Design and Optimization of Low-thrust Orbit Transfers Using Q-law and Evolutionary Algorithms

NASA Technical Reports Server (NTRS)

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

2005-01-01

Future space missions will depend more on low-thrust propulsion (such as ion engines) thanks to its high specific impulse. Yet, the design of low-thrust trajectories is complex and challenging. Third-body perturbations often dominate the thrust, and a significant change to the orbit requires a long duration of thrust. In order to guide the early design phases, we have developed an efficient and efficacious method to obtain approximate propellant and flight-time requirements (i.e., the Pareto front) for orbit transfers. A search for the Pareto-optimal trajectories is done in two levels: optimal thrust angles and locations are determined by Q-law, while the Q-law is optimized with two evolutionary algorithms: a genetic algorithm and a simulated-annealing-related algorithm. The examples considered are several types of orbit transfers around the Earth and the asteroid Vesta.

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.

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.

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.

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.

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.

Status of Low Thrust Work at JSC

NASA Technical Reports Server (NTRS)

Condon, Gerald L.

2004-01-01

High performance low thrust (solar electric, nuclear electric, variable specific impulse magnetoplasma rocket) propulsion offers a significant benefit to NASA missions beyond low Earth orbit. As NASA (e.g., Prometheus Project) endeavors to develop these propulsion systems and associated power supplies, it becomes necessary to develop a refined trajectory design capability that will allow engineers to develop future robotic and human mission designs that take advantage of this new technology. This ongoing work addresses development of a trajectory design and optimization tool for assessing low thrust (and other types) trajectories. This work targets to advance the state of the art, enable future NASA missions, enable science drivers, and enhance education. This presentation provides a summary of the low thrust-related JSC activities under the ISP program and specifically, provides a look at a new release of a multi-gravity, multispacecraft trajectory optimization tool (Copernicus) along with analysis performed using this tool over the past year.

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.

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.

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.

Approximate approach for optimization space flights with a low thrust on the basis of sufficient optimality conditions

NASA Astrophysics Data System (ADS)

Salmin, Vadim V.

2017-01-01

Flight mechanics with a low-thrust is a new chapter of mechanics of space flight, considered plurality of all problems trajectory optimization and movement control laws and the design parameters of spacecraft. Thus tasks associated with taking into account the additional factors in mathematical models of the motion of spacecraft becomes increasingly important, as well as additional restrictions on the possibilities of the thrust vector control. The complication of the mathematical models of controlled motion leads to difficulties in solving optimization problems. Author proposed methods of finding approximate optimal control and evaluating their optimality based on analytical solutions. These methods are based on the principle of extending the class of admissible states and controls and sufficient conditions for the absolute minimum. Developed procedures of the estimation enabling to determine how close to the optimal founded solution, and indicate ways to improve them. Authors describes procedures of estimate for approximately optimal control laws for space flight mechanics problems, in particular for optimization flight low-thrust between the circular non-coplanar orbits, optimization the control angle and trajectory movement of the spacecraft during interorbital flights, optimization flights with low-thrust between arbitrary elliptical orbits Earth satellites.

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.

Computation of optimal Mars trajectories via combined chemical/electrical propulsion, Part 3: Compromise solutions

NASA Astrophysics Data System (ADS)

Miele, A.; Wang, T.; Williams, P. N.

