both are needed to minimize delta-v spent for station keeping. A Python I/F to NPOPT has been written to be used from an LTool script. In vertical hovering, the spacecraft stays along the line joining the Sun and a small body. An instantaneous delta-v toward the anti- Sun direction is applied at the closest approach to the small body for station keeping. For example, the spacecraft hovers between the minimum range (2 km) point and the maximum range (2.5 km) point from the asteroid 1989ML. Horizontal hovering buys more time for a spacecraft to recover if, for any reason, a planned thrust fails, by returning almost to the initial position after some time later via a near elliptical orbit around the small body. The mapping or staging orbit may be similarly generated using T-LDC with a set of constraints. Some delta-v tables are generated for several different asteroid masses.

Unraveling the Processing Parameters in Friction Stir Welding

NASA Technical Reports Server (NTRS)

Schneider, Judy; Nunes, Arthur C., Jr.

2005-01-01

In friction stir welding (FSW), a rotating threaded pin tool is translated along a weld seam, literally stirring the edges of the seam together. To determine optimal processing parameters for producing a defect free weld, a better understanding of the resulting metal deformation flow path or paths is required. In this study, various markers are used to trace the flow paths of the metal. X-ray radiographs record the segmentation and position of the wire. Several variations in the trajectories can be differentiated within the weld zone.

Transferable Output ASCII Data (TOAD) gateway: Version 1.0 user's guide

NASA Technical Reports Server (NTRS)

Bingel, Bradford D.

1991-01-01

The Transferable Output ASCII Data (TOAD) Gateway, release 1.0 is described. This is a software tool for converting tabular data from one format into another via the TOAD format. This initial release of the Gateway allows free data interchange among the following file formats: TOAD; Standard Interface File (SIF); Program to Optimize Simulated Trajectories (POST) input; Comma Separated Value (TSV); and a general free-form file format. As required, additional formats can be accommodated quickly and easily.

Coordinated trajectory planning of dual-arm space robot using constrained particle swarm optimization

NASA Astrophysics Data System (ADS)

Wang, Mingming; Luo, Jianjun; Yuan, Jianping; Walter, Ulrich

2018-05-01

Application of the multi-arm space robot will be more effective than single arm especially when the target is tumbling. This paper investigates the application of particle swarm optimization (PSO) strategy to coordinated trajectory planning of the dual-arm space robot in free-floating mode. In order to overcome the dynamics singularities issue, the direct kinematics equations in conjunction with constrained PSO are employed for coordinated trajectory planning of dual-arm space robot. The joint trajectories are parametrized with Bézier curve to simplify the calculation. Constrained PSO scheme with adaptive inertia weight is implemented to find the optimal solution of joint trajectories while specific objectives and imposed constraints are satisfied. The proposed method is not sensitive to the singularity issue due to the application of forward kinematic equations. Simulation results are presented for coordinated trajectory planning of two kinematically redundant manipulators mounted on a free-floating spacecraft and demonstrate the effectiveness of the proposed method.

Trajectory planning of free-floating space robot using Particle Swarm Optimization (PSO)

NASA Astrophysics Data System (ADS)

Wang, Mingming; Luo, Jianjun; Walter, Ulrich

2015-07-01

This paper investigates the application of Particle Swarm Optimization (PSO) strategy to trajectory planning of the kinematically redundant space robot in free-floating mode. Due to the path dependent dynamic singularities, the volume of available workspace of the space robot is limited and enormous joint velocities are required when such singularities are met. In order to overcome this effect, the direct kinematics equations in conjunction with PSO are employed for trajectory planning of free-floating space robot. The joint trajectories are parametrized with the Bézier curve to simplify the calculation. Constrained PSO scheme with adaptive inertia weight is implemented to find the optimal solution of joint trajectories while specific objectives and imposed constraints are satisfied. The proposed method is not sensitive to the singularity issue due to the application of forward kinematic equations. Simulation results are presented for trajectory planning of 7 degree-of-freedom (DOF) redundant manipulator mounted on a free-floating spacecraft and demonstrate the effectiveness of the proposed method.

Optimization of cooling strategy and seeding by FBRM analysis of batch crystallization

NASA Astrophysics Data System (ADS)

Zhang, Dejiang; Liu, Lande; Xu, Shijie; Du, Shichao; Dong, Weibing; Gong, Junbo

2018-03-01

A method is presented for optimizing the cooling strategy and seed loading simultaneously. Focused beam reflectance measurement (FBRM) was used to determine the approximating optimal cooling profile. Using these results in conjunction with constant growth rate assumption, modified Mullin-Nyvlt trajectory could be calculated. This trajectory could suppress secondary nucleation and has the potential to control product's polymorph distribution. Comparing with linear and two step cooling, modified Mullin-Nyvlt trajectory have a larger size distribution and a better morphology. Based on the calculating results, the optimized seed loading policy was also developed. This policy could be useful for guiding the batch crystallization process.

Global, Multi-Objective Trajectory Optimization With Parametric Spreading

NASA Technical Reports Server (NTRS)

Vavrina, Matthew A.; Englander, Jacob A.; Phillips, Sean M.; Hughes, Kyle M.

2017-01-01

Mission design problems are often characterized by multiple, competing trajectory optimization objectives. Recent multi-objective trajectory optimization formulations enable generation of globally-optimal, Pareto solutions via a multi-objective genetic algorithm. A byproduct of these formulations is that clustering in design space can occur in evolving the population towards the Pareto front. This clustering can be a drawback, however, if parametric evaluations of design variables are desired. This effort addresses clustering by incorporating operators that encourage a uniform spread over specified design variables while maintaining Pareto front representation. The algorithm is demonstrated on a Neptune orbiter mission, and enhanced multidimensional visualization strategies are presented.

Ground Contact Model for Mars Science Laboratory Mission Simulations

NASA Technical Reports Server (NTRS)

Raiszadeh, Behzad; Way, David

2012-01-01

The Program to Optimize Simulated Trajectories II (POST 2) has been successful in simulating the flight of launch vehicles and entry bodies on earth and other planets. POST 2 has been the primary simulation tool for the Entry Descent, and Landing (EDL) phase of numerous Mars lander missions such as Mars Pathfinder in 1997, the twin Mars Exploration Rovers (MER-A and MER-B) in 2004, Mars Phoenix lander in 2007, and it is now the main trajectory simulation tool for Mars Science Laboratory (MSL) in 2012. In all previous missions, the POST 2 simulation ended before ground impact, and a tool other than POST 2 simulated landing dynamics. It would be ideal for one tool to simulate the entire EDL sequence, thus avoiding errors that could be introduced by handing off position, velocity, or other fight parameters from one simulation to the other. The desire to have one continuous end-to-end simulation was the motivation for developing the ground interaction model in POST 2. Rover landing, including the detection of the postlanding state, is a very critical part of the MSL mission, as the EDL landing sequence continues for a few seconds after landing. The method explained in this paper illustrates how a simple ground force interaction model has been added to POST 2, which allows simulation of the entire EDL from atmospheric entry through touchdown.

Minimum impulse three-body trajectories.

NASA Technical Reports Server (NTRS)

D'Amario, L.; Edelbaum, T. N.

1973-01-01

A rapid and accurate method of calculating optimal impulsive transfers in the restricted problem of three bodies has been developed. The technique combines a multi-conic method of trajectory integration with primer vector theory and an accelerated gradient method of trajectory optimization. A unique feature is that the state transition matrix and the primer vector are found analytical without additional integrations or differentiations. The method has been applied to the determination of optimal two and three impulse transfers between the L2 libration point and circular orbits about both the earth and the moon.

Optimal flight trajectories in the presence of windshear, 1984-86

NASA Technical Reports Server (NTRS)

Miele, A.

1986-01-01

Optimal flight trajectories were determined in the presence of windshear and guidance schemes were developed for near optimum flight in a windshear. This is a wind characterized by sharp change in intensity and direction over a relatively small region of space. This problem is important in the takeoff and landing of both civilian airplanes and military airplanes and is key to aircraft saftey. The topics covered in reference to takeoff problems are: equations of motion, problem formulation, algorithms, optimal flight trajectories, advanced guidance schemes, simplified guidance schemes, and piloting strategies.

General Methodology for Designing Spacecraft Trajectories

NASA Technical Reports Server (NTRS)

Condon, Gerald; Ocampo, Cesar; Mathur, Ravishankar; Morcos, Fady; Senent, Juan; Williams, Jacob; Davis, Elizabeth C.

2012-01-01

A methodology for designing spacecraft trajectories in any gravitational environment within the solar system has been developed. The methodology facilitates modeling and optimization for problems ranging from that of a single spacecraft orbiting a single celestial body to that of a mission involving multiple spacecraft and multiple propulsion systems operating in gravitational fields of multiple celestial bodies. The methodology consolidates almost all spacecraft trajectory design and optimization problems into a single conceptual framework requiring solution of either a system of nonlinear equations or a parameter-optimization problem with equality and/or inequality constraints.

Fuzzy physical programming for Space Manoeuvre Vehicles trajectory optimization based on hp-adaptive pseudospectral method

NASA Astrophysics Data System (ADS)

Chai, Runqi; Savvaris, Al; Tsourdos, Antonios

2016-06-01

In this paper, a fuzzy physical programming (FPP) method has been introduced for solving multi-objective Space Manoeuvre Vehicles (SMV) skip trajectory optimization problem based on hp-adaptive pseudospectral methods. The dynamic model of SMV is elaborated and then, by employing hp-adaptive pseudospectral methods, the problem has been transformed to nonlinear programming (NLP) problem. According to the mission requirements, the solutions were calculated for each single-objective scenario. To get a compromised solution for each target, the fuzzy physical programming (FPP) model is proposed. The preference function is established with considering the fuzzy factor of the system such that a proper compromised trajectory can be acquired. In addition, the NSGA-II is tested to obtain the Pareto-optimal solution set and verify the Pareto optimality of the FPP solution. Simulation results indicate that the proposed method is effective and feasible in terms of dealing with the multi-objective skip trajectory optimization for the SMV.

HILTOP supplement: Heliocentric interplanetary low thrust trajectory optimization program, supplement 1

NASA Technical Reports Server (NTRS)

Mann, F. I.; Horsewood, J. L.

1974-01-01

Modifications and improvements are described that were made to the HILTOP electric propulsion trajectory optimization computer program during calendar years 1973 and 1974. New program features include the simulation of power degradation, housekeeping power, launch asymptote declination optimization, and powered and unpowered ballistic multiple swingby missions with an optional deep space burn.

Optimal Trajectories for the Helicopter in One-Engine-Inoperative Terminal-Area Operations

NASA Technical Reports Server (NTRS)

Zhao, Yiyuan; Chen, Robert T. N.

1996-01-01

This paper presents a summary of a series of recent analytical studies conducted to investigate One-Engine-Inoperative (OEI) optimal control strategies and the associated optimal trajectories for a twin engine helicopter in Category-A terminal-area operations. These studies also examine the associated heliport size requirements and the maximum gross weight capability of the helicopter. Using an eight states, two controls, augmented point-mass model representative of the study helicopter, Continued TakeOff (CTO), Rejected TakeOff (RTO), Balked Landing (BL), and Continued Landing (CL) are investigated for both Vertical-TakeOff-and-Landing (VTOL) and Short-TakeOff-and-Landing (STOL) terminal-area operations. The formulation of the nonlinear optimal control problems with considerations for realistic constraints, solution methods for the two-point boundary-value problem, a new real-time generation method for the optimal OEI trajectories, and the main results of this series of trajectory optimization studies are presented. In particular, a new balanced- weight concept for determining the takeoff decision point for VTOL Category-A operations is proposed, extending the balanced-field length concept used for STOL operations.

Optimizing the way kinematical feed chains with great distance between slides are chosen for CNC machine tools

NASA Astrophysics Data System (ADS)

Lucian, P.; Gheorghe, S.

2017-08-01

This paper presents a new method, based on FRISCO formula, for optimizing the choice of the best control system for kinematical feed chains with great distance between slides used in computer numerical controlled machine tools. Such machines are usually, but not limited to, used for machining large and complex parts (mostly in the aviation industry) or complex casting molds. For such machine tools the kinematic feed chains are arranged in a dual-parallel drive structure that allows the mobile element to be moved by the two kinematical branches and their related control systems. Such an arrangement allows for high speed and high rigidity (a critical requirement for precision machining) during the machining process. A significant issue for such an arrangement it’s the ability of the two parallel control systems to follow the same trajectory accurately in order to address this issue it is necessary to achieve synchronous motion control for the two kinematical branches ensuring that the correct perpendicular position it’s kept by the mobile element during its motion on the two slides.

Optimal starting conditions for the rendezvous maneuver: Analytical and computational approach

NASA Astrophysics Data System (ADS)

Ciarcia, Marco

The three-dimensional rendezvous between two spacecraft is considered: a target spacecraft on a circular orbit around the Earth and a chaser spacecraft initially on some elliptical orbit yet to be determined. The chaser spacecraft has variable mass, limited thrust, and its trajectory is governed by three controls, one determining the thrust magnitude and two determining the thrust direction. We seek the time history of the controls in such a way that the propellant mass required to execute the rendezvous maneuver is minimized. Two cases are considered: (i) time-to-rendezvous free and (ii) time-to-rendezvous given, respectively equivalent to (i) free angular travel and (ii) fixed angular travel for the target spacecraft. The above problem has been studied by several authors under the assumption that the initial separation coordinates and the initial separation velocities are given, hence known initial conditions for the chaser spacecraft. In this paper, it is assumed that both the initial separation coordinates and initial separation velocities are free except for the requirement that the initial chaser-to-target distance is given so as to prevent the occurrence of trivial solutions. Two approaches are employed: optimal control formulation (Part A) and mathematical programming formulation (Part B). In Part A, analyses are performed with the multiple-subarc sequential gradient-restoration algorithm for optimal control problems. They show that the fuel-optimal trajectory is zero-bang, namely it is characterized by two subarcs: a long coasting zero-thrust subarc followed by a short powered max-thrust braking subarc. While the thrust direction of the powered subarc is continuously variable for the optimal trajectory, its replacement with a constant (yet optimized) thrust direction produces a very efficient guidance trajectory. Indeed, for all values of the initial distance, the fuel required by the guidance trajectory is within less than one percent of the fuel required by the optimal trajectory. For the guidance trajectory, because of the replacement of the variable thrust direction of the powered subarc with a constant thrust direction, the optimal control problem degenerates into a mathematical programming problem with a relatively small number of degrees of freedom, more precisely: three for case (i) time-to-rendezvous free and two for case (ii) time-to-rendezvous given. In particular, we consider the rendezvous between the Space Shuttle (chaser) and the International Space Station (target). Once a given initial distance SS-to-ISS is preselected, the present work supplies not only the best initial conditions for the rendezvous trajectory, but simultaneously the corresponding final conditions for the ascent trajectory. In Part B, an analytical solution of the Clohessy-Wiltshire equations is presented (i) neglecting the change of the spacecraft mass due to the fuel consumption and (ii) and assuming that the thrust is finite, that is, the trajectory includes powered subarcs flown with max thrust and coasting subarc flown with zero thrust. Then, employing the found analytical solution, we study the rendezvous problem under the assumption that the initial separation coordinates and initial separation velocities are free except for the requirement that the initial chaser-to-target distance is given. The main contribution of Part B is the development of analytical solutions for the powered subarcs, an important extension of the analytical solutions already available for the coasting subarcs. One consequence is that the entire optimal trajectory can be described analytically. Another consequence is that the optimal control problems degenerate into mathematical programming problems. A further consequence is that, vis-a-vis the optimal control formulation, the mathematical programming formulation reduces the CPU time by a factor of order 1000. Key words. Space trajectories, rendezvous, optimization, guidance, optimal control, calculus of variations, Mayer problems, Bolza problems, transformation techniques, multiple-subarc sequential gradient-restoration algorithm.

Trajectory Optimization for Crewed Missions to an Earth-Moon L2 Halo Orbit

NASA Astrophysics Data System (ADS)

Dowling, Jennifer

Baseline trajectories to an Earth-Moon L2 halo orbit and round trip trajectories for crewed missions have been created in support of an advanced Orion mission concept. Various transfer durations and orbit insertion locations have been evaluated. The trajectories often include a deterministic mid-course maneuver that decreases the overall change in velocity in the trajectory. This paper presents the application of primer vector theory to study the existence, location, and magnitude of the mid-course maneuver in order to understand how to build an optimal round trip trajectory to an Earth-Moon L2 halo orbit. The lessons learned about when to add mid-course maneuvers can be applied to other mission designs.

Interplanetary Program to Optimize Simulated Trajectories (IPOST). Volume 3: Programmer's manual

NASA Technical Reports Server (NTRS)

Hong, P. E.; Kent, P. D.; Olson, D. W.; Vallado, C. A.

1992-01-01

The Interplanetary Program to Optimize Space Trajectories (IPOST) is intended to support many analysis phases, from early interplanetary feasibility studies through spacecraft development and operations. Here, information is given on the IPOST code.

Launch Vehicle Ascent Trajectory Simulation Using the Program to Optimize Simulated Trajectories II (POST2)

NASA Technical Reports Server (NTRS)

Lugo, Rafael A.; Shidner, Jeremy D.; Powell, Richard W.; Marsh, Steven M.; Hoffman, James A.; Litton, Daniel K.; Schmitt, Terri L.

2017-01-01

The Program to Optimize Simulated Trajectories II (POST2) has been continuously developed for over 40 years and has been used in many flight and research projects. Recently, there has been an effort to improve the POST2 architecture by promoting modularity, flexibility, and ability to support multiple simultaneous projects. The purpose of this paper is to provide insight into the development of trajectory simulation in POST2 by describing methods and examples of various improved models for a launch vehicle liftoff and ascent.

Trajectory optimization for the National aerospace plane

NASA Technical Reports Server (NTRS)

Lu, Ping

1993-01-01

While continuing the application of the inverse dynamics approach in obtaining the optimal numerical solutions, the research during the past six months has been focused on the formulation and derivation of closed-form solutions for constrained hypersonic flight trajectories. Since it was found in the research of the first year that a dominant portion of the optimal ascent trajectory of the aerospace plane is constrained by dynamic pressure and heating constraints, the application of the analytical solutions significantly enhances the efficiency in trajectory optimization, provides a better insight to understanding of the trajectory and conceivably has great potential in guidance of the vehicle. Work of this period has been reported in four technical papers. Two of the papers were presented in the AIAA Guidance, Navigation, and Control Conference (Hilton Head, SC, August, 1992) and Fourth International Aerospace Planes Conference (Orlando, FL, December, 1992). The other two papers have been accepted for publication by Journal of Guidance, Control, and Dynamics, and will appear in 1993. This report briefly summarizes the work done in the past six months and work currently underway.

Ares-I-X Vehicle Preliminary Range Safety Malfunction Turn Analysis

NASA Technical Reports Server (NTRS)

Beaty, James R.; Starr, Brett R.; Gowan, John W., Jr.

2008-01-01

Ares-I-X is the designation given to the flight test version of the Ares-I rocket (also known as the Crew Launch Vehicle - CLV) being developed by NASA. As part of the preliminary flight plan approval process for the test vehicle, a range safety malfunction turn analysis was performed to support the launch area risk assessment and vehicle destruct criteria development processes. Several vehicle failure scenarios were identified which could cause the vehicle trajectory to deviate from its normal flight path, and the effects of these failures were evaluated with an Ares-I-X 6 degrees-of-freedom (6-DOF) digital simulation, using the Program to Optimize Simulated Trajectories Version 2 (POST2) simulation framework. The Ares-I-X simulation analysis provides output files containing vehicle state information, which are used by other risk assessment and vehicle debris trajectory simulation tools to determine the risk to personnel and facilities in the vicinity of the launch area at Kennedy Space Center (KSC), and to develop the vehicle destruct criteria used by the flight test range safety officer. The simulation analysis approach used for this study is described, including descriptions of the failure modes which were considered and the underlying assumptions and ground rules of the study, and preliminary results are presented, determined by analysis of the trajectory deviation of the failure cases, compared with the expected vehicle trajectory.

Intrapartum fetal heart rate classification from trajectory in Sparse SVM feature space.

PubMed

Spilka, J; Frecon, J; Leonarduzzi, R; Pustelnik, N; Abry, P; Doret, M

2015-01-01

Intrapartum fetal heart rate (FHR) constitutes a prominent source of information for the assessment of fetal reactions to stress events during delivery. Yet, early detection of fetal acidosis remains a challenging signal processing task. The originality of the present contribution are three-fold: multiscale representations and wavelet leader based multifractal analysis are used to quantify FHR variability ; Supervised classification is achieved by means of Sparse-SVM that aim jointly to achieve optimal detection performance and to select relevant features in a multivariate setting ; Trajectories in the feature space accounting for the evolution along time of features while labor progresses are involved in the construction of indices quantifying fetal health. The classification performance permitted by this combination of tools are quantified on a intrapartum FHR large database (≃ 1250 subjects) collected at a French academic public hospital.

A study of variable thrust, variable specific impulse trajectories for solar system exploration

NASA Astrophysics Data System (ADS)

Sakai, Tadashi

A study has been performed to determine the advantages and disadvantages of variable thrust and variable Isp (specific impulse) trajectories for solar system exploration. There have been several numerical research efforts for variable thrust, variable Isp, power-limited trajectory optimization problems. All of these results conclude that variable thrust, variable Isp (variable specific impulse, or VSI) engines are superior to constant thrust, constant Isp (constant specific impulse; or CSI) engines. However, most of these research efforts assume a mission from Earth to Mars, and some of them further assume that these planets are circular and coplanar. Hence they still lack the generality. This research has been conducted to answer the following questions: (1) Is a VSI engine always better than a CSI engine or a high thrust engine for any mission to any planet with any time of flight considering lower propellant mass as the sole criterion? (2) If a planetary swing-by is used for a VSI trajectory, is the fuel savings of a VSI swing-by trajectory better than that of a CSI swing-by or high thrust swing-by trajectory? To support this research, an unique, new computer-based interplanetary trajectory calculation program has been created. This program utilizes a calculus of variations algorithm to perform overall optimization of thrust, Isp, and thrust vector direction along a trajectory that minimizes fuel consumption for interplanetary travel. It is assumed that the propulsion system is power-limited, and thus the compromise between thrust and Isp is a variable to be optimized along the flight path. This program is capable of optimizing not only variable thrust trajectories but also constant thrust trajectories in 3-D space using a planetary ephemeris database. It is also capable of conducting planetary swing-bys. Using this program, various Earth-originating trajectories have been investigated and the optimized results have been compared to traditional CSI and high thrust trajectory solutions. Results show that VSI rocket engines reduce fuel requirements for any mission compared to CSI rocket engines. Fuel can be saved by applying swing-by maneuvers for VSI engines; but the effects of swing-bys due to VSI engines are smaller than that of CSI or high thrust engines.

Complexity Science Applications to Dynamic Trajectory Management: Research Strategies

NASA Technical Reports Server (NTRS)

Sawhill, Bruce; Herriot, James; Holmes, Bruce J.; Alexandrov, Natalia

2009-01-01

The promise of the Next Generation Air Transportation System (NextGen) is strongly tied to the concept of trajectory-based operations in the national airspace system. Existing efforts to develop trajectory management concepts are largely focused on individual trajectories, optimized independently, then de-conflicted among each other, and individually re-optimized, as possible. The benefits in capacity, fuel, and time are valuable, though perhaps could be greater through alternative strategies. The concept of agent-based trajectories offers a strategy for automation of simultaneous multiple trajectory management. The anticipated result of the strategy would be dynamic management of multiple trajectories with interacting and interdependent outcomes that satisfy multiple, conflicting constraints. These constraints would include the business case for operators, the capacity case for the Air Navigation Service Provider (ANSP), and the environmental case for noise and emissions. The benefits in capacity, fuel, and time might be improved over those possible under individual trajectory management approaches. The proposed approach relies on computational agent-based modeling (ABM), combinatorial mathematics, as well as application of "traffic physics" concepts to the challenge, and modeling and simulation capabilities. The proposed strategy could support transforming air traffic control from managing individual aircraft behaviors to managing systemic behavior of air traffic in the NAS. A system built on the approach could provide the ability to know when regions of airspace approach being "full," that is, having non-viable local solution space for optimizing trajectories in advance.

A six degree of freedom, plume-fuel optimal trajectory planner for spacecraft proximity operations using an A* node search. M.S. Thesis - MIT

NASA Technical Reports Server (NTRS)

Jackson, Mark Charles

1994-01-01

Spacecraft proximity operations are complicated by the fact that exhaust plume impingement from the reaction control jets of space vehicles can cause structural damage, contamination of sensitive arrays and instruments, or attitude misalignment during docking. The occurrence and effect of jet plume impingement can be reduced by planning approach trajectories with plume effects considered. An A* node search is used to find plume-fuel optimal trajectories through a discretized six dimensional attitude-translation space. A plume cost function which approximates jet plume isopressure envelopes is presented. The function is then applied to find relative costs for predictable 'trajectory altering' firings and unpredictable 'deadbanding' firings. Trajectory altering firings are calculated by running the spacecraft jet selection algorithm and summing the cost contribution from each jet fired. A 'deadbanding effects' function is defined and integrated to determine the potential for deadbanding impingement along candidate trajectories. Plume costs are weighed against fuel costs in finding the optimal solution. A* convergence speed is improved by solving approach trajectory problems in reverse time. Results are obtained on a high fidelity space shuttle/space station simulation. Trajectory following is accomplished by a six degree of freedom autopilot. Trajectories planned with, and without, plume costs are compared in terms of force applied to the target structure.

Optimism and Pessimism as Predictors of Alcohol Use Trajectories in Adolescence

ERIC Educational Resources Information Center

Wray, Tyler B.; Dvorak, Rob D.; Hsia, Jennifer F.; Arens, Ashley M.; Schweinle, William E.

2013-01-01

A range of research has recognized the benefits of optimism in a variety of health-related outcomes. Pessimism has received less attention but may be a distinct concept that is uniquely related to certain health behaviors, including drug use. The present study examined relationships between optimism and pessimism and alcohol use trajectories of…

A Robust Method to Integrate End-to-End Mission Architecture Optimization Tools

NASA Technical Reports Server (NTRS)

Lugo, Rafael; Litton, Daniel; Qu, Min; Shidner, Jeremy; Powell, Richard

2016-01-01

End-to-end mission simulations include multiple phases of flight. For example, an end-to-end Mars mission simulation may include launch from Earth, interplanetary transit to Mars and entry, descent and landing. Each phase of flight is optimized to meet specified constraints and often depend on and impact subsequent phases. The design and optimization tools and methodologies used to combine different aspects of end-to-end framework and their impact on mission planning are presented. This work focuses on a robust implementation of a Multidisciplinary Design Analysis and Optimization (MDAO) method that offers the flexibility to quickly adapt to changing mission design requirements. Different simulations tailored to the liftoff, ascent, and atmospheric entry phases of a trajectory are integrated and optimized in the MDAO program Isight, which provides the user a graphical interface to link simulation inputs and outputs. This approach provides many advantages to mission planners, as it is easily adapted to different mission scenarios and can improve the understanding of the integrated system performance within a particular mission configuration. A Mars direct entry mission using the Space Launch System (SLS) is presented as a generic end-to-end case study. For the given launch period, the SLS launch performance is traded for improved orbit geometry alignment, resulting in an optimized a net payload that is comparable to that in the SLS Mission Planner's Guide.

SU-F-BRB-16: A Spreadsheet Based Automatic Trajectory GEnerator (SAGE): An Open Source Tool for Automatic Creation of TrueBeam Developer Mode Robotic Trajectories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Etmektzoglou, A; Mishra, P; Svatos, M

Purpose: To automate creation and delivery of robotic linac trajectories with TrueBeam Developer Mode, an open source spreadsheet-based trajectory generation tool has been developed, tested and made freely available. The computing power inherent in a spreadsheet environment plus additional functions programmed into the tool insulate users from the underlying schema tedium and allow easy calculation, parameterization, graphical visualization, validation and finally automatic generation of Developer Mode XML scripts which are directly loadable on a TrueBeam linac. Methods: The robotic control system platform that allows total coordination of potentially all linac moving axes with beam (continuous, step-and-shoot, or combination thereof) becomesmore » available in TrueBeam Developer Mode. Many complex trajectories are either geometric or can be described in analytical form, making the computational power, graphing and programmability available in a spreadsheet environment an easy and ideal vehicle for automatic trajectory generation. The spreadsheet environment allows also for parameterization of trajectories thus enabling the creation of entire families of trajectories using only a few variables. Standard spreadsheet functionality has been extended for powerful movie-like dynamic graphic visualization of the gantry, table, MLC, room, lasers, 3D observer placement and beam centerline all as a function of MU or time, for analysis of the motions before requiring actual linac time. Results: We used the tool to generate and deliver extended SAD “virtual isocenter” trajectories of various shapes such as parameterized circles and ellipses. We also demonstrated use of the tool in generating linac couch motions that simulate respiratory motion using analytical parameterized functions. Conclusion: The SAGE tool is a valuable resource to experiment with families of complex geometric trajectories for a TrueBeam Linac. It makes Developer Mode more accessible as a vehicle to quickly translate research ideas into machine readable scripts without programming knowledge. As an open source initiative, it also enables researcher collaboration on future developments. I am a full time employee at Varian Medical Systems, Palo Alto, California.« less

An Interpolation Approach to Optimal Trajectory Planning for Helicopter Unmanned Aerial Vehicles

DTIC Science & Technology

2012-06-01

Armament Data Line DOF Degree of Freedom PS Pseudospectral LGL Legendre -Gauss-Lobatto quadrature nodes ODE Ordinary Differential Equation xiv...low order polynomials patched together in such away so that the resulting trajectory has several continuous derivatives at all points. In [7], Murray...claims that splines are ideal for optimal control problems because each segment of the spline’s piecewise polynomials approximate the trajectory

Optimal trajectory planning of free-floating space manipulator using differential evolution algorithm

NASA Astrophysics Data System (ADS)

Wang, Mingming; Luo, Jianjun; Fang, Jing; Yuan, Jianping

2018-03-01

The existence of the path dependent dynamic singularities limits the volume of available workspace of free-floating space robot and induces enormous joint velocities when such singularities are met. In order to overcome this demerit, this paper presents an optimal joint trajectory planning method using forward kinematics equations of free-floating space robot, while joint motion laws are delineated with application of the concept of reaction null-space. Bézier curve, in conjunction with the null-space column vectors, are applied to describe the joint trajectories. Considering the forward kinematics equations of the free-floating space robot, the trajectory planning issue is consequently transferred to an optimization issue while the control points to construct the Bézier curve are the design variables. A constrained differential evolution (DE) scheme with premature handling strategy is implemented to find the optimal solution of the design variables while specific objectives and imposed constraints are satisfied. Differ from traditional methods, we synthesize null-space and specialized curve to provide a novel viewpoint for trajectory planning of free-floating space robot. Simulation results are presented for trajectory planning of 7 degree-of-freedom (DOF) kinematically redundant manipulator mounted on a free-floating spacecraft and demonstrate the feasibility and effectiveness of the proposed method.

Gamma guidance of trajectories for coplanar, aeroassisted orbital transfer

NASA Technical Reports Server (NTRS)

Miele, A.; Wang, T.

1990-01-01

The optimization and guidance of trajectories for coplaner, aeroassisted orbital transfer (AOT) from high Earth orbit (HEO) to low Earth orbit (LEO) are examined. In particular, HEO can be a geosynchronous Earth orbit (GEO). It is assumed that the initial and final orbits are circular, that the gravitational field is central and is governed by the inverse square law, and that at most three impulses are employed: one at HEO exit, one at atmospheric exit, and one at LEO entry. It is also assumed that, during the atmospheric pass, the trajectory is controlled via the lift coefficient. The presence of upper and lower bounds on the lift coefficient is considered. First, optimal trajectories are computed by minimizing the total velocity impulse (hence, the propellant consumption) required for AOT transfer. The sequential gradient-restoration algorithm (SGRA) is used for optimal control problems. The optimal trajectory is shown to include two branches: a relatively short descending flight branch (branch 1) and a long ascending flight branch (branch 2). Next, attention is focused on guidance trajectories capable of approximating the optimal trajectories in real time, while retaining the essential characteristics of simplicity, ease of implementation, and reliability. For the atmospheric pass, a feedback control scheme is employed and the lift coefficient is adjusted according to a two-stage gamma guidance law. Further improvements are possible via a modified gamma guidance which is more stable with respect to dispersion effects arising from navigation errors, variations of the atmospheric density, and uncertainties in the aerodynamic coefficients than gamma guidance trajectory. A byproduct of the studies on dispersion effects is the following design concept. For coplaner aeroassisted orbital transfer, the lift-range-to-weight ratio appears to play a more important role than the lift-to-drag ratio. This is because the lift-range-to-weight ratio controls mainly the minimum altitude (hence, the peak heating rate) of the guidance trajectory; on the other hand, the lift-to-drag ratio controls mainly the duration of the atmospheric pass of the guidance trajectory.

Trajectory Tracking of a Planer Parallel Manipulator by Using Computed Force Control Method

NASA Astrophysics Data System (ADS)

Bayram, Atilla

2017-03-01

Despite small workspace, parallel manipulators have some advantages over their serial counterparts in terms of higher speed, acceleration, rigidity, accuracy, manufacturing cost and payload. Accordingly, this type of manipulators can be used in many applications such as in high-speed machine tools, tuning machine for feeding, sensitive cutting, assembly and packaging. This paper presents a special type of planar parallel manipulator with three degrees of freedom. It is constructed as a variable geometry truss generally known planar Stewart platform. The reachable and orientation workspaces are obtained for this manipulator. The inverse kinematic analysis is solved for the trajectory tracking according to the redundancy and joint limit avoidance. Then, the dynamics model of the manipulator is established by using Virtual Work method. The simulations are performed to follow the given planar trajectories by using the dynamic equations of the variable geometry truss manipulator and computed force control method. In computed force control method, the feedback gain matrices for PD control are tuned with fixed matrices by trail end error and variable ones by means of optimization with genetic algorithm.

Implementation of optimal trajectory control of series resonant converter

NASA Technical Reports Server (NTRS)

Oruganti, Ramesh; Yang, James J.; Lee, Fred C.

1987-01-01

Due to the presence of a high-frequency LC tank circuit, the dynamics of a resonant converter are unpredictable. There is often a large surge of tank energy during transients. Using state-plane analysis technique, an optimal trajectory control utilizing the desired solution trajectory as the control law was previously proposed for the series resonant converters. The method predicts the fastest response possible with minimum energy surge in the resonant tank. The principle of the control and its experimental implementation are described here. The dynamics of the converter are shown to be close to time-optimal.

Constrained Burn Optimization for the International Space Station

NASA Technical Reports Server (NTRS)

Brown, Aaron J.; Jones, Brandon A.

2017-01-01

In long-term trajectory planning for the International Space Station (ISS), translational burns are currently targeted sequentially to meet the immediate trajectory constraints, rather than simultaneously to meet all constraints, do not employ gradient-based search techniques, and are not optimized for a minimum total deltav (v) solution. An analytic formulation of the constraint gradients is developed and used in an optimization solver to overcome these obstacles. Two trajectory examples are explored, highlighting the advantage of the proposed method over the current approach, as well as the potential v and propellant savings in the event of propellant shortages.

Trajectory Browser Website

NASA Technical Reports Server (NTRS)

Foster, Cyrus; Jaroux, Belgacem A.

2012-01-01

The Trajectory Browser is a web-based tool developed at the NASA Ames Research Center to be used for the preliminary assessment of trajectories to small-bodies and planets and for providing relevant launch date, time-of-flight and V requirements. The site hosts a database of transfer trajectories from Earth to asteroids and planets for various types of missions such as rendezvous, sample return or flybys. A search engine allows the user to find trajectories meeting desired constraints on the launch window, mission duration and delta V capability, while a trajectory viewer tool allows the visualization of the heliocentric trajectory and the detailed mission itinerary. The anticipated user base of this tool consists primarily of scientists and engineers designing interplanetary missions in the context of pre-phase A studies, particularly for performing accessibility surveys to large populations of small-bodies. The educational potential of the website is also recognized for academia and the public with regards to trajectory design, a field that has generally been poorly understood by the public. The website is currently hosted on NASA-internal URL http://trajbrowser.arc.nasa.gov/ with plans for a public release as soon as development is complete.

Identification of optimal feedback control rules from micro-quadrotor and insect flight trajectories.

PubMed

Faruque, Imraan A; Muijres, Florian T; Macfarlane, Kenneth M; Kehlenbeck, Andrew; Humbert, J Sean

2018-06-01

This paper presents "optimal identification," a framework for using experimental data to identify the optimality conditions associated with the feedback control law implemented in the measurements. The technique compares closed loop trajectory measurements against a reduced order model of the open loop dynamics, and uses linear matrix inequalities to solve an inverse optimal control problem as a convex optimization that estimates the controller optimality conditions. In this study, the optimal identification technique is applied to two examples, that of a millimeter-scale micro-quadrotor with an engineered controller on board, and the example of a population of freely flying Drosophila hydei maneuvering about forward flight. The micro-quadrotor results show that the performance indices used to design an optimal flight control law for a micro-quadrotor may be recovered from the closed loop simulated flight trajectories, and the Drosophila results indicate that the combined effect of the insect longitudinal flight control sensing and feedback acts principally to regulate pitch rate.