2005-12-01

The success of the solar-electric ion engine powering the DS1 spacecraft has paved the way toward the use of low-thrust electrical engines in future planetary/interplanetary missions. Vis-à-vis a chemical engine, an electrical engine has a higher specific impulse, implying a possible decrease in propellant mass; however, the low-thrust aspect discourages the use of an electrical engine in the near-planet phases of a trip, since this might result in an increase in flight time. Therefore, a fundamental design problem is to find the best combination of chemical propulsion and electrical propulsion for a given mission, for example, a mission from Earth to Mars. With this in mind, this paper is the third of a series dealing with the optimization of Earth Mars missions via the use of hybrid engines, namely the combination of high-thrust chemical engines for planetary flight and low-thrust electrical engines for interplanetary flight. We look at the deep-space interplanetary portion of the trajectory under rather idealized conditions. The two major performance indexes, the propellant mass and the flight time, are in conflict with one another for the following reason: any attempt at reducing the former causes an increase in the latter and vice versa. Therefore, it is natural to consider a compromise performance index involving the scaled values of the propellant mass and flight time weighted respectively by the compromise factor C and its complement 1-C. We use the compromise factor as the parameter of the one-parameter family of compromise trajectories. Analyses carried out with the sequential gradient-restoration algorithm for optimal control problems lead to results which can be highlighted as follows. Thrust profile. Generally speaking, the thrust profile of the compromise trajectory includes three subarcs: the first subarc is characterized by maximum thrust in conjunction with positive (upward) thrust direction; the second subarc is characterized by zero thrust (coasting flight); the third subarc is characterized by maximum thrust in conjunction with negative (downward) thrust direction. Effect of the compromise factor. As the compromise factor increases, the propellant mass decreases and the flight time increases; correspondingly, the following changes in the thrust profile take place: (a) the time lengths of the first and third subarcs (powered phases) decrease slightly, meaning that thrust application occurs for shorter duration; also, the average value of the thrust direction in the first and third subarcs decreases, implying higher efficiency of thrust application wrt the spacecraft energy level; as a result, the total propellant mass decreases; (b) the time length of the second subarc (coasting) increases considerably, resulting in total time increase. Minimum time trajectory. If C=0, the resulting minimum time trajectory has the following characteristics: (a) the time length of the coasting subarc reduces to zero and the three-subarc trajectory degenerates into a two-subarc trajectory; (b) maximum thrust is applied at all times and the thrust direction switches from upward to downward at midcourse. Minimum propellant mass trajectory. If C=1, the resulting minimum propellant mass trajectory has the following characteristics: (a) the thrust magnitude has a bang-zero-bang profile; (b) for the powered subarcs, the thrust direction is tangent to the flight path at all times.

Comparison of Performance Predictions for New Low-Thrust Trajectory Tools

NASA Technical Reports Server (NTRS)

Polsgrove, Tara; Kos, Larry; Hopkins, Randall; Crane, Tracie

2006-01-01

Several low thrust trajectory optimization tools have been developed over the last 3% years by the Low Thrust Trajectory Tools development team. This toolset includes both low-medium fidelity and high fidelity tools which allow the analyst to quickly research a wide mission trade space and perform advanced mission design. These tools were tested using a set of reference trajectories that exercised each tool s unique capabilities. This paper compares the performance predictions of the various tools against several of the reference trajectories. The intent is to verify agreement between the high fidelity tools and to quantify the performance prediction differences between tools of different fidelity levels.

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.

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.

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.

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.

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.

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.

Optimization of transfer trajectories to the Apophis asteroid for spacecraft with high and low thrust

NASA Astrophysics Data System (ADS)

Ivashkin, V. V.; Krylov, I. V.

2014-03-01

The problem of optimization of a spacecraft transfer to the Apophis asteroid is investigated. The scheme of transfer under analysis includes a geocentric stage of boosting the spacecraft with high thrust, a heliocentric stage of control by a low thrust engine, and a stage of deceleration with injection to an orbit of the asteroid's satellite. In doing this, the problem of optimal control is solved for cases of ideal and piecewise-constant low thrust, and the optimal magnitude and direction of spacecraft's hyperbolic velocity "at infinity" during departure from the Earth are determined. The spacecraft trajectories are found based on a specially developed comprehensive method of optimization. This method combines the method of dynamic programming at the first stage of analysis and the Pontryagin maximum principle at the concluding stage, together with the parameter continuation method. The estimates are obtained for the spacecraft's final mass and for the payload mass that can be delivered to the asteroid using the Soyuz-Fregat carrier launcher.

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.

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.

Algorithm for fuel conservative horizontal capture trajectories

NASA Technical Reports Server (NTRS)

Neuman, F.; Erzberger, H.

1981-01-01

A real time algorithm for computing constant altitude fuel-conservative approach trajectories for aircraft is described. The characteristics of the trajectory computed were chosen to approximate the extremal trajectories obtained from the optimal control solution to the problem and showed a fuel difference of only 0.5 to 2 percent for the real time algorithm in favor of the extremals. The trajectories may start at any initial position, heading, and speed and end at any other final position, heading, and speed. They consist of straight lines and a series of circular arcs of varying radius to approximate constant bank-angle decelerating turns. Throttle control is maximum thrust, nominal thrust, or zero thrust. Bank-angle control is either zero or aproximately 30 deg.

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.

Optimal thrust level for orbit insertion

NASA Astrophysics Data System (ADS)

Cerf, Max

2017-07-01

The minimum-fuel orbital transfer is analyzed in the case of a launcher upper stage using a constantly thrusting engine. The thrust level is assumed to be constant and its value is optimized together with the thrust direction. A closed-loop solution for the thrust direction is derived from the extremal analysis for a planar orbital transfer. The optimal control problem reduces to two unknowns, namely the thrust level and the final time. Guessing and propagating the costates is no longer necessary and the optimal trajectory is easily found from a rough initialization. On the other hand the initial costates are assessed analytically from the initial conditions and they can be used as initial guess for transfers at different thrust levels. The method is exemplified on a launcher upper stage targeting a geostationary transfer orbit.

Rapid space trajectory generation using a Fourier series shape-based approach

NASA Astrophysics Data System (ADS)

Taheri, Ehsan

With the insatiable curiosity of human beings to explore the universe and our solar system, it is essential to benefit from larger propulsion capabilities to execute efficient transfers and carry more scientific equipments. In the field of space trajectory optimization the fundamental advances in using low-thrust propulsion and exploiting the multi-body dynamics has played pivotal role in designing efficient space mission trajectories. The former provides larger cumulative momentum change in comparison with the conventional chemical propulsion whereas the latter results in almost ballistic trajectories with negligible amount of propellant. However, the problem of space trajectory design translates into an optimal control problem which is, in general, time-consuming and very difficult to solve. Therefore, the goal of the thesis is to address the above problem by developing a methodology to simplify and facilitate the process of finding initial low-thrust trajectories in both two-body and multi-body environments. This initial solution will not only provide mission designers with a better understanding of the problem and solution but also serves as a good initial guess for high-fidelity optimal control solvers and increases their convergence rate. Almost all of the high-fidelity solvers enjoy the existence of an initial guess that already satisfies the equations of motion and some of the most important constraints. Despite the nonlinear nature of the problem, it is sought to find a robust technique for a wide range of typical low-thrust transfers with reduced computational intensity. Another important aspect of our developed methodology is the representation of low-thrust trajectories by Fourier series with which the number of design variables reduces significantly. Emphasis is given on simplifying the equations of motion to the possible extent and avoid approximating the controls. These facts contribute to speeding up the solution finding procedure. Several example applications of two and three-dimensional two-body low-thrust transfers are considered. In addition, in the multi-body dynamic, and in particular the restricted-three-body dynamic, several Earth-to-Moon low-thrust transfers are investigated.

Parallel Monotonic Basin Hopping for Low Thrust Trajectory Optimization

NASA Technical Reports Server (NTRS)

McCarty, Steven L.; McGuire, Melissa L.

2018-01-01

Monotonic Basin Hopping has been shown to be an effective method of solving low thrust trajectory optimization problems. This paper outlines an extension to the common serial implementation by parallelizing it over any number of available compute cores. The Parallel Monotonic Basin Hopping algorithm described herein is shown to be an effective way to more quickly locate feasible solutions, and improve locally optimal solutions in an automated way without requiring a feasible initial guess. The increased speed achieved through parallelization enables the algorithm to be applied to more complex problems that would otherwise be impractical for a serial implementation. Low thrust cislunar transfers and a hybrid Mars example case demonstrate the effectiveness of the algorithm. Finally, a preliminary scaling study quantifies the expected decrease in solve time compared to a serial implementation.,

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.