Configuration optimization and experimental accuracy evaluation of a bone-attached, parallel robot for skull surgery.

PubMed

Kobler, Jan-Philipp; Nuelle, Kathrin; Lexow, G Jakob; Rau, Thomas S; Majdani, Omid; Kahrs, Lueder A; Kotlarski, Jens; Ortmaier, Tobias

2016-03-01

Minimally invasive cochlear implantation is a novel surgical technique which requires highly accurate guidance of a drilling tool along a trajectory from the mastoid surface toward the basal turn of the cochlea. The authors propose a passive, reconfigurable, parallel robot which can be directly attached to bone anchors implanted in a patient's skull, avoiding the need for surgical tracking systems. Prior to clinical trials, methods are necessary to patient specifically optimize the configuration of the mechanism with respect to accuracy and stability. Furthermore, the achievable accuracy has to be determined experimentally. A comprehensive error model of the proposed mechanism is established, taking into account all relevant error sources identified in previous studies. Two optimization criteria to exploit the given task redundancy and reconfigurability of the passive robot are derived from the model. The achievable accuracy of the optimized robot configurations is first estimated with the help of a Monte Carlo simulation approach and finally evaluated in drilling experiments using synthetic temporal bone specimen. Experimental results demonstrate that the bone-attached mechanism exhibits a mean targeting accuracy of [Formula: see text] mm under realistic conditions. A systematic targeting error is observed, which indicates that accurate identification of the passive robot's kinematic parameters could further reduce deviations from planned drill trajectories. The accuracy of the proposed mechanism demonstrates its suitability for minimally invasive cochlear implantation. Future work will focus on further evaluation experiments on temporal bone specimen.

OTIS 3.2 Software Released

NASA Technical Reports Server (NTRS)

Riehl, John P.; Sjauw, Waldy K.

2004-01-01

Trajectory, mission, and vehicle engineers concern themselves with finding the best way for an object to get from one place to another. These engineers rely upon special software to assist them in this. For a number of years, many engineers have used the OTIS program for this assistance. With OTIS, an engineer can fully optimize trajectories for airplanes, launch vehicles like the space shuttle, interplanetary spacecraft, and orbital transfer vehicles. OTIS provides four modes of operation, with each mode providing successively stronger optimization capability. The most powerful mode uses a mathematical method called implicit integration to solve what engineers and mathematicians call the optimal control problem. OTIS 3.2, which was developed at the NASA Glenn Research Center, is the latest release of this industry workhorse and features new capabilities for parameter optimization and mission design. OTIS stands for Optimal Control by Implicit Simulation, and it is implicit integration that makes OTIS so powerful at solving trajectory optimization problems. Why is this so important? The optimization process not only determines how to get from point A to point B, but it can also determine how to do this with the least amount of propellant, with the lightest starting weight, or in the fastest time possible while avoiding certain obstacles along the way. There are numerous conditions that engineers can use to define optimal, or best. OTIS provides a framework for defining the starting and ending points of the trajectory (point A and point B), the constraints on the trajectory (requirements like "avoid these regions where obstacles occur"), and what is being optimized (e.g., minimize propellant). The implicit integration method can find solutions to very complicated problems when there is not a lot of information available about what the optimal trajectory might be. The method was first developed for solving two-point boundary value problems and was adapted for use in OTIS. Implicit integration usually allows OTIS to find solutions to problems much faster than programs that use explicit integration and parametric methods. Consequently, OTIS is best suited to solving very complicated and highly constrained problems.

Trajectory planning and optimal tracking for an industrial mobile robot

NASA Astrophysics Data System (ADS)

Hu, Huosheng; Brady, J. Michael; Probert, Penelope J.

1994-02-01

This paper introduces a unified approach to trajectory planning and tracking for an industrial mobile robot subject to non-holonomic constraints. We show (1) how a smooth trajectory is generated that takes into account the constraints from the dynamic environment and the robot kinematics; and (2) how a general predictive controller works to provide optimal tracking capability for nonlinear systems. The tracking performance of the proposed guidance system is analyzed by simulation.

Multi-Target Tracking via Mixed Integer Optimization

DTIC Science & Technology

2016-05-13

solving these two problems separately, however few algorithms attempt to solve these simultaneously and even fewer utilize optimization. In this paper we...introduce a new mixed integer optimization (MIO) model which solves the data association and trajectory estimation problems simultaneously by minimizing...Kalman filter [5], which updates the trajectory estimates before the algorithm progresses forward to the next scan. This process repeats sequentially

MARS Science Laboratory Post-Landing Location Estimation Using Post2 Trajectory Simulation

NASA Technical Reports Server (NTRS)

Davis, J. L.; Shidner, Jeremy D.; Way, David W.

2013-01-01

The Mars Science Laboratory (MSL) Curiosity rover landed safely on Mars August 5th, 2012 at 10:32 PDT, Earth Received Time. Immediately following touchdown confirmation, best estimates of position were calculated to assist in determining official MSL locations during entry, descent and landing (EDL). Additionally, estimated balance mass impact locations were provided and used to assess how predicted locations compared to actual locations. For MSL, the Program to Optimize Simulated Trajectories II (POST2) was the primary trajectory simulation tool used to predict and assess EDL performance from cruise stage separation through rover touchdown and descent stage impact. This POST2 simulation was used during MSL operations for EDL trajectory analyses in support of maneuver decisions and imaging MSL during EDL. This paper presents the simulation methodology used and results of pre/post-landing MSL location estimates and associated imagery from Mars Reconnaissance Orbiter s (MRO) High Resolution Imaging Science Experiment (HiRISE) camera. To generate these estimates, the MSL POST2 simulation nominal and Monte Carlo data, flight telemetry from onboard navigation, relay orbiter positions from MRO and Mars Odyssey and HiRISE generated digital elevation models (DEM) were utilized. A comparison of predicted rover and balance mass location estimations against actual locations are also presented.

Understanding transient uncoupling induced synchronization through modified dynamic coupling

NASA Astrophysics Data System (ADS)

Ghosh, Anupam; Godara, Prakhar; Chakraborty, Sagar

2018-05-01

An important aspect of the recently introduced transient uncoupling scheme is that it induces synchronization for large values of coupling strength at which the coupled chaotic systems resist synchronization when continuously coupled. However, why this is so is an open problem? To answer this question, we recall the conventional wisdom that the eigenvalues of the Jacobian of the transverse dynamics measure whether a trajectory at a phase point is locally contracting or diverging with respect to another nearby trajectory. Subsequently, we go on to highlight a lesser appreciated fact that even when, under the corresponding linearised flow, the nearby trajectory asymptotically diverges away, its distance from the reference trajectory may still be contracting for some intermediate period. We term this phenomenon transient decay in line with the phenomenon of the transient growth. Using these facts, we show that an optimal coupling region, i.e., a region of the phase space where coupling is on, should ideally be such that at any of the constituent phase point either the maximum of the real parts of the eigenvalues is negative or the magnitude of the positive maximum is lesser than that of the negative minimum. We also invent and employ a modified dynamics coupling scheme—a significant improvement over the well-known dynamic coupling scheme—as a decisive tool to justify our results.

Real-time control of optimal low-thrust transfer to the Sun-Earth L 1 halo orbit in the bicircular four-body problem

NASA Astrophysics Data System (ADS)

Salmani, Majid; Büskens, Christof

2011-11-01

In this article, after describing a procedure to construct trajectories for a spacecraft in the four-body model, a method to correct the trajectory violations is presented. To construct the trajectories, periodic orbits as the solutions of the three-body problem are used. On the other hand, the bicircular model based on the Sun-Earth rotating frame governs the dynamics of the spacecraft and other bodies. A periodic orbit around the first libration-point L1 is the destination of the mission which is one of the equilibrium points in the Sun-Earth/Moon three-body problem. In the way to reach such a far destination, there are a lot of disturbances such as solar radiation and winds that make the plans untrustworthy. However, the solar radiation pressure is considered in the system dynamics. To prevail over these difficulties, considering the whole transfer problem as an optimal control problem makes the designer to be able to correct the unavoidable violations from the pre-designed trajectory and strategies. The optimal control problem is solved by a direct method, transcribing it into a nonlinear programming problem. This transcription gives an unperturbed optimal trajectory and its sensitivities with respect perturbations. Modeling these perturbations as parameters embedded in a parametric optimal control problem, one can take advantage of the parametric sensitivity analysis of nonlinear programming problem to recalculate the optimal trajectory with a very smaller amount of computation costs. This is obtained by evaluating a first-order Taylor expansion of the perturbed solution in an iterative process which is aimed to achieve an admissible solution. At the end, the numerical results show the applicability of the presented method.

A Real-Time Brain-Machine Interface Combining Motor Target and Trajectory Intent Using an Optimal Feedback Control Design

PubMed Central

Shanechi, Maryam M.; Williams, Ziv M.; Wornell, Gregory W.; Hu, Rollin C.; Powers, Marissa; Brown, Emery N.

2013-01-01

Real-time brain-machine interfaces (BMI) have focused on either estimating the continuous movement trajectory or target intent. However, natural movement often incorporates both. Additionally, BMIs can be modeled as a feedback control system in which the subject modulates the neural activity to move the prosthetic device towards a desired target while receiving real-time sensory feedback of the state of the movement. We develop a novel real-time BMI using an optimal feedback control design that jointly estimates the movement target and trajectory of monkeys in two stages. First, the target is decoded from neural spiking activity before movement initiation. Second, the trajectory is decoded by combining the decoded target with the peri-movement spiking activity using an optimal feedback control design. This design exploits a recursive Bayesian decoder that uses an optimal feedback control model of the sensorimotor system to take into account the intended target location and the sensory feedback in its trajectory estimation from spiking activity. The real-time BMI processes the spiking activity directly using point process modeling. We implement the BMI in experiments consisting of an instructed-delay center-out task in which monkeys are presented with a target location on the screen during a delay period and then have to move a cursor to it without touching the incorrect targets. We show that the two-stage BMI performs more accurately than either stage alone. Correct target prediction can compensate for inaccurate trajectory estimation and vice versa. The optimal feedback control design also results in trajectories that are smoother and have lower estimation error. The two-stage decoder also performs better than linear regression approaches in offline cross-validation analyses. Our results demonstrate the advantage of a BMI design that jointly estimates the target and trajectory of movement and more closely mimics the sensorimotor control system. PMID:23593130

Multi-objective trajectory optimization for the space exploration vehicle

NASA Astrophysics Data System (ADS)

Qin, Xiaoli; Xiao, Zhen

2016-07-01

The research determines temperature-constrained optimal trajectory for the space exploration vehicle by developing an optimal control formulation and solving it using a variable order quadrature collocation method with a Non-linear Programming(NLP) solver. The vehicle is assumed to be the space reconnaissance aircraft that has specified takeoff/landing locations, specified no-fly zones, and specified targets for sensor data collections. A three degree of freedom aircraft model is adapted from previous work and includes flight dynamics, and thermal constraints.Vehicle control is accomplished by controlling angle of attack, roll angle, and propellant mass flow rate. This model is incorporated into an optimal control formulation that includes constraints on both the vehicle and mission parameters, such as avoidance of no-fly zones and exploration of space targets. In addition, the vehicle models include the environmental models(gravity and atmosphere). How these models are appropriately employed is key to gaining confidence in the results and conclusions of the research. Optimal trajectories are developed using several performance costs in the optimal control formation,minimum time,minimum time with control penalties,and maximum distance.The resulting analysis demonstrates that optimal trajectories that meet specified mission parameters and constraints can be quickly determined and used for large-scale space exloration.

Desensitized Optimal Filtering and Sensor Fusion Toolkit

NASA Technical Reports Server (NTRS)

Karlgaard, Christopher D.

2015-01-01

Analytical Mechanics Associates, Inc., has developed a software toolkit that filters and processes navigational data from multiple sensor sources. A key component of the toolkit is a trajectory optimization technique that reduces the sensitivity of Kalman filters with respect to model parameter uncertainties. The sensor fusion toolkit also integrates recent advances in adaptive Kalman and sigma-point filters for non-Gaussian problems with error statistics. This Phase II effort provides new filtering and sensor fusion techniques in a convenient package that can be used as a stand-alone application for ground support and/or onboard use. Its modular architecture enables ready integration with existing tools. A suite of sensor models and noise distribution as well as Monte Carlo analysis capability are included to enable statistical performance evaluations.

Impact of Airspace Charges on Transatlantic Aircraft Trajectories

NASA Technical Reports Server (NTRS)

Sridhar, Banavar; Ng, Hok K.; Linke, Florian; Chen, Neil Y.

2015-01-01

Aircraft flying over the airspace of different countries are subject to over-flight charges. These charges vary from country to country. Airspace charges, while necessary to support the communication, navigation and surveillance services, may lead to aircraft flying routes longer than wind-optimal routes and produce additional carbon dioxide and other gaseous emissions. This paper develops an optimal route between city pairs by modifying the cost function to include an airspace cost whenever an aircraft flies through a controlled airspace without landing or departing from that airspace. It is assumed that the aircraft will fly the trajectory at a constant cruise altitude and constant speed. The computationally efficient optimal trajectory is derived by solving a non-linear optimal control problem. The operational strategies investigated in this study for minimizing aircraft fuel burn and emissions include flying fuel-optimal routes and flying cost-optimal routes that may completely or partially reduce airspace charges en route. The results in this paper use traffic data for transatlantic flights during July 2012. The mean daily savings in over-flight charges, fuel cost and total operation cost during the period are 17.6 percent, 1.6 percent, and 2.4 percent respectively, along the cost- optimal trajectories. The transatlantic flights can potentially save $600,000 in fuel cost plus $360,000 in over-flight charges daily by flying the cost-optimal trajectories. In addition, the aircraft emissions can be potentially reduced by 2,070 metric tons each day. The airport pairs and airspace regions that have the highest potential impacts due to airspace charges are identified for possible reduction of fuel burn and aircraft emissions for the transatlantic flights. The results in the paper show that the impact of the variation in fuel price on the optimal routes is to reduce the difference between wind-optimal and cost-optimal routes as the fuel price increases. The additional fuel consumption is quantified using the 30 percent variation in fuel prices during March 2014 to March 2015.

An Efficient Method of Sharing Mass Spatio-Temporal Trajectory Data Based on Cloudera Impala for Traffic Distribution Mapping in an Urban City.

PubMed

Zhou, Lianjie; Chen, Nengcheng; Yuan, Sai; Chen, Zeqiang

2016-10-29

The efficient sharing of spatio-temporal trajectory data is important to understand traffic congestion in mass data. However, the data volumes of bus networks in urban cities are growing rapidly, reaching daily volumes of one hundred million datapoints. Accessing and retrieving mass spatio-temporal trajectory data in any field is hard and inefficient due to limited computational capabilities and incomplete data organization mechanisms. Therefore, we propose an optimized and efficient spatio-temporal trajectory data retrieval method based on the Cloudera Impala query engine, called ESTRI, to enhance the efficiency of mass data sharing. As an excellent query tool for mass data, Impala can be applied for mass spatio-temporal trajectory data sharing. In ESTRI we extend the spatio-temporal trajectory data retrieval function of Impala and design a suitable data partitioning method. In our experiments, the Taiyuan BeiDou (BD) bus network is selected, containing 2300 buses with BD positioning sensors, producing 20 million records every day, resulting in two difficulties as described in the Introduction section. In addition, ESTRI and MongoDB are applied in experiments. The experiments show that ESTRI achieves the most efficient data retrieval compared to retrieval using MongoDB for data volumes of fifty million, one hundred million, one hundred and fifty million, and two hundred million. The performance of ESTRI is approximately seven times higher than that of MongoDB. The experiments show that ESTRI is an effective method for retrieving mass spatio-temporal trajectory data. Finally, bus distribution mapping in Taiyuan city is achieved, describing the buses density in different regions at different times throughout the day, which can be applied in future studies of transport, such as traffic scheduling, traffic planning and traffic behavior management in intelligent public transportation systems.

Program to Optimize Simulated Trajectories (POST). Volume 3: Programmer's manual

NASA Technical Reports Server (NTRS)

Brauer, G. L.; Cornick, D. E.; Habeger, A. R.; Petersen, F. M.; Stevenson, R.

1975-01-01

Information pertinent to the programmer and relating to the program to optimize simulated trajectories (POST) is presented. Topics discussed include: program structure and logic, subroutine listings and flow charts, and internal FORTRAN symbols. The POST core requirements are summarized along with program macrologic.

Optimal aeroassisted coplanar orbital transfer using an energy model

NASA Technical Reports Server (NTRS)

Halyo, Nesim; Taylor, Deborah B.

1989-01-01

The atmospheric portion of the trajectories for the aeroassisted coplanar orbit transfer was investigated. The equations of motion for the problem are expressed using reduced order model and total vehicle energy, kinetic plus potential, as the independent variable rather than time. The order reduction is achieved analytically without an approximation of the vehicle dynamics. In this model, the problem of coplanar orbit transfer is seen as one in which a given amount of energy must be transferred from the vehicle to the atmosphere during the trajectory without overheating the vehicle. An optimal control problem is posed where a linear combination of the integrated square of the heating rate and the vehicle drag is the cost function to be minimized. The necessary conditions for optimality are obtained. These result in a 4th order two-point-boundary-value problem. A parametric study of the optimal guidance trajectory in which the proportion of the heating rate term versus the drag varies is made. Simulations of the guidance trajectories are presented.

Developmental Trajectories of Subjective Social Status.

PubMed

Goodman, Elizabeth; Maxwell, Sarah; Malspeis, Susan; Adler, Nancy

2015-09-01

Subjective social status (SSS), a person's sense of their (or for youth, abstract their family's) position in the socioeconomic hierarchy, is strongly related to health in adults but not health in adolescence. Understanding this developmental discrepancy requires first understanding the developmental trajectory of SSS. The objective of this study was to identify the number and shape of SSS trajectories as adolescents transition to adulthood and explore if trajectory membership affects health. Using data from 7436 assessments from the Princeton School District Study, a decade long cohort study of non-Hispanic black and white youth, latent class growth models with 3 to 7 SSS trajectories were developed. Model fit, trajectory structure, and shape were used to guide optimal model selection. Using this optimal model, the associations of trajectory membership with BMI and depressive symptoms in young adulthood were explored. The 5-class model was optimal. In this model, trajectories were persistent high (7.8%),mid–high (32.2%), middle (43.4%), low–lower (7.4%), and high–low (9.1%). Non-Hispanic black race/ethnicity, lower household income, and low parent education were associated with membership in this high–low trajectory. High–low trajectory membership was associated with higher BMI and depressive symptoms in non-Hispanic white subjects but was not associated with depressive symptoms. It was associated with lower BMI only after adjustment for BMI in adolescence in non-Hispanic black subjects. SSS is relatively stable in adolescence and the transition to adulthood, and it generally reflects objective markers of social advantage. However, socially disadvantaged youth with high SSS in early adolescence may be at increased health risk.

Conjugate gradient optimization programs for shuttle reentry

NASA Technical Reports Server (NTRS)

Powers, W. F.; Jacobson, R. A.; Leonard, D. A.

1972-01-01

Two computer programs for shuttle reentry trajectory optimization are listed and described. Both programs use the conjugate gradient method as the optimization procedure. The Phase 1 Program is developed in cartesian coordinates for a rotating spherical earth, and crossrange, downrange, maximum deceleration, total heating, and terminal speed, altitude, and flight path angle are included in the performance index. The programs make extensive use of subroutines so that they may be easily adapted to other atmospheric trajectory optimization problems.

On the Nature of Earth-Mars Porkchop Plots

NASA Technical Reports Server (NTRS)

Woolley, Ryan C.; Whetsel, Charles W.

2013-01-01

Porkchop plots are a quick and convenient tool to help mission designers plan ballistic trajectories between two bodies. Parameter contours give rise to the familiar 'porkchop' shape. Each synodic period the pattern repeats, but not exactly, primarily due to differences in inclination and non-zero eccentricity. In this paper we examine the morphological features of Earth-to-Mars porkchop plots and the orbital characteristics that create them. These results are compared to idealistic and optimized transfers. Conclusions are drawn about 'good' opportunities versus 'bad' opportunities for different mission applications.

Kinetic constrained optimization of the golf swing hub path.

PubMed

Nesbit, Steven M; McGinnis, Ryan S

2014-12-01

This study details an optimization of the golf swing, where the hand path and club angular trajectories are manipulated. The optimization goal was to maximize club head velocity at impact within the interaction kinetic limitations (force, torque, work, and power) of the golfer as determined through the analysis of a typical swing using a two-dimensional dynamic model. The study was applied to four subjects with diverse swing capabilities and styles. It was determined that it is possible for all subjects to increase their club head velocity at impact within their respective kinetic limitations through combined modifications to their respective hand path and club angular trajectories. The manner of the modifications, the degree of velocity improvement, the amount of kinetic reduction, and the associated kinetic limitation quantities were subject dependent. By artificially minimizing selected kinetic inputs within the optimization algorithm, it was possible to identify swing trajectory characteristics that indicated relative kinetic weaknesses of a subject. Practical implications are offered based upon the findings of the study. Key PointsThe hand path trajectory is an important characteristic of the golf swing and greatly affects club head velocity and golfer/club energy transfer.It is possible to increase the energy transfer from the golfer to the club by modifying the hand path and swing trajectories without increasing the kinetic output demands on the golfer.It is possible to identify relative kinetic output strengths and weakness of a golfer through assessment of the hand path and swing trajectories.Increasing any one of the kinetic outputs of the golfer can potentially increase the club head velocity at impact.The hand path trajectory has important influences over the club swing trajectory.

Kinetic Constrained Optimization of the Golf Swing Hub Path

PubMed Central

Nesbit, Steven M.; McGinnis, Ryan S.

2014-01-01

This study details an optimization of the golf swing, where the hand path and club angular trajectories are manipulated. The optimization goal was to maximize club head velocity at impact within the interaction kinetic limitations (force, torque, work, and power) of the golfer as determined through the analysis of a typical swing using a two-dimensional dynamic model. The study was applied to four subjects with diverse swing capabilities and styles. It was determined that it is possible for all subjects to increase their club head velocity at impact within their respective kinetic limitations through combined modifications to their respective hand path and club angular trajectories. The manner of the modifications, the degree of velocity improvement, the amount of kinetic reduction, and the associated kinetic limitation quantities were subject dependent. By artificially minimizing selected kinetic inputs within the optimization algorithm, it was possible to identify swing trajectory characteristics that indicated relative kinetic weaknesses of a subject. Practical implications are offered based upon the findings of the study. Key Points The hand path trajectory is an important characteristic of the golf swing and greatly affects club head velocity and golfer/club energy transfer. It is possible to increase the energy transfer from the golfer to the club by modifying the hand path and swing trajectories without increasing the kinetic output demands on the golfer. It is possible to identify relative kinetic output strengths and weakness of a golfer through assessment of the hand path and swing trajectories. Increasing any one of the kinetic outputs of the golfer can potentially increase the club head velocity at impact. The hand path trajectory has important influences over the club swing trajectory. PMID:25435779

Physics-based statistical learning approach to mesoscopic model selection.

PubMed

Taverniers, Søren; Haut, Terry S; Barros, Kipton; Alexander, Francis J; Lookman, Turab

2015-11-01

In materials science and many other research areas, models are frequently inferred without considering their generalization to unseen data. We apply statistical learning using cross-validation to obtain an optimally predictive coarse-grained description of a two-dimensional kinetic nearest-neighbor Ising model with Glauber dynamics (GD) based on the stochastic Ginzburg-Landau equation (sGLE). The latter is learned from GD "training" data using a log-likelihood analysis, and its predictive ability for various complexities of the model is tested on GD "test" data independent of the data used to train the model on. Using two different error metrics, we perform a detailed analysis of the error between magnetization time trajectories simulated using the learned sGLE coarse-grained description and those obtained using the GD model. We show that both for equilibrium and out-of-equilibrium GD training trajectories, the standard phenomenological description using a quartic free energy does not always yield the most predictive coarse-grained model. Moreover, increasing the amount of training data can shift the optimal model complexity to higher values. Our results are promising in that they pave the way for the use of statistical learning as a general tool for materials modeling and discovery.

Dynamic trajectory-based couch motion for improvement of radiation therapy trajectories in cranial SRT

DOE Office of Scientific and Technical Information (OSTI.GOV)

MacDonald, R. Lee; Thomas, Christopher G., E-mail: Chris.Thomas@cdha.nshealth.ca; Department of Medical Physics, Nova Scotia Cancer Centre, Queen Elizabeth II Health Sciences Centre, Halifax, Nova Scotia B3H 1V7

2015-05-15

Purpose: To investigate potential improvement in external beam stereotactic radiation therapy plan quality for cranial cases using an optimized dynamic gantry and patient support couch motion trajectory, which could minimize exposure to sensitive healthy tissue. Methods: Anonymized patient anatomy and treatment plans of cranial cancer patients were used to quantify the geometric overlap between planning target volumes and organs-at-risk (OARs) based on their two-dimensional projection from source to a plane at isocenter as a function of gantry and couch angle. Published dose constraints were then used as weighting factors for the OARs to generate a map of couch-gantry coordinate space,more » indicating degree of overlap at each point in space. A couch-gantry collision space was generated by direct measurement on a linear accelerator and couch using an anthropomorphic solid-water phantom. A dynamic, fully customizable algorithm was written to generate a navigable ideal trajectory for the patient specific couch-gantry space. The advanced algorithm can be used to balance the implementation of absolute minimum values of overlap with the clinical practicality of large-scale couch motion and delivery time. Optimized cranial cancer treatment trajectories were compared to conventional treatment trajectories. Results: Comparison of optimized treatment trajectories with conventional treatment trajectories indicated an average decrease in mean dose to the OARs of 19% and an average decrease in maximum dose to the OARs of 12%. Degradation was seen for homogeneity index (6.14% ± 0.67%–5.48% ± 0.76%) and conformation number (0.82 ± 0.02–0.79 ± 0.02), but neither was statistically significant. Removal of OAR constraints from volumetric modulated arc therapy optimization reveals that reduction in dose to OARs is almost exclusively due to the optimized trajectory and not the OAR constraints. Conclusions: The authors’ study indicated that simultaneous couch and gantry motion during radiation therapy to minimize the geometrical overlap in the beams-eye-view of target volumes and the organs-at-risk can have an appreciable dose reduction to organs-at-risk.« less

Solar Sail Spaceflight Simulation

NASA Technical Reports Server (NTRS)

Lisano, Michael; Evans, James; Ellis, Jordan; Schimmels, John; Roberts, Timothy; Rios-Reyes, Leonel; Scheeres, Daniel; Bladt, Jeff; Lawrence, Dale; Piggott, Scott

2007-01-01

The Solar Sail Spaceflight Simulation Software (S5) toolkit provides solar-sail designers with an integrated environment for designing optimal solar-sail trajectories, and then studying the attitude dynamics/control, navigation, and trajectory control/correction of sails during realistic mission simulations. Unique features include a high-fidelity solar radiation pressure model suitable for arbitrarily-shaped solar sails, a solar-sail trajectory optimizer, capability to develop solar-sail navigation filter simulations, solar-sail attitude control models, and solar-sail high-fidelity force models.

Air traffic management evaluation tool

NASA Technical Reports Server (NTRS)

Sheth, Kapil S. (Inventor); Sridhar, Banavar (Inventor); Bilimoria, Karl D. (Inventor); Grabbe, Shon (Inventor); Chatterji, Gano Broto (Inventor); Schipper, John F. (Inventor)

2010-01-01

Method and system for evaluating and implementing air traffic management tools and approaches for managing and avoiding an air traffic incident before the incident occurs. The invention provides flight plan routing and direct routing or wind optimal routing, using great circle navigation and spherical Earth geometry. The invention provides for aircraft dynamics effects, such as wind effects at each altitude, altitude changes, airspeed changes and aircraft turns to provide predictions of aircraft trajectory (and, optionally, aircraft fuel use). A second system provides several aviation applications using the first system. These applications include conflict detection and resolution, miles-in trail or minutes-in-trail aircraft separation, flight arrival management, flight re-routing, weather prediction and analysis and interpolation of weather variables based upon sparse measurements.

Generalized gradient algorithm for trajectory optimization

NASA Technical Reports Server (NTRS)

Zhao, Yiyuan; Bryson, A. E.; Slattery, R.

1990-01-01

The generalized gradient algorithm presented and verified as a basis for the solution of trajectory optimization problems improves the performance index while reducing path equality constraints, and terminal equality constraints. The algorithm is conveniently divided into two phases, of which the first, 'feasibility' phase yields a solution satisfying both path and terminal constraints, while the second, 'optimization' phase uses the results of the first phase as initial guesses.

Linearization methods for optimizing the low thrust spacecraft trajectory: Theoretical aspects

NASA Astrophysics Data System (ADS)

Kazmerchuk, P. V.

2016-12-01

The theoretical aspects of the modified linearization method, which makes it possible to solve a wide class of nonlinear problems on optimizing low-thrust spacecraft trajectories (V. V. Efanov et al., 2009; V. V. Khartov et al., 2010) are examined. The main modifications of the linearization method are connected with its refinement for optimizing the main dynamic systems and design parameters of the spacecraft.

Optimal lunar soft landing trajectories using taboo evolutionary programming

NASA Astrophysics Data System (ADS)

Mutyalarao, M.; Raj, M. Xavier James

A safe lunar landing is a key factor to undertake an effective lunar exploration. Lunar lander consists of four phases such as launch phase, the earth-moon transfer phase, circumlunar phase and landing phase. The landing phase can be either hard landing or soft landing. Hard landing means the vehicle lands under the influence of gravity without any deceleration measures. However, soft landing reduces the vertical velocity of the vehicle before landing. Therefore, for the safety of the astronauts as well as the vehicle lunar soft landing with an acceptable velocity is very much essential. So it is important to design the optimal lunar soft landing trajectory with minimum fuel consumption. Optimization of Lunar Soft landing is a complex optimal control problem. In this paper, an analysis related to lunar soft landing from a parking orbit around Moon has been carried out. A two-dimensional trajectory optimization problem is attempted. The problem is complex due to the presence of system constraints. To solve the time-history of control parameters, the problem is converted into two point boundary value problem by using the maximum principle of Pontrygen. Taboo Evolutionary Programming (TEP) technique is a stochastic method developed in recent years and successfully implemented in several fields of research. It combines the features of taboo search and single-point mutation evolutionary programming. Identifying the best unknown parameters of the problem under consideration is the central idea for many space trajectory optimization problems. The TEP technique is used in the present methodology for the best estimation of initial unknown parameters by minimizing objective function interms of fuel requirements. The optimal estimation subsequently results into an optimal trajectory design of a module for soft landing on the Moon from a lunar parking orbit. Numerical simulations demonstrate that the proposed approach is highly efficient and it reduces the minimum fuel consumption. The results are compared with the available results in literature shows that the solution of present algorithm is better than some of the existing algorithms. Keywords: soft landing, trajectory optimization, evolutionary programming, control parameters, Pontrygen principle.

Costs of Limiting Route Optimization to Published Waypoints in the Traffic Aware Planner

NASA Technical Reports Server (NTRS)

Karr, David A.; Vivona, Robert A.; Wing, David J.

2013-01-01

The Traffic Aware Planner (TAP) is an airborne advisory tool that generates optimized, traffic-avoiding routes to support the aircraft crew in making strategic reroute requests to Air Traffic Control (ATC). TAP is derived from a research-prototype self-separation tool, the Autonomous Operations Planner (AOP), in which optimized route modifications that avoid conflicts with traffic and weather, using waypoints at explicit latitudes and longitudes (a technique supported by self-separation concepts), are generated by maneuver patterns applied to the existing route. For use in current-day operations in which trajectory changes must be requested from ATC via voice communication, TAP produces optimized routes described by advisories that use only published waypoints prior to a reconnection waypoint on the existing route. We describe how the relevant algorithms of AOP have been modified to implement this requirement. The modifications include techniques for finding appropriate published waypoints in a maneuver pattern and a method for combining the genetic algorithm of AOP with an exhaustive search of certain types of advisory. We demonstrate methods to investigate the increased computation required by these techniques and to estimate other costs (measured in terms such as time to destination and fuel burned) that may be incurred when only published waypoints are used.

Design and Evaluation of the Terminal Area Precision Scheduling and Spacing System

NASA Technical Reports Server (NTRS)

Swenson, Harry N.; Thipphavong, Jane; Sadovsky, Alex; Chen, Liang; Sullivan, Chris; Martin, Lynne

2011-01-01

This paper describes the design, development and results from a high fidelity human-in-the-loop simulation of an integrated set of trajectory-based automation tools providing precision scheduling, sequencing and controller merging and spacing functions. These integrated functions are combined into a system called the Terminal Area Precision Scheduling and Spacing (TAPSS) system. It is a strategic and tactical planning tool that provides Traffic Management Coordinators, En Route and Terminal Radar Approach Control air traffic controllers the ability to efficiently optimize the arrival capacity of a demand-impacted airport while simultaneously enabling fuel-efficient descent procedures. The TAPSS system consists of four-dimensional trajectory prediction, arrival runway balancing, aircraft separation constraint-based scheduling, traffic flow visualization and trajectory-based advisories to assist controllers in efficient metering, sequencing and spacing. The TAPSS system was evaluated and compared to today's ATC operation through extensive series of human-in-the-loop simulations for arrival flows into the Los Angeles International Airport. The test conditions included the variation of aircraft demand from a baseline of today's capacity constrained periods through 5%, 10% and 20% increases. Performance data were collected for engineering and human factor analysis and compared with similar operations both with and without the TAPSS system. The engineering data indicate operations with the TAPSS show up to a 10% increase in airport throughput during capacity constrained periods while maintaining fuel-efficient aircraft descent profiles from cruise to landing.

Research in navigation and optimization for space trajectories

NASA Technical Reports Server (NTRS)

Pines, S.; Kelley, H. J.

1979-01-01

Topics covered include: (1) initial Cartesian coordinates for rapid precision orbit prediction; (2) accelerating convergence in optimization methods using search routines by applying curvilinear projection ideas; (3) perturbation-magnitude control for difference-quotient estimation of derivatives; and (4) determining the accelerometer bias for in-orbit shuttle trajectories.

Multi-Objective Trajectory Optimization of a Hypersonic Reconnaissance Vehicle with Temperature Constraints

NASA Astrophysics Data System (ADS)

Masternak, Tadeusz J.

This research determines temperature-constrained optimal trajectories for a scramjet-based hypersonic reconnaissance vehicle by developing an optimal control formulation and solving it using a variable order Gauss-Radau quadrature collocation method with a Non-Linear Programming (NLP) solver. The vehicle is assumed to be an air-breathing reconnaissance aircraft that has specified takeoff/landing locations, airborne refueling constraints, specified no-fly zones, and specified targets for sensor data collections. A three degree of freedom scramjet aircraft model is adapted from previous work and includes flight dynamics, aerodynamics, and thermal constraints. Vehicle control is accomplished by controlling angle of attack, roll angle, and propellant mass flow rate. This model is incorporated into an optimal control formulation that includes constraints on both the vehicle and mission parameters, such as avoidance of no-fly zones and coverage of high-value targets. To solve the optimal control formulation, a MATLAB-based package called General Pseudospectral Optimal Control Software (GPOPS-II) is used, which transcribes continuous time optimal control problems into an NLP problem. In addition, since a mission profile can have varying vehicle dynamics and en-route imposed constraints, the optimal control problem formulation can be broken up into several "phases" with differing dynamics and/or varying initial/final constraints. Optimal trajectories are developed using several different performance costs in the optimal control formulation: minimum time, minimum time with control penalties, and maximum range. The resulting analysis demonstrates that optimal trajectories that meet specified mission parameters and constraints can be quickly determined and used for larger-scale operational and campaign planning and execution.

Locally optimal transfer trajectories between libration point orbits using invariant manifolds

NASA Astrophysics Data System (ADS)

Davis, Kathryn E.

2009-12-01

Techniques from dynamical systems theory and primer vector theory have been applied to the construction of locally optimal transfer trajectories between libration point orbits. When two libration point orbits have different energies, it has been found that the unstable manifold of the first orbit can be connected to the stable manifold of the second orbit with a bridging trajectory. A bounding sphere centered on the secondary, with a radius less than the radius of the sphere of influence of the secondary, was used to study the stable and unstable manifold trajectories. It was numerically demonstrated that within the bounding sphere, the two-body parameters of the unstable and stable manifold trajectories could be analyzed to locate low transfer costs. It was shown that as the two-body parameters of an unstable manifold trajectory more closely matched the two-body parameters of a stable manifold trajectory, the total DeltaV necessary to complete the transfer decreased. Primer vector theory was successfully applied to a transfer to determine the optimal maneuvers required to create the bridging trajectory that connected the unstable manifold of the first orbit to the stable manifold of the second orbit. Transfer trajectories were constructed between halo orbits in the Sun-Earth and Earth-Moon three-body systems. Multiple solutions were found between the same initial and final orbits, where certain solutions retraced interior portions of the trajectory. All of the trajectories created satisfied the conditions for optimality. The costs of transfers constructed using invariant manifolds were compared to the costs of transfers constructed without the use of invariant manifolds, when data was available. In all cases, the total cost of the transfers were significantly lower when invariant manifolds were used in the transfer construction. In many cases, the transfers that employed invariant manifolds were three to four times more efficient, in terms of fuel expenditure, than the transfer that did not. The decrease in transfer cost was accompanied by an increase in transfer time of flight. Transfers constructed in the Earth-Moon system were shown to be particularly viable for lunar navigation and communication constellations, as excellent coverage of the lunar surface can be achieved during the transfer.

SU-E-T-436: Fluence-Based Trajectory Optimization for Non-Coplanar VMAT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smyth, G; Bamber, JC; Bedford, JL

2015-06-15

Purpose: To investigate a fluence-based trajectory optimization technique for non-coplanar VMAT for brain cancer. Methods: Single-arc non-coplanar VMAT trajectories were determined using a heuristic technique for five patients. Organ at risk (OAR) volume intersected during raytracing was minimized for two cases: absolute volume and the sum of relative volumes weighted by OAR importance. These trajectories and coplanar VMAT formed starting points for the fluence-based optimization method. Iterative least squares optimization was performed on control points 24° apart in gantry rotation. Optimization minimized the root-mean-square (RMS) deviation of PTV dose from the prescription (relative importance 100), maximum dose to the brainstemmore » (10), optic chiasm (5), globes (5) and optic nerves (5), plus mean dose to the lenses (5), hippocampi (3), temporal lobes (2), cochleae (1) and brain excluding other regions of interest (1). Control point couch rotations were varied in steps of up to 10° and accepted if the cost function improved. Final treatment plans were optimized with the same objectives in an in-house planning system and evaluated using a composite metric - the sum of optimization metrics weighted by importance. Results: The composite metric decreased with fluence-based optimization in 14 of the 15 plans. In the remaining case its overall value, and the PTV and OAR components, were unchanged but the balance of OAR sparing differed. PTV RMS deviation was improved in 13 cases and unchanged in two. The OAR component was reduced in 13 plans. In one case the OAR component increased but the composite metric decreased - a 4 Gy increase in OAR metrics was balanced by a reduction in PTV RMS deviation from 2.8% to 2.6%. Conclusion: Fluence-based trajectory optimization improved plan quality as defined by the composite metric. While dose differences were case specific, fluence-based optimization improved both PTV and OAR dosimetry in 80% of cases.« less

Solar Electric Propulsion Triple-Satellite-Aided Capture With Mars Flyby

NASA Astrophysics Data System (ADS)

Patrick, Sean

Triple-Satellite-aided-capture sequences use gravity-assists at three of Jupiter's four massive Galilean moons to reduce the DeltaV required to enter into Jupiter orbit. A triple-satellite-aided capture at Callisto, Ganymede, and Io is proposed to capture a SEP spacecraft into Jupiter orbit from an interplanetary Earth-Jupiter trajectory that employs low-thrust maneuvers. The principal advantage of this method is that it combines the ISP efficiency of ion propulsion with nearly impulsive but propellant-free gravity assists. For this thesis, two main chapters are devoted to the exploration of low-thrust triple-flyby capture trajectories. Specifically, the design and optimization of these trajectories are explored heavily. The first chapter explores the design of two solar electric propulsion (SEP), low-thrust trajectories developed using the JPL's MALTO software. The two trajectories combined represent a full Earth to Jupiter capture split into a heliocentric Earth to Jupiter Sphere of Influence (SOI) trajectory and a Joviocentric capture trajectory. The Joviocentric trajectory makes use of gravity assist flybys of Callisto, Ganymede, and Io to capture into Jupiter orbit with a period of 106.3 days. Following this, in chapter two, three more SEP low-thrust trajectories were developed based upon those in chapter one. These trajectories, devised using the high-fidelity Mystic software, also developed by JPL, improve upon the original trajectories developed in chapter one. Here, the developed trajectories are each three separate, full Earth to Jupiter capture orbits. As in chapter one, a Mars gravity assist is used to augment the heliocentric trajectories. Gravity-assist flybys of Callisto, Ganymede, and Io or Europa are used to capture into Jupiter Orbit. With between 89.8 and 137.2-day periods, the orbits developed in chapters one and two are shorter than most Jupiter capture orbits achieved using low-thrust propulsion techniques. Finally, chapter 3 presents an original trajectory design for a Very-Long-Baseline Interferometry (VLBI) satellite constellation. The design was created for the 8th Global Trajectory Optimization Competition (GTOC8) in which participants are tasked with creating and optimizing low-thrust trajectories to place a series of three space craft into formation to map given radio sources.

A Final Approach Trajectory Model for Current Operations

NASA Technical Reports Server (NTRS)

Gong, Chester; Sadovsky, Alexander

2010-01-01

Predicting accurate trajectories with limited intent information is a challenge faced by air traffic management decision support tools in operation today. One such tool is the FAA's Terminal Proximity Alert system which is intended to assist controllers in maintaining safe separation of arrival aircraft during final approach. In an effort to improve the performance of such tools, two final approach trajectory models are proposed; one based on polynomial interpolation, the other on the Fourier transform. These models were tested against actual traffic data and used to study effects of the key final approach trajectory modeling parameters of wind, aircraft type, and weight class, on trajectory prediction accuracy. Using only the limited intent data available to today's ATM system, both the polynomial interpolation and Fourier transform models showed improved trajectory prediction accuracy over a baseline dead reckoning model. Analysis of actual arrival traffic showed that this improved trajectory prediction accuracy leads to improved inter-arrival separation prediction accuracy for longer look ahead times. The difference in mean inter-arrival separation prediction error between the Fourier transform and dead reckoning models was 0.2 nmi for a look ahead time of 120 sec, a 33 percent improvement, with a corresponding 32 percent improvement in standard deviation.

Partial Validation of Multibody Program to Optimize Simulated Trajectories II (POST II) Parachute Simulation With Interacting Forces

NASA Technical Reports Server (NTRS)

Raiszadeh, Ben; Queen, Eric M.

2002-01-01

A capability to simulate trajectories Of Multiple interacting rigid bodies has been developed. This capability uses the Program to Optimize Simulated Trajectories II (POST II). Previously, POST II had the ability to simulate multiple bodies without interacting forces. The current implementation is used for the Simulation of parachute trajectories, in which the parachute and suspended bodies can be treated as rigid bodies. An arbitrary set of connecting lines can be included in the model and are treated as massless spring-dampers. This paper discusses details of the connection line modeling and results of several test cases used to validate the capability.

Outer-Planet Mission Analysis Using Solar-Electric Ion Propulsion

NASA Technical Reports Server (NTRS)

Woo, Byoungsam; Coverstone, Victoria L.; Hartmann, John W.; Cupples, Michael

2003-01-01

Outer-planet mission analysis was performed using three next generation solar-electric ion thruster models. Optimal trajectories are presented that maximize the delivered mass to the designated outer planet. Trajectories to Saturn and Neptune with a single Venus gravity assist are investigated. For each thruster model, the delivered mass versus flight time curve was generated to obtain thruster model performance. The effects of power to the thrusters and resonance ratio of Venutian orbital periods to spacecraft period were also studied. Multiple locally optimal trajectories to Saturn and Neptune have been discovered in different regions of the parameter search space. The characteristics of each trajectory are noted.

A multi target approach to control chemical reactions in their inhomogeneous solvent environment

NASA Astrophysics Data System (ADS)

Keefer, Daniel; Thallmair, Sebastian; Zauleck, Julius P. P.; de Vivie-Riedle, Regina

2015-12-01

Shaped laser pulses offer a powerful tool to manipulate molecular quantum systems. Their application to chemical reactions in solution is a promising concept to redesign chemical synthesis. Along this road, theoretical developments to include the solvent surrounding are necessary. An appropriate theoretical treatment is helpful to understand the underlying mechanisms. In our approach we simulate the solvent by randomly selected snapshots from molecular dynamics trajectories. We use multi target optimal control theory to optimize pulses for the various arrangements of explicit solvent molecules simultaneously. This constitutes a major challenge for the control algorithm, as the solvent configurations introduce a large inhomogeneity to the potential surfaces. We investigate how the algorithm handles the new challenges and how well the controllability of the system is preserved with increasing complexity. Additionally, we introduce a way to statistically estimate the efficiency of the optimized laser pulses in the complete thermodynamical ensemble.

Decision-Aiding and Optimization for Vertical Navigation of Long-Haul Aircraft

NASA Technical Reports Server (NTRS)

Patrick, Nicholas J. M.; Sheridan, Thomas B.

1996-01-01

Most decisions made in the cockpit are related to safety, and have therefore been proceduralized in order to reduce risk. There are very few which are made on the basis of a value metric such as economic cost. One which can be shown to be value based, however, is the selection of a flight profile. Fuel consumption and flight time both have a substantial effect on aircraft operating cost, but they cannot be minimized simultaneously. In addition, winds, turbulence, and performance vary widely with altitude and time. These factors make it important and difficult for pilots to (a) evaluate the outcomes associated with a particular trajectory before it is flown and (b) decide among possible trajectories. The two elements of this problem considered here are: (1) determining what constitutes optimality, and (2) finding optimal trajectories. Pilots and dispatchers from major u.s. airlines were surveyed to determine which attributes of the outcome of a flight they considered the most important. Avoiding turbulence-for passenger comfort-topped the list of items which were not safety related. Pilots' decision making about the selection of flight profile on the basis of flight time, fuel burn, and exposure to turbulence was then observed. Of the several behavioral and prescriptive decision models invoked to explain the pilots' choices, utility maximization is shown to best reproduce the pilots' decisions. After considering more traditional methods for optimizing trajectories, a novel method is developed using a genetic algorithm (GA) operating on a discrete representation of the trajectory search space. The representation is a sequence of command altitudes, and was chosen to be compatible with the constraints imposed by Air Traffic Control, and with the training given to pilots. Since trajectory evaluation for the GA is performed holistically, a wide class of objective functions can be optimized easily. Also, using the GA it is possible to compare the costs associated with different airspace design and air traffic management policies. A decision aid is proposed which would combine the pilot's notion of optimality with the GA-based optimization, provide the pilot with a number of alternative pareto-optimal trajectories, and allow him to consider unmodelled attributes and constraints in choosing among them. A solution to the problem of displaying alternatives in a multi-attribute decision space is also presented.

Parallelization of Program to Optimize Simulated Trajectories (POST3D)

NASA Technical Reports Server (NTRS)

Hammond, Dana P.; Korte, John J. (Technical Monitor)

2001-01-01

This paper describes the parallelization of the Program to Optimize Simulated Trajectories (POST3D). POST3D uses a gradient-based optimization algorithm that reaches an optimum design point by moving from one design point to the next. The gradient calculations required to complete the optimization process, dominate the computational time and have been parallelized using a Single Program Multiple Data (SPMD) on a distributed memory NUMA (non-uniform memory access) architecture. The Origin2000 was used for the tests presented.

Optimization of the interplanetary trajectories of spacecraft with a solar electric propulsion power plant of minimal power

NASA Astrophysics Data System (ADS)

Ivanyukhin, A. V.; Petukhov, V. G.

2016-12-01

The problem of optimizing the interplanetary trajectories of a spacecraft (SC) with a solar electric propulsion system (SEPS) is examined. The problem of investigating the permissible power minimum of the solar electric propulsion power plant required for a successful flight is studied. Permissible ranges of thrust and exhaust velocity are analyzed for the given range of flight time and final mass of the spacecraft. The optimization is performed according to Portnyagin's maximum principle, and the continuation method is used for reducing the boundary problem of maximal principle to the Cauchy problem and to study the solution/ parameters dependence. Such a combination results in the robust algorithm that reduces the problem of trajectory optimization to the numerical integration of differential equations by the continuation method.

Sensory Agreement Guides Kinetic Energy Optimization of Arm Movements during Object Manipulation.

PubMed

Farshchiansadegh, Ali; Melendez-Calderon, Alejandro; Ranganathan, Rajiv; Murphey, Todd D; Mussa-Ivaldi, Ferdinando A

2016-04-01

The laws of physics establish the energetic efficiency of our movements. In some cases, like locomotion, the mechanics of the body dominate in determining the energetically optimal course of action. In other tasks, such as manipulation, energetic costs depend critically upon the variable properties of objects in the environment. Can the brain identify and follow energy-optimal motions when these motions require moving along unfamiliar trajectories? What feedback information is required for such optimal behavior to occur? To answer these questions, we asked participants to move their dominant hand between different positions while holding a virtual mechanical system with complex dynamics (a planar double pendulum). In this task, trajectories of minimum kinetic energy were along curvilinear paths. Our findings demonstrate that participants were capable of finding the energy-optimal paths, but only when provided with veridical visual and haptic information pertaining to the object, lacking which the trajectories were executed along rectilinear paths.

Rapid near-optimal aerospace plane trajectory generation and guidance

NASA Technical Reports Server (NTRS)

Calise, A. J.; Corban, J. E.; Markopoulos, N.

1991-01-01

Effort was directed toward the problems of the real time trajectory optimization and guidance law development for the National Aerospace Plane (NASP) applications. In particular, singular perturbation methods were used to develop guidance algorithms suitable for onboard, real time implementation. The progress made in this research effort is reported.

Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

NASA Technical Reports Server (NTRS)

Pinson, Robin M.; Lu, Ping

2016-01-01

Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from the ground control. The propellant optimal control problem in this work is to determine the optimal finite thrust vector to land the spacecraft at a specified location, in the presence of a highly nonlinear gravity field, subject to various mission and operational constraints. The proposed solution uses convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process for a fixed final time problem. In addition, a second optimization method is wrapped around the convex optimization problem to determine the optimal flight time that yields the lowest propellant usage over all flight times. Gravity models designed for irregularly shaped asteroids are investigated. Success of the algorithm is demonstrated by designing powered descent trajectories for the elongated binary asteroid Castalia.

Low-energy Lunar Trajectories with Lunar Flybys

NASA Astrophysics Data System (ADS)

Wei, B. W.; Li, Y. S.

2017-09-01

The low-energy lunar trajectories with lunar flybys are investigated in the Sun-Earth-Moon bicircular problem (BCP). Accordingly, the characteristics of the distribution of trajectories in the phase space are summarized. To begin with, by using invariant manifolds of the BCP system, the low-energy lunar trajectories with lunar flybys are sought based on the BCP model. Secondly, through the treating time as an augmented dimension in the phase space of nonautonomous system, the state space map that reveals the distribution of these lunar trajectories in the phase space is given. As a result, it is become clear that low-energy lunar trajectories exist in families, and every moment of a Sun-Earth-Moon synodic period can be the departure date. Finally, the changing rule of departure impulse, midcourse impulse at Poincaré section, transfer duration, and system energy of different families are analyzed. Consequently, the impulse optimal family and transfer duration optimal family are obtained respectively.

Optimizing Aircraft Trajectories with Multiple Cruise Altitudes in the Presence of Winds

NASA Technical Reports Server (NTRS)

Ng, Hok K.; Sridhar, Banavar; Grabbe, Shon

2014-01-01

This study develops a trajectory optimization algorithm for approximately minimizing aircraft travel time and fuel burn by combining a method for computing minimum-time routes in winds on multiple horizontal planes, and an aircraft fuel burn model for generating fuel-optimal vertical profiles. It is applied to assess the potential benefits of flying user-preferred routes for commercial cargo flights operating between Anchorage, Alaska and major airports in Asia and the contiguous United States. Flying wind optimal trajectories with a fuel-optimal vertical profile reduces average fuel burn of international flights cruising at a single altitude by 1-3 percent. The potential fuel savings of performing en-route step climbs are not significant for many shorter domestic cargo flights that have only one step climb. Wind-optimal trajectories reduce fuel burn and travel time relative to the flight plan route by up to 3 percent for the domestic cargo flights. However, for trans-oceanic traffic, the fuel burn savings could be as much as 10 percent. The actual savings in operations will vary from the simulation results due to differences in the aircraft models and user defined cost indices. In general, the savings are proportional to trip length, and depend on the en-route wind conditions and aircraft types.

Low-thrust trajectory optimization of asteroid sample return mission with multiple revolutions and moon gravity assists

NASA Astrophysics Data System (ADS)

Tang, Gao; Jiang, FanHuag; Li, JunFeng

2015-11-01

Near-Earth asteroids have gained a lot of interest and the development in low-thrust propulsion technology makes complex deep space exploration missions possible. A mission from low-Earth orbit using low-thrust electric propulsion system to rendezvous with near-Earth asteroid and bring sample back is investigated. By dividing the mission into five segments, the complex mission is solved separately. Then different methods are used to find optimal trajectories for every segment. Multiple revolutions around the Earth and multiple Moon gravity assists are used to decrease the fuel consumption to escape from the Earth. To avoid possible numerical difficulty of indirect methods, a direct method to parameterize the switching moment and direction of thrust vector is proposed. To maximize the mass of sample, optimal control theory and homotopic approach are applied to find the optimal trajectory. Direct methods of finding proper time to brake the spacecraft using Moon gravity assist are also proposed. Practical techniques including both direct and indirect methods are investigated to optimize trajectories for different segments and they can be easily extended to other missions and more precise dynamic model.

Developmental Trajectories of Subjective Social Status

PubMed Central

Maxwell, Sarah; Malspeis, Susan; Adler, Nancy

2015-01-01

BACKGROUND AND OBJECTIVE: Subjective social status (SSS), a person’s sense of their (or for youth, their family’s) position in the socioeconomic hierarchy, is strongly related to health in adults but not health in adolescence. Understanding this developmental discrepancy requires first understanding the developmental trajectory of SSS. The objective of this study was to identify the number and shape of SSS trajectories as adolescents transition to adulthood and explore if trajectory membership affects health. METHODS: Using data from 7436 assessments from the Princeton School District Study, a decade-long cohort study of non-Hispanic black and white youth, latent class growth models with 3 to 7 SSS trajectories were developed. Model fit, trajectory structure, and shape were used to guide optimal model selection. Using this optimal model, the associations of trajectory membership with BMI and depressive symptoms in young adulthood were explored. RESULTS: The 5-class model was optimal. In this model, trajectories were persistent high (7.8%), mid–high (32.2%), middle (43.4%), low–lower (7.4%), and high–low (9.1%). Non-Hispanic black race/ethnicity, lower household income, and low parent education were associated with membership in this high–low trajectory. High–low trajectory membership was associated with higher BMI and depressive symptoms in non-Hispanic white subjects but was not associated with depressive symptoms. It was associated with lower BMI only after adjustment for BMI in adolescence in non-Hispanic black subjects. CONCLUSIONS: SSS is relatively stable in adolescence and the transition to adulthood, and it generally reflects objective markers of social advantage. However, socially disadvantaged youth with high SSS in early adolescence may be at increased health risk. PMID:26324868

Deep Brain Stimulation for Essential Tremor: Aligning Thalamic and Posterior Subthalamic Targets in 1 Surgical Trajectory.

PubMed

Bot, Maarten; van Rootselaar, Fleur; Contarino, Maria Fiorella; Odekerken, Vincent; Dijk, Joke; de Bie, Rob; Schuurman, Richard; van den Munckhof, Pepijn

2017-12-21

Ventral intermediate nucleus (VIM) deep brain stimulation (DBS) and posterior subthalamic area (PSA) DBS suppress tremor in essential tremor (ET) patients, but it is not clear which target is optimal. Aligning both targets in 1 surgical trajectory would facilitate exploring stimulation of either target in a single patient. To evaluate aligning VIM and PSA in 1 surgical trajectory for DBS in ET. Technical aspects of trajectories, intraoperative stimulation findings, final electrode placement, target used for chronic stimulation, and adverse and beneficial effects were evaluated. In 17 patients representing 33 trajectories, we successfully aligned VIM and PSA targets in 26 trajectories. Trajectory distance between targets averaged 7.2 (range 6-10) mm. In all but 4 aligned trajectories, optimal intraoperative tremor suppression was obtained in the PSA. During follow-up, active electrode contacts were located in PSA in the majority of cases. Overall, successful tremor control was achieved in 69% of patients. Stimulation-induced dysarthria or gait ataxia occurred in, respectively, 56% and 44% of patients. Neither difference in tremor suppression or side effects was noted between aligned and nonaligned leads nor between the different locations of chronic stimulation. Alignment of VIM and PSA for DBS in ET is feasible and enables intraoperative exploration of both targets in 1 trajectory. This facilitates positioning of electrode contacts in both areas, where multiple effective points of stimulation can be found. In the majority of aligned leads, optimal intraoperative and chronic stimulation were located in the PSA. Copyright © 2017 by the Congress of Neurological Surgeons

NASA Advanced Concepts Office, Earth-To-Orbit Team Design Process and Tools

NASA Technical Reports Server (NTRS)

Waters, Eric D.; Creech, Dennis M.; Garcia, Jessica; Threet, Grady E., Jr.; Phillips, Alan

2012-01-01

The Earth-to-Orbit Team (ETO) of the Advanced Concepts Office (ACO) at NASA Marshall Space Flight Center (MSFC) is considered the pre-eminent go-to group for pre-phase A and phase A concept definition. Over the past several years the ETO team has evaluated thousands of launch vehicle concept variations for a significant number of studies including agency-wide efforts such as the Exploration Systems Architecture Study (ESAS), Constellation, Heavy Lift Launch Vehicle (HLLV), Augustine Report, Heavy Lift Propulsion Technology (HLPT), Human Exploration Framework Team (HEFT), and Space Launch System (SLS). The ACO ETO Team is called upon to address many needs in NASA s design community; some of these are defining extremely large trade-spaces, evaluating advanced technology concepts which have not been addressed by a large majority of the aerospace community, and the rapid turn-around of highly time critical actions. It is the time critical actions, those often limited by schedule or little advanced warning, that have forced the five member ETO team to develop a design process robust enough to handle their current output level in order to meet their customer s needs. Based on the number of vehicle concepts evaluated over the past year this output level averages to four completed vehicle concepts per day. Each of these completed vehicle concepts includes a full mass breakdown of the vehicle to a tertiary level of subsystem components and a vehicle trajectory analysis to determine optimized payload delivery to specified orbital parameters, flight environments, and delta v capability. A structural analysis of the vehicle to determine flight loads based on the trajectory output, material properties, and geometry of the concept is also performed. Due to working in this fast-paced and sometimes rapidly changing environment, the ETO Team has developed a finely tuned process to maximize their delivery capabilities. The objective of this paper is to describe the interfaces between the three disciplines used in the design process: weights and sizing, trajectory, and structural analysis. The tools used to perform such analysis are INtegrated Rocket Sizing (INTROS), Program to Optimize Simulated Trajectories (POST), and Launch Vehicle Analysis (LVA) respectively. The methods each discipline uses to streamline their particular part of the design process will also be discussed.

NASA Advanced Concepts Office, Earth-To-Orbit Team Design Process and Tools

NASA Technical Reports Server (NTRS)

Waters, Eric D.; Garcia, Jessica; Threet, Grady E., Jr.; Phillips, Alan

2013-01-01

The Earth-to-Orbit Team (ETO) of the Advanced Concepts Office (ACO) at NASA Marshall Space Flight Center (MSFC) is considered the pre-eminent "go-to" group for pre-phase A and phase A concept definition. Over the past several years the ETO team has evaluated thousands of launch vehicle concept variations for a significant number of studies including agency-wide efforts such as the Exploration Systems Architecture Study (ESAS), Constellation, Heavy Lift Launch Vehicle (HLLV), Augustine Report, Heavy Lift Propulsion Technology (HLPT), Human Exploration Framework Team (HEFT), and Space Launch System (SLS). The ACO ETO Team is called upon to address many needs in NASA's design community; some of these are defining extremely large trade-spaces, evaluating advanced technology concepts which have not been addressed by a large majority of the aerospace community, and the rapid turn-around of highly time critical actions. It is the time critical actions, those often limited by schedule or little advanced warning, that have forced the five member ETO team to develop a design process robust enough to handle their current output level in order to meet their customer's needs. Based on the number of vehicle concepts evaluated over the past year this output level averages to four completed vehicle concepts per day. Each of these completed vehicle concepts includes a full mass breakdown of the vehicle to a tertiary level of subsystem components and a vehicle trajectory analysis to determine optimized payload delivery to specified orbital parameters, flight environments, and delta v capability. A structural analysis of the vehicle to determine flight loads based on the trajectory output, material properties, and geometry of the concept is also performed. Due to working in this fast-paced and sometimes rapidly changing environment, the ETO Team has developed a finely tuned process to maximize their delivery capabilities. The objective of this paper is to describe the interfaces between the three disciplines used in the design process: weights and sizing, trajectory, and structural analysis. The tools used to perform such analysis are INtegrated Rocket Sizing (INTROS), Program to Optimize Simulated Trajectories (POST), and Launch Vehicle Analysis (LVA) respectively. The methods each discipline uses to streamline their particular part of the design process will also be discussed.

Rapid Preliminary Design of Interplanetary Trajectories Using the Evolutionary Mission Trajectory Generator

NASA Technical Reports Server (NTRS)

Englander, Jacob

2016-01-01

Preliminary design of interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. In addition, a time-history of control variables must be chosen that defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated. This can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a hybrid optimal control problem. The method is demonstrated on notional high-thrust chemical and low-thrust electric propulsion missions. In the low-thrust case, the hybrid optimal control problem is augmented to include systems design optimization.

Optimal transfers between libration-point orbits in the elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Hiday, Lisa Ann

1992-09-01

A strategy is formulated to design optimal impulsive transfers between three-dimensional libration-point orbits in the vicinity of the interior L(1) libration point of the Sun-Earth/Moon barycenter system. Two methods of constructing nominal transfers, for which the fuel cost is to be minimized, are developed; both inferior and superior transfers between two halo orbits are considered. The necessary conditions for an optimal transfer trajectory are stated in terms of the primer vector. The adjoint equation relating reference and perturbed trajectories in this formulation of the elliptic restricted three-body problem is shown to be distinctly different from that obtained in the analysis of trajectories in the two-body problem. Criteria are established whereby the cost on a nominal transfer can be improved by the addition of an interior impulse or by the implementation of coastal arcs in the initial and final orbits. The necessary conditions for the local optimality of a time-fixed transfer trajectory possessing additional impulses are satisfied by requiring continuity of the Hamiltonian and the derivative of the primer vector at all interior impulses. The optimality of a time-free transfer containing coastal arcs is surmised by examination of the slopes at the endpoints of a plot of the magnitude of the primer vector over the duration of the transfer path. If the initial and final slopes of the primer magnitude are zero, the transfer trajectory is optimal; otherwise, the execution of coasts is warranted. The position and timing of each interior impulse applied to a time-fixed transfer as well as the direction and length of coastal periods implemented on a time-free transfer are specified by the unconstrained minimization of the appropriate variation in cost utilizing a multivariable search technique. Although optimal solutions in some instances are elusive, the time-fixed and time-free optimization algorithms prove to be very successful in diminishing costs on nominal transfer trajectories. The inclusion of coastal arcs on time-free superior and inferior transfers results in significant modification of the transfer time of flight caused by shifts in departure and arrival locations on the halo orbits.

Large scale nonlinear programming for the optimization of spacecraft trajectories

NASA Astrophysics Data System (ADS)

Arrieta-Camacho, Juan Jose

Despite the availability of high fidelity mathematical models, the computation of accurate optimal spacecraft trajectories has never been an easy task. While simplified models of spacecraft motion can provide useful estimates on energy requirements, sizing, and cost; the actual launch window and maneuver scheduling must rely on more accurate representations. We propose an alternative for the computation of optimal transfers that uses an accurate representation of the spacecraft dynamics. Like other methodologies for trajectory optimization, this alternative is able to consider all major disturbances. In contrast, it can handle explicitly equality and inequality constraints throughout the trajectory; it requires neither the derivation of costate equations nor the identification of the constrained arcs. The alternative consist of two steps: (1) discretizing the dynamic model using high-order collocation at Radau points, which displays numerical advantages, and (2) solution to the resulting Nonlinear Programming (NLP) problem using an interior point method, which does not suffer from the performance bottleneck associated with identifying the active set, as required by sequential quadratic programming methods; in this way the methodology exploits the availability of sound numerical methods, and next generation NLP solvers. In practice the methodology is versatile; it can be applied to a variety of aerospace problems like homing, guidance, and aircraft collision avoidance; the methodology is particularly well suited for low-thrust spacecraft trajectory optimization. Examples are presented which consider the optimization of a low-thrust orbit transfer subject to the main disturbances due to Earth's gravity field together with Lunar and Solar attraction. Other example considers the optimization of a multiple asteroid rendezvous problem. In both cases, the ability of our proposed methodology to consider non-standard objective functions and constraints is illustrated. Future research directions are identified, involving the automatic scheduling and optimization of trajectory correction maneuvers. The sensitivity information provided by the methodology is expected to be invaluable in such research pursuit. The collocation scheme and nonlinear programming algorithm presented in this work, complement other existing methodologies by providing reliable and efficient numerical methods able to handle large scale, nonlinear dynamic models.

Optimal transfers between unstable periodic orbits using invariant manifolds

NASA Astrophysics Data System (ADS)

Davis, Kathryn E.; Anderson, Rodney L.; Scheeres, Daniel J.; Born, George H.

2011-03-01

This paper presents a method to construct optimal transfers between unstable periodic orbits of differing energies using invariant manifolds. The transfers constructed in this method asymptotically depart the initial orbit on a trajectory contained within the unstable manifold of the initial orbit and later, asymptotically arrive at the final orbit on a trajectory contained within the stable manifold of the final orbit. Primer vector theory is applied to a transfer to determine the optimal maneuvers required to create the bridging trajectory that connects the unstable and stable manifold trajectories. Transfers are constructed between unstable periodic orbits in the Sun-Earth, Earth-Moon, and Jupiter-Europa three-body systems. Multiple solutions are found between the same initial and final orbits, where certain solutions retrace interior portions of the trajectory. All transfers created satisfy the conditions for optimality. The costs of transfers constructed using manifolds are compared to the costs of transfers constructed without the use of manifolds. In all cases, the total cost of the transfer is significantly lower when invariant manifolds are used in the transfer construction. In many cases, the transfers that employ invariant manifolds are three times more efficient, in terms of fuel expenditure, than the transfer that do not. The decrease in transfer cost is accompanied by an increase in transfer time of flight.

Validation of a Low-Thrust Mission Design Tool Using Operational Navigation Software

NASA Technical Reports Server (NTRS)

Englander, Jacob A.; Knittel, Jeremy M.; Williams, Ken; Stanbridge, Dale; Ellison, Donald H.

2017-01-01

Design of flight trajectories for missions employing solar electric propulsion requires a suitably high-fidelity design tool. In this work, the Evolutionary Mission Trajectory Generator (EMTG) is presented as a medium-high fidelity design tool that is suitable for mission proposals. EMTG is validated against the high-heritage deep-space navigation tool MIRAGE, demonstrating both the accuracy of EMTG's model and an operational mission design and navigation procedure using both tools. The validation is performed using a benchmark mission to the Jupiter Trojans.

Modelling mid-course corrections for optimality conditions along interplanetary transfers

NASA Astrophysics Data System (ADS)

Iorfida, Elisabetta; Palmer, Phil; Roberts, Mark

2014-12-01

Within the field of trajectory optimisation, Lawden developed the primer vector theory, which defines a set of necessary conditions to characterise whether a transfer trajectory, in the two-body problem context, is optimum with respect to propellant usage. If the conditions are not satisfied, a region of the transfer trajectory is identified in which one or more potential intermediate impulses are performed in order to lower the overall cost. The method is computationally complex owing to having to solve a boundary value problem. In this paper is presented a new propagator that reduces the mathematical complexity and the computational cost of the problem, in particular it exploits a separation between the in-plane and out-of-plane components of the primer vector along the transfer trajectory. Using this propagator, the optimality of the transfer arc has been investigated, varying the departure and arrival orbits. In particular, keeping fixed the transfer trajectory, the optimality has been extensively analysed varying both the initial and final positions on the orbit, together with the directions of the initial and final thrust impulses.

From Basking Ridge to the Jupiter Trojans

NASA Technical Reports Server (NTRS)

Englander, Jacob

2017-01-01

This presentation describes the activities of the Global Trajectory Optimization Lab, a subdivision of the Navigation and Mission Design Branch at NASA GSFC. The students will learn the basics of interplanetary trajectory optimization and then, as an example, the Lucy mission to the Jupiter Trojans will be described from both a science and engineering perspective.

Trajectory Approaches for Launching Hypersonic Flight Tests (Preprint)

DTIC Science & Technology

2014-08-01

This paper presents some approaches toward designing trajectories for hypersonic testing at up to Mach 10 speed using a reusable rocket -powered first...Program to Optimize Simulated Trajectories (POST) code to look at different ways of flying to Mach 10 with a reusable first stage rocket . These trajectories...are good starting points for how to setup a trajectory simulation to meet hypersonic testing needs. 15. SUBJECT TERMS responsive and reusable rocket

Analytical Approach to the Fuel Optimal Impulsive Transfer Problem Using Primer Vector Method

NASA Astrophysics Data System (ADS)

Fitrianingsih, E.; Armellin, R.

2018-04-01

One of the objectives of mission design is selecting an optimum orbital transfer which often translated as a transfer which requires minimum propellant consumption. In order to assure the selected trajectory meets the requirement, the optimality of transfer should first be analyzed either by directly calculating the ΔV of the candidate trajectories and select the one that gives a minimum value or by evaluating the trajectory according to certain criteria of optimality. The second method is performed by analyzing the profile of the modulus of the thrust direction vector which is known as primer vector. Both methods come with their own advantages and disadvantages. However, it is possible to use the primer vector method to verify if the result from the direct method is truly optimal or if the ΔV can be reduced further by implementing correction maneuver to the reference trajectory. In addition to its capability to evaluate the transfer optimality without the need to calculate the transfer ΔV, primer vector also enables us to identify the time and position to apply correction maneuver in order to optimize a non-optimum transfer. This paper will present the analytical approach to the fuel optimal impulsive transfer using primer vector method. The validity of the method is confirmed by comparing the result to those from the numerical method. The investigation of the optimality of direct transfer is used to give an example of the application of the method. The case under study is the prograde elliptic transfers from Earth to Mars. The study enables us to identify the optimality of all the possible transfers.

Global Optimization of N-Maneuver, High-Thrust Trajectories Using Direct Multiple Shooting

NASA Technical Reports Server (NTRS)

Vavrina, Matthew A.; Englander, Jacob A.; Ellison, Donald H.

2016-01-01

The performance of impulsive, gravity-assist trajectories often improves with the inclusion of one or more maneuvers between flybys. However, grid-based scans over the entire design space can become computationally intractable for even one deep-space maneuver, and few global search routines are capable of an arbitrary number of maneuvers. To address this difficulty a trajectory transcription allowing for any number of maneuvers is developed within a multi-objective, global optimization framework for constrained, multiple gravity-assist trajectories. The formulation exploits a robust shooting scheme and analytic derivatives for computational efficiency. The approach is applied to several complex, interplanetary problems, achieving notable performance without a user-supplied initial guess.

MGA trajectory planning with an ACO-inspired algorithm

NASA Astrophysics Data System (ADS)

Ceriotti, Matteo; Vasile, Massimiliano

2010-11-01

Given a set of celestial bodies, the problem of finding an optimal sequence of swing-bys, deep space manoeuvres (DSM) and transfer arcs connecting the elements of the set is combinatorial in nature. The number of possible paths grows exponentially with the number of celestial bodies. Therefore, the design of an optimal multiple gravity assist (MGA) trajectory is a NP-hard mixed combinatorial-continuous problem. Its automated solution would greatly improve the design of future space missions, allowing the assessment of a large number of alternative mission options in a short time. This work proposes to formulate the complete automated design of a multiple gravity assist trajectory as an autonomous planning and scheduling problem. The resulting scheduled plan will provide the optimal planetary sequence and a good estimation of the set of associated optimal trajectories. The trajectory model consists of a sequence of celestial bodies connected by two-dimensional transfer arcs containing one DSM. For each transfer arc, the position of the planet and the spacecraft, at the time of arrival, are matched by varying the pericentre of the preceding swing-by, or the magnitude of the launch excess velocity, for the first arc. For each departure date, this model generates a full tree of possible transfers from the departure to the destination planet. Each leaf of the tree represents a planetary encounter and a possible way to reach that planet. An algorithm inspired by ant colony optimization (ACO) is devised to explore the space of possible plans. The ants explore the tree from departure to destination adding one node at the time: every time an ant is at a node, a probability function is used to select a feasible direction. This approach to automatic trajectory planning is applied to the design of optimal transfers to Saturn and among the Galilean moons of Jupiter. Solutions are compared to those found through more traditional genetic-algorithm techniques.

Optimal trajectories for hypersonic launch vehicles

NASA Technical Reports Server (NTRS)

Ardema, Mark D.; Bowles, Jeffrey V.; Whittaker, Thomas

1992-01-01

In this paper, we derive a near-optimal guidance law for the ascent trajectory from Earth surface to Earth orbit of a hypersonic, dual-mode propulsion, lifting vehicle. Of interest are both the optimal flight path and the optimal operation of the propulsion system. The guidance law is developed from the energy-state approximation of the equations of motion. The performance objective is a weighted sum of fuel mass and volume, with the weighting factor selected to give minimum gross take-off weight for a specific payload mass and volume.