Fuel-optimal low-thrust formation reconfiguration via Radau pseudospectral method

NASA Astrophysics Data System (ADS)

Li, Jing

2016-07-01

This paper investigates fuel-optimal low-thrust formation reconfiguration near circular orbit. Based on the Clohessy-Wiltshire equations, first-order necessary optimality conditions are derived from the Pontryagin's maximum principle. The fuel-optimal impulsive solution is utilized to divide the low-thrust trajectory into thrust and coast arcs. By introducing the switching times as optimization variables, the fuel-optimal low-thrust formation reconfiguration is posed as a nonlinear programming problem (NLP) via direct transcription using multiple-phase Radau pseudospectral method (RPM), which is then solved by a sparse nonlinear optimization software SNOPT. To facilitate optimality verification and, if necessary, further refinement of the optimized solution of the NLP, formulas for mass costate estimation and initial costates scaling are presented. Numerical examples are given to show the application of the proposed optimization method. To fix the problem, generic fuel-optimal low-thrust formation reconfiguration can be simplified as reconfiguration without any initial and terminal coast arcs, whose optimal solutions can be efficiently obtained from the multiple-phase RPM at the cost of a slight fuel increment. Finally, influence of the specific impulse and maximum thrust magnitude on the fuel-optimal low-thrust formation reconfiguration is analyzed. Numerical results shown the links and differences between the fuel-optimal impulsive and low-thrust solutions.

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.

Optimal Trajectories For Orbital Transfers Using Low And Medium Thrust Propulsion Systems

NASA Technical Reports Server (NTRS)

Cobb, Shannon S.

1992-01-01

For many problems it is reasonable to expect that the minimum time solution is also the minimum fuel solution. However, if one allows the propulsion system to be turned off and back on, it is clear that these two solutions may differ. In general, high thrust transfers resemble the well-known impulsive transfers where the burn arcs are of very short duration. The low and medium thrust transfers differ in that their thrust acceleration levels yield longer burn arcs which will require more revolutions, thus making the low thrust transfer computational intensive. Here, we consider optimal low and medium thrust orbital transfers.

Design space pruning heuristics and global optimization method for conceptual design of low-thrust asteroid tour missions

NASA Astrophysics Data System (ADS)

Alemany, Kristina

Electric propulsion has recently become a viable technology for spacecraft, enabling shorter flight times, fewer required planetary gravity assists, larger payloads, and/or smaller launch vehicles. With the maturation of this technology, however, comes a new set of challenges in the area of trajectory design. Because low-thrust trajectory optimization has historically required long run-times and significant user-manipulation, mission design has relied on expert-based knowledge for selecting departure and arrival dates, times of flight, and/or target bodies and gravitational swing-bys. These choices are generally based on known configurations that have worked well in previous analyses or simply on trial and error. At the conceptual design level, however, the ability to explore the full extent of the design space is imperative to locating the best solutions in terms of mass and/or flight times. Beginning in 2005, the Global Trajectory Optimization Competition posed a series of difficult mission design problems, all requiring low-thrust propulsion and visiting one or more asteroids. These problems all had large ranges on the continuous variables---launch date, time of flight, and asteroid stay times (when applicable)---as well as being characterized by millions or even billions of possible asteroid sequences. Even with recent advances in low-thrust trajectory optimization, full enumeration of these problems was not possible within the stringent time limits of the competition. This investigation develops a systematic methodology for determining a broad suite of good solutions to the combinatorial, low-thrust, asteroid tour problem. The target application is for conceptual design, where broad exploration of the design space is critical, with the goal being to rapidly identify a reasonable number of promising solutions for future analysis. The proposed methodology has two steps. The first step applies a three-level heuristic sequence developed from the physics of the problem, which allows for efficient pruning of the design space. The second phase applies a global optimization scheme to locate a broad suite of good solutions to the reduced problem. The global optimization scheme developed combines a novel branch-and-bound algorithm with a genetic algorithm and an industry-standard low-thrust trajectory optimization program to solve for the following design variables: asteroid sequence, launch date, times of flight, and asteroid stay times. The methodology is developed based on a small sample problem, which is enumerated and solved so that all possible discretized solutions are known. The methodology is then validated by applying it to a larger intermediate sample problem, which also has a known solution. Next, the methodology is applied to several larger combinatorial asteroid rendezvous problems, using previously identified good solutions as validation benchmarks. These problems include the 2nd and 3rd Global Trajectory Optimization Competition problems. The methodology is shown to be capable of achieving a reduction in the number of asteroid sequences of 6-7 orders of magnitude, in terms of the number of sequences that require low-thrust optimization as compared to the number of sequences in the original problem. More than 70% of the previously known good solutions are identified, along with several new solutions that were not previously reported by any of the competitors. Overall, the methodology developed in this investigation provides an organized search technique for the low-thrust mission design of asteroid rendezvous problems.