Decision-Aiding and Optimization for Vertical Navigation of Long-Haul Aircraft

NASA Technical Reports Server (NTRS)

Patrick, Nicholas J. M.; Sheridan, Thomas B.

1996-01-01

Most decisions made in the cockpit are related to safety, and have therefore been proceduralized in order to reduce risk. There are very few which are made on the basis of a value metric such as economic cost. One which can be shown to be value based, however, is the selection of a flight profile. Fuel consumption and flight time both have a substantial effect on aircraft operating cost, but they cannot be minimized simultaneously. In addition, winds, turbulence, and performance x,ary widely with altitude and time. These factors make it important and difficult for pilots to (a) evaluate the outcomes associated with a particular trajectory before it is flown and (b) decide among possible trajectories. The two elements of this problem considered here are (1) determining, what constitutes optimality, and (2) finding optimal trajectories. Pilots and dispatchers from major U.S. airlines were surveyed to determine which attributes of the outcome of a flight they considered the most important. Avoiding turbulence-for passenger comfort topped the list of items which were not safety related. Pilots' decision making about the selection of flight profile on the basis of flight time, fuel burn, and exposure to turbulence was then observed. Of the several behavioral and prescriptive decision models invoked to explain the pilots' choices, utility maximization is shown to best reproduce the pilots' decisions. After considering more traditional methods for optimizing trajectories, a novel method is developed using a genetic algorithm (GA) operating on a discrete representation of the trajectory search space. The representation is a sequence of command altitudes, and was chosen to be compatible with the constraints imposed by Air Traffic Control, and with the training given to pilots. Since trajectory evaluation for the GA is performed holistically, a wide class of objective functions can be optimized easily. Also, using the GA it is possible to compare the costs associated with different airspace design and air traffic management policies. A decision aid is proposed which would combine the pilot's notion of optimility with the GA-based optimization, provide the pilot with a number of alternative pareto-optimal trajectories, and allow him to consider un-modelled attributes and constraints in choosing among them. A solution to the problem of displaying alternatives in a multi-attribute decision space is also presented.

Analysis of Chemical, REP, and SEP missions to the Trojan asteroids

NASA Technical Reports Server (NTRS)

Bonfiglio, Eugene P.; Oh, David; Yen, Chen-Wan

2005-01-01

Recent studies suggest significant benefits from using 1st and 2nd generation Radioisotope Power Systems (RPS) as a power source for electric propulsion (EP) missions to the outer planets. This study focuses on trajectories to the Trojan asteroids. A high level analysis is performed with chemical trajectories to determine potential canidates for REP trajectory optimization. Extensive analysis of direct trajectories using REP is performed on these candidates. Solar Electric Propulsion (SEP) trajectories are also considered for comparison against REP trajectories.

Shaping low-thrust trajectories with thrust-handling feature

NASA Astrophysics Data System (ADS)

Taheri, Ehsan; Kolmanovsky, Ilya; Atkins, Ella

2018-02-01

Shape-based methods are becoming popular in low-thrust trajectory optimization due to their fast computation speeds. In existing shape-based methods constraints are treated at the acceleration level but not at the thrust level. These two constraint types are not equivalent since spacecraft mass decreases over time as fuel is expended. This paper develops a shape-based method based on a Fourier series approximation that is capable of representing trajectories defined in spherical coordinates and that enforces thrust constraints. An objective function can be incorporated to minimize overall mission cost, i.e., achieve minimum ΔV . A representative mission from Earth to Mars is studied. The proposed Fourier series technique is demonstrated capable of generating feasible and near-optimal trajectories. These attributes can facilitate future low-thrust mission designs where different trajectory alternatives must be rapidly constructed and evaluated.

Multi Sector Planning Tools for Trajectory-Based Operations

NASA Technical Reports Server (NTRS)

Prevot, Thomas; Mainini, Matthew; Brasil, Connie

2010-01-01

This paper discusses a suite of multi sector planning tools for trajectory-based operations that were developed and evaluated in the Airspace Operations Laboratory (AOL) at the NASA Ames Research Center. The toolset included tools for traffic load and complexity assessment as well as trajectory planning and coordination. The situation assessment tools included an integrated suite of interactive traffic displays, load tables, load graphs, and dynamic aircraft filters. The planning toolset allowed for single and multi aircraft trajectory planning and data communication-based coordination of trajectories between operators. Also newly introduced was a real-time computation of sector complexity into the toolset that operators could use in lieu of aircraft count to better estimate and manage sector workload, especially in situations with convective weather. The tools were used during a joint NASA/FAA multi sector planner simulation in the AOL in 2009 that had multiple objectives with the assessment of the effectiveness of the tools being one of them. Current air traffic control operators who were experienced as area supervisors and traffic management coordinators used the tools throughout the simulation and provided their usefulness and usability ratings in post simulation questionnaires. This paper presents these subjective assessments as well as the actual usage data that was collected during the simulation. The toolset was rated very useful and usable overall. Many elements received high scores by the operators and were used frequently and successfully. Other functions were not used at all, but various requests for new functions and capabilities were received that could be added to the toolset.

Optimal trajectory generation for mechanical arms. M.S. Thesis

NASA Technical Reports Server (NTRS)

Iemenschot, J. A.

1972-01-01

A general method of generating optimal trajectories between an initial and a final position of an n degree of freedom manipulator arm with nonlinear equations of motion is proposed. The method is based on the assumption that the time history of each of the coordinates can be expanded in a series of simple time functions. By searching over the coefficients of the terms in the expansion, trajectories which minimize the value of a given cost function can be obtained. The method has been applied to a planar three degree of freedom arm.

A Smoothed Eclipse Model for Solar Electric Propulsion Trajectory Optimization

NASA Technical Reports Server (NTRS)

Aziz, Jonathan D.; Scheeres, Daniel J.; Parker, Jeffrey S.; Englander, Jacob A.

2017-01-01

Solar electric propulsion (SEP) is the dominant design option for employing low-thrust propulsion on a space mission. Spacecraft solar arrays power the SEP system but are subject to blackout periods during solar eclipse conditions. Discontinuity in power available to the spacecraft must be accounted for in trajectory optimization, but gradient-based methods require a differentiable power model. This work presents a power model that smooths the eclipse transition from total eclipse to total sunlight with a logistic function. Example trajectories are computed with differential dynamic programming, a second-order gradient-based method.

Nonlinear dynamic analysis and optimal trajectory planning of a high-speed macro-micro manipulator

NASA Astrophysics Data System (ADS)

Yang, Yi-ling; Wei, Yan-ding; Lou, Jun-qiang; Fu, Lei; Zhao, Xiao-wei

2017-09-01

This paper reports the nonlinear dynamic modeling and the optimal trajectory planning for a flexure-based macro-micro manipulator, which is dedicated to the large-scale and high-speed tasks. In particular, a macro- micro manipulator composed of a servo motor, a rigid arm and a compliant microgripper is focused. Moreover, both flexure hinges and flexible beams are considered. By combining the pseudorigid-body-model method, the assumed mode method and the Lagrange equation, the overall dynamic model is derived. Then, the rigid-flexible-coupling characteristics are analyzed by numerical simulations. After that, the microscopic scale vibration excited by the large-scale motion is reduced through the trajectory planning approach. Especially, a fitness function regards the comprehensive excitation torque of the compliant microgripper is proposed. The reference curve and the interpolation curve using the quintic polynomial trajectories are adopted. Afterwards, an improved genetic algorithm is used to identify the optimal trajectory by minimizing the fitness function. Finally, the numerical simulations and experiments validate the feasibility and the effectiveness of the established dynamic model and the trajectory planning approach. The amplitude of the residual vibration reduces approximately 54.9%, and the settling time decreases 57.1%. Therefore, the operation efficiency and manipulation stability are significantly improved.

POST II Trajectory Animation Tool Using MATLAB, V1.0

NASA Technical Reports Server (NTRS)

Raiszadeh, Behzad

2005-01-01

A trajectory animation tool has been developed for accurately depicting position and the attitude of the bodies in flight. The movies generated from This MATLAB based tool serve as an engineering analysis aid to gain further understanding into the dynamic behavior of bodies in flight. This tool has been designed to interface with the output generated from POST II simulations, and is able to animate a single as well as multiple vehicles in flight.

Potential for Integrating Entry Guidance into the Multi-Disciplinary Entry Vehicle Optimization Environment

NASA Technical Reports Server (NTRS)

D'souza, Sarah N.; Kinney, David J.; Garcia, Joseph A.; Sarigul-Klijn, Nesrin

2014-01-01

The state-of-the-art in vehicle design decouples flight feasible trajectory generation from the optimization process of an entry spacecraft shape. The disadvantage to this decoupled process is seen when a particular aeroshell does not meet in-flight requirements when integrated into Guidance, Navigation, and Control simulations. It is postulated that the integration of a guidance algorithm into the design process will provide a real-time, rapid trajectory generation technique to enhance the robustness of vehicle design solutions. The potential benefit of this integration is a reduction in design cycles (possible cost savings) and increased accuracy in the aerothermal environment (possible mass savings). This work examines two aspects: 1) the performance of a reference tracking guidance algorithm for five different geometries with the same reference trajectory and 2) the potential of mass savings from improved aerothermal predictions. An Apollo Derived Guidance (ADG) algorithm is used in this study. The baseline geometry and five test case geometries were flown using the same baseline trajectory. The guided trajectory results are compared to separate trajectories determined in a vehicle optimization study conducted for NASA's Mars Entry, Descent, and Landing System Analysis. This study revealed several aspects regarding the potential gains and required developments for integrating a guidance algorithm into the vehicle optimization environment. First, the generation of flight feasible trajectories is only as good as the robustness of the guidance algorithm. The set of dispersed geometries modelled aerodynamic dispersions that ranged from +/-1% to +/-17% and a single extreme case was modelled where the aerodynamics were approximately 80% less than the baseline geometry. The ADG, as expected, was able to guide the vehicle into the aeroshell separation box at the target location for dispersions up to 17%, but failed for the 80% dispersion cases. Finally, the results revealed that including flight feasible trajectories for a set of dispersed geometries has the potential to save mass up to 430 kg.

MADS Users' Guide

NASA Technical Reports Server (NTRS)

Moerder, Daniel D.

2014-01-01

MADS (Minimization Assistant for Dynamical Systems) is a trajectory optimization code in which a user-specified performance measure is directly minimized, subject to constraints placed on a low-order discretization of user-supplied plant ordinary differential equations. This document describes the mathematical formulation of the set of trajectory optimization problems for which MADS is suitable, and describes the user interface. Usage examples are provided.

Two-phase framework for near-optimal multi-target Lambert rendezvous

NASA Astrophysics Data System (ADS)

Bang, Jun; Ahn, Jaemyung

2018-03-01

This paper proposes a two-phase framework to obtain a near-optimal solution of multi-target Lambert rendezvous problem. The objective of the problem is to determine the minimum-cost rendezvous sequence and trajectories to visit a given set of targets within a maximum mission duration. The first phase solves a series of single-target rendezvous problems for all departure-arrival object pairs to generate the elementary solutions, which provides candidate rendezvous trajectories. The second phase formulates a variant of traveling salesman problem (TSP) using the elementary solutions prepared in the first phase and determines the final rendezvous sequence and trajectories of the multi-target rendezvous problem. The validity of the proposed optimization framework is demonstrated through an asteroid exploration case study.

Optimizing interplanetary trajectories with deep space maneuvers. M.S. Thesis

NASA Technical Reports Server (NTRS)

Navagh, John

1993-01-01

Analysis of interplanetary trajectories is a crucial area for both manned and unmanned missions of the Space Exploration Initiative. A deep space maneuver (DSM) can improve a trajectory in much the same way as a planetary swingby. However, instead of using a gravitational field to alter the trajectory, the on-board propulsion system of the spacecraft is used when the vehicle is not near a planet. The purpose is to develop an algorithm to determine where and when to use deep space maneuvers to reduce the cost of a trajectory. The approach taken to solve this problem uses primer vector theory in combination with a non-linear optimizing program to minimize Delta(V). A set of necessary conditions on the primer vector is shown to indicate whether a deep space maneuver will be beneficial. Deep space maneuvers are applied to a round trip mission to Mars to determine their effect on the launch opportunities. Other studies which were performed include cycler trajectories and Mars mission abort scenarios. It was found that the software developed was able to locate quickly DSM's which lower the total Delta(V) on these trajectories.

Optimizing interplanetary trajectories with deep space maneuvers

NASA Astrophysics Data System (ADS)

Navagh, John

1993-09-01

Analysis of interplanetary trajectories is a crucial area for both manned and unmanned missions of the Space Exploration Initiative. A deep space maneuver (DSM) can improve a trajectory in much the same way as a planetary swingby. However, instead of using a gravitational field to alter the trajectory, the on-board propulsion system of the spacecraft is used when the vehicle is not near a planet. The purpose is to develop an algorithm to determine where and when to use deep space maneuvers to reduce the cost of a trajectory. The approach taken to solve this problem uses primer vector theory in combination with a non-linear optimizing program to minimize Delta(V). A set of necessary conditions on the primer vector is shown to indicate whether a deep space maneuver will be beneficial. Deep space maneuvers are applied to a round trip mission to Mars to determine their effect on the launch opportunities. Other studies which were performed include cycler trajectories and Mars mission abort scenarios. It was found that the software developed was able to locate quickly DSM's which lower the total Delta(V) on these trajectories.

Automatic determination of optimal linear drilling trajectories for cochlear access accounting for drill-positioning error.

PubMed

Noble, Jack H; Majdani, Omid; Labadie, Robert F; Dawant, Benoit; Fitzpatrick, J Michael

2010-09-01

Cochlear implantation is a surgical procedure in which an electrode array is permanently implanted into the cochlea to stimulate the auditory nerve and allow deaf people to hear. Percutaneous cochlear access, a new minimally invasive implantation approach, requires drilling a single linear channel from the skull surface to the cochlea. The focus of this paper addresses a major challenge with this approach, which is the ability to determine, in a pre-operative CT, a safe and effective drilling trajectory. A measure of the safety and effectiveness of a given trajectory relative to sensitive structures is derived using a Monte Carlo approach. The drilling trajectory that maximizes this measure is found using an optimization algorithm. In tests on 13 ears, the technique was shown to find approximately twice as many acceptable trajectories as those found manually by an experienced surgeon. Using this method, safe trajectories can be automatically determined quickly and consistently. Copyright 2010 John Wiley & Sons, Ltd.

Optimization of dynamic soaring maneuvers to enhance endurance of a versatile UAV

NASA Astrophysics Data System (ADS)

Mir, Imran; Maqsood, Adnan; Akhtar, Suhail

2017-06-01

Dynamic soaring is a process of acquiring energy available in atmospheric wind shears and is commonly exhibited by soaring birds to perform long distance flights. This paper aims to demonstrate a viable algorithm which can be implemented in near real time environment to formulate optimal trajectories for dynamic soaring maneuvers for a small scale Unmanned Aerial Vehicle (UAV). The objective is to harness maximum energy from atmosphere wind shear to improve loiter time for Intelligence, Surveillance and Reconnaissance (ISR) missions. Three-dimensional point-mass UAV equations of motion and linear wind gradient profile are used to model flight dynamics. Utilizing UAV states, controls, operational constraints, initial and terminal conditions that enforce a periodic flight, dynamic soaring problem is formulated as an optimal control problem. Optimized trajectories of the maneuver are subsequently generated employing pseudo spectral techniques against distant UAV performance parameters. The discussion also encompasses the requirement for generation of optimal trajectories for dynamic soaring in real time environment and the ability of the proposed algorithm for speedy solution generation. Coupled with the fact that dynamic soaring is all about immediately utilizing the available energy from the wind shear encountered, the proposed algorithm promises its viability for practical on board implementations requiring computation of trajectories in near real time.

An inverse dynamics approach to trajectory optimization and guidance for an aerospace plane

NASA Technical Reports Server (NTRS)

Lu, Ping

1992-01-01

The optimal ascent problem for an aerospace planes is formulated as an optimal inverse dynamic problem. Both minimum-fuel and minimax type of performance indices are considered. Some important features of the optimal trajectory and controls are used to construct a nonlinear feedback midcourse controller, which not only greatly simplifies the difficult constrained optimization problem and yields improved solutions, but is also suited for onboard implementation. Robust ascent guidance is obtained by using combination of feedback compensation and onboard generation of control through the inverse dynamics approach. Accurate orbital insertion can be achieved with near-optimal control of the rocket through inverse dynamics even in the presence of disturbances.

Low-thrust trajectory optimization in a full ephemeris model

NASA Astrophysics Data System (ADS)

Cai, Xing-Shan; Chen, Yang; Li, Jun-Feng

2014-10-01

The low-thrust trajectory optimization with complicated constraints must be considered in practical engineering. In most literature, this problem is simplified into a two-body model in which the spacecraft is subject to the gravitational force at the center of mass and the spacecraft's own electric propulsion only, and the gravity assist (GA) is modeled as an instantaneous velocity increment. This paper presents a method to solve the fuel-optimal problem of low-thrust trajectory with complicated constraints in a full ephemeris model, which is closer to practical engineering conditions. First, it introduces various perturbations, including a third body's gravity, the nonspherical perturbation and the solar radiation pressure in a dynamic equation. Second, it builds two types of equivalent inner constraints to describe the GA. At the same time, the present paper applies a series of techniques, such as a homotopic approach, to enhance the possibility of convergence of the global optimal solution.

Optimal Control of Induction Machines to Minimize Transient Energy Losses

NASA Astrophysics Data System (ADS)

Plathottam, Siby Jose

Induction machines are electromechanical energy conversion devices comprised of a stator and a rotor. Torque is generated due to the interaction between the rotating magnetic field from the stator, and the current induced in the rotor conductors. Their speed and torque output can be precisely controlled by manipulating the magnitude, frequency, and phase of the three input sinusoidal voltage waveforms. Their ruggedness, low cost, and high efficiency have made them ubiquitous component of nearly every industrial application. Thus, even a small improvement in their energy efficient tend to give a large amount of electrical energy savings over the lifetime of the machine. Hence, increasing energy efficiency (reducing energy losses) in induction machines is a constrained optimization problem that has attracted attention from researchers. The energy conversion efficiency of induction machines depends on both the speed-torque operating point, as well as the input voltage waveform. It also depends on whether the machine is in the transient or steady state. Maximizing energy efficiency during steady state is a Static Optimization problem, that has been extensively studied, with commercial solutions available. On the other hand, improving energy efficiency during transients is a Dynamic Optimization problem that is sparsely studied. This dissertation exclusively focuses on improving energy efficiency during transients. This dissertation treats the transient energy loss minimization problem as an optimal control problem which consists of a dynamic model of the machine, and a cost functional. The rotor field oriented current fed model of the induction machine is selected as the dynamic model. The rotor speed and rotor d-axis flux are the state variables in the dynamic model. The stator currents referred to as d-and q-axis currents are the control inputs. A cost functional is proposed that assigns a cost to both the energy losses in the induction machine, as well as the deviations from desired speed-torque-magnetic flux setpoints. Using Pontryagin's minimum principle, a set of necessary conditions that must be satisfied by the optimal control trajectories are derived. The conditions are in the form a two-point boundary value problem, that can be solved numerically. The conjugate gradient method that was modified using the Hestenes-Stiefel formula was used to obtain the numerical solution of both the control and state trajectories. Using the distinctive shape of the numerical trajectories as inspiration, analytical expressions were derived for the state, and control trajectories. It was shown that the trajectory could be fully described by finding the solution of a one-dimensional optimization problem. The sensitivity of both the optimal trajectory and the optimal energy efficiency to different induction machine parameters were analyzed. A non-iterative solution that can use feedback for generating optimal control trajectories in real time was explored. It was found that an artificial neural network could be trained using the numerical solutions and made to emulate the optimal control trajectories with a high degree of accuracy. Hence a neural network along with a supervisory logic was implemented and used in a real-time simulation to control the Finite Element Method model of the induction machine. The results were compared with three other control regimes and the optimal control system was found to have the highest energy efficiency for the same drive cycle.

Numerical approach of collision avoidance and optimal control on robotic manipulators

NASA Technical Reports Server (NTRS)

Wang, Jyhshing Jack

1990-01-01

Collision-free optimal motion and trajectory planning for robotic manipulators are solved by a method of sequential gradient restoration algorithm. Numerical examples of a two degree-of-freedom (DOF) robotic manipulator are demonstrated to show the excellence of the optimization technique and obstacle avoidance scheme. The obstacle is put on the midway, or even further inward on purpose, of the previous no-obstacle optimal trajectory. For the minimum-time purpose, the trajectory grazes by the obstacle and the minimum-time motion successfully avoids the obstacle. The minimum-time is longer for the obstacle avoidance cases than the one without obstacle. The obstacle avoidance scheme can deal with multiple obstacles in any ellipsoid forms by using artificial potential fields as penalty functions via distance functions. The method is promising in solving collision-free optimal control problems for robotics and can be applied to any DOF robotic manipulators with any performance indices and mobile robots as well. Since this method generates optimum solution based on Pontryagin Extremum Principle, rather than based on assumptions, the results provide a benchmark against which any optimization techniques can be measured.

Optimization of fixed-range trajectories for supersonic transport aircraft

NASA Astrophysics Data System (ADS)

Windhorst, Robert Dennis

1999-11-01

This thesis develops near-optimal guidance laws that generate minimum fuel, time, or direct operating cost fixed-range trajectories for supersonic transport aircraft. The approach uses singular perturbation techniques to time-scale de-couple the equations of motion into three sets of dynamics, two of which are analyzed in the main body of this thesis and one of which is analyzed in the Appendix. The two-point-boundary-value-problems obtained by application of the maximum principle to the dynamic systems are solved using the method of matched asymptotic expansions. Finally, the two solutions are combined using the matching principle and an additive composition rule to form a uniformly valid approximation of the full fixed-range trajectory. The approach is used on two different time-scale formulations. The first holds weight constant, and the second allows weight and range dynamics to propagate on the same time-scale. Solutions for the first formulation are only carried out to zero order in the small parameter, while solutions for the second formulation are carried out to first order. Calculations for a HSCT design were made to illustrate the method. Results show that the minimum fuel trajectory consists of three segments: a minimum fuel energy-climb, a cruise-climb, and a minimum drag glide. The minimum time trajectory also has three segments: a maximum dynamic pressure ascent, a constant altitude cruise, and a maximum dynamic pressure glide. The minimum direct operating cost trajectory is an optimal combination of the two. For realistic costs of fuel and flight time, the minimum direct operating cost trajectory is very similar to the minimum fuel trajectory. Moreover, the HSCT has three local optimum cruise speeds, with the globally optimum cruise point at the highest allowable speed, if range is sufficiently long. The final range of the trajectory determines which locally optimal speed is best. Ranges of 500 to 6,000 nautical miles, subsonic and supersonic mixed flight, and varying fuel efficiency cases are analyzed. Finally, the payload-range curve of the HSCT design is determined.

Spiking, Bursting, and Population Dynamics in a Network of Growth Transform Neurons.

PubMed

Gangopadhyay, Ahana; Chakrabartty, Shantanu

2018-06-01

This paper investigates the dynamical properties of a network of neurons, each of which implements an asynchronous mapping based on polynomial growth transforms. In the first part of this paper, we present a geometric approach for visualizing the dynamics of the network where each of the neurons traverses a trajectory in a dual optimization space, whereas the network itself traverses a trajectory in an equivalent primal optimization space. We show that as the network learns to solve basic classification tasks, different choices of primal-dual mapping produce unique but interpretable neural dynamics like noise shaping, spiking, and bursting. While the proposed framework is general enough, in this paper, we demonstrate its use for designing support vector machines (SVMs) that exhibit noise-shaping properties similar to those of modulators, and for designing SVMs that learn to encode information using spikes and bursts. It is demonstrated that the emergent switching, spiking, and burst dynamics produced by each neuron encodes its respective margin of separation from a classification hyperplane whose parameters are encoded by the network population dynamics. We believe that the proposed growth transform neuron model and the underlying geometric framework could serve as an important tool to connect well-established machine learning algorithms like SVMs to neuromorphic principles like spiking, bursting, population encoding, and noise shaping.

Conformational and functional analysis of molecular dynamics trajectories by Self-Organising Maps

PubMed Central

2011-01-01

Background Molecular dynamics (MD) simulations are powerful tools to investigate the conformational dynamics of proteins that is often a critical element of their function. Identification of functionally relevant conformations is generally done clustering the large ensemble of structures that are generated. Recently, Self-Organising Maps (SOMs) were reported performing more accurately and providing more consistent results than traditional clustering algorithms in various data mining problems. We present a novel strategy to analyse and compare conformational ensembles of protein domains using a two-level approach that combines SOMs and hierarchical clustering. Results The conformational dynamics of the α-spectrin SH3 protein domain and six single mutants were analysed by MD simulations. The Cα's Cartesian coordinates of conformations sampled in the essential space were used as input data vectors for SOM training, then complete linkage clustering was performed on the SOM prototype vectors. A specific protocol to optimize a SOM for structural ensembles was proposed: the optimal SOM was selected by means of a Taguchi experimental design plan applied to different data sets, and the optimal sampling rate of the MD trajectory was selected. The proposed two-level approach was applied to single trajectories of the SH3 domain independently as well as to groups of them at the same time. The results demonstrated the potential of this approach in the analysis of large ensembles of molecular structures: the possibility of producing a topological mapping of the conformational space in a simple 2D visualisation, as well as of effectively highlighting differences in the conformational dynamics directly related to biological functions. Conclusions The use of a two-level approach combining SOMs and hierarchical clustering for conformational analysis of structural ensembles of proteins was proposed. It can easily be extended to other study cases and to conformational ensembles from other sources. PMID:21569575

Particle Swarm Optimization of Low-Thrust, Geocentric-to-Halo-Orbit Transfers

NASA Astrophysics Data System (ADS)

Abraham, Andrew J.

Missions to Lagrange points are becoming increasingly popular amongst spacecraft mission planners. Lagrange points are locations in space where the gravity force from two bodies, and the centrifugal force acting on a third body, cancel. To date, all spacecraft that have visited a Lagrange point have done so using high-thrust, chemical propulsion. Due to the increasing availability of low-thrust (high efficiency) propulsive devices, and their increasing capability in terms of fuel efficiency and instantaneous thrust, it has now become possible for a spacecraft to reach a Lagrange point orbit without the aid of chemical propellant. While at any given time there are many paths for a low-thrust trajectory to take, only one is optimal. The traditional approach to spacecraft trajectory optimization utilizes some form of gradient-based algorithm. While these algorithms offer numerous advantages, they also have a few significant shortcomings. The three most significant shortcomings are: (1) the fact that an initial guess solution is required to initialize the algorithm, (2) the radius of convergence can be quite small and can allow the algorithm to become trapped in local minima, and (3) gradient information is not always assessable nor always trustworthy for a given problem. To avoid these problems, this dissertation is focused on optimizing a low-thrust transfer trajectory from a geocentric orbit to an Earth-Moon, L1, Lagrange point orbit using the method of Particle Swarm Optimization (PSO). The PSO method is an evolutionary heuristic that was originally written to model birds swarming to locate hidden food sources. This PSO method will enable the exploration of the invariant stable manifold of the target Lagrange point orbit in an effort to optimize the spacecraft's low-thrust trajectory. Examples of these optimized trajectories are presented and contrasted with those found using traditional, gradient-based approaches. In summary, the results of this dissertation find that the PSO method does, indeed, successfully optimize the low-thrust trajectory transfer problem without the need for initial guessing. Furthermore, a two-degree-of-freedom PSO problem formulation significantly outperformed a one-degree-of-freedom formulation by at least an order of magnitude, in terms of CPU time. Finally, the PSO method is also used to solve a traditional, two-burn, impulsive transfer to a Lagrange point orbit using a hybrid optimization algorithm that incorporates a gradient-based shooting algorithm as a pre-optimizer. Surprisingly, the results of this study show that "fast" transfers outperform "slow" transfers in terms of both Deltav and time of flight.

Design of Quiet Rotorcraft Approach Trajectories

NASA Technical Reports Server (NTRS)

Padula, Sharon L.; Burley, Casey L.; Boyd, D. Douglas, Jr.; Marcolini, Michael A.

2009-01-01

A optimization procedure for identifying quiet rotorcraft approach trajectories is proposed and demonstrated. The procedure employs a multi-objective genetic algorithm in order to reduce noise and create approach paths that will be acceptable to pilots and passengers. The concept is demonstrated by application to two different helicopters. The optimized paths are compared with one another and to a standard 6-deg approach path. The two demonstration cases validate the optimization procedure but highlight the need for improved noise prediction techniques and for additional rotorcraft acoustic data sets.

Hodograph analysis in aircraft trajectory optimization

NASA Technical Reports Server (NTRS)

Cliff, Eugene M.; Seywald, Hans; Bless, Robert R.

1993-01-01

An account is given of key geometrical concepts involved in the use of a hodograph as an optimal control theory resource which furnishes a framework for geometrical interpretation of the minimum principle. Attention is given to the effects of different convexity properties on the hodograph, which bear on the existence of solutions and such types of controls as chattering controls, 'bang-bang' control, and/or singular control. Illustrative aircraft trajectory optimization problems are examined in view of this use of the hodograph.

Singular perturbation analysis of AOTV-related trajectory optimization problems

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Bae, Gyoung H.

1990-01-01

The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality constraint was imposed on the full order AOTV point mass equations of motion, using a simple aerodynamic heating rate model.

A Collaborative Analysis Tool for Thermal Protection Systems for Single Stage to Orbit Launch Vehicles

NASA Technical Reports Server (NTRS)

Alexander, Reginald A.; Stanley, Thomas Troy

1999-01-01

Presented is a design tool and process that connects several disciplines which are needed in the complex and integrated design of high performance reusable single stage to orbit (SSTO) vehicles. Every system is linked to every other system and in the case of SSTO vehicles with air breathing propulsion, which is currently being studied by the National Aeronautics and Space Administration (NASA); the thermal protection system (TPS) is linked directly to almost every major system. The propulsion system pushes the vehicle to velocities on the order of 15 times the speed of sound in the atmosphere before pulling up to go to orbit which results high temperatures on the external surfaces of the vehicle. Thermal protection systems to maintain the structural integrity of the vehicle must be able to mitigate the heat transfer to the structure and be lightweight. Herein lies the interdependency, in that as the vehicle's speed increases, the TPS requirements are increased. And as TPS masses increase the effect on the propulsion system and all other systems is compounded. To adequately determine insulation masses for a vehicle such as the one described above, the aeroheating loads must be calculated and the TPS thicknesses must be calculated for the entire vehicle. To accomplish this an ascent or reentry trajectory is obtained using the computer code Program to Optimize Simulated Trajectories (POST). The trajectory is then used to calculate the convective heat rates on several locations on the vehicles using the Miniature Version of the JA70 Aerodynamic Heating Computer Program (MINIVER). Once the heat rates are defined for each body point on the vehicle, then insulation thicknesses that are required to maintain the vehicle within structural limits are calculated using Systems Improved Numerical Differencing Analyzer (SINDA) models. If the TPS masses are too heavy for the performance of the vehicle the process may be repeated altering the trajectory or some other input to reduce the TPS mass. The problem described is an example of the need for collaborative design and analysis. Analysis tools are being developed to facilitate these collaborative efforts. RECIPE is a cross-platform application capable of hosting a number of engineers and designers across the Internet for distributed and collaborative engineering environments. Such integrated system design environments allow for collaborative team design analysis for performing individual or reduced team studies. The analysis tools mentioned earlier are commonly run on different platforms and are usually run by different people. To facilitate the larger number of potential runs that may need to be made, RECIPE connects the computer codes that calculate the trajectory data, heat rate data, and TPS masses so that the output from each tool is easily transferred to the model input files that need it. This methodology is being applied to solve launch vehicle thermal design problems to shorten the design cycle, and enable the project team to evaluate design options. Results will be presented indicating the effectiveness of this as a collaborative design tool.

Guidance trajectories for aeroassisted orbital transfer

NASA Technical Reports Server (NTRS)

Miele, A.

1990-01-01

Research on aerobraking guidance schemes is presented. The intent is to produce aerobraking guidance trajectories exhibiting many of the desirable characteristics of optimal aerobraking trajectories. Both one-control schemes and two-control schemes are studied. The research is in the interest of aeroassisted flight experiment vehicles (AFE) and aeroassisted orbital transfer (AOT) vehicles.

An Efficient Method of Sharing Mass Spatio-Temporal Trajectory Data Based on Cloudera Impala for Traffic Distribution Mapping in an Urban City

PubMed Central

Zhou, Lianjie; Chen, Nengcheng; Yuan, Sai; Chen, Zeqiang

2016-01-01

The efficient sharing of spatio-temporal trajectory data is important to understand traffic congestion in mass data. However, the data volumes of bus networks in urban cities are growing rapidly, reaching daily volumes of one hundred million datapoints. Accessing and retrieving mass spatio-temporal trajectory data in any field is hard and inefficient due to limited computational capabilities and incomplete data organization mechanisms. Therefore, we propose an optimized and efficient spatio-temporal trajectory data retrieval method based on the Cloudera Impala query engine, called ESTRI, to enhance the efficiency of mass data sharing. As an excellent query tool for mass data, Impala can be applied for mass spatio-temporal trajectory data sharing. In ESTRI we extend the spatio-temporal trajectory data retrieval function of Impala and design a suitable data partitioning method. In our experiments, the Taiyuan BeiDou (BD) bus network is selected, containing 2300 buses with BD positioning sensors, producing 20 million records every day, resulting in two difficulties as described in the Introduction section. In addition, ESTRI and MongoDB are applied in experiments. The experiments show that ESTRI achieves the most efficient data retrieval compared to retrieval using MongoDB for data volumes of fifty million, one hundred million, one hundred and fifty million, and two hundred million. The performance of ESTRI is approximately seven times higher than that of MongoDB. The experiments show that ESTRI is an effective method for retrieving mass spatio-temporal trajectory data. Finally, bus distribution mapping in Taiyuan city is achieved, describing the buses density in different regions at different times throughout the day, which can be applied in future studies of transport, such as traffic scheduling, traffic planning and traffic behavior management in intelligent public transportation systems. PMID:27801869

Collaborative Analysis Tool for Thermal Protection Systems for Single Stage to Orbit Launch Vehicles

NASA Technical Reports Server (NTRS)

Alexander, Reginald Andrew; Stanley, Thomas Troy

1999-01-01

Presented is a design tool and process that connects several disciplines which are needed in the complex and integrated design of high performance reusable single stage to orbit (SSTO) vehicles. Every system is linked to every other system and in the case of SSTO vehicles with air breathing propulsion, which is currently being studied by the National Aeronautics and Space Administration (NASA); the thermal protection system (TPS) is linked directly to almost every major system. The propulsion system pushes the vehicle to velocities on the order of 15 times the speed of sound in the atmosphere before pulling up to go to orbit which results high temperatures on the external surfaces of the vehicle. Thermal protection systems to maintain the structural integrity of the vehicle must be able to mitigate the heat transfer to the structure and be lightweight. Herein lies the interdependency, in that as the vehicle's speed increases, the TPS requirements are increased. And as TPS masses increase the effect on the propulsion system and all other systems is compounded. To adequately determine insulation masses for a vehicle such as the one described above, the aeroheating loads must be calculated and the TPS thicknesses must be calculated for the entire vehicle. To accomplish this an ascent or reentry trajectory is obtained using the computer code Program to Optimize Simulated Trajectories (POST). The trajectory is then used to calculate the convective heat rates on several locations on the vehicles using the Miniature Version of the JA70 Aerodynamic Heating Computer Program (MINIVER). Once the heat rates are defined for each body point on the vehicle, then insulation thickness that are required to maintain the vehicle within structural limits are calculated using Systems Improved Numerical Differencing Analyzer (SINDA) models. If the TPS masses are too heavy for the performance of the vehicle the process may be repeated altering the trajectory or some other input to reduce the TPS mass.

An explicit solution to the exoatmospheric powered flight guidance and trajectory optimization problem for rocket propelled vehicles

NASA Technical Reports Server (NTRS)

Jaggers, R. F.

1977-01-01

A derivation of an explicit solution to the two point boundary-value problem of exoatmospheric guidance and trajectory optimization is presented. Fixed initial conditions and continuous burn, multistage thrusting are assumed. Any number of end conditions from one to six (throttling is required in the case of six) can be satisfied in an explicit and practically optimal manner. The explicit equations converge for off nominal conditions such as engine failure, abort, target switch, etc. The self starting, predictor/corrector solution involves no Newton-Rhapson iterations, numerical integration, or first guess values, and converges rapidly if physically possible. A form of this algorithm has been chosen for onboard guidance, as well as real time and preflight ground targeting and trajectory shaping for the NASA Space Shuttle Program.

A Global Approach to the Optimal Trajectory Based on an Improved Ant Colony Algorithm for Cold Spray

NASA Astrophysics Data System (ADS)

Cai, Zhenhua; Chen, Tingyang; Zeng, Chunnian; Guo, Xueping; Lian, Huijuan; Zheng, You; Wei, Xiaoxu

2016-12-01

This paper is concerned with finding a global approach to obtain the shortest complete coverage trajectory on complex surfaces for cold spray applications. A slicing algorithm is employed to decompose the free-form complex surface into several small pieces of simple topological type. The problem of finding the optimal arrangement of the pieces is translated into a generalized traveling salesman problem (GTSP). Owing to its high searching capability and convergence performance, an improved ant colony algorithm is then used to solve the GTSP. Through off-line simulation, a robot trajectory is generated based on the optimized result. The approach is applied to coat real components with a complex surface by using the cold spray system with copper as the spraying material.

Measurement Learning Trajectories: A Tool for Professional Development

ERIC Educational Resources Information Center

McCool, Jenni K.

2009-01-01

This study investigated the ways in which a teacher developed conceptions of measurement teaching and learning as she collaborated with a researcher to learn and implement a measurement learning trajectory with two of her students. Teachers need tools that effectively address the content area of measurement and can be used to improve their…

A near-optimal guidance for cooperative docking maneuvers

NASA Astrophysics Data System (ADS)

Ciarcià, Marco; Grompone, Alessio; Romano, Marcello

2014-09-01

In this work we study the problem of minimum energy docking maneuvers between two Floating Spacecraft Simulators. The maneuvers are planar and conducted autonomously in a cooperative mode. The proposed guidance strategy is based on the direct method known as Inverse Dynamics in the Virtual Domain, and the nonlinear programming solver known as Sequential Gradient-Restoration Algorithm. The combination of these methods allows for the quick prototyping of near-optimal trajectories, and results in an implementable tool for real-time closed-loop maneuvering. The experimental results included in this paper were obtained by exploiting the recently upgraded Floating Spacecraft-Simulator Testbed of the Spacecraft Robotics Laboratory at the Naval Postgraduate School. A direct performances comparison, in terms of maneuver energy and propellant mass, between the proposed guidance strategy and a LQR controller, demonstrates the effectiveness of the method.

A trajectory planning scheme for spacecraft in the space station environment. M.S. Thesis - University of California

NASA Technical Reports Server (NTRS)

Soller, Jeffrey Alan; Grunwald, Arthur J.; Ellis, Stephen R.

1991-01-01

Simulated annealing is used to solve a minimum fuel trajectory problem in the space station environment. The environment is special because the space station will define a multivehicle environment in space. The optimization surface is a complex nonlinear function of the initial conditions of the chase and target crafts. Small permutations in the input conditions can result in abrupt changes to the optimization surface. Since no prior knowledge about the number or location of local minima on the surface is available, the optimization must be capable of functioning on a multimodal surface. It was reported in the literature that the simulated annealing algorithm is more effective on such surfaces than descent techniques using random starting points. The simulated annealing optimization was found to be capable of identifying a minimum fuel, two-burn trajectory subject to four constraints which are integrated into the optimization using a barrier method. The computations required to solve the optimization are fast enough that missions could be planned on board the space station. Potential applications for on board planning of missions are numerous. Future research topics may include optimal planning of multi-waypoint maneuvers using a knowledge base to guide the optimization, and a study aimed at developing robust annealing schedules for potential on board missions.

Optimization of Composite Structures with Curved Fiber Trajectories

NASA Astrophysics Data System (ADS)

Lemaire, Etienne; Zein, Samih; Bruyneel, Michael

2014-06-01

This paper studies the problem of optimizing composites shells manufactured using Automated Tape Layup (ATL) or Automated Fiber Placement (AFP) processes. The optimization procedure relies on a new approach to generate equidistant fiber trajectories based on Fast Marching Method. Starting with a (possibly curved) reference fiber direction defined on a (possibly curved) meshed surface, the new method allows determining fibers orientation resulting from a uniform thickness layup. The design variables are the parameters defining the position and the shape of the reference curve which results in very few design variables. Thanks to this efficient parameterization, maximum stiffness optimization numerical applications are proposed. The shape of the design space is discussed, regarding local and global optimal solutions.

Preliminary Analysis of Optimal Round Trip Lunar Missions

NASA Astrophysics Data System (ADS)

Gagg Filho, L. A.; da Silva Fernandes, S.

2015-10-01

A study of optimal bi-impulsive trajectories of round trip lunar missions is presented in this paper. The optimization criterion is the total velocity increment. The dynamical model utilized to describe the motion of the space vehicle is a full lunar patched-conic approximation, which embraces the lunar patched-conic of the outgoing trip and the lunar patched-conic of the return mission. Each one of these parts is considered separately to solve an optimization problem of two degrees of freedom. The Sequential Gradient Restoration Algorithm (SGRA) is employed to achieve the optimal solutions, which show a good agreement with the ones provided by literature, and, proved to be consistent with the image trajectories theorem.

Noncoplanar VMAT for nasopharyngeal tumors: Plan quality versus treatment time.

PubMed

Wild, Esther; Bangert, Mark; Nill, Simeon; Oelfke, Uwe

2015-05-01

The authors investigated the potential of optimized noncoplanar irradiation trajectories for volumetric modulated arc therapy (VMAT) treatments of nasopharyngeal patients and studied the trade-off between treatment plan quality and delivery time in radiation therapy. For three nasopharyngeal patients, the authors generated treatment plans for nine different delivery scenarios using dedicated optimization methods. They compared these scenarios according to dose characteristics, number of beam directions, and estimated delivery times. In particular, the authors generated the following treatment plans: (1) a 4π plan, which is a not sequenced, fluence optimized plan that uses beam directions from approximately 1400 noncoplanar directions and marks a theoretical upper limit of the treatment plan quality, (2) a coplanar 2π plan with 72 coplanar beam directions as pendant to the noncoplanar 4π plan, (3) a coplanar VMAT plan, (4) a coplanar step and shoot (SnS) plan, (5) a beam angle optimized (BAO) coplanar SnS IMRT plan, (6) a noncoplanar BAO SnS plan, (7) a VMAT plan with rotated treatment couch, (8) a noncoplanar VMAT plan with an optimized great circle around the patient, and (9) a noncoplanar BAO VMAT plan with an arbitrary trajectory around the patient. VMAT using optimized noncoplanar irradiation trajectories reduced the mean and maximum doses in organs at risk compared to coplanar VMAT plans by 19% on average while the target coverage remains constant. A coplanar BAO SnS plan was superior to coplanar SnS or VMAT; however, noncoplanar plans like a noncoplanar BAO SnS plan or noncoplanar VMAT yielded a better plan quality than the best coplanar 2π plan. The treatment plan quality of VMAT plans depended on the length of the trajectory. The delivery times of noncoplanar VMAT plans were estimated to be 6.5 min in average; 1.6 min longer than a coplanar plan but on average 2.8 min faster than a noncoplanar SnS plan with comparable treatment plan quality. The authors' study reconfirms the dosimetric benefits of noncoplanar irradiation of nasopharyngeal tumors. Both SnS using optimized noncoplanar beam ensembles and VMAT using an optimized, arbitrary, noncoplanar trajectory enabled dose reductions in organs at risk compared to coplanar SnS and VMAT. Using great circles or simple couch rotations to implement noncoplanar VMAT, however, was not sufficient to yield meaningful improvements in treatment plan quality. The authors estimate that noncoplanar VMAT using arbitrary optimized irradiation trajectories comes at an increased delivery time compared to coplanar VMAT yet at a decreased delivery time compared to noncoplanar SnS IMRT.

Development of a Smooth Trajectory Maneuver Method to Accommodate the Ares I Flight Control Constraints

NASA Technical Reports Server (NTRS)

Pinson, Robin M.; Schmitt, Terri L.; Hanson, John M.

2008-01-01

Six degree-of-freedom (DOF) launch vehicle trajectories are designed to follow an optimized 3-DOF reference trajectory. A vehicle has a finite amount of control power that it can allocate to performing maneuvers. Therefore, the 3-DOF trajectory must be designed to refrain from using 100% of the allowable control capability to perform maneuvers, saving control power for handling off-nominal conditions, wind gusts and other perturbations. During the Ares I trajectory analysis, two maneuvers were found to be hard for the control system to implement; a roll maneuver prior to the gravity turn and an angle of attack maneuver immediately after the J-2X engine start-up. It was decided to develop an approach for creating smooth maneuvers in the optimized reference trajectories that accounts for the thrust available from the engines. A feature of this method is that no additional angular velocity in the direction of the maneuver has been added to the vehicle after the maneuver completion. This paper discusses the equations behind these new maneuvers and their implementation into the Ares I trajectory design cycle. Also discussed is a possible extension to adjusting closed-loop guidance.

Utilization of UARS Data in Validation of Photochemical and Dynamical Mechanism in Stratospheric Models

NASA Technical Reports Server (NTRS)

Rodriquez, Jose M.; Hu, Wenjie; Ko, Malcolm K. W.

1995-01-01

We proposed model-data intercomparison studies for UARS data. In the past three months, we have been working on constructing analysis tools to diagnose the UARS data. The 'Trajectory mapping' technique, which was developed by Morris (1994), is adaptable to generate synoptic maps of trace gas data from asynoptic observations. An in-house trajectory model (kinematic methods following Merrill et al., 1986 and Pickering et al., 1994) has been developed in AER under contract with NASA/ACMAP and the trajectory mapping tool has been applied to analyze UARS measurement.

Application of Metaheuristic and Deterministic Algorithms for Aircraft Reference Trajectory Optimization =

NASA Astrophysics Data System (ADS)

Murrieta Mendoza, Alejandro

Aircraft reference trajectory is an alternative method to reduce fuel consumption, thus the pollution released to the atmosphere. Fuel consumption reduction is of special importance for two reasons: first, because the aeronautical industry is responsible of 2% of the CO2 released to the atmosphere, and second, because it will reduce the flight cost. The aircraft fuel model was obtained from a numerical performance database which was created and validated by our industrial partner from flight experimental test data. A new methodology using the numerical database was proposed in this thesis to compute the fuel burn for a given trajectory. Weather parameters such as wind and temperature were taken into account as they have an important effect in fuel burn. The open source model used to obtain the weather forecast was provided by Weather Canada. A combination of linear and bi-linear interpolations allowed finding the required weather data. The search space was modelled using different graphs: one graph was used for mapping the different flight phases such as climb, cruise and descent, and another graph was used for mapping the physical space in which the aircraft would perform its flight. The trajectory was optimized in its vertical reference trajectory using the Beam Search algorithm, and a combination of the Beam Search algorithm with a search space reduction technique. The trajectory was optimized simultaneously for the vertical and lateral reference navigation plans while fulfilling a Required Time of Arrival constraint using three different metaheuristic algorithms: the artificial bee's colony, and the ant colony optimization. Results were validated using the software FlightSIMRTM, a commercial Flight Management System, an exhaustive search algorithm, and as flown flights obtained from flightawareRTM. All algorithms were able to reduce the fuel burn, and the flight costs. None None None None None None None

A mathematical tool to generate complex whole body motor tasks and test hypotheses on underlying motor planning.

PubMed

Tagliabue, Michele; Pedrocchi, Alessandra; Pozzo, Thierry; Ferrigno, Giancarlo

2008-01-01

In spite of the complexity of human motor behavior, difficulties in mathematical modeling have restricted to rather simple movements attempts to identify the motor planning criterion used by the central nervous system. This paper presents a novel-simulation technique able to predict the "desired trajectory" corresponding to a wide range of kinematic and kinetic optimality criteria for tasks involving many degrees of freedom and the coordination between goal achievement and balance maintenance. Employment of proper time discretization, inverse dynamic methods and constrained optimization technique are combined. The application of this simulator to a planar whole body pointing movement shows its effectiveness in managing system nonlinearities and instability as well as in ensuring the anatomo-physiological feasibility of predicted motor plans. In addition, the simulator's capability to simultaneously optimize competing movement aspects represents an interesting opportunity for the motor control community, in which the coexistence of several controlled variables has been hypothesized.

Real-time terminal area trajectory planning for runway independent aircraft

NASA Astrophysics Data System (ADS)

Xue, Min

The increasing demand for commercial air transportation results in delays due to traffic queues that form bottlenecks along final approach and departure corridors. In urban areas, it is often infeasible to build new runways, and regardless of automation upgrades traffic must remain separated to avoid the wakes of previous aircraft. Vertical or short takeoff and landing aircraft as Runway Independent Aircraft (RIA) can increase passenger throughput at major urban airports via the use of vertiports or stub runways. The concept of simultaneous non-interfering (SNI) operations has been proposed to reduce traffic delays by creating approach and departure corridors that do not intersect existing fixed-wing routes. However, SNI trajectories open new routes that may overfly noise-sensitive areas, and RIA may generate more noise than traditional jet aircraft, particularly on approach. In this dissertation, we develop efficient SNI noise abatement procedures applicable to RIA. First, we introduce a methodology based on modified approximated cell-decomposition and Dijkstra's search algorithm to optimize longitudinal plane (2-D) RIA trajectories over a cost function that minimizes noise, time, and fuel use. Then, we extend the trajectory optimization model to 3-D with a k-ary tree as the discrete search space. We incorporate geography information system (GIS) data, specifically population, into our objective function, and focus on a practical case study: the design of SNI RIA approach procedures to Baltimore-Washington International airport. Because solutions were represented as trim state sequences, we incorporated smooth transition between segments to enable more realistic cost estimates. Due to the significant computational complexity, we investigated alternative more efficient optimization techniques applicable to our nonlinear, non-convex, heavily constrained, and discontinuous objective function. Comparing genetic algorithm (GA) and adaptive simulated annealing (ASA) with our original Dijkstra's algorithm, ASA is identified as the most efficient algorithm for terminal area trajectory optimization. The effects of design parameter discretization are analyzed, with results indicating a SNI procedure with 3-4 segments effectively balances simplicity with cost minimization. Finally, pilot control commands were implemented and generated via optimization-base inverse simulation to validate execution of the optimal approach trajectories.

Trajectory optimization for dynamic couch rotation during volumetric modulated arc radiotherapy

NASA Astrophysics Data System (ADS)

Smyth, Gregory; Bamber, Jeffrey C.; Evans, Philip M.; Bedford, James L.

2013-11-01

Non-coplanar radiation beams are often used in three-dimensional conformal and intensity modulated radiotherapy to reduce dose to organs at risk (OAR) by geometric avoidance. In volumetric modulated arc radiotherapy (VMAT) non-coplanar geometries are generally achieved by applying patient couch rotations to single or multiple full or partial arcs. This paper presents a trajectory optimization method for a non-coplanar technique, dynamic couch rotation during VMAT (DCR-VMAT), which combines ray tracing with a graph search algorithm. Four clinical test cases (partial breast, brain, prostate only, and prostate and pelvic nodes) were used to evaluate the potential OAR sparing for trajectory-optimized DCR-VMAT plans, compared with standard coplanar VMAT. In each case, ray tracing was performed and a cost map reflecting the number of OAR voxels intersected for each potential source position was generated. The least-cost path through the cost map, corresponding to an optimal DCR-VMAT trajectory, was determined using Dijkstra’s algorithm. Results show that trajectory optimization can reduce dose to specified OARs for plans otherwise comparable to conventional coplanar VMAT techniques. For the partial breast case, the mean heart dose was reduced by 53%. In the brain case, the maximum lens doses were reduced by 61% (left) and 77% (right) and the globes by 37% (left) and 40% (right). Bowel mean dose was reduced by 15% in the prostate only case. For the prostate and pelvic nodes case, the bowel V50 Gy and V60 Gy were reduced by 9% and 45% respectively. Future work will involve further development of the algorithm and assessment of its performance over a larger number of cases in site-specific cohorts.

Strategies for the sustained human exploration of Mars

NASA Astrophysics Data System (ADS)

Landau, Damon Frederick

A variety of mission scenarios are compared in this thesis to assess the strengths and weaknesses of options for Mars exploration. The mission design space is modeled along two dimensions: trajectory architectures and propulsion system technologies. Direct, semi-direct, stop-over, semi-cycler, and cycler architectures are examined, and electric propulsion, nuclear thermal rockets, methane and oxygen production on Mars, Mars water excavation, aerocapture, and reusable propulsion systems are included in the technology assessment. The mission sensitivity to crew size, vehicle masses, and crew travel time is also examined. The primary figure of merit for a mission scenario is the injected mass to low-Earth orbit (IMLEO), though technology readiness levels (TRL) are also included. Several elements in the architecture dimension are explored in more detail. The Earth-Mars semi-cycler architecture is introduced and five families of Earth-Mars semi-cycler trajectories are presented along with optimized itineraries. Optimized cycler trajectories are also presented. In addition to Earth-Mars semi-cycler and cycler trajectories, conjunction-class, free-return, Mars-Earth semi-cycler, and low-thrust trajectories are calculated. Design parameters for optimal DeltaV trajectories are provided over a range of flight times (from 120 to 270 days) and launch years (between 2009 and 2022). Unlike impulsive transfers, the mass-optimal low-thrust trajectory depends strongly on the thrust and specific impulse of the propulsion system. A low-thrust version of the rocket equation is provided where the initial mass or thrust may be minimized by varying the initial acceleration and specific impulse. Planet-centered operations are also examined. A method to rotate a parking orbit about the line of apsides to achieve the proper orientation at departure is discussed, thus coupling the effects of parking-orbit orientation with the interplanetary trajectories. Also, a guidance algorithm for rendezvous during flybys in semi-cycler and cycler missions is presented with a control law for final approach. A forty-year plan to establish a permanent base on Mars is detailed and methods to expand the base are discussed. Once a large base is established, one-, two-, or three-vehicle systems may sustain the colonization of Mars.

Ares I-X Test Flight Reference Trajectory Development

NASA Technical Reports Server (NTRS)

Starr, Brett R.; Gumbert, Clyde R.; Tartabini, Paul V.

2011-01-01

Ares I-X was the first test flight of NASA's Constellation Program's Ares I crew launch vehicle. Ares I is a two stage to orbit launch vehicle that provides crew access to low Earth orbit for NASA's future manned exploration missions. The Ares I first stage consists of a Shuttle solid rocket motor (SRM) modified to include an additional propellant segment and a liquid propellant upper stage with an Apollo J2X engine modified to increase its thrust capability. The modified propulsion systems were not available for the first test flight, thus the test had to be conducted with an existing Shuttle 4 segment reusable solid rocket motor (RSRM) and an inert Upper Stage. The test flight's primary objective was to demonstrate controllability of an Ares I vehicle during first stage boost and the ability to perform a successful separation. In order to demonstrate controllability, the Ares I-X ascent control algorithms had to maintain stable flight throughout a flight environment equivalent to Ares I. The goal of the test flight reference trajectory development was to design a boost trajectory using the existing RSRM that results in a flight environment equivalent to Ares I. A trajectory similarity metric was defined as the integrated difference between the Ares I and Ares I-X Mach versus dynamic pressure relationships. Optimization analyses were performed that minimized the metric by adjusting the inert upper stage weight and the ascent steering profile. The sensitivity of the optimal upper stage weight and steering profile to launch month was also investigated. A response surface approach was used to verify the optimization results. The analyses successfully defined monthly ascent trajectories that matched the Ares I reference trajectory dynamic pressure versus Mach number relationship to within 10% through Mach 3.5. The upper stage weight required to achieve the match was found to be feasible and varied less than 5% throughout the year. The paper will discuss the flight test requirements, provide Ares I-X vehicle background, discuss the optimization analyses used to meet the requirements, present analysis results, and compare the reference trajectory to the reconstructed flight trajectory.

Modeling human decision making behavior in supervisory control

NASA Technical Reports Server (NTRS)

Tulga, M. K.; Sheridan, T. B.

1977-01-01

An optimal decision control model was developed, which is based primarily on a dynamic programming algorithm which looks at all the available task possibilities, charts an optimal trajectory, and commits itself to do the first step (i.e., follow the optimal trajectory during the next time period), and then iterates the calculation. A Bayesian estimator was included which estimates the tasks which might occur in the immediate future and provides this information to the dynamic programming routine. Preliminary trials comparing the human subject's performance to that of the optimal model show a great similarity, but indicate that the human skips certain movements which require quick change in strategy.

Walking the Filament of Feasibility: Global Optimization of Highly-Constrained, Multi-Modal Interplanetary Trajectories Using a Novel Stochastic Search Technique

NASA Technical Reports Server (NTRS)

Englander, Arnold C.; Englander, Jacob A.

2017-01-01

Interplanetary trajectory optimization problems are highly complex and are characterized by a large number of decision variables and equality and inequality constraints as well as many locally optimal solutions. Stochastic global search techniques, coupled with a large-scale NLP solver, have been shown to solve such problems but are inadequately robust when the problem constraints become very complex. In this work, we present a novel search algorithm that takes advantage of the fact that equality constraints effectively collapse the solution space to lower dimensionality. This new approach walks the filament'' of feasibility to efficiently find the global optimal solution.

WE-AB-209-06: Dynamic Collimator Trajectory Algorithm for Use in VMAT Treatment Deliveries

DOE Office of Scientific and Technical Information (OSTI.GOV)

MacDonald, L; Thomas, C; Syme, A

2016-06-15

Purpose: To develop advanced dynamic collimator positioning algorithms for optimal beam’s-eye-view (BEV) fitting of targets in VMAT procedures, including multiple metastases stereotactic radiosurgery procedures. Methods: A trajectory algorithm was developed, which can dynamically modify the angle of the collimator as a function of VMAT control point to provide optimized collimation of target volume(s). Central to this algorithm is a concept denoted “whitespace”, defined as area within the jaw-defined BEV field, outside of the PTV, and not shielded by the MLC when fit to the PTV. Calculating whitespace at all collimator angles and every control point, a two-dimensional topographical map depictingmore » the tightness-of-fit of the MLC was generated. A variety of novel searching algorithms identified a number of candidate trajectories of continuous collimator motion. Ranking these candidate trajectories according to their accrued whitespace value produced an optimal solution for navigation of this map. Results: All trajectories were normalized to minimum possible (i.e. calculated without consideration of collimator motion constraints) accrued whitespace. On an acoustic neuroma case, a random walk algorithm generated a trajectory with 151% whitespace; random walk including a mandatory anchor point improved this to 148%; gradient search produced a trajectory with 137%; and bi-directional gradient search generated a trajectory with 130% whitespace. For comparison, a fixed collimator angle of 30° and 330° accumulated 272% and 228% of whitespace, respectively. The algorithm was tested on a clinical case with two metastases (single isocentre) and identified collimator angles that allow for simultaneous irradiation of the PTVs while minimizing normal tissue irradiation. Conclusion: Dynamic collimator trajectories have the potential to improve VMAT deliveries through increased efficiency and reduced normal tissue dose, especially in treatment of multiple cranial metastases, without significant safety concerns that hinder immediate clinical implementation.« less

Fast state transfer in a Λ-system: a shortcut-to-adiabaticity approach to robust and resource optimized control

NASA Astrophysics Data System (ADS)

Mortensen, Henrik Lund; Sørensen, Jens Jakob W. H.; Mølmer, Klaus; Sherson, Jacob Friis

2018-02-01

We propose an efficient strategy to find optimal control functions for state-to-state quantum control problems. Our procedure first chooses an input state trajectory, that can realize the desired transformation by adiabatic variation of the system Hamiltonian. The shortcut-to-adiabaticity formalism then provides a control Hamiltonian that realizes the reference trajectory exactly but on a finite time scale. As the final state is achieved with certainty, we define a cost functional that incorporates the resource requirements and a perturbative expression for robustness. We optimize this functional by systematically varying the reference trajectory. We demonstrate the method by application to population transfer in a laser driven three-level Λ-system, where we find solutions that are fast and robust against perturbations while maintaining a low peak laser power.

Primer vector theory applied to the linear relative-motion equations. [for N-impulse space trajectory optimization

NASA Technical Reports Server (NTRS)

Jezewski, D.

1980-01-01

Prime vector theory is used in analyzing a set of linear relative-motion equations - the Clohessy-Wiltshire (C/W) equations - to determine the criteria and necessary conditions for an optimal N-impulse trajectory. The analysis develops the analytical criteria for improving a solution by: (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of: (1) fixed-end conditions, two impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized renezvous problem.

Optimal reorientation of asymmetric underactuated spacecraft using differential flatness and receding horizon control

NASA Astrophysics Data System (ADS)

Cai, Wei-wei; Yang, Le-ping; Zhu, Yan-wei

2015-01-01

This paper presents a novel method integrating nominal trajectory optimization and tracking for the reorientation control of an underactuated spacecraft with only two available control torque inputs. By employing a pseudo input along the uncontrolled axis, the flatness property of a general underactuated spacecraft is extended explicitly, by which the reorientation trajectory optimization problem is formulated into the flat output space with all the differential constraints eliminated. Ultimately, the flat output optimization problem is transformed into a nonlinear programming problem via the Chebyshev pseudospectral method, which is improved by the conformal map and barycentric rational interpolation techniques to overcome the side effects of the differential matrix's ill-conditions on numerical accuracy. Treating the trajectory tracking control as a state regulation problem, we develop a robust closed-loop tracking control law using the receding-horizon control method, and compute the feedback control at each control cycle rapidly via the differential transformation method. Numerical simulation results show that the proposed control scheme is feasible and effective for the reorientation maneuver.

Route Sanitizer: Connected Vehicle Trajectory De-Identification Tool

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carter, Jason M; Ferber, Aaron E

Route Sanitizer is ORNL's connected vehicle moving object database de-identification tool and a graphical user interface to ORNL's connected vehicle de-identification algorithm. It uses the Google Chrome (soon to be Electron) platform so it will run on different computing platforms. The basic de-identification strategy is record redaction: portions of a vehicle trajectory (e.g. sequences of precise temporal spatial records) are removed. It does not alter retained records. The algorithm uses custom techniques to find areas within trajectories that may be considered private, then it suppresses those in addition to enough of the trajectory surrounding those locations to protect against "inferencemore » attacks" in a mathematically sound way. Map data is integrated into the process to make this possible.« less

System and method for bullet tracking and shooter localization

DOEpatents

Roberts, Randy S [Livermore, CA; Breitfeller, Eric F [Dublin, CA

2011-06-21

A system and method of processing infrared imagery to determine projectile trajectories and the locations of shooters with a high degree of accuracy. The method includes image processing infrared image data to reduce noise and identify streak-shaped image features, using a Kalman filter to estimate optimal projectile trajectories, updating the Kalman filter with new image data, determining projectile source locations by solving a combinatorial least-squares solution for all optimal projectile trajectories, and displaying all of the projectile source locations. Such a shooter-localization system is of great interest for military and law enforcement applications to determine sniper locations, especially in urban combat scenarios.

Optimal design of near-Earth asteroid sample-return trajectories in the Sun-Earth-Moon system

NASA Astrophysics Data System (ADS)

He, Shengmao; Zhu, Zhengfan; Peng, Chao; Ma, Jian; Zhu, Xiaolong; Gao, Yang

2016-08-01

In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi-body dynamics, considering the gravitational forces of the Sun, Earth, and Moon. It is proposed that an electric-propulsion spacecraft initially parking in a circular 200-km-altitude low Earth orbit is expected to rendezvous with an asteroid and carry as much sample as possible back to the Earth in a 10-year time frame. The team from the Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences has reported a solution with an asteroid sample mass of 328 tons, which is ranked first in the competition. In this article, we will present our design and optimization methods, primarily including overall analysis, target selection, escape from and capture by the Earth-Moon system, and optimization of impulsive and low-thrust trajectories that are modeled in multi-body dynamics. The orbital resonance concept and lunar gravity assists are considered key techniques employed for trajectory design. The reported solution, preliminarily revealing the feasibility of returning a hundreds-of-tons asteroid or asteroid sample, envisions future space missions relating to near-Earth asteroid exploration.

A study of numerical methods for computing reentry trajectories for shuttle-type space vehicles

NASA Technical Reports Server (NTRS)

1972-01-01

The reuseable exterior insulation system (REI) is studied to determine the optimal reentry trajectory for a space shuttle, which minimizes the heat input to the fuselage. The REI is composed of titanium, covered by a surface insulation material. The method of perturbation functions was used to generate the trajectories, and proved to be an effective technique for generating families of solutions, once an initial trajectory has been obtained.

Single-particle trajectories reveal two-state diffusion-kinetics of hOGG1 proteins on DNA.

PubMed

Vestergaard, Christian L; Blainey, Paul C; Flyvbjerg, Henrik

2018-03-16

We reanalyze trajectories of hOGG1 repair proteins diffusing on DNA. A previous analysis of these trajectories with the popular mean-squared-displacement approach revealed only simple diffusion. Here, a new optimal estimator of diffusion coefficients reveals two-state kinetics of the protein. A simple, solvable model, in which the protein randomly switches between a loosely bound, highly mobile state and a tightly bound, less mobile state is the simplest possible dynamic model consistent with the data. It yields accurate estimates of hOGG1's (i) diffusivity in each state, uncorrupted by experimental errors arising from shot noise, motion blur and thermal fluctuations of the DNA; (ii) rates of switching between states and (iii) rate of detachment from the DNA. The protein spends roughly equal time in each state. It detaches only from the loosely bound state, with a rate that depends on pH and the salt concentration in solution, while its rates for switching between states are insensitive to both. The diffusivity in the loosely bound state depends primarily on pH and is three to ten times higher than in the tightly bound state. We propose and discuss some new experiments that take full advantage of the new tools of analysis presented here.

A computational intelligence approach to the Mars Precision Landing problem

NASA Astrophysics Data System (ADS)

Birge, Brian Kent, III

Various proposed Mars missions, such as the Mars Sample Return Mission (MRSR) and the Mars Smart Lander (MSL), require precise re-entry terminal position and velocity states. This is to achieve mission objectives including rendezvous with a previous landed mission, or reaching a particular geographic landmark. The current state of the art footprint is in the magnitude of kilometers. For this research a Mars Precision Landing is achieved with a landed footprint of no more than 100 meters, for a set of initial entry conditions representing worst guess dispersions. Obstacles to reducing the landed footprint include trajectory dispersions due to initial atmospheric entry conditions (entry angle, parachute deployment height, etc.), environment (wind, atmospheric density, etc.), parachute deployment dynamics, unavoidable injection error (propagated error from launch on), etc. Weather and atmospheric models have been developed. Three descent scenarios have been examined. First, terminal re-entry is achieved via a ballistic parachute with concurrent thrusting events while on the parachute, followed by a gravity turn. Second, terminal re-entry is achieved via a ballistic parachute followed by gravity turn to hover and then thrust vector to desired location. Third, a guided parafoil approach followed by vectored thrusting to reach terminal velocity is examined. The guided parafoil is determined to be the best architecture. The purpose of this study is to examine the feasibility of using a computational intelligence strategy to facilitate precision planetary re-entry, specifically to take an approach that is somewhat more intuitive and less rigid, and see where it leads. The test problems used for all research are variations on proposed Mars landing mission scenarios developed by NASA. A relatively recent method of evolutionary computation is Particle Swarm Optimization (PSO), which can be considered to be in the same general class as Genetic Algorithms. An improvement over the regular PSO algorithm, allowing tracking of nonstationary error functions is detailed. Continued refinement of PSO in the larger research community comes from attempts to understand human-human social interaction as well as analysis of the emergent behavior. Using PSO and the parafoil scenario, optimized reference trajectories are created for an initial condition set of 76 states, representing the convex hull of 2001 states from an early Monte Carlo analysis. The controls are a set series of bank angles followed by a set series of 3DOF thrust vectoring. The reference trajectories are used to train an Artificial Neural Network Reference Trajectory Generator (ANNTraG), with the (marginal) ability to generalize a trajectory from initial conditions it has never been presented. The controls here allow continuous change in bank angle as well as thrust vector. The optimized reference trajectories represent the best achievable trajectory given the initial condition. Steps toward a closed loop neural controller with online learning updates are examined. The inner loop of the simulation employs the Program to Optimize Simulated Trajectories (POST) as the basic model, containing baseline dynamics and state generation. This is controlled from a MATLAB shell that directs the optimization, learning, and control strategy. Using mainly bank angle guidance coupled with CI strategies, the set of achievable reference trajectories are shown to be 88% under 10 meters, a significant improvement in the state of the art. Further, the automatic real-time generation of realistic reference trajectories in the presence of unknown initial conditions is shown to have promise. The closed loop CI guidance strategy is outlined. An unexpected advance came from the effort to optimize the optimization, where the PSO algorithm was improved with the capability for tracking a changing error environment.

Application of dynamic programming to control khuzestan water resources system

USGS Publications Warehouse

Jamshidi, M.; Heidari, M.

1977-01-01

An approximate optimization technique based on discrete dynamic programming called discrete differential dynamic programming (DDDP), is employed to obtain the near optimal operation policies of a water resources system in the Khuzestan Province of Iran. The technique makes use of an initial nominal state trajectory for each state variable, and forms corridors around the trajectories. These corridors represent a set of subdomains of the entire feasible domain. Starting with such a set of nominal state trajectories, improvements in objective function are sought within the corridors formed around them. This leads to a set of new nominal trajectories upon which more improvements may be sought. Since optimization is confined to a set of subdomains, considerable savings in memory and computer time are achieved over that of conventional dynamic programming. The Kuzestan water resources system considered in this study is located in southwest Iran, and consists of two rivers, three reservoirs, three hydropower plants, and three irrigable areas. Data and cost benefit functions for the analysis were obtained either from the historical records or from similar studies. ?? 1977.

A New Maneuver for Escape Trajectories

NASA Technical Reports Server (NTRS)

Adams, Robert B.

2008-01-01

This presentation put forth a new maneuver for escape trajectories and specifically sought to find an analytical approximation for medium thrust trajectories. In most low thrust derivations the idea is that escape velocity is best achieved by accelerating along the velocity vector. The reason for this is that change in specific orbital energy is a function of velocity and acceleration. However, Levin (1952) suggested that while this is a locally optimal solution it might not be a globally optimal one. Turning acceleration inward would drop periapse giving a higher velocity later in the trajectory. Acceleration at that point would be dotted against a higher magnitude V giving a greater rate of change of mechanical energy. The author then hypothesized that decelerating from the initial orbit and then accelerating at periapse would not lead to a gain in greater specific orbital energy--however, the hypothesis was incorrect. After considerable derivation it was determined that this new maneuver outperforms a direct burn when the overall DeltaV budget exceeds the initial orbital velocity (the author has termed this the Heinlein maneuver). The author provides a physical explanation for this maneuver and presents optimization analyses.

Earth-to-Orbit Laser Launch Simulation for a Lightcraft Technology Demonstrator

NASA Astrophysics Data System (ADS)

Richard, J. C.; Morales, C.; Smith, W. L.; Myrabo, L. N.

2006-05-01

Optimized laser launch trajectories have been developed for a 1.4 m diameter, 120 kg (empty mass) Lightcraft Technology Demonstrator (LTD). The lightcraft's combined-cycle airbreathing/rocket engine is designed for single-stage-to-orbit flights with a mass ratio of 2 propelled by a 100 MW class ground-based laser built on a 3 km mountain peak. Once in orbit, the vehicle becomes an autonomous micro-satellite. Two types of trajectories were simulated with the SORT (Simulation and Optimization of Rocket Trajectories) software package: a) direct GBL boost to orbit, and b) GBL boost aided by laser relay satellite. Several new subroutines were constructed for SORT to input engine performance (as a function of Mach number and altitude), vehicle aerodynamics, guidance algorithms, and mass history. A new guidance/steering option required the lightcraft to always point at the GBL or laser relay satellite. SORT iterates on trajectory parameters to optimize vehicle performance, achieve a desired criteria, or constrain the solution to avoid some specific limit. The predicted laser-boost performance for the LTD is undoubtedly revolutionary, and SORT simulations have helped to define this new frontier.

Multidisciplinary Optimization Branch Experience Using iSIGHT Software

NASA Technical Reports Server (NTRS)

Padula, S. L.; Korte, J. J.; Dunn, H. J.; Salas, A. O.

1999-01-01

The Multidisciplinary Optimization (MDO) Branch at NASA Langley is investigating frameworks for supporting multidisciplinary analysis and optimization research. A framework provides software and system services to integrate computational tasks and allows the researcher to concentrate more on the application and less on the programming details. A framework also provides a common working environment and a full range of optimization tools, and so increases the productivity of multidisciplinary research teams. Finally, a framework enables staff members to develop applications for use by disciplinary experts in other organizations. This year, the MDO Branch has gained experience with the iSIGHT framework. This paper describes experiences with four aerospace applications, including: (1) reusable launch vehicle sizing, (2) aerospike nozzle design, (3) low-noise rotorcraft trajectories, and (4) acoustic liner design. Brief overviews of each problem are provided, including the number and type of disciplinary codes and computation time estimates. In addition, the optimization methods, objective functions, design variables, and constraints are described for each problem. For each case, discussions on the advantages and disadvantages of using the iSIGHT framework are provided as well as notes on the ease of use of various advanced features and suggestions for areas of improvement.