Flight trajectories with maximum tangential thrust in a central Newtonian field

NASA Astrophysics Data System (ADS)

Azizov, A. G.; Korshunova, N. A.

1983-07-01

The paper examines the two-dimensional problem of determining the optimal trajectories of a point moving with a limited per-second mass consumption in a central Newtonian field. It is shown that one of the cases in which the variational equations in the Meier formulation can be integrated in quadratures is motion with maximum tangential thrust. Trajectories corresponding to this motion are determined. By way of application, attention is given to the problem of determining the thrust which assures maximum kinetic energy for the point at the moment t = t1, corresponding to the mass consumption M0 - M1, where M0 and M1 are, respectively, the initial and final mass.

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.

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.

Preliminary Design of Low-Thrust Interplanetary Missions

NASA Technical Reports Server (NTRS)

Sims, Jon A.; Flanagan, Steve N.

1997-01-01

For interplanetary missions, highly efficient electric propulsion systems can be used to increase the mass delivered to the destination and/or reduce the trip time over typical chemical propulsion systems. This technology is being demonstrated on the Deep Space 1 mission - part of NASA's New Millennium Program validating technologies which can lower the cost and risk and enhance the performance of future missions. With the successful demonstration on Deep Space 1, future missions can consider electric propulsion as a viable propulsion option. Electric propulsion systems, while highly efficient, produce only a small amount of thrust. As a result, the engines operate during a significant fraction of the trajectory. This characteristic makes it much more difficult to find optimal trajectories. The methods for optimizing low-thrust trajectories are typically categorized as either indirect, or direct. Indirect methods are based on calculus of variations, resulting in a two-point boundary value problem that is solved by satisfying terminal constraints and targeting conditions. These methods are subject to extreme sensitivity to the initial guess of the variables - some of which are not physically intuitive. Adding a gravity assist to the trajectory compounds the sensitivity. Direct methods parameterize the problem and use nonlinear programming techniques to optimize an objective function by adjusting a set of variables. A variety of methods of this type have been examined with varying results. These methods are subject to the limitations of the nonlinear programming techniques. In this paper we present a direct method intended to be used primarily for preliminary design of low-thrust interplanetary trajectories, including those with multiple gravity assists. Preliminary design implies a willingness to accept limited accuracy to achieve an efficient algorithm that executes quickly.

Low thrust spacecraft transfers optimization method with the stepwise control structure in the Earth-Moon system in terms of the L1-L2 transfer

NASA Astrophysics Data System (ADS)

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

2016-04-01

The paper outlines the method for determination of the locally optimal stepwise control structure in the problem of the low thrust spacecraft transfer optimization in the Earth-Moon system, including the L1-L2 transfer. The total flight time as an optimization criterion is considered. The optimal control programs were obtained by using the Pontryagin's maximum principle. As a result of optimization, optimal control programs, corresponding trajectories, and minimal total flight times were determined.

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.

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.

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.

Space tug geosynchronous mission simulation

NASA Technical Reports Server (NTRS)

Lang, T. J.

1973-01-01

Near-optimal three dimensional trajectories from a low earth park orbit inclined at 28.5 deg to a synchronous-equatorial mission orbit were developed for both the storable (thrust = 28,912 N (6,500 lbs), I sub sp = 339 sec) and cryogenic (thrust = 44,480 N (10,000 lbs), I sub sp = 470 sec) space tug using the iterative cost function minimization technique contained within the modularized vehicle simulation (MVS) program. The finite burn times, due to low thrust-to-weight ratios, and the associated gravity losses are accounted for in the trajectory simulation and optimization. The use of an ascent phasing orbit to achieve burnout in synchronous orbit at any longitude is investigated. The ascent phasing orbit is found to offer the additional advantage of significantly reducing the overall delta velocity by splitting the low altitude burn into two parts and thereby reducing gravity losses.

Accurate approximation