Development of a new integrated local trajectory planning and tracking control framework for autonomous ground vehicles

NASA Astrophysics Data System (ADS)

Li, Xiaohui; Sun, Zhenping; Cao, Dongpu; Liu, Daxue; He, Hangen

2017-03-01

This study proposes a novel integrated local trajectory planning and tracking control (ILTPTC) framework for autonomous vehicles driving along a reference path with obstacles avoidance. For this ILTPTC framework, an efficient state-space sampling-based trajectory planning scheme is employed to smoothly follow the reference path. A model-based predictive path generation algorithm is applied to produce a set of smooth and kinematically-feasible paths connecting the initial state with the sampling terminal states. A velocity control law is then designed to assign a speed value at each of the points along the generated paths. An objective function considering both safety and comfort performance is carefully formulated for assessing the generated trajectories and selecting the optimal one. For accurately tracking the optimal trajectory while overcoming external disturbances and model uncertainties, a combined feedforward and feedback controller is developed. Both simulation analyses and vehicle testing are performed to verify the effectiveness of the proposed ILTPTC framework, and future research is also briefly discussed.

Designing for Cost

NASA Technical Reports Server (NTRS)

Dean, Edwin B.; Unal, Resit

1991-01-01

Designing for cost is a state of mind. Of course, a lot of technical knowledge is required and the use of appropriate tools will improve the process. Unfortunately, the extensive use of weight based cost estimating relationships has generated a perception in the aerospace community that the primary way to reduce cost is to reduce weight. Wrong! Based upon an approximation of an industry accepted formula, the PRICE H (tm) production-production equation, Dean demonstrated theoretically that the optimal trajectory for cost reduction is predominantly in the direction of system complexity reduction, not system weight reduction. Thus the phrase "keep it simple" is a primary state of mind required for reducing cost throughout the design process.

An aircraft noise pollution model for trajectory optimization

NASA Technical Reports Server (NTRS)

Barkana, A.; Cook, G.

1976-01-01

A mathematical model describing the generation of aircraft noise is developed with the ultimate purpose of reducing noise (noise-optimizing landing trajectories) in terminal areas. While the model is for a specific aircraft (Boeing 737), the methodology would be applicable to a wide variety of aircraft. The model is used to obtain a footprint on the ground inside of which the noise level is at or above 70 dB.

Time-optimal control of the spacecraft trajectories in the Earth-Moon system

NASA Astrophysics Data System (ADS)

Starinova, O. L.; Fain, M. K.; Materova, I. L.

2017-01-01

This paper outlines the multiparametric optimization of the L1-L2 and L2-L1 missions in the Earth-Moon system using electric propulsion. The optimal control laws are obtained using the Fedorenko successful linearization method to estimate the derivatives and the gradient method to optimize the control laws. The study of the transfers is based on the restricted circular three-body problem. The mathematical model of the missions is described within the barycentric system of coordinates. The optimization criterion is the total flight time. The perturbation from the Earth, the Moon and the Sun are taking into account. The impact of the shaded areas, induced by the Earth and the Moon, is also accounted. As the results of the optimization we obtained optimal control laws, corresponding trajectories and minimal total flight times.

An Evaluation of a Flight Deck Interval Management Algorithm Including Delayed Target Trajectories

NASA Technical Reports Server (NTRS)

Swieringa, Kurt A.; Underwood, Matthew C.; Barmore, Bryan; Leonard, Robert D.

2014-01-01

NASA's first Air Traffic Management (ATM) Technology Demonstration (ATD-1) was created to facilitate the transition of mature air traffic management technologies from the laboratory to operational use. The technologies selected for demonstration are the Traffic Management Advisor with Terminal Metering (TMA-TM), which provides precise timebased scheduling in the terminal airspace; Controller Managed Spacing (CMS), which provides controllers with decision support tools enabling precise schedule conformance; and Interval Management (IM), which consists of flight deck automation that enables aircraft to achieve or maintain precise in-trail spacing. During high demand operations, TMA-TM may produce a schedule and corresponding aircraft trajectories that include delay to ensure that a particular aircraft will be properly spaced from other aircraft at each schedule waypoint. These delayed trajectories are not communicated to the automation onboard the aircraft, forcing the IM aircraft to use the published speeds to estimate the target aircraft's estimated time of arrival. As a result, the aircraft performing IM operations may follow an aircraft whose TMA-TM generated trajectories have substantial speed deviations from the speeds expected by the spacing algorithm. Previous spacing algorithms were not designed to handle this magnitude of uncertainty. A simulation was conducted to examine a modified spacing algorithm with the ability to follow aircraft flying delayed trajectories. The simulation investigated the use of the new spacing algorithm with various delayed speed profiles and wind conditions, as well as several other variables designed to simulate real-life variability. The results and conclusions of this study indicate that the new spacing algorithm generally exhibits good performance; however, some types of target aircraft speed profiles can cause the spacing algorithm to command less than optimal speed control behavior.

Optimizing Mars Sphere of Influence Maneuvers for NASA's Evolvable Mars Campaign

NASA Technical Reports Server (NTRS)

Merrill, Raymond G.; Komar, D. R.; Chai, Patrick; Qu, Min

2016-01-01

NASA's Human Spaceflight Architecture Team is refining human exploration architectures that will extend human presence to the Martian surface. For both Mars orbital and surface missions, NASA's Evolvable Mars Campaign assumes that cargo and crew can be delivered repeatedly to the same destination. Up to this point, interplanetary trajectories have been optimized to minimize the total propulsive requirements of the in-space transportation systems, while the pre-deployed assets and surface systems are optimized to minimize their respective propulsive requirements separate from the in-space transportation system. There is a need to investigate the coupled problem of optimizing the interplanetary trajectory and optimizing the maneuvers within Mars's sphere of influence. This paper provides a description of the ongoing method development, analysis and initial results of the effort to resolve the discontinuity between the interplanetary trajectory and the Mars sphere of influence trajectories. Assessment of Phobos and Deimos orbital missions shows the in-space transportation and crew taxi allocations are adequate for missions in the 2030s. Because the surface site has yet to be selected, the transportation elements must be sized to provide enough capability to provide surface access to all landing sites under consideration. Analysis shows access to sites from elliptical parking orbits with a lander that is designed for sub-periapsis landing location is either infeasible or requires expensive orbital maneuvers for many latitude ranges. In this case the locus of potential arrival perigee vectors identifies the potential maximum north or south latitudes accessible. Higher arrival velocities can decrease reorientation costs and increase landing site availability. Utilizing hyperbolic arrival and departure vectors in the optimization scheme will increase transportation site accessibility and provide more optimal solutions.

Common aero vehicle autonomous reentry trajectory optimization satisfying waypoint and no-fly zone constraints

NASA Astrophysics Data System (ADS)

Jorris, Timothy R.

2007-12-01

To support the Air Force's Global Reach concept, a Common Aero Vehicle is being designed to support the Global Strike mission. "Waypoints" are specified for reconnaissance or multiple payload deployments and "no-fly zones" are specified for geopolitical restrictions or threat avoidance. Due to time critical targets and multiple scenario analysis, an autonomous solution is preferred over a time-intensive, manually iterative one. Thus, a real-time or near real-time autonomous trajectory optimization technique is presented to minimize the flight time, satisfy terminal and intermediate constraints, and remain within the specified vehicle heating and control limitations. This research uses the Hypersonic Cruise Vehicle (HCV) as a simplified two-dimensional platform to compare multiple solution techniques. The solution techniques include a unique geometric approach developed herein, a derived analytical dynamic optimization technique, and a rapidly emerging collocation numerical approach. This up-and-coming numerical technique is a direct solution method involving discretization then dualization, with pseudospectral methods and nonlinear programming used to converge to the optimal solution. This numerical approach is applied to the Common Aero Vehicle (CAV) as the test platform for the full three-dimensional reentry trajectory optimization problem. The culmination of this research is the verification of the optimality of this proposed numerical technique, as shown for both the two-dimensional and three-dimensional models. Additionally, user implementation strategies are presented to improve accuracy and enhance solution convergence. Thus, the contributions of this research are the geometric approach, the user implementation strategies, and the determination and verification of a numerical solution technique for the optimal reentry trajectory problem that minimizes time to target while satisfying vehicle dynamics and control limitation, and heating, waypoint, and no-fly zone constraints.

Effects of inclination and eccentricity on optimal trajectories between earth and Venus

NASA Technical Reports Server (NTRS)

Gravier, J.-P.; Marchal, C.; Culp, R. D.

1973-01-01

The true optimal transfers, including the effects of the inclination and eccentricity of the planets' orbits, between earth and Venus are presented as functions of the corresponding idealized Hohmann transfers. The method of determining the optimal transfers using the calculus of variations is presented. For every possible Hohmann window, specified as a continuous function of the longitude of perihelion of the Hohmann trajectory, the corresponding numerically exact optimal two-impulse transfers are given in graphical form. The cases for which the optimal two-impulse transfer is the absolute optimal, and those for which a three-impulse transfer provides the absolute optimal transfer are indicated. This information furnishes everything necessary for quick and accurate orbit calculations for preliminary Venus mission analysis. This makes it possible to use the actual optimal transfers for advanced planning in place of the standard Hohmann transfers.

Broken-Plane Maneuver Applications for Earth to Mars Trajectories

NASA Technical Reports Server (NTRS)

Abilleira, Fernando

2007-01-01

Optimization techniques are critical when investigating Earth to Mars trajectories since they have the potential of reducing the total (delta)V of a mission. A deep space maneuver (DSM) executed during the cruise may improve a trajectory by reducing the total mission V. Nonetheless, DSMs not only may improve trajectory performance (from an energetic point of view) but also open up new families of trajectories that would satisfy very specific mission requirements not achievable with ballistic trajectories. In the following pages, various specific examples showing the potential advantages of the usage of broken plane maneuvers will be introduced. These examples correspond to possible scenarios for Earth to Mars trajectories during the next decade (2010-2020).

Safe Onboard Guidance and Control Under Probabilistic Uncertainty

NASA Technical Reports Server (NTRS)

Blackmore, Lars James

2011-01-01

An algorithm was developed that determines the fuel-optimal spacecraft guidance trajectory that takes into account uncertainty, in order to guarantee that mission safety constraints are satisfied with the required probability. The algorithm uses convex optimization to solve for the optimal trajectory. Convex optimization is amenable to onboard solution due to its excellent convergence properties. The algorithm is novel because, unlike prior approaches, it does not require time-consuming evaluation of multivariate probability densities. Instead, it uses a new mathematical bounding approach to ensure that probability constraints are satisfied, and it is shown that the resulting optimization is convex. Empirical results show that the approach is many orders of magnitude less conservative than existing set conversion techniques, for a small penalty in computation time.

An Exploration Of Fuel Optimal Two-impulse Transfers To Cyclers in the Earth-Moon System

NASA Astrophysics Data System (ADS)

Hosseinisianaki, Saghar

2011-12-01

This research explores the optimum two-impulse transfers between a low Earth orbit and cycler orbits in the Earth-Moon circular restricted three-body framework, emphasizing the optimization strategy. Cyclers are those types of periodic orbits that meet both the Earth and the Moon periodically. A spacecraft on such trajectories are under the influence of both the Earth and the Moon gravitational fields. Cyclers have gained recent interest as baseline orbits for several Earth-Moon mission concepts, notably in relation to human exploration. In this thesis it is shown that a direct optimization starting from the classic lambert initial guess may not be adequate for these problems and propose a three-step optimization solver to improve the domain of convergence toward an optimal solution. The first step consists of finding feasible trajectories with a given transfer time. I employ Lambert's problem to provide initial guess to optimize the error in arrival position. This includes the analysis of the liability of Lambert's solution as an initial guess. Once a feasible trajectory is found, the velocity impulse is only a function of transfer time, departure, and arrival points' phases. The second step consists of the optimization of impulse over transfer time which results in the minimum impulse transfer for fixed end points. Finally, the third step is mapping the optimal solutions as the end points are varied.

An Exploration Of Fuel Optimal Two-impulse Transfers To Cyclers in the Earth-Moon System

NASA Astrophysics Data System (ADS)

Hosseinisianaki, Saghar

This research explores the optimum two-impulse transfers between a low Earth orbit and cycler orbits in the Earth-Moon circular restricted three-body framework, emphasizing the optimization strategy. Cyclers are those types of periodic orbits that meet both the Earth and the Moon periodically. A spacecraft on such trajectories are under the influence of both the Earth and the Moon gravitational fields. Cyclers have gained recent interest as baseline orbits for several Earth-Moon mission concepts, notably in relation to human exploration. In this thesis it is shown that a direct optimization starting from the classic lambert initial guess may not be adequate for these problems and propose a three-step optimization solver to improve the domain of convergence toward an optimal solution. The first step consists of finding feasible trajectories with a given transfer time. I employ Lambert's problem to provide initial guess to optimize the error in arrival position. This includes the analysis of the liability of Lambert's solution as an initial guess. Once a feasible trajectory is found, the velocity impulse is only a function of transfer time, departure, and arrival points' phases. The second step consists of the optimization of impulse over transfer time which results in the minimum impulse transfer for fixed end points. Finally, the third step is mapping the optimal solutions as the end points are varied.

Optimized x-ray source scanning trajectories for iterative reconstruction in high cone-angle tomography

NASA Astrophysics Data System (ADS)

Kingston, Andrew M.; Myers, Glenn R.; Latham, Shane J.; Li, Heyang; Veldkamp, Jan P.; Sheppard, Adrian P.

2016-10-01

With the GPU computing becoming main-stream, iterative tomographic reconstruction (IR) is becoming a com- putationally viable alternative to traditional single-shot analytical methods such as filtered back-projection. IR liberates one from the continuous X-ray source trajectories required for analytical reconstruction. We present a family of novel X-ray source trajectories for large-angle CBCT. These discrete (sparsely sampled) trajectories optimally fill the space of possible source locations by maximising the degree of mutually independent information. They satisfy a discrete equivalent of Tuy's sufficiency condition and allow high cone-angle (high-flux) tomog- raphy. The highly isotropic nature of the trajectory has several advantages: (1) The average source distance is approximately constant throughout the reconstruction volume, thus avoiding the differential-magnification artefacts that plague high cone-angle helical computed tomography; (2) Reduced streaking artifacts due to e.g. X-ray beam-hardening; (3) Misalignment and component motion manifests as blur in the tomogram rather than double-edges, which is easier to automatically correct; (4) An approximately shift-invariant point-spread-function which enables filtering as a pre-conditioner to speed IR convergence. We describe these space-filling trajectories and demonstrate their above-mentioned properties compared with a traditional helical trajectories.

Ascent trajectory optimization for stratospheric airship with thermal effects

NASA Astrophysics Data System (ADS)

Guo, Xiao; Zhu, Ming

2013-09-01

Ascent trajectory optimization with thermal effects is addressed for a stratospheric airship. Basic thermal characteristics of the stratospheric airship are introduced. Besides, the airship’s equations of motion are constructed by including the factors about aerodynamic force, added mass and wind profiles which are developed based on horizontal-wind model. For both minimum-time and minimum-energy flights during ascent, the trajectory optimization problem is described with the path and terminal constraints in different scenarios and then, is converted into a parameter optimization problem by a direct collocation method. Sparse Nonlinear OPTimizer(SNOPT) is employed as a nonlinear programming solver and two scenarios are adopted. The solutions obtained illustrate that the trajectories are greatly affected by the thermal behaviors which prolong the daytime minimum-time flights of about 20.8% compared with that of nighttime in scenario 1 and of about 10.5% in scenario 2. And there is the same trend for minimum-energy flights. For the energy consumption of minimum-time flights, 6% decrease is abstained in scenario 1 and 5% decrease in scenario 2. However, a few energy consumption reduction is achieved for minimum-energy flights. Solar radiation is the principal component and the natural wind also affects the thermal behaviors of stratospheric airship during ascent. The relationship between take-off time and performance of airship during ascent is discussed. it is found that the take-off time at dusk is best choice for stratospheric airship. And in addition, for saving energy, airship prefers to fly downwind.

A reverse engineering approach to optimize experiments for the construction of biological regulatory networks.

PubMed

Zhang, Xiaomeng; Shao, Bin; Wu, Yangle; Qi, Ouyang

2013-01-01

One of the major objectives in systems biology is to understand the relation between the topological structures and the dynamics of biological regulatory networks. In this context, various mathematical tools have been developed to deduct structures of regulatory networks from microarray expression data. In general, from a single data set, one cannot deduct the whole network structure; additional expression data are usually needed. Thus how to design a microarray expression experiment in order to get the most information is a practical problem in systems biology. Here we propose three methods, namely, maximum distance method, trajectory entropy method, and sampling method, to derive the optimal initial conditions for experiments. The performance of these methods is tested and evaluated in three well-known regulatory networks (budding yeast cell cycle, fission yeast cell cycle, and E. coli. SOS network). Based on the evaluation, we propose an efficient strategy for the design of microarray expression experiments.

JacksonBot - Design, Simulation and Optimal Control of an Action Painting Robot

NASA Astrophysics Data System (ADS)

Raschke, Michael; Mombaur, Katja; Schubert, Alexander

We present the robotics platform JacksonBot which is capable to produce paintings inspired by the Action Painting style of Jackson Pollock. A dynamically moving robot arm splashes color from a container at the end effector on the canvas. The paintings produced by this platform rely on a combination of the algorithmic generation of robot arm motions with random effects of the splashing color. The robot can be considered as a complex and powerful tool to generate art works programmed by a user. Desired end effector motions can be prescribed either by mathematical functions, by point sequences or by data glove motions. We have evaluated the effect of different shapes of input motions on the resulting painting. In order to compute the robot joint trajectories necessary to move along a desired end effector path, we use an optimal control based approach to solve the inverse kinematics problem.

A Computational Intelligence (CI) Approach to the Precision Mars Lander Problem

NASA Technical Reports Server (NTRS)

Birge, Brian; Walberg, Gerald

2002-01-01

A Mars precision landing requires a landed footprint of no more than 100 meters. Obstacles to reducing the landed footprint include trajectory dispersions due to initial atmospheric entry conditions such as entry angle, parachute deployment height, environment parameters such as wind, atmospheric density, parachute deployment dynamics, unavoidable injection error or propagated error from launch, etc. Computational Intelligence (CI) techniques such as Artificial Neural Nets and Particle Swarm Optimization have been shown to have great success with other control problems. The research period extended previous work on investigating applicability of the computational intelligent approaches. The focus of this investigation was on Particle Swarm Optimization and basic Neural Net architectures. The research investigating these issues was performed for the grant cycle from 5/15/01 to 5/15/02. Matlab 5.1 and 6.0 along with NASA's POST were the primary computational tools.

User's guide to four-body and three-body trajectory optimization programs

NASA Technical Reports Server (NTRS)

Pu, C. L.; Edelbaum, T. N.

1974-01-01

A collection of computer programs and subroutines written in FORTRAN to calculate 4-body (sun-earth-moon-space) and 3-body (earth-moon-space) optimal trajectories is presented. The programs incorporate a variable step integration technique and a quadrature formula to correct single step errors. The programs provide capability to solve initial value problem, two point boundary value problem of a transfer from a given initial position to a given final position in fixed time, optimal 2-impulse transfer from an earth parking orbit of given inclination to a given final position and velocity in fixed time and optimal 3-impulse transfer from a given position to a given final position and velocity in fixed time.

Rocket ascent G-limited moment-balanced optimization program (RAGMOP)

NASA Technical Reports Server (NTRS)

Lyons, J. T.; Woltosz, W. S.; Abercrombie, G. E.; Gottlieb, R. G.

1972-01-01

This document describes the RAGMOP (Rocket Ascent G-limited Momentbalanced Optimization Program) computer program for parametric ascent trajectory optimization. RAGMOP computes optimum polynomial-form attitude control histories, launch azimuth, engine burn-time, and gross liftoff weight for space shuttle type vehicles using a search-accelerated, gradient projection parameter optimization technique. The trajectory model available in RAGMOP includes a rotating oblate earth model, the option of input wind tables, discrete and/or continuous throttling for the purposes of limiting the thrust acceleration and/or the maximum dynamic pressure, limitation of the structural load indicators (the product of dynamic pressure with angle-of-attack and sideslip angle), and a wide selection of intermediate and terminal equality constraints.

Optimization of the production process using virtual model of a workspace

NASA Astrophysics Data System (ADS)

Monica, Z.

2015-11-01

Optimization of the production process is an element of the design cycle consisting of: problem definition, modelling, simulation, optimization and implementation. Without the use of simulation techniques, the only thing which could be achieved is larger or smaller improvement of the process, not the optimization (i.e., the best result it is possible to get for the conditions under which the process works). Optimization is generally management actions that are ultimately bring savings in time, resources, and raw materials and improve the performance of a specific process. It does not matter whether it is a service or manufacturing process. Optimizing the savings generated by improving and increasing the efficiency of the processes. Optimization consists primarily of organizational activities that require very little investment, or rely solely on the changing organization of work. Modern companies operating in a market economy shows a significant increase in interest in modern methods of production management and services. This trend is due to the high competitiveness among companies that want to achieve success are forced to continually modify the ways to manage and flexible response to changing demand. Modern methods of production management, not only imply a stable position of the company in the sector, but also influence the improvement of health and safety within the company and contribute to the implementation of more efficient rules for standardization work in the company. This is why in the paper is presented the application of such developed environment like Siemens NX to create the virtual model of a production system and to simulate as well as optimize its work. The analyzed system is the robotized workcell consisting of: machine tools, industrial robots, conveyors, auxiliary equipment and buffers. In the program could be defined the control program realizing the main task in the virtual workcell. It is possible, using this tool, to optimize both the object trajectory and the cooperation process.

Continuous performance measurement in flight systems. [sequential control model

NASA Technical Reports Server (NTRS)

Connelly, E. M.; Sloan, N. A.; Zeskind, R. M.

1975-01-01

The desired response of many man machine control systems can be formulated as a solution to an optimal control synthesis problem where the cost index is given and the resulting optimal trajectories correspond to the desired trajectories of the man machine system. Optimal control synthesis provides the reference criteria and the significance of error information required for performance measurement. The synthesis procedure described provides a continuous performance measure (CPM) which is independent of the mechanism generating the control action. Therefore, the technique provides a meaningful method for online evaluation of man's control capability in terms of total man machine performance.

An optimal control strategy for collision avoidance of mobile robots in non-stationary environments

NASA Technical Reports Server (NTRS)

Kyriakopoulos, K. J.; Saridis, G. N.

1991-01-01

An optimal control formulation of the problem of collision avoidance of mobile robots in environments containing moving obstacles is presented. Collision avoidance is guaranteed if the minimum distance between the robot and the objects is nonzero. A nominal trajectory is assumed to be known from off-line planning. The main idea is to change the velocity along the nominal trajectory so that collisions are avoided. Furthermore, time consistency with the nominal plan is desirable. A numerical solution of the optimization problem is obtained. Simulation results verify the value of the proposed strategy.

Optimization methods of laws control of electric propulsion spacecraft in the restricted three-body task

NASA Astrophysics Data System (ADS)

Starinova, Olga L.

2014-12-01

This paper outlines the optimization methods of the control law of the low thrust spacecraft for the restrict problem of three-body. The conditions for fragmentation trajectory on the specific parts of trajectory are formulated. The mathematical statement and methods to solve the optimal control problem on these parts are stated. Results of the decision of applied problems for various classes of spacecrafts which are carrying out maneuvers with low thrust are presented. In particular, the non-coplanar maneuvers of the low thrust spacecraft in the Earth-Moon system are viewed.

Optimal trajectories for hypersonic launch vehicles

NASA Technical Reports Server (NTRS)

Ardema, Mark D.; Bowles, Jeffrey V.; Whittaker, Thomas

1994-01-01

In this paper, we derive a near-optimal guidance law for the ascent trajectory from earth surface to earth orbit of a hypersonic, dual-mode propulsion, lifting vehicle. Of interest are both the optical flight path and the optimal operation of the propulsion system. The guidance law is developed from the energy-state approximation of the equations of motion. Because liquid hydrogen fueled hypersonic aircraft are volume sensitive, as well as weight sensitive, the cost functional is a weighted sum of fuel mass and volume; the weighting factor is chosen to minimize gross take-off weight for a given payload mass and volume in orbit.

Noncoplanar VMAT for nasopharyngeal tumors: Plan quality versus treatment time

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wild, Esther, E-mail: e.wild@dkfz.de; Bangert, Mark; Nill, Simeon

Purpose: The authors investigated the potential of optimized noncoplanar irradiation trajectories for volumetric modulated arc therapy (VMAT) treatments of nasopharyngeal patients and studied the trade-off between treatment plan quality and delivery time in radiation therapy. Methods: For three nasopharyngeal patients, the authors generated treatment plans for nine different delivery scenarios using dedicated optimization methods. They compared these scenarios according to dose characteristics, number of beam directions, and estimated delivery times. In particular, the authors generated the following treatment plans: (1) a 4π plan, which is a not sequenced, fluence optimized plan that uses beam directions from approximately 1400 noncoplanar directionsmore » and marks a theoretical upper limit of the treatment plan quality, (2) a coplanar 2π plan with 72 coplanar beam directions as pendant to the noncoplanar 4π plan, (3) a coplanar VMAT plan, (4) a coplanar step and shoot (SnS) plan, (5) a beam angle optimized (BAO) coplanar SnS IMRT plan, (6) a noncoplanar BAO SnS plan, (7) a VMAT plan with rotated treatment couch, (8) a noncoplanar VMAT plan with an optimized great circle around the patient, and (9) a noncoplanar BAO VMAT plan with an arbitrary trajectory around the patient. Results: VMAT using optimized noncoplanar irradiation trajectories reduced the mean and maximum doses in organs at risk compared to coplanar VMAT plans by 19% on average while the target coverage remains constant. A coplanar BAO SnS plan was superior to coplanar SnS or VMAT; however, noncoplanar plans like a noncoplanar BAO SnS plan or noncoplanar VMAT yielded a better plan quality than the best coplanar 2π plan. The treatment plan quality of VMAT plans depended on the length of the trajectory. The delivery times of noncoplanar VMAT plans were estimated to be 6.5 min in average; 1.6 min longer than a coplanar plan but on average 2.8 min faster than a noncoplanar SnS plan with comparable treatment plan quality. Conclusions: The authors’ study reconfirms the dosimetric benefits of noncoplanar irradiation of nasopharyngeal tumors. Both SnS using optimized noncoplanar beam ensembles and VMAT using an optimized, arbitrary, noncoplanar trajectory enabled dose reductions in organs at risk compared to coplanar SnS and VMAT. Using great circles or simple couch rotations to implement noncoplanar VMAT, however, was not sufficient to yield meaningful improvements in treatment plan quality. The authors estimate that noncoplanar VMAT using arbitrary optimized irradiation trajectories comes at an increased delivery time compared to coplanar VMAT yet at a decreased delivery time compared to noncoplanar SnS IMRT.« less

A New Theory of Trajectory Design and NASA's Vision

NASA Technical Reports Server (NTRS)

Folta, David

2006-01-01

This new theory is defined as the use of chaos to design trajectories and orbits that can be used to meet complex mission goals. The benefits are; a) minimizes fuel costs; b) optimizes trajectory profiles; c) provides non-standard and new orbit designs; and d) mitigates operational risks. Other synonymous terms include dynamical systems, invariant manifolds, capture orbits and ballistic orbits.

Multivariant function model generation

NASA Technical Reports Server (NTRS)

1974-01-01

The development of computer programs applicable to space vehicle guidance was conducted. The subjects discussed are as follows: (1) determination of optimum reentry trajectories, (2) development of equations for performance of trajectory computation, (3) vehicle control for fuel optimization, (4) development of equations for performance trajectory computations, (5) applications and solution of Hamilton-Jacobi equation, and (6) stresses in dome shaped shells with discontinuities at the apex.

Global Optimization of Low-Thrust Interplanetary Trajectories Subject to Operational Constraints

NASA Technical Reports Server (NTRS)

Englander, Jacob Aldo; Vavrina, Matthew; Hinckley, David

2016-01-01

Low-thrust electric propulsion provides many advantages for mission to difficult targets-Comets and asteroids-Mercury-Outer planets (with sufficient power supply)Low-thrust electric propulsion is characterized by high power requirements but also very high specific impulse (Isp), leading to very good mass fractions. Low-thrust trajectory design is a very different process from chemical trajectory.

An optimal control strategy for two-dimensional motion camouflage with non-holonimic constraints.

PubMed

Rañó, Iñaki

2012-07-01

Motion camouflage is a stealth behaviour observed both in hover-flies and in dragonflies. Existing controllers for mimicking motion camouflage generate this behaviour on an empirical basis or without considering the kinematic motion restrictions present in animal trajectories. This study summarises our formal contributions to solve the generation of motion camouflage as a non-linear optimal control problem. The dynamics of the system capture the kinematic restrictions to motion of the agents, while the performance index ensures camouflage trajectories. An extensive set of simulations support the technique, and a novel analysis of the obtained trajectories contributes to our understanding of possible mechanisms to obtain sensor based motion camouflage, for instance, in mobile robots.

Trajectories for High Specific Impulse High Specific Power Deep Space Exploration

NASA Technical Reports Server (NTRS)

Polsgrove, T.; Adams, R. B.; Brady, Hugh J. (Technical Monitor)

2002-01-01

Preliminary results are presented for two methods to approximate the mission performance of high specific impulse high specific power vehicles. The first method is based on an analytical approximation derived by Williams and Shepherd and can be used to approximate mission performance to outer planets and interstellar space. The second method is based on a parametric analysis of trajectories created using the well known trajectory optimization code, VARITOP. This parametric analysis allows the reader to approximate payload ratios and optimal power requirements for both one-way and round-trip missions. While this second method only addresses missions to and from Jupiter, future work will encompass all of the outer planet destinations and some interstellar precursor missions.

Optimization of Thermal Object Nonlinear Control Systems by Energy Efficiency Criterion.

NASA Astrophysics Data System (ADS)

Velichkin, Vladimir A.; Zavyalov, Vladimir A.

2018-03-01

This article presents the results of thermal object functioning control analysis (heat exchanger, dryer, heat treatment chamber, etc.). The results were used to determine a mathematical model of the generalized thermal control object. The appropriate optimality criterion was chosen to make the control more energy-efficient. The mathematical programming task was formulated based on the chosen optimality criterion, control object mathematical model and technological constraints. The “maximum energy efficiency” criterion helped avoid solving a system of nonlinear differential equations and solve the formulated problem of mathematical programming in an analytical way. It should be noted that in the case under review the search for optimal control and optimal trajectory reduces to solving an algebraic system of equations. In addition, it is shown that the optimal trajectory does not depend on the dynamic characteristics of the control object.

Simulation-Based Analysis of Reentry Dynamics for the Sharp Atmospheric Entry Vehicle

NASA Technical Reports Server (NTRS)

Tillier, Clemens Emmanuel

1998-01-01

This thesis describes the analysis of the reentry dynamics of a high-performance lifting atmospheric entry vehicle through numerical simulation tools. The vehicle, named SHARP, is currently being developed by the Thermal Protection Materials and Systems branch of NASA Ames Research Center, Moffett Field, California. The goal of this project is to provide insight into trajectory tradeoffs and vehicle dynamics using simulation tools that are powerful, flexible, user-friendly and inexpensive. Implemented Using MATLAB and SIMULINK, these tools are developed with an eye towards further use in the conceptual design of the SHARP vehicle's trajectory and flight control systems. A trajectory simulator is used to quantify the entry capabilities of the vehicle subject to various operational constraints. Using an aerodynamic database computed by NASA and a model of the earth, the simulator generates the vehicle trajectory in three-dimensional space based on aerodynamic angle inputs. Requirements for entry along the SHARP aerothermal performance constraint are evaluated for different control strategies. Effect of vehicle mass on entry parameters is investigated, and the cross range capability of the vehicle is evaluated. Trajectory results are presented and interpreted. A six degree of freedom simulator builds on the trajectory simulator and provides attitude simulation for future entry controls development. A Newtonian aerodynamic model including control surfaces and a mass model are developed. A visualization tool for interpreting simulation results is described. Control surfaces are roughly sized. A simple controller is developed to fly the vehicle along its aerothermal performance constraint using aerodynamic flaps for control. This end-to-end demonstration proves the suitability of the 6-DOF simulator for future flight control system development. Finally, issues surrounding real-time simulation with hardware in the loop are discussed.

A study of unmanned mission opportunities to comets and asteroids

NASA Technical Reports Server (NTRS)

Mann, F. I.; Horsewood, J. L.; Bjorkman, W.

1974-01-01

Several unmanned multiple-target mission opportunities to comets and asteroids were studied. The targets investigated include Grigg-Skjellerup, Giacobini-Zinner, Tuttle-Giacobini-Kresak, Borrelly, Halley, Schaumasse, Geographos, Eros, Icarus, and Toro, and the trajectories consist of purely ballistic flight, except that powered swingbys and deep space burns are employed when necessary. Optimum solar electric rendezvous trajectories to the comets Giacobini-Zinner/85, Borrelly/87, and Temple (2)/83 and /88 employing the 8.67 kw Sert III spacecraft modified for interplanetary flight were also investigated. The problem of optimizing electric propulsion heliocentric trajectories, including the effects of geocentric launch asymptote declination on launch vehicle performance capability, was formulated, and a solution developed using variational calculus techniques. Improvements were made to the HILTOP trajectory optimization computer program. An error analysis of high-thrust maneuvers involving spin-stabilized spacecraft was developed and applied to a synchronous meteorological satellite mission.

Non-Rigid Structure Estimation in Trajectory Space from Monocular Vision

PubMed Central

Wang, Yaming; Tong, Lingling; Jiang, Mingfeng; Zheng, Junbao

2015-01-01

In this paper, the problem of non-rigid structure estimation in trajectory space from monocular vision is investigated. Similar to the Point Trajectory Approach (PTA), based on characteristic points’ trajectories described by a predefined Discrete Cosine Transform (DCT) basis, the structure matrix was also calculated by using a factorization method. To further optimize the non-rigid structure estimation from monocular vision, the rank minimization problem about structure matrix is proposed to implement the non-rigid structure estimation by introducing the basic low-rank condition. Moreover, the Accelerated Proximal Gradient (APG) algorithm is proposed to solve the rank minimization problem, and the initial structure matrix calculated by the PTA method is optimized. The APG algorithm can converge to efficient solutions quickly and lessen the reconstruction error obviously. The reconstruction results of real image sequences indicate that the proposed approach runs reliably, and effectively improves the accuracy of non-rigid structure estimation from monocular vision. PMID:26473863

A New Unified Analysis of Estimate Errors by Model-Matching Phase-Estimation Methods for Sensorless Drive of Permanent-Magnet Synchronous Motors and New Trajectory-Oriented Vector Control, Part II

NASA Astrophysics Data System (ADS)

Shinnaka, Shinji

This paper presents a new unified analysis of estimate errors by model-matching extended-back-EMF estimation methods for sensorless drive of permanent-magnet synchronous motors. Analytical solutions about estimate errors, whose validity is confirmed by numerical experiments, are rich in universality and applicability. As an example of universality and applicability, a new trajectory-oriented vector control method is proposed, which can realize directly quasi-optimal strategy minimizing total losses with no additional computational loads by simply orienting one of vector-control coordinates to the associated quasi-optimal trajectory. The coordinate orientation rule, which is analytically derived, is surprisingly simple. Consequently the trajectory-oriented vector control method can be applied to a number of conventional vector control systems using model-matching extended-back-EMF estimation methods.

Multi-Objective Hybrid Optimal Control for Interplanetary Mission Planning

NASA Technical Reports Server (NTRS)

Englander, Jacob; Vavrina, Matthew; Ghosh, Alexander

2015-01-01

Preliminary design of low-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed and in some cases the final destination. In addition, a time-history of control variables must be chosen which defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated. The customer who commissions a trajectory design is not usually interested in a point solution, but rather the exploration of the trade space of trajectories between several different objective functions. This can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very diserable. This work presents such as an approach by posing the mission design problem as a multi-objective hybrid optimal control problem. The method is demonstrated on a hypothetical mission to the main asteroid belt.

Mission Design, Guidance, and Navigation of a Callisto-Io-Ganymede Triple Flyby Jovian Capture

NASA Astrophysics Data System (ADS)

Didion, Alan M.

Use of a triple-satellite-aided capture maneuver to enter Jovian orbit reduces insertion DeltaV and provides close flyby science opportunities at three of Jupiter's four large Galilean moons. This capture can be performed while maintaining appropriate Jupiter standoff distance and setting up a suitable apojove for plotting an extended tour. This paper has three main chapters, the first of which discusses the design and optimization of a triple-flyby capture trajectory. A novel triple-satellite-aided capture uses sequential flybys of Callisto, Io, and Ganymede to reduce the DeltaV required to capture into orbit about Jupiter. An optimal broken-plane maneuver is added between Earth and Jupiter to form a complete chemical/impulsive interplanetary trajectory from Earth to Jupiter. Such a trajectory can yield significant fuel savings over single and double-flyby capture schemes while maintaining a brief and simple interplanetary transfer phase. The second chapter focuses on the guidance and navigation of such trajectories in the presence of spacecraft navigation errors, ephemeris errors, and maneuver execution errors. A powered-flyby trajectory correction maneuver (TCM) is added to the nominal trajectory at Callisto and the nominal Jupiter orbit insertion (JOI) maneuver is modified to both complete the capture and target the Ganymede flyby. A third TCM is employed after all the flybys to act as a JOI cleanup maneuver. A Monte Carlo simulation shows that the statistical DeltaV required to correct the trajectory is quite manageable and the flyby characteristics are very consistent. The developed methods maintain flexibility for adaptation to similar launch, cruise, and capture conditions. The third chapter details the methodology and results behind a completely separate project to design and optimize an Earth-orbiting three satellite constellation to perform very long baseline interferometry (VLBI) as part of the 8th annual Global Trajectory Optimisation Competition (GTOC8). A script is designed to simulate the prescribed constellation and record its observations; the observations made are scored according to a provided performance index.

Impulsive time-free transfers between halo orbits

NASA Astrophysics Data System (ADS)

Hiday, L. A.; Howell, K. C.

1992-08-01

A methodology is developed to design optimal time-free impulsive transfers between three-dimensional halo orbits in the vicinity of the interior L1 libration point of the sun-earth/moon barycenter system. The transfer trajectories are optimal in the sense that the total characteristics velocity required to implement the transfer exhibits a local minimum. Criteria are established whereby the implementation of a coast in the initial orbit, a coast in the final orbit, or dual coasts accomplishes a reduction in fuel expenditure. The optimality of a reference two-impulse transfer can be determined by examining the slope at the endpoints of a plot of the magnitude of the primer vector on the reference trajectory. If the initial and final slopes of the primer magnitude are zero, the transfer trajectory is optimal; otherwise, the execution of coasts is warranted. The optimal time of flight on the time-free transfer, and consequently, the departure and arrival locations on the halo orbits are determined by the unconstrained minimization of a function of two variables using a multivariable search technique. Results indicate that the cost can be substantially diminished by the allowance for coasts in the initial and final libration-point orbits.

Impulsive Time-Free Transfers Between Halo Orbits

NASA Astrophysics Data System (ADS)

Hiday-Johnston, L. A.; Howell, K. C.

1996-12-01

A methodology is developed to design optimal time-free impulsive transfers between three-dimensional halo orbits in the vicinity of the interior L 1 libration point of the Sun-Earth/Moon barycenter system. The transfer trajectories are optimal in the sense that the total characteristic velocity required to implement the transfer exhibits a local minimum. Criteria are established whereby the implementation of a coast in the initial orbit, a coast in the final orbit, or dual coasts accomplishes a reduction in fuel expenditure. The optimality of a reference two-impulse transfer can be determined by examining the slope at the endpoints of a plot of the magnitude of the primer vector on the reference trajectory. If the initial and final slopes of the primer magnitude are zero, the transfer trajectory is optimal; otherwise, the execution of coasts is warranted. The optimal time of flight on the time-free transfer, and consequently, the departure and arrival locations on the halo orbits are determined by the unconstrained minimization of a function of two variables using a multivariable search technique. Results indicate that the cost can be substantially diminished by the allowance for coasts in the initial and final libration-point orbits.

Parameterized data-driven fuzzy model based optimal control of a semi-batch reactor.

PubMed

Kamesh, Reddi; Rani, K Yamuna

2016-09-01

A parameterized data-driven fuzzy (PDDF) model structure is proposed for semi-batch processes, and its application for optimal control is illustrated. The orthonormally parameterized input trajectories, initial states and process parameters are the inputs to the model, which predicts the output trajectories in terms of Fourier coefficients. Fuzzy rules are formulated based on the signs of a linear data-driven model, while the defuzzification step incorporates a linear regression model to shift the domain from input to output domain. The fuzzy model is employed to formulate an optimal control problem for single rate as well as multi-rate systems. Simulation study on a multivariable semi-batch reactor system reveals that the proposed PDDF modeling approach is capable of capturing the nonlinear and time-varying behavior inherent in the semi-batch system fairly accurately, and the results of operating trajectory optimization using the proposed model are found to be comparable to the results obtained using the exact first principles model, and are also found to be comparable to or better than parameterized data-driven artificial neural network model based optimization results. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Multiple-hopping trajectories near a rotating asteroid

NASA Astrophysics Data System (ADS)

Shen, Hong-Xin; Zhang, Tian-Jiao; Li, Zhao; Li, Heng-Nian

2017-03-01

We present a study of the transfer orbits connecting landing points of irregular-shaped asteroids. The landing points do not touch the surface of the asteroids and are chosen several meters above the surface. The ant colony optimization technique is used to calculate the multiple-hopping trajectories near an arbitrary irregular asteroid. This new method has three steps which are as follows: (1) the search of the maximal clique of candidate target landing points; (2) leg optimization connecting all landing point pairs; and (3) the hopping sequence optimization. In particular this method is applied to asteroids 433 Eros and 216 Kleopatra. We impose a critical constraint on the target landing points to allow for extensive exploration of the asteroid: the relative distance between all the arrived target positions should be larger than a minimum allowed value. Ant colony optimization is applied to find the set and sequence of targets, and the differential evolution algorithm is used to solve for the hopping orbits. The minimum-velocity increment tours of hopping trajectories connecting all the landing positions are obtained by ant colony optimization. The results from different size asteroids indicate that the cost of the minimum velocity-increment tour depends on the size of the asteroids.

Automation of POST Cases via External Optimizer and "Artificial p2" Calculation

NASA Technical Reports Server (NTRS)

Dees, Patrick D.; Zwack, Mathew R.; Michelson, Diane K.

2017-01-01

During conceptual design speed and accuracy are often at odds. Specifically in the realm of launch vehicles, optimizing the ascent trajectory requires a larger pool of analytical power and expertise. Experienced analysts working on familiar vehicles can produce optimal trajectories in a short time frame, however whenever either "experienced" or "familiar " is not applicable the optimization process can become quite lengthy. In order to construct a vehicle agnostic method an established global optimization algorithm is needed. In this work the authors develop an "artificial" error term to map arbitrary control vectors to non-zero error by which a global method can operate. Two global methods are compared alongside Design of Experiments and random sampling and are shown to produce comparable results to analysis done by a human expert.

Optimal trajectories for an aerospace plane. Part 2: Data, tables, and graphs

NASA Technical Reports Server (NTRS)

Miele, Angelo; Lee, W. Y.; Wu, G. D.

1990-01-01

Data, tables, and graphs relative to the optimal trajectories for an aerospace plane are presented. A single-stage-to-orbit (SSTO) configuration is considered, and the transition from low supersonic speeds to orbital speeds is studied for a single aerodynamic model (GHAME) and three engine models. Four optimization problems are solved using the sequential gradient-restoration algorithm for optimal control problems: (1) minimization of the weight of fuel consumed; (2) minimization of the peak dynamic pressure; (3) minimization of the peak heating rate; and (4) minimization of the peak tangential acceleration. The above optimization studies are carried out for different combinations of constraints, specifically: initial path inclination that is either free or given; dynamic pressure that is either free or bounded; and tangential acceleration that is either free or bounded.

Creation of an Upper Stage Trajectory Capability Boundary to Enable Booster System Trade Space Exploration

NASA Technical Reports Server (NTRS)

Walsh, Ptrick; Coulon, Adam; Edwards, Stephen; Mavris, Dimitri N.

2012-01-01

The problem of trajectory optimization is important in all space missions. The solution of this problem enables one to specify the optimum thrust steering program which should be followed to achieve a specified mission objective, simultaneously satisfying the constraints.1 It is well known that whether or not the ascent trajectory is optimal can have a significant impact on propellant usage for a given payload, or on payload weight for the same gross vehicle weight.2 Consequently, ascent guidance commands are usually optimized in some fashion. Multi-stage vehicles add complexity to this analysis process as changes in vehicle properties in one stage propagate to the other stages through gear ratios and changes in the optimal trajectory. These effects can cause an increase in analysis time as more variables are added and convergence of the optimizer to system closure requires more analysis iterations. In this paper, an approach to simplifying this multi-stage problem through the creation of an upper stage capability boundary is presented. This work was completed as part of a larger study focused on trade space exploration for the advanced booster system that will eventually form a part of NASA s new Space Launch System.3 The approach developed leverages Design of Experiments and Surrogate Modeling4 techniques to create a predictive model of the SLS upper stage performance. The design of the SLS core stages is considered fixed for the purposes of this study, which results in trajectory parameters such as staging conditions being the only variables relevant to the upper stage. Through the creation of a surrogate model, which takes staging conditions as inputs and predicts the payload mass delivered by the SLS upper stage to a reference orbit as the response, it is possible to identify a "surface" of staging conditions which all satisfy the SLS requirement of placing 130 metric tons into low-Earth orbit (LEO).3 This identified surface represents the 130 metric ton capability boundary for the upper stage, such that if the combined first stage and boosters can achieve any one staging point on that surface, then the design is identified as feasible. With the surrogate model created, design and analysis of advanced booster concepts is streamlined, as optimization of the upper stage trajectory is no longer required in every design loop.

The Trajectory Synthesizer Generalized Profile Interface

NASA Technical Reports Server (NTRS)

Lee, Alan G.; Bouyssounouse, Xavier; Murphy, James R.

2010-01-01

The Trajectory Synthesizer is a software program that generates aircraft predictions for Air Traffic Management decision support tools. The Trajectory Synthesizer being used by researchers at NASA Ames Research Center was restricted in the number of trajectory types that could be generated. This limitation was not sufficient to support the rapidly changing Air Traffic Management research requirements. The Generalized Profile Interface was developed to address this issue. It provides a flexible approach to describe the constraints applied to trajectory generation and may provide a method for interoperability between trajectory generators. It also supports the request and generation of new types of trajectory profiles not possible with the previous interface to the Trajectory Synthesizer. Other enhancements allow the Trajectory Synthesizer to meet the current and future needs of Air Traffic Management research.

Improvement of Automated POST Case Success Rate Using Support Vector Machines

NASA Technical Reports Server (NTRS)

Zwack, Matthew R.; Dees, Patrick D.

2017-01-01

During early conceptual design of complex systems, concept down selection can have a large impact upon program life-cycle cost. Therefore, any concepts selected during early design will inherently commit program costs and affect the overall probability of program success. For this reason it is important to consider as large a design space as possible in order to better inform the down selection process. For conceptual design of launch vehicles, trajectory analysis and optimization often presents the largest obstacle to evaluating large trade spaces. This is due to the sensitivity of the trajectory discipline to changes in all other aspects of the vehicle design. Small deltas in the performance of other subsystems can result in relatively large fluctuations in the ascent trajectory because the solution space is non-linear and multi-modal [1]. In order to help capture large design spaces for new launch vehicles, the authors have performed previous work seeking to automate the execution of the industry standard tool, Program to Optimize Simulated Trajectories (POST). This work initially focused on implementation of analyst heuristics to enable closure of cases in an automated fashion, with the goal of applying the concepts of design of experiments (DOE) and surrogate modeling to enable near instantaneous throughput of vehicle cases [2]. Additional work was then completed to improve the DOE process by utilizing a graph theory based approach to connect similar design points [3]. The conclusion of the previous work illustrated the utility of the graph theory approach for completing a DOE through POST. However, this approach was still dependent upon the use of random repetitions to generate seed points for the graph. As noted in [3], only 8% of these random repetitions resulted in converged trajectories. This ultimately affects the ability of the random reps method to confidently approach the global optima for a given vehicle case in a reasonable amount of time. With only an 8% pass rate, tens or hundreds of thousands of reps may be needed to be confident that the best repetition is at least close to the global optima. However, typical design study time constraints require that fewer repetitions be attempted, sometimes resulting in seed points that have only a handful of successful completions. If a small number of successful repetitions are used to generate a seed point, the graph method may inherit some inaccuracies as it chains DOE cases from the non-global-optimal seed points. This creates inherent noise in the graph data, which can limit the accuracy of the resulting surrogate models. For this reason, the goal of this work is to improve the seed point generation method and ultimately the accuracy of the resulting POST surrogate model. The work focuses on increasing the case pass rate for seed point generation.

Enhanced Fuel-Optimal Trajectory-Generation Algorithm for Planetary Pinpoint Landing

NASA Technical Reports Server (NTRS)

Acikmese, Behcet; Blackmore, James C.; Scharf, Daniel P.

2011-01-01

An enhanced algorithm is developed that builds on a previous innovation of fuel-optimal powered-descent guidance (PDG) for planetary pinpoint landing. The PDG problem is to compute constrained, fuel-optimal trajectories to land a craft at a prescribed target on a planetary surface, starting from a parachute cut-off point and using a throttleable descent engine. The previous innovation showed the minimal-fuel PDG problem can be posed as a convex optimization problem, in particular, as a Second-Order Cone Program, which can be solved to global optimality with deterministic convergence properties, and hence is a candidate for onboard implementation. To increase the speed and robustness of this convex PDG algorithm for possible onboard implementation, the following enhancements are incorporated: 1) Fast detection of infeasibility (i.e., control authority is not sufficient for soft-landing) for subsequent fault response. 2) The use of a piecewise-linear control parameterization, providing smooth solution trajectories and increasing computational efficiency. 3) An enhanced line-search algorithm for optimal time-of-flight, providing quicker convergence and bounding the number of path-planning iterations needed. 4) An additional constraint that analytically guarantees inter-sample satisfaction of glide-slope and non-sub-surface flight constraints, allowing larger discretizations and, hence, faster optimization. 5) Explicit incorporation of Mars rotation rate into the trajectory computation for improved targeting accuracy. These enhancements allow faster convergence to the fuel-optimal solution and, more importantly, remove the need for a "human-in-the-loop," as constraints will be satisfied over the entire path-planning interval independent of step-size (as opposed to just at the discrete time points) and infeasible initial conditions are immediately detected. Finally, while the PDG stage is typically only a few minutes, ignoring the rotation rate of Mars can introduce 10s of meters of error. By incorporating it, the enhanced PDG algorithm becomes capable of pinpoint targeting.

Optimization of ramp area aircraft push back time windows in the presence of uncertainty

NASA Astrophysics Data System (ADS)

Coupe, William Jeremy

It is well known that airport surface traffic congestion at major airports is responsible for increased taxi-out times, fuel burn and excess emissions and there is potential to mitigate these negative consequences through optimizing airport surface traffic operations. Due to a highly congested voice communication channel between pilots and air traffic controllers and a data communication channel that is used only for limited functions, one of the most viable near-term strategies for improvement of the surface traffic is issuing a push back advisory to each departing aircraft. This dissertation focuses on the optimization of a push back time window for each departing aircraft. The optimization takes into account both spatial and temporal uncertainties of ramp area aircraft trajectories. The uncertainties are described by a stochastic kinematic model of aircraft trajectories, which is used to infer distributions of combinations of push back times that lead to conflict among trajectories from different gates. The model is validated and the distributions are included in the push back time window optimization. Under the assumption of a fixed taxiway spot schedule, the computed push back time windows can be integrated with a higher level taxiway scheduler to optimize the flow of traffic from the gate to the departure runway queue. To enable real-time decision making the computational time of the push back time window optimization is critical and is analyzed throughout.

Optimal integration of gravity in trajectory planning of vertical pointing movements.

PubMed

Crevecoeur, Frédéric; Thonnard, Jean-Louis; Lefèvre, Philippe

2009-08-01

The planning and control of motor actions requires knowledge of the dynamics of the controlled limb to generate the appropriate muscular commands and achieve the desired goal. Such planning and control imply that the CNS must be able to deal with forces and constraints acting on the limb, such as the omnipresent force of gravity. The present study investigates the effect of hypergravity induced by parabolic flights on the trajectory of vertical pointing movements to test the hypothesis that motor commands are optimized with respect to the effect of gravity on the limb. Subjects performed vertical pointing movements in normal gravity and hypergravity. We use a model based on optimal control to identify the role played by gravity in the optimal arm trajectory with minimal motor costs. First, the simulations in normal gravity reproduce the asymmetry in the velocity profiles (the velocity reaches its maximum before half of the movement duration), which typically characterizes the vertical pointing movements performed on Earth, whereas the horizontal movements present symmetrical velocity profiles. Second, according to the simulations, the optimal trajectory in hypergravity should present an increase in the peak acceleration and peak velocity despite the increase in the arm weight. In agreement with these predictions, the subjects performed faster movements in hypergravity with significant increases in the peak acceleration and peak velocity, which were accompanied by a significant decrease in the movement duration. This suggests that movement kinematics change in response to an increase in gravity, which is consistent with the hypothesis that motor commands are optimized and the action of gravity on the limb is taken into account. The results provide evidence for an internal representation of gravity in the central planning process and further suggest that an adaptation to altered dynamics can be understood as a reoptimization process.

Optimizing highly noncoplanar VMAT trajectories: the NoVo method.

PubMed

Langhans, Marco; Unkelbach, Jan; Bortfeld, Thomas; Craft, David

2018-01-16

We introduce a new method called NoVo (Noncoplanar VMAT Optimization) to produce volumetric modulated arc therapy (VMAT) treatment plans with noncoplanar trajectories. While the use of noncoplanar beam arrangements for intensity modulated radiation therapy (IMRT), and in particular high fraction stereotactic radiosurgery (SRS), is common, noncoplanar beam trajectories for VMAT are less common as the availability of treatment machines handling these is limited. For both IMRT and VMAT, the beam angle selection problem is highly nonconvex in nature, which is why automated beam angle selection procedures have not entered mainstream clinical usage. NoVo determines a noncoplanar VMAT solution (i.e. the simultaneous trajectories of the gantry and the couch) by first computing a [Formula: see text] solution (beams from every possible direction, suitably discretized) and then eliminating beams by examing fluence contributions. Also all beam angles are scored via geometrical considerations only to find out the usefulness of the whole beam space in a very short time. A custom path finding algorithm is applied to find an optimized, continuous trajectory through the most promising beam angles using the calculated score of the beam space. Finally, using this trajectory a VMAT plan is optimized. For three clinical cases, a lung, brain, and liver case, we compare NoVo to the ideal [Formula: see text] solution, nine beam noncoplanar IMRT, coplanar VMAT, and a recently published noncoplanar VMAT algorithm. NoVo comes closest to the [Formula: see text] solution considering the lung case (brain and liver case: second), as well as improving the solution time by using geometrical considerations, followed by a time effective iterative process reducing the [Formula: see text] solution. Compared to a recently published noncoplanar VMAT algorithm, using NoVo the computation time is reduced by a factor of 2-3 (depending on the case). Compared to coplanar VMAT, NoVo reduces the objective function value by 24%, 49% and 6% for the lung, brain and liver cases, respectively.

Optimizing highly noncoplanar VMAT trajectories: the NoVo method

NASA Astrophysics Data System (ADS)

Langhans, Marco; Unkelbach, Jan; Bortfeld, Thomas; Craft, David

2018-01-01

We introduce a new method called NoVo (Noncoplanar VMAT Optimization) to produce volumetric modulated arc therapy (VMAT) treatment plans with noncoplanar trajectories. While the use of noncoplanar beam arrangements for intensity modulated radiation therapy (IMRT), and in particular high fraction stereotactic radiosurgery (SRS), is common, noncoplanar beam trajectories for VMAT are less common as the availability of treatment machines handling these is limited. For both IMRT and VMAT, the beam angle selection problem is highly nonconvex in nature, which is why automated beam angle selection procedures have not entered mainstream clinical usage. NoVo determines a noncoplanar VMAT solution (i.e. the simultaneous trajectories of the gantry and the couch) by first computing a 4π solution (beams from every possible direction, suitably discretized) and then eliminating beams by examing fluence contributions. Also all beam angles are scored via geometrical considerations only to find out the usefulness of the whole beam space in a very short time. A custom path finding algorithm is applied to find an optimized, continuous trajectory through the most promising beam angles using the calculated score of the beam space. Finally, using this trajectory a VMAT plan is optimized. For three clinical cases, a lung, brain, and liver case, we compare NoVo to the ideal 4π solution, nine beam noncoplanar IMRT, coplanar VMAT, and a recently published noncoplanar VMAT algorithm. NoVo comes closest to the 4π solution considering the lung case (brain and liver case: second), as well as improving the solution time by using geometrical considerations, followed by a time effective iterative process reducing the 4π solution. Compared to a recently published noncoplanar VMAT algorithm, using NoVo the computation time is reduced by a factor of 2-3 (depending on the case). Compared to coplanar VMAT, NoVo reduces the objective function value by 24%, 49% and 6% for the lung, brain and liver cases, respectively.

The primer vector in linear, relative-motion equations. [spacecraft trajectory optimization

NASA Technical Reports Server (NTRS)

1980-01-01

Primer vector theory is used in analyzing a set of linear, relative-motion equations - the Clohessy-Wiltshire equations - to determine the criteria and necessary conditions for an optimal, N-impulse trajectory. Since the state vector for these equations is defined in terms of a linear system of ordinary differential equations, all fundamental relations defining the solution of the state and costate equations, and the necessary conditions for optimality, can be expressed in terms of elementary functions. The analysis develops the analytical criteria for improving a solution by (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of (1) fixed-end conditions, two-impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized rendezvous problem. A sequence of rendezvous problems is solved to illustrate the analysis and the computational procedure.

Optimal trajectories based on linear equations

NASA Technical Reports Server (NTRS)

Carter, Thomas E.

1990-01-01

The Principal results of a recent theory of fuel optimal space trajectories for linear differential equations are presented. Both impulsive and bounded-thrust problems are treated. A new form of the Lawden Primer vector is found that is identical for both problems. For this reason, starting iteratives from the solution of the impulsive problem are highly effective in the solution of the two-point boundary-value problem associated with bounded thrust. These results were applied to the problem of fuel optimal maneuvers of a spacecraft near a satellite in circular orbit using the Clohessy-Wiltshire equations. For this case two-point boundary-value problems were solved using a microcomputer, and optimal trajectory shapes displayed. The results of this theory can also be applied if the satellite is in an arbitrary Keplerian orbit through the use of the Tschauner-Hempel equations. A new form of the solution of these equations has been found that is identical for elliptical, parabolic, and hyperbolic orbits except in the way that a certain integral is evaluated. For elliptical orbits this integral is evaluated through the use of the eccentric anomaly. An analogous evaluation is performed for hyperbolic orbits.

Optimal trajectories for solar bow shock mission

NASA Astrophysics Data System (ADS)

Pizzurro, S.; Circi, C.

2012-11-01

This paper deals a Solar Bow Shock mission, a phenomenon of interaction between the solar wind and the interstellar medium, due to the relative motion of our star with respect to the enormous interstellar matter cloud that contains it. This phenomenon occurs at boundary of the solar system (200 AU), and it is preferable a mission in situ that could examine in detail what actually happens on-the-spot, to understand its effect on the planets of the solar system. Voyager 1 & 2 reached the area where the phenomenon takes place after 30 years. The target is to arrive there optimizing both the transfer time, and the propellant mass consumption. Therefore, the trajectory will be optimized using different propulsion systems and appropriate flyby sequences.. The approach techniques that will be used foresee executions of impulsive or ballistic gravity assists with the utilisation of high thrust engine only, or low thrust engine only, or both engines in two different phases of the mission. By comparing all the solutions obtained imposing different initial conditions the optimal trajectory to arrive at Solar Bow Shock is presented.

Lagrangian Approach to Jet Mixing and Optimization of the Reactor for Production of Carbon Nanotubes

NASA Technical Reports Server (NTRS)

Povitsky, Alex; Salas, Manuel D.

2001-01-01

This study was motivated by an attempt to optimize the High Pressure carbon oxide (HiPco) process for the production of carbon nanotubes from gaseous carbon oxide, The goal is to achieve rapid and uniform heating of catalyst particles by an optimal arrangement of jets. A mixed Eulerian and Lagrangian approach is implemented to track the temperature of catalyst particles along their trajectories as a function of time. The FLUENT CFD software with second-order upwind approximation of convective terms and an algebraic multigrid-based solver is used. The poor performance of the original reactor configuration is explained in terms of features of particle trajectories. The trajectories most exposed to the hot jets appear to be the most problematic for heating because they either bend towards the cold jet interior or rotate upwind of the mixing zone. To reduce undesirable slow and/or oscillatory heating of catalyst particles, a reactor configuration with three central jets is proposed and the optimal location of the central and peripheral nozzles is determined.

Traj_opt User's Guide

NASA Technical Reports Server (NTRS)

Saunders, David A.

2005-01-01

Trajectory optimization program Traj_opt was developed at Ames Research Center to help assess the potential benefits of ultrahigh temperature ceramic materials applied to reusable space vehicles with sharp noses and wing leading edges. Traj_opt loosely couples the Ames three-degrees-of-freedom trajectory package Traj (see NASA-TM-2004-212847) with the SNOPT optimization package (Stanford University Technical Report SOL 98-1). Traj_opt version January 22, 2003 is covered by this user guide. The program has been applied extensively to entry and ascent abort trajectory calculations for sharp and blunt crew transfer vehicles. The main optimization variables are control points for the angle of attack and bank angle time histories. No propulsion options are provided, but numerous objective functions may be specified and the nonlinear constraints implemented include a distributed surface heating constraint capability. Aero-capture calculations are also treated with an option to minimize orbital eccentricity at apoapsis. Traj_opt runs efficiently on a single processor, using forward or central differences for the gradient calculations. Results may be displayed conveniently with Gnuplot scripts. Control files recommended for five standard reentry and ascent abort trajectories are included along with detailed descriptions of the inputs and outputs.

Traffic Aware Strategic Aircrew Requests (TASAR)

NASA Technical Reports Server (NTRS)

Ballin, Mark G.; Wing, David J.

2012-01-01

Under Instrument Flight Rules, pilots are not permitted to make changes to their approved trajectory without first receiving permission from Air Traffic Control (ATC). Referred to as "user requests," trajectory change requests from aircrews are often denied or deferred by controllers because they have awareness of traffic and airspace constraints not currently available to flight crews. With the introduction of Automatic Dependent Surveillance-Broadcast (ADS-B) and other information services, a rich traffic, weather, and airspace information environment is becoming available on the flight deck. Automation developed by NASA uses this information to aid flight crews in the identification and formulation of optimal conflict-free trajectory requests. The concept of Traffic Aware Strategic Aircrew Requests (TASAR) combines ADS-B and airborne automation to enable user-optimal in-flight trajectory replanning and to increase the likelihood of ATC approval for the resulting trajectory change request. TASAR may improve flight efficiency or other user-desired attributes of the flight while not impacting and potentially benefiting the air traffic controller. This paper describes the TASAR concept of operations, its enabling automation technology which is currently under development, and NASA s plans for concept assessment and maturation.

Multi-Objective Hybrid Optimal Control for Interplanetary Mission Planning

NASA Technical Reports Server (NTRS)

Englander, Jacob

2015-01-01

Preliminary design of low-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. Because low-thrust trajectory design is tightly coupled with systems design, power and propulsion characteristics must be chosen as well. In addition, a time-history of control variables must be chosen which defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated. The customer who commissions a trajectory design is not usually interested in a point solution, but rather the exploration of the trade space of trajectories between several different objective functions. This can be very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a multi-objective hybrid optimal control problem. The methods is demonstrated on hypothetical mission to the main asteroid belt and to Deimos.

Multi-Objective Hybrid Optimal Control for Interplanetary Mission Planning

NASA Technical Reports Server (NTRS)

Englander, Jacob A.

2014-01-01

Preliminary design of low-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. Because low-thrust trajectory design is tightly coupled with systems design, power and propulsion characteristics must be chosen as well. In addition, a time-history of control variables must be chosen which defines the trajectory. There are often may thousands, if not millions, of possible trajectories to be evaluated. The customer who commissions a trajectory design is not usually interested in a point solution, but rather the exploration of the trade space of trajectories between several different objective functions. This can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a multi-objective hybrid optimal control problem. The method is demonstrated on hypothetical mission to the main asteroid belt and to Deimos.

International Space Station (ISS) External Thermal Control System (ETCS) Loop A Pump Module (PM) Jettison Options Assessment

NASA Technical Reports Server (NTRS)

Murri, Daniel G.; Dwyer Cianciolo, Alicia; Shidner, Jeremy D.; Powell, Richard W.

2014-01-01

On December 11, 2013, the International Space Station (ISS) experienced a failure of the External Thermal Control System (ETCS) Loop A Pump Module (PM). To minimize the number of extravehicular activities (EVA) required to replace the PM, jettisoning the faulty pump was evaluated. The objective of this study was to independently evaluate the jettison options considered by the ISS Trajectory Operations Officer (TOPO) and to provide recommendations for safe jettison of the ETCS Loop A PM. The simulation selected to evaluate the TOPO options was the NASA Engineering and Safety Center's (NESC) version of Program to Optimize Simulated Trajectories II (POST2) developed to support another NESC assessment. The objective of the jettison analysis was twofold: (1) to independently verify TOPO posigrade and retrograde jettison results, and (2) to determine jettison guidelines based on additional sensitivity, trade study, and Monte Carlo (MC) analysis that would prevent PM recontact. Recontact in this study designates a propagated PM trajectory that comes within 500 m of the ISS propagated trajectory. An additional simulation using Systems Tool Kit (STK) was run for independent verification of the POST2 simulation results. Ultimately, the ISS Program removed the PM jettison option from consideration. However, prior to the Program decision, the retrograde jettison option remained part of the EVA contingency plan. The jettison analysis presented showed that, in addition to separation velocity/direction and the atmosphere conditions, the key variables in determining the time to recontact the ISS is highly dependent on the ballistic number (BN) difference between the object being jettisoned and the ISS.

Skip trajectory flight of a ramjet-powered hypersonic vehicle

NASA Astrophysics Data System (ADS)

Fomin, V. M.; Aulchenko, S. M.; Zvegintsev, V. I.

2010-07-01

Possible skip trajectories of a flying vehicle with a periodically actuated ramjet are numerically simulated. An optimal choice of ramjet actuation areas and duration is demonstrated to ensure the maximum flight range with a given amount of the fuel. The main advantage of skip trajectories is found to be a significant (by an order of magnitude) decrease in thermal loads on the flying vehicle.

TH-EF-BRB-10: Dosimetric Validation of a Trajectory Based Cranial SRS Treatment Technique On a Varian TrueBeam Linac

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wilson, B; Vancouver Cancer Centre, Vancouver, BC; Gete, E

2016-06-15

Purpose: This work investigates the dosimetric accuracy of a trajectory based delivery technique in which an optimized radiation beam is delivered along a Couch-Gantry trajectory that is formed by simultaneous rotation of the linac gantry and the treatment couch. Methods: Nine trajectory based cranial SRS treatment plans were created using in-house optimization software. The plans were calculated for delivery on the TrueBeam STx linac with 6MV photon beam. Dose optimization was performed along a user-defined trajectory using MLC modulation, dose rate modulation and jaw tracking. The pre-defined trajectory chosen for this study is formed by a couch rotation through itsmore » full range of 180 degrees while the gantry makes four partial arc sweeps which are 170 degrees each. For final dose calculation, the trajectory based plans were exported to the Varian Eclipse Treatment Planning System. The plans were calculated on a homogeneous cube phantom measuring 18.2×18.2×18.2 cm3 with the analytical anisotropic algorithm (AAA) using a 1mm3 calculation voxel. The plans were delivered on the TrueBeam linac via the developer’s mode. Point dose measurements were performed on 9 patients with the IBA CC01 mini-chamber with a sensitive volume of 0.01 cc. Gafchromic film measurements along the sagittal and coronal planes were performed on three of the 9 treatment plans. Point dose values were compared with ion chamber measurements. Gamma analysis comparing film measurement and AAA calculations was performed using FilmQA Pro. Results: The AAA calculations and measurements were in good agreement. The point dose difference between AAA and ion chamber measurements were within 2.2%. Gamma analysis test pass rates (2%, 2mm passing criteria) for the Gafchromic film measurements were >95%. Conclusion: We have successfully tested TrueBeam’s ability to deliver accurate trajectory based treatments involving simultaneous gantry and couch rotation with MLC and dose rate modulation along the trajectory.« less

From medico-administrative databases analysis to care trajectories analytics: an example with the French SNDS.

PubMed

Drezen, Erwan; Guyet, Thomas; Happe, André

2018-02-01

Medico-administrative data like SNDS (Système National de Données de Santé) are not collected initially for epidemiological purposes. Moreover, the data model and the tools proposed to SNDS users make their in-depth exploitation difficult. We propose a data model, called the ePEPS model, based on healthcare trajectories to provide a medical view of raw data. A data abstraction process enables the clinician to have an intuitive medical view of raw data and to design a study-specific view. This view is based on a generic model of care trajectory, that is a sequence of time stamped medical events for a given patient. This model is combined with tools to manipulate care trajectories efficiently. © 2017 Société Française de Pharmacologie et de Thérapeutique.

Spinal pedicle screw planning using deformable atlas registration

NASA Astrophysics Data System (ADS)

Goerres, J.; Uneri, A.; De Silva, T.; Ketcha, M.; Reaungamornrat, S.; Jacobson, M.; Vogt, S.; Kleinszig, G.; Osgood, G.; Wolinsky, J.-P.; Siewerdsen, J. H.

2017-04-01

Spinal screw placement is a challenging task due to small bone corridors and high risk of neurological or vascular complications, benefiting from precision guidance/navigation and quality assurance (QA). Implicit to both guidance and QA is the definition of a surgical plan—i.e. the desired trajectories and device selection for target vertebrae—conventionally requiring time-consuming manual annotations by a skilled surgeon. We propose automation of such planning by deriving the pedicle trajectory and device selection from a patient’s preoperative CT or MRI. An atlas of vertebrae surfaces was created to provide the underlying basis for automatic planning—in this work, comprising 40 exemplary vertebrae at three levels of the spine (T7, T8, and L3). The atlas was enriched with ideal trajectory annotations for 60 pedicles in total. To define trajectories for a given patient, sparse deformation fields from the atlas surfaces to the input (CT or MR image) are applied on the annotated trajectories. Mean value coordinates are used to interpolate dense deformation fields. The pose of a straight trajectory is optimized by image-based registration to an accumulated volume of the deformed annotations. For evaluation, input deformation fields were created using coherent point drift (CPD) to perform a leave-one-out analysis over the atlas surfaces. CPD registration demonstrated surface error of 0.89  ±  0.10 mm (median  ±  interquartile range) for T7/T8 and 1.29  ±  0.15 mm for L3. At the pedicle center, registered trajectories deviated from the expert reference by 0.56  ±  0.63 mm (T7/T8) and 1.12  ±  0.67 mm (L3). The predicted maximum screw diameter differed by 0.45  ±  0.62 mm (T7/T8), and 1.26  ±  1.19 mm (L3). The automated planning method avoided screw collisions in all cases and demonstrated close agreement overall with expert reference plans, offering a potentially valuable tool in support of surgical guidance and QA.

Spinal pedicle screw planning using deformable atlas registration.

PubMed

Goerres, J; Uneri, A; De Silva, T; Ketcha, M; Reaungamornrat, S; Jacobson, M; Vogt, S; Kleinszig, G; Osgood, G; Wolinsky, J-P; Siewerdsen, J H

2017-04-07

Spinal screw placement is a challenging task due to small bone corridors and high risk of neurological or vascular complications, benefiting from precision guidance/navigation and quality assurance (QA). Implicit to both guidance and QA is the definition of a surgical plan-i.e. the desired trajectories and device selection for target vertebrae-conventionally requiring time-consuming manual annotations by a skilled surgeon. We propose automation of such planning by deriving the pedicle trajectory and device selection from a patient's preoperative CT or MRI. An atlas of vertebrae surfaces was created to provide the underlying basis for automatic planning-in this work, comprising 40 exemplary vertebrae at three levels of the spine (T7, T8, and L3). The atlas was enriched with ideal trajectory annotations for 60 pedicles in total. To define trajectories for a given patient, sparse deformation fields from the atlas surfaces to the input (CT or MR image) are applied on the annotated trajectories. Mean value coordinates are used to interpolate dense deformation fields. The pose of a straight trajectory is optimized by image-based registration to an accumulated volume of the deformed annotations. For evaluation, input deformation fields were created using coherent point drift (CPD) to perform a leave-one-out analysis over the atlas surfaces. CPD registration demonstrated surface error of 0.89  ±  0.10 mm (median  ±  interquartile range) for T7/T8 and 1.29  ±  0.15 mm for L3. At the pedicle center, registered trajectories deviated from the expert reference by 0.56  ±  0.63 mm (T7/T8) and 1.12  ±  0.67 mm (L3). The predicted maximum screw diameter differed by 0.45  ±  0.62 mm (T7/T8), and 1.26  ±  1.19 mm (L3). The automated planning method avoided screw collisions in all cases and demonstrated close agreement overall with expert reference plans, offering a potentially valuable tool in support of surgical guidance and QA.

A study of the influence of the sun on optimal two-impulse Earth-to-Moon trajectories with moderate time of flight in the three-body and four-body models

NASA Astrophysics Data System (ADS)

Filho, Luiz Arthur Gagg; da Silva Fernandes, Sandro

2017-05-01

In this work, a study about the influence of the Sun on optimal two-impulse Earth-to-Moon trajectories for interior transfers with moderate time of flight is presented considering the three-body and the four-body models. The optimization criterion is the total characteristic velocity which represents the fuel consumption of an infinite thrust propulsion system. The optimization problem has been formulated using the classic planar circular restricted three-body problem (PCR3BP) and the planar bi-circular restricted four-body problem (PBR4BP), and, it consists of transferring a spacecraft from a circular low Earth orbit (LEO) to a circular low Moon orbit (LMO) with minimum fuel consumption. The Sequential Gradient Restoration Algorithm (SGRA) is applied to determine the optimal solutions. Numerical results are presented for several final altitudes of a clockwise or a counterclockwise circular low Moon orbit considering a specified altitude of a counterclockwise circular low Earth orbit. Two types of analysis are performed: in the first one, the initial position of the Sun is taken as a parameter and the major parameters describing the optimal trajectories are obtained by solving an optimization problem of one degree of freedom. In the second analysis, an optimization problem with two degrees of freedom is considered and the initial position of the Sun is taken as an additional unknown.

Optimal motion planning for collision avoidance of mobile robots in non-stationary environments

NASA Technical Reports Server (NTRS)

Kyriakopoulos, K. J.; Saridis, G. N.

1992-01-01

An optimal control formulation of the problem of collision avoidance of mobile robots moving in general terrains containing moving obstacles is presented. A dynamic model of the mobile robot and the dynamic constraints are derived. Collision avoidance is guaranteed if the minimum distance between the robot and the object is nonzero. A nominal trajectory is assumed to be known from off-line planning. The main idea is to change the velocity along the nominal trajectory so that collisions are avoided. Time consistency with the nominal plan is desirable. A numerical solution of the optimization problem is obtained. A perturbation control type of approach is used to update the optimal plan. Simulation results verify the value of the proposed strategy.

Optimization of extended propulsion time nuclear-electric propulsion trajectories

NASA Technical Reports Server (NTRS)

Sauer, C. G., Jr.

1981-01-01

This paper presents the methodology used in optimizing extended propulsion time NEP missions considering realistic thruster lifetime constraints. These missions consist of a powered spiral escape from a 700-km circular orbit at the earth, followed by a powered heliocentric transfer with an optimized coast phase, and terminating in a spiral capture phase at the target planet. This analysis is most applicable to those missions with very high energy requirements such as outer planet orbiter missions or sample return missions where the total propulsion time could greatly exceed the expected lifetime of an individual thruster. This methodology has been applied to the investigation of NEP missions to the outer planets where examples are presented of both constrained and optimized trajectories.

Optimality of affine control system of several species in competition on a sequential batch reactor

NASA Astrophysics Data System (ADS)

Rodríguez, J. C.; Ramírez, H.; Gajardo, P.; Rapaport, A.

2014-09-01

In this paper, we analyse the optimality of affine control system of several species in competition for a single substrate on a sequential batch reactor, with the objective being to reach a given (low) level of the substrate. We allow controls to be bounded measurable functions of time plus possible impulses. A suitable modification of the dynamics leads to a slightly different optimal control problem, without impulsive controls, for which we apply different optimality conditions derived from Pontryagin principle and the Hamilton-Jacobi-Bellman equation. We thus characterise the singular trajectories of our problem as the extremal trajectories keeping the substrate at a constant level. We also establish conditions for which an immediate one impulse (IOI) strategy is optimal. Some numerical experiences are then included in order to illustrate our study and show that those conditions are also necessary to ensure the optimality of the IOI strategy.

Multi-step optimization strategy for fuel-optimal orbital transfer of low-thrust spacecraft

NASA Astrophysics Data System (ADS)

Rasotto, M.; Armellin, R.; Di Lizia, P.

2016-03-01

An effective method for the design of fuel-optimal transfers in two- and three-body dynamics is presented. The optimal control problem is formulated using calculus of variation and primer vector theory. This leads to a multi-point boundary value problem (MPBVP), characterized by complex inner constraints and a discontinuous thrust profile. The first issue is addressed by embedding the MPBVP in a parametric optimization problem, thus allowing a simplification of the set of transversality constraints. The second problem is solved by representing the discontinuous control function by a smooth function depending on a continuation parameter. The resulting trajectory optimization method can deal with different intermediate conditions, and no a priori knowledge of the control structure is required. Test cases in both the two- and three-body dynamics show the capability of the method in solving complex trajectory design problems.

Trajectory planning of mobile robots using indirect solution of optimal control method in generalized point-to-point task

NASA Astrophysics Data System (ADS)

Nazemizadeh, M.; Rahimi, H. N.; Amini Khoiy, K.

2012-03-01

This paper presents an optimal control strategy for optimal trajectory planning of mobile robots by considering nonlinear dynamic model and nonholonomic constraints of the system. The nonholonomic constraints of the system are introduced by a nonintegrable set of differential equations which represent kinematic restriction on the motion. The Lagrange's principle is employed to derive the nonlinear equations of the system. Then, the optimal path planning of the mobile robot is formulated as an optimal control problem. To set up the problem, the nonlinear equations of the system are assumed as constraints, and a minimum energy objective function is defined. To solve the problem, an indirect solution of the optimal control method is employed, and conditions of the optimality derived as a set of coupled nonlinear differential equations. The optimality equations are solved numerically, and various simulations are performed for a nonholonomic mobile robot to illustrate effectiveness of the proposed method.

A new measuring method for motion accuracy of 3-axis NC equipments based on composite trajectory of circle and non-circle

NASA Astrophysics Data System (ADS)

Yang, Fan; Du, Zhengchun; Yang, Jiangguo; Hong, Maisheng

2011-12-01

Geometric motion error measurement has been considered as an important task for accuracy enhancement and quality assurance of NC machine tools and CMMs. In consideration of the disadvantages of traditional measuring methods,a new measuring method for motion accuracy of 3-axis NC equipments based on composite trajectory including circle and non-circle(straight line and/or polygonal line) is proposed. The principles and techniques of the new measuring method are discussed in detail. 8 feasible measuring strategies based on different measuring groupings are summarized and optimized. The experiment of the most preferable strategy is carried out on the 3-axis CNC vertical machining center Cincinnati 750 Arrow by using cross grid encoder. The whole measuring time of 21 error components of the new method is cut down to 1-2 h because of easy installation, adjustment, operation and the characteristics of non-contact measurement. Result shows that the new method is suitable for `on machine" measurement and has good prospects of wide application.

Optimal bipedal interactions with dynamic terrain: synthesis and analysis via nonlinear programming

NASA Astrophysics Data System (ADS)

Hubicki, Christian; Goldman, Daniel; Ames, Aaron

In terrestrial locomotion, gait dynamics and motor control behaviors are tuned to interact efficiently and stably with the dynamics of the terrain (i.e. terradynamics). This controlled interaction must be particularly thoughtful in bipeds, as their reduced contact points render them highly susceptible to falls. While bipedalism under rigid terrain assumptions is well-studied, insights for two-legged locomotion on soft terrain, such as sand and dirt, are comparatively sparse. We seek an understanding of how biological bipeds stably and economically negotiate granular media, with an eye toward imbuing those abilities in bipedal robots. We present a trajectory optimization method for controlled systems subject to granular intrusion. By formulating a large-scale nonlinear program (NLP) with reduced-order resistive force theory (RFT) models and jamming cone dynamics, the optimized motions are informed and shaped by the dynamics of the terrain. Using a variant of direct collocation methods, we can express all optimization objectives and constraints in closed-form, resulting in rapid solving by standard NLP solvers, such as IPOPT. We employ this tool to analyze emergent features of bipedal locomotion in granular media, with an eye toward robotic implementation.

Trajectory Optimization of an Interstellar Mission Using Solar Electric Propulsion

NASA Technical Reports Server (NTRS)

Kluever, Craig A.

1996-01-01

This paper presents several mission designs for heliospheric boundary exploration using spacecraft with low-thrust ion engines as the primary mode of propulsion The mission design goal is to transfer a 200-kg spacecraft to the heliospheric boundary in minimum time. The mission design is a combined trajectory and propulsion system optimization problem. Trajectory design variables include launch date, launch energy, burn and coast arc switch times, thrust steering direction, and planetary flyby conditions. Propulsion system design parameters include input power and specific impulse. Both SEP and NEP spacecraft arc considered and a wide range of launch vehicle options are investigated. Numerical results are presented and comparisons with the all chemical heliospheric missions from Ref 9 are made.

The large deviation function for entropy production: the optimal trajectory and the role of fluctuations

NASA Astrophysics Data System (ADS)

Speck, Thomas; Engel, Andreas; Seifert, Udo

2012-12-01

We study the large deviation function for the entropy production rate in two driven one-dimensional systems: the asymmetric random walk on a discrete lattice and Brownian motion in a continuous periodic potential. We compare two approaches: using the Donsker-Varadhan theory and using the Freidlin-Wentzell theory. We show that the wings of the large deviation function are dominated by a single optimal trajectory: either in the forward direction (positive rate) or in the backward direction (negative rate). The joining of the two branches at zero entropy production implies a non-differentiability and thus the appearance of a ‘kink’. However, around zero entropy production, many trajectories contribute and thus the ‘kink’ is smeared out.

Transfers between libration-point orbits in the elliptic restricted problem

NASA Astrophysics Data System (ADS)

Hiday, L. A.; Howell, K. C.

The present time-fixed impulsive transfers between 3D libration point orbits in the vicinity of the interior L(1) libration point of the sun-earth-moon barycenter system are 'optimal' in that the total characteristic velocity required for implementation of the transfer exhibits a local minimum. The conditions necessary for a time-fixed, two-impulse transfer trajectory to be optimal are stated in terms of the primer vector, and the conditions necessary for satisfying the local optimality of a transfer trajectory containing additional impulses are addressed by requiring continuity of the Hamiltonian and the derivative of the primer vector at all interior impulses.

Air breathing engine/rocket trajectory optimization

NASA Technical Reports Server (NTRS)

Smith, V. K., III

1979-01-01

This research has focused on improving the mathematical models of the air-breathing propulsion systems, which can be mated with the rocket engine model and incorporated in trajectory optimization codes. Improved engine simulations provided accurate representation of the complex cycles proposed for advanced launch vehicles, thereby increasing the confidence in propellant use and payload calculations. The versatile QNEP (Quick Navy Engine Program) was modified to allow treatment of advanced turboaccelerator cycles using hydrogen or hydrocarbon fuels and operating in the vehicle flow field.

NASP guidance design for vehicle autonomy

NASA Astrophysics Data System (ADS)

Wagner, E. A.; Li, I.; Nguyen, D. D.; Nguyen, P. L.

1990-10-01

Vehicle guidance for General Dynamics' NASP vehicle is planned to be self-contained onboard the vehicle, and independent of any ground support during the mission. It will include real-time onboard abort and ascent trajectory optimization capability. Although these features should be considered a natural outgrowth of research in guidance and trajectory optimization and advances in computation, facilitating full vehicle autonomy for NASP represents a significant advance relative to any flight-demonstrated guidance. Algorithms and processing requirements for autonomous NASP vehicle guidance are considered.

Conceptual Design and Structural Analysis of an Open Rotor Hybrid Wing Body Aircraft

NASA Technical Reports Server (NTRS)

Gern, Frank H.

2013-01-01

Through a recent NASA contract, Boeing Research and Technology in Huntington Beach, CA developed and optimized a conceptual design of an open rotor hybrid wing body aircraft (HWB). Open rotor engines offer a significant potential for fuel burn savings over turbofan engines, while the HWB configuration potentially allows to offset noise penalties through possible engine shielding. Researchers at NASA Langley converted the Boeing design to a FLOPS model which will be used to develop take-off and landing trajectories for community noise analyses. The FLOPS model was calibrated using Boeing data and shows good agreement with the original Boeing design. To complement Boeing s detailed aerodynamics and propulsion airframe integration work, a newly developed and validated conceptual structural analysis and optimization tool was used for a conceptual loads analysis and structural weights estimate. Structural optimization and weight calculation are based on a Nastran finite element model of the primary HWB structure, featuring centerbody, mid section, outboard wing, and aft body. Results for flight loads, deformations, wing weight, and centerbody weight are presented and compared to Boeing and FLOPS analyses.

A real-time guidance algorithm for aerospace plane optimal ascent to low earth orbit

NASA Technical Reports Server (NTRS)

Calise, A. J.; Flandro, G. A.; Corban, J. E.

1989-01-01

Problems of onboard trajectory optimization and synthesis of suitable guidance laws for ascent to low Earth orbit of an air-breathing, single-stage-to-orbit vehicle are addressed. A multimode propulsion system is assumed which incorporates turbojet, ramjet, Scramjet, and rocket engines. An algorithm for generating fuel-optimal climb profiles is presented. This algorithm results from the application of the minimum principle to a low-order dynamic model that includes angle-of-attack effects and the normal component of thrust. Maximum dynamic pressure and maximum aerodynamic heating rate constraints are considered. Switching conditions are derived which, under appropriate assumptions, govern optimal transition from one propulsion mode to another. A nonlinear transformation technique is employed to derived a feedback controller for tracking the computed trajectory. Numerical results illustrate the nature of the resulting fuel-optimal climb paths.

Simulated annealing in orbital flight planning

NASA Technical Reports Server (NTRS)

Soller, Jeffrey

1990-01-01

Simulated annealing is used to solve a minimum fuel trajectory problem in the space station environment. The environment is unique because the space station will define the first true multivehicle environment in space. The optimization yields surfaces which are potentially complex, with multiple local minima. Because of the likelihood of these local minima, descent techniques are unable to offer robust solutions. Other deterministic optimization techniques were explored without success. The simulated annealing optimization is capable of identifying a minimum-fuel, two-burn trajectory subject to four constraints. Furthermore, the computational efforts involved in the optimization are such that missions could be planned on board the space station. Potential applications could include the on-site planning of rendezvous with a target craft of the emergency rescue of an astronaut. Future research will include multiwaypoint maneuvers, using a knowledge base to guide the optimization.

A Computationally Inexpensive Optimal Guidance via Radial-Basis-Function Neural Network for Autonomous Soft Landing on Asteroids

PubMed Central

Zhang, Peng; Liu, Keping; Zhao, Bo; Li, Yuanchun

2015-01-01

Optimal guidance is essential for the soft landing task. However, due to its high computational complexities, it is hardly applied to the autonomous guidance. In this paper, a computationally inexpensive optimal guidance algorithm based on the radial basis function neural network (RBFNN) is proposed. The optimization problem of the trajectory for soft landing on asteroids is formulated and transformed into a two-point boundary value problem (TPBVP). Combining the database of initial states with the relative initial co-states, an RBFNN is trained offline. The optimal trajectory of the soft landing is determined rapidly by applying the trained network in the online guidance. The Monte Carlo simulations of soft landing on the Eros433 are performed to demonstrate the effectiveness of the proposed guidance algorithm. PMID:26367382

Selection and trajectory design to mission secondary targets

NASA Astrophysics Data System (ADS)

Victorino Sarli, Bruno; Kawakatsu, Yasuhiro

2017-02-01

Recently, with new trajectory design techniques and use of low-thrust propulsion systems, missions have become more efficient and cheaper with respect to propellant. As a way to increase the mission's value and scientific return, secondary targets close to the main trajectory are often added with a small change in the transfer trajectory. As a result of their large number, importance and facility to perform a flyby, asteroids are commonly used as such targets. This work uses the Primer Vector theory to define the direction and magnitude of the thrust for a minimum fuel consumption problem. The design of a low-thrust trajectory with a midcourse asteroid flyby is not only challenging for the low-thrust problem solution, but also with respect to the selection of a target and its flyby point. Currently more than 700,000 minor bodies have been identified, which generates a very large number of possible flyby points. This work uses a combination of reachability, reference orbit, and linear theory to select appropriate candidates, drastically reducing the simulation time, to be later included in the main trajectory and optimized. Two test cases are presented using the aforementioned selection process and optimization to add and design a secondary flyby to a mission with the primary objective of 3200 Phaethon flyby and 25143 Itokawa rendezvous.

Trajectory Assessment and Modification Tools for Next Generation Air Traffic Management Operations

NASA Technical Reports Server (NTRS)

Brasil, Connie; Lee, Paul; Mainini, Matthew; Lee, Homola; Lee, Hwasoo; Prevot, Thomas; Smith, Nancy

2011-01-01

This paper reviews three Next Generation Air Transportation System (NextGen) based high fidelity air traffic control human-in-the-loop (HITL) simulations, with a focus on the expected requirement of enhanced automated trajectory assessment and modification tools to support future air traffic flow management (ATFM) planning positions. The simulations were conducted at the National Aeronautics and Space Administration (NASA) Ames Research Centers Airspace Operations Laboratory (AOL) in 2009 and 2010. The test airspace for all three simulations assumed the mid-term NextGenEn-Route high altitude environment utilizing high altitude sectors from the Kansas City and Memphis Air Route Traffic Control Centers. Trajectory assessment, modification and coordination decision support tools were developed at the AOL in order to perform future ATFM tasks. Overall tool usage results and user acceptability ratings were collected across three areas of NextGen operatoins to evaluate the tools. In addition to the usefulness and usability feedback, feasibility issues, benefits, and future requirements were also addressed. Overall, the tool sets were rated very useful and usable, and many elements of the tools received high scores and were used frequently and successfully. Tool utilization results in all three HITLs showed both user and system benefits including better airspace throughput, reduced controller workload, and highly effective communication protocols in both full Data Comm and mixed-equipage environments.

ANALYTiC: An Active Learning System for Trajectory Classification.

PubMed

Soares Junior, Amilcar; Renso, Chiara; Matwin, Stan

2017-01-01

The increasing availability and use of positioning devices has resulted in large volumes of trajectory data. However, semantic annotations for such data are typically added by domain experts, which is a time-consuming task. Machine-learning algorithms can help infer semantic annotations from trajectory data by learning from sets of labeled data. Specifically, active learning approaches can minimize the set of trajectories to be annotated while preserving good performance measures. The ANALYTiC web-based interactive tool visually guides users through this annotation process.

Trajectory-Based Takeoff Time Predictions Applied to Tactical Departure Scheduling: Concept Description, System Design, and Initial Observations

NASA Technical Reports Server (NTRS)

Engelland, Shawn A.; Capps, Alan

2011-01-01

Current aircraft departure release times are based on manual estimates of aircraft takeoff times. Uncertainty in takeoff time estimates may result in missed opportunities to merge into constrained en route streams and lead to lost throughput. However, technology exists to improve takeoff time estimates by using the aircraft surface trajectory predictions that enable air traffic control tower (ATCT) decision support tools. NASA s Precision Departure Release Capability (PDRC) is designed to use automated surface trajectory-based takeoff time estimates to improve en route tactical departure scheduling. This is accomplished by integrating an ATCT decision support tool with an en route tactical departure scheduling decision support tool. The PDRC concept and prototype software have been developed, and an initial test was completed at air traffic control facilities in Dallas/Fort Worth. This paper describes the PDRC operational concept, system design, and initial observations.

Splash: a software tool for stereotactic planning of recording chamber placement and electrode trajectories.

PubMed

Sperka, Daniel J; Ditterich, Jochen

2011-01-01

While computer-aided planning of human neurosurgeries is becoming more and more common, animal researchers still largely rely on paper atlases for planning their approach before implanting recording chambers to perform invasive recordings of neural activity, which makes this planning process tedious and error-prone. Here we present SPLASh (Stereotactic PLAnning Software), an interactive software tool for the stereotactic planning of recording chamber placement and electrode trajectories. SPLASh has been developed for monkey cortical recordings and relies on a combination of structural MRIs and electronic brain atlases. Since SPLASh is based on the neuroanatomy software Caret, it should also be possible to use it for other parts of the brain or other species for which Caret atlases are available. The tool allows the user to interactively evaluate different possible placements of recording chambers and to simulate electrode trajectories.

Splash: A Software Tool for Stereotactic Planning of Recording Chamber Placement and Electrode Trajectories

PubMed Central

Sperka, Daniel J.; Ditterich, Jochen

2011-01-01

While computer-aided planning of human neurosurgeries is becoming more and more common, animal researchers still largely rely on paper atlases for planning their approach before implanting recording chambers to perform invasive recordings of neural activity, which makes this planning process tedious and error-prone. Here we present SPLASh (Stereotactic PLAnning Software), an interactive software tool for the stereotactic planning of recording chamber placement and electrode trajectories. SPLASh has been developed for monkey cortical recordings and relies on a combination of structural MRIs and electronic brain atlases. Since SPLASh is based on the neuroanatomy software Caret, it should also be possible to use it for other parts of the brain or other species for which Caret atlases are available. The tool allows the user to interactively evaluate different possible placements of recording chambers and to simulate electrode trajectories. PMID:21472085

Conflict Resolution for Wind-Optimal Aircraft Trajectories in North Atlantic Oceanic Airspace with Wind Uncertainties

NASA Technical Reports Server (NTRS)

Rodionova, Olga; Sridhar, Banavar; Ng, Hok K.

2016-01-01

Air traffic in the North Atlantic oceanic airspace (NAT) experiences very strong winds caused by jet streams. Flying wind-optimal trajectories increases individual flight efficiency, which is advantageous when operating in the NAT. However, as the NAT is highly congested during peak hours, a large number of potential conflicts between flights are detected for the sets of wind-optimal trajectories. Conflict resolution performed at the strategic level of flight planning can significantly reduce the airspace congestion. However, being completed far in advance, strategic planning can only use predicted environmental conditions that may significantly differ from the real conditions experienced further by aircraft. The forecast uncertainties result in uncertainties in conflict prediction, and thus, conflict resolution becomes less efficient. This work considers wind uncertainties in order to improve the robustness of conflict resolution in the NAT. First, the influence of wind uncertainties on conflict prediction is investigated. Then, conflict resolution methods accounting for wind uncertainties are proposed.

Publications | Grid Modernization | NREL

Science.gov Websites

Photovoltaics: Trajectories and Challenges Cover of Efficient Relaxations for Joint Chance Constrained AC Optimal Power Flow publication Efficient Relaxations for Joint Chance Constrained AC Optimal Power Flow

Using Static Percentiles of AE9/AP9 to Approximate Dynamic Monte Carlo Runs for Radiation Analysis of Spiral Transfer Orbits

NASA Astrophysics Data System (ADS)

Kwan, Betty P.; O'Brien, T. Paul

2015-06-01

The Aerospace Corporation performed a study to determine whether static percentiles of AE9/AP9 can be used to approximate dynamic Monte Carlo runs for radiation analysis of spiral transfer orbits. Solar panel degradation is a major concern for solar-electric propulsion because solar-electric propulsion depends on the power output of the solar panel. Different spiral trajectories have different radiation environments that could lead to solar panel degradation. Because the spiral transfer orbits only last weeks to months, an average environment does not adequately address the possible transient enhancements of the radiation environment that must be accounted for in optimizing the transfer orbit trajectory. Therefore, to optimize the trajectory, an ensemble of Monte Carlo simulations of AE9/AP9 would normally be run for every spiral trajectory to determine the 95th percentile radiation environment. To avoid performing lengthy Monte Carlo dynamic simulations for every candidate spiral trajectory in the optimization, we found a static percentile that would be an accurate representation of the full Monte Carlo simulation for a representative set of spiral trajectories. For 3 LEO to GEO and 1 LEO to MEO trajectories, a static 90th percentile AP9 is a good approximation of the 95th percentile fluence with dynamics for 4-10 MeV protons, and a static 80th percentile AE9 is a good approximation of the 95th percentile fluence with dynamics for 0.5-2 MeV electrons. While the specific percentiles chosen cannot necessarily be used in general for other orbit trade studies, the concept of determining a static percentile as a quick approximation to a full Monte Carlo ensemble of simulations can likely be applied to other orbit trade studies. We expect the static percentile to depend on the region of space traversed, the mission duration, and the radiation effect considered.

Hierarchical Motion Planning for Autonomous Aerial and Terrestrial Vehicles

NASA Astrophysics Data System (ADS)

Cowlagi, Raghvendra V.

Autonomous mobile robots---both aerial and terrestrial vehicles---have gained immense importance due to the broad spectrum of their potential military and civilian applications. One of the indispensable requirements for the autonomy of a mobile vehicle is the vehicle's capability of planning and executing its motion, that is, finding appropriate control inputs for the vehicle such that the resulting vehicle motion satisfies the requirements of the vehicular task. The motion planning and control problem is inherently complex because it involves two disparate sub-problems: (1) satisfaction of the vehicular task requirements, which requires tools from combinatorics and/or formal methods, and (2) design of the vehicle control laws, which requires tools from dynamical systems and control theory. Accordingly, this problem is usually decomposed and solved over two levels of hierarchy. The higher level, called the geometric path planning level, finds a geometric path that satisfies the vehicular task requirements, e.g., obstacle avoidance. The lower level, called the trajectory planning level, involves sufficient smoothening of this geometric path followed by a suitable time parametrization to obtain a reference trajectory for the vehicle. Although simple and efficient, such hierarchical decomposition suffers a serious drawback: the geometric path planner has no information of the kinematical and dynamical constraints of the vehicle. Consequently, the geometric planner may produce paths that the trajectory planner cannot transform into a feasible reference trajectory. Two main ideas appear in the literature to remedy this problem: (a) randomized sampling-based planning, which eliminates the geometric planner altogether by planning in the vehicle state space, and (b) geometric planning supported by feedback control laws. The former class of methods suffer from a lack of optimality of the resultant trajectory, while the latter class of methods makes a restrictive assumption concerning the vehicle kinematical model. We propose a hierarchical motion planning framework based on a novel mode of interaction between these two levels of planning. This interaction rests on the solution of a special shortest-path problem on graphs, namely, one using costs defined on multiple edge transitions in the path instead of the usual single edge transition costs. These costs are provided by a local trajectory generation algorithm, which we implement using model predictive control and the concept of effective target sets for simplifying the non-convex constraints involved in the problem. The proposed motion planner ensures "consistency" between the two levels of planning, i.e., a guarantee that the higher level geometric path is always associated with a kinematically and dynamically feasible trajectory. The main contributions of this thesis are: 1. A motion planning framework based on history-dependent costs (H-costs) in cell decomposition graphs for incorporating vehicle dynamical constraints: this framework offers distinct advantages in comparison with the competing approaches of discretization of the state space, of randomized sampling-based motion planning, and of local feedback-based, decoupled hierarchical motion planning, 2. An efficient and flexible algorithm for finding optimal H-cost paths, 3. A precise and general formulation of a local trajectory problem (the tile motion planning problem) that allows independent development of the discrete planner and the trajectory planner, while maintaining "compatibility" between the two planners, 4. A local trajectory generation algorithm using mpc, and the application of the concept of effective target sets for a significant simplification of the local trajectory generation problem, 5. The geometric analysis of curvature-bounded traversal of rectangular channels, leading to less conservative results in comparison with a result reported in the literature, and also to the efficient construction of effective target sets for the solution of the tile motion planning problem, 6. A wavelet-based multi-resolution path planning scheme, and a proof of completeness of the proposed scheme: such proofs are altogether absent from other works on multi-resolution path planning, 7. A technique for extracting all information about cells---namely, the locations, the sizes, and the associated image intensities---directly from the set of significant detail coefficients considered for path planning at a given iteration, and 8. The extension of the multi-resolution path planning scheme to include vehicle dynamical constraints using the aforementioned history-dependent costs approach. The future work includes an implementation of the proposed framework involving a discrete planner that solves classical planning problems more general than the single-query path planning problem considered thus far, and involving trajectory generation schemes for realistic vehicle dynamical models such as the bicycle model.

Huygens probe entry, descent, and landing trajectory reconstruction using the Program to Optimize Simulated Trajectories II

NASA Astrophysics Data System (ADS)

Striepe, Scott Allen

The objectives of this research were to develop a reconstruction capability using the Program to Optimize Simulated Trajectories II (POST2), apply this capability to reconstruct the Huygens Titan probe entry, descent, and landing (EDL) trajectory, evaluate the newly developed POST2 reconstruction module, analyze the reconstructed trajectory, and assess the pre-flight simulation models used for Huygens EDL simulation. An extended Kalman filter (EKF) module was developed and integrated into POST2 to enable trajectory reconstruction (especially when using POST2-based mission specific simulations). Several validation cases, ranging from a single, constant parameter estimate to multivariable estimation cases similar to an actual mission flight, were executed to test the POST2 reconstruction module. Trajectory reconstruction of the Huygens entry probe at Titan was accomplished using accelerometer measurements taken during flight to adjust an estimated state (e.g., position, velocity, parachute drag, wind velocity, etc.) in a POST2-based simulation developed to support EDL analyses and design prior to entry. Although the main emphasis of the trajectory reconstruction was to evaluate models used in the NASA pre-entry trajectory simulation, the resulting reconstructed trajectory was also assessed to provide an independent evaluation of the ESA result. Major findings from this analysis include: Altitude profiles from this analysis agree well with other NASA and ESA results but not with Radar data, whereas a scale factor of about 0.93 would bring the radar measurements into compliance with these results; entry capsule aerodynamics predictions (axial component only) were well within 3-sigma bounds established pre-flight for most of the entry when compared to reconstructed values; Main parachute drag of 9% to 19% above ESA model was determined from the reconstructed trajectory; based on the tilt sensor and accelerometer data, the conclusion from this assessment was that the probe was tilted about 10 degrees during the Drogue parachute phase.

Monte Carlo tree search -based non-coplanar trajectory design for station parameter optimized radiation therapy (SPORT).

PubMed

Dong, Peng; Liu, Hongcheng; Xing, Lei

2018-06-04

An important yet challenging problem in LINAC-based rotational arc radiation therapy is the design of beam trajectory, which requires simultaneous consideration of delivery efficiency and final dose distribution. In this work, we propose a novel trajectory selection strategy by developing a Monte Carlo tree search (MCTS) algorithm during the beam trajectory selection process. Methods: To search through the vast number of possible trajectories, MCTS algorithm was implemented. In this approach, a candidate trajectory is explored by starting from a leaf node and sequentially examining the next level of linked nodes with consideration of geometric and physical constraints. The maximum Upper Confidence Bounds for Trees, which is a function of average objective function value and the number of times the node under testing has been visited, was employed to intelligently select the trajectory. For each candidate trajectory, we run an inverse fluence map optimization with an infinity norm regularization. The ranking of the plan as measured by the corresponding objective function value was then fed back to update the statistics of the nodes on the trajectory. The method was evaluated with a chest wall and a brain case, and the results were compared with the coplanar and noncoplanar 4pi beam configurations. Results: For both clinical cases, the MCTS method found effective and easy-to-deliver trajectories within an hour. As compared with the coplanar plans, it offers much better sparing of the OARs while maintaining the PTV coverage. The quality of the MCTS-generated plan is found to be comparable to the 4pi plans. Conclusion: AI based on MCTS is valuable to facilitate the design of beam trajectory and paves the way for future clinical use of non-coplanar treatment delivery. . © 2018 Institute of Physics and Engineering in Medicine.

A Parallel Processing and Diversified-Hidden-Gene-Based Genetic Algorithm Framework for Fuel-Optimal Trajectory Design for Interplanetary Spacecraft Missions

NASA Astrophysics Data System (ADS)

Somavarapu, Dhathri H.

This thesis proposes a new parallel computing genetic algorithm framework for designing fuel-optimal trajectories for interplanetary spacecraft missions. The framework can capture the deep search space of the problem with the use of a fixed chromosome structure and hidden-genes concept, can explore the diverse set of candidate solutions with the use of the adaptive and twin-space crowding techniques and, can execute on any high-performance computing (HPC) platform with the adoption of the portable message passing interface (MPI) standard. The algorithm is implemented in C++ with the use of the MPICH implementation of the MPI standard. The algorithm uses a patched-conic approach with two-body dynamics assumptions. New procedures are developed for determining trajectories in the Vinfinity-leveraging legs of the flight from the launch and non-launch planets and, deep-space maneuver legs of the flight from the launch and non-launch planets. The chromosome structure maintains the time of flight as a free parameter within certain boundaries. The fitness or the cost function of the algorithm uses only the mission Delta V, and does not include time of flight. The optimization is conducted with two variations for the minimum mission gravity-assist sequence, the 4-gravity-assist, and the 3-gravity-assist, with a maximum of 5 gravity-assists allowed in both the cases. The optimal trajectories discovered using the framework in both of the cases demonstrate the success of this framework.

Kinematic Optimization of Robot Trajectories for Thermal Spray Coating Application

NASA Astrophysics Data System (ADS)

Deng, Sihao; Liang, Hong; Cai, Zhenhua; Liao, Hanlin; Montavon, Ghislain

2014-12-01

Industrial robots are widely used in the field of thermal spray nowadays. Due to their characteristics of high-accuracy and programmable flexibility, spraying on complex geometrical workpieces can be realized in the equipped spray room. However, in some cases, the robots cannot guarantee the process parameters defined by the robot movement, such as the scanning trajectory, spray angle, relative speed between the torch and the substrate, etc., which have distinct influences on heat and mass transfer during the generation of any thermally sprayed coatings. In this study, an investigation on the robot kinematics was proposed to find the rules of motion in a common case. The results showed that the motion behavior of each axis of robot permits to identify the motion problems in the trajectory. This approach allows to optimize the robot trajectory generation in a limited working envelop. It also minimizes the influence of robot performance to achieve a more constant relative scanning speed which is represented as a key parameter in thermal spraying.

Program manual for HILTOP, a heliocentric interplanetary low thrust trajectory optimization program. Part 1: User's guide

NASA Technical Reports Server (NTRS)

Mann, F. I.; Horsewood, J. L.

1974-01-01

A performance-analysis computer program, that was developed explicitly to generate optimum electric propulsion trajectory data for missions of interest in the exploration of the solar system is presented. The program was primarily designed to evaluate the performance capabilities of electric propulsion systems, and in the simulation of a wide variety of interplanetary missions. A numerical integration of the two-body, three-dimensional equations of motion and the Euler-Lagrange equations was used in the program. Transversality conditions which permit the rapid generation of converged maximum-payload trajectory data, and the optimization of numerous other performance indices for which no transversality conditions exist are included. The ability to simulate constrained optimum solutions, including trajectories having specified propulsion time and constant thrust cone angle, is also in the program. The program was designed to handle multiple-target missions with various types of encounters, such as rendezvous, stopover, orbital capture, and flyby. Performance requirements for a variety of launch vehicles can be determined.

Six-Degree-of-Freedom Trajectory Optimization Utilizing a Two-Timescale Collocation Architecture

NASA Technical Reports Server (NTRS)

Desai, Prasun N.; Conway, Bruce A.

2005-01-01

Six-degree-of-freedom (6DOF) trajectory optimization of a reentry vehicle is solved using a two-timescale collocation methodology. This class of 6DOF trajectory problems are characterized by two distinct timescales in their governing equations, where a subset of the states have high-frequency dynamics (the rotational equations of motion) while the remaining states (the translational equations of motion) vary comparatively slowly. With conventional collocation methods, the 6DOF problem size becomes extraordinarily large and difficult to solve. Utilizing the two-timescale collocation architecture, the problem size is reduced significantly. The converged solution shows a realistic landing profile and captures the appropriate high-frequency rotational dynamics. A large reduction in the overall problem size (by 55%) is attained with the two-timescale architecture as compared to the conventional single-timescale collocation method. Consequently, optimum 6DOF trajectory problems can now be solved efficiently using collocation, which was not previously possible for a system with two distinct timescales in the governing states.

A New Unified Analysis of Estimate Errors by Model-Matching Phase-Estimation Methods for Sensorless Drive of Permanent-Magnet Synchronous Motors and New Trajectory-Oriented Vector Control, Part I

NASA Astrophysics Data System (ADS)

Shinnaka, Shinji; Sano, Kousuke

This paper presents a new unified analysis of estimate errors by model-matching phase-estimation methods such as rotor-flux state-observers, back EMF state-observers, and back EMF disturbance-observers, for sensorless drive of permanent-magnet synchronous motors. Analytical solutions about estimate errors, whose validity is confirmed by numerical experiments, are rich in universality and applicability. As an example of universality and applicability, a new trajectory-oriented vector control method is proposed, which can realize directly quasi-optimal strategy minimizing total losses with no additional computational loads by simply orienting one of vector-control coordinates to the associated quasi-optimal trajectory. The coordinate orientation rule, which is analytically derived, is surprisingly simple. Consequently the trajectory-oriented vector control method can be applied to a number of conventional vector control systems using one of the model-matching phase-estimation methods.

Automatic trajectory measurement of large numbers of crowded objects

NASA Astrophysics Data System (ADS)

Li, Hui; Liu, Ye; Chen, Yan Qiu

2013-06-01

Complex motion patterns of natural systems, such as fish schools, bird flocks, and cell groups, have attracted great attention from scientists for years. Trajectory measurement of individuals is vital for quantitative and high-throughput study of their collective behaviors. However, such data are rare mainly due to the challenges of detection and tracking of large numbers of objects with similar visual features and frequent occlusions. We present an automatic and effective framework to measure trajectories of large numbers of crowded oval-shaped objects, such as fish and cells. We first use a novel dual ellipse locator to detect the coarse position of each individual and then propose a variance minimization active contour method to obtain the optimal segmentation results. For tracking, cost matrix of assignment between consecutive frames is trainable via a random forest classifier with many spatial, texture, and shape features. The optimal trajectories are found for the whole image sequence by solving two linear assignment problems. We evaluate the proposed method on many challenging data sets.

Multi-Objective Hybrid Optimal Control for Multiple-Flyby Low-Thrust Mission Design

NASA Technical Reports Server (NTRS)

Englander, Jacob A.; Vavrina, Matthew A.; Ghosh, Alexander R.

2015-01-01

Preliminary design of low-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. In addition, a time-history of control variables must be chosen that defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated. The customer who commissions a trajectory design is not usually interested in a point solution, but rather the exploration of the trade space of trajectories between several different objective functions. This can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a multi-objective hybrid optimal control problem. The method is demonstrated on a hypothetical mission to the main asteroid belt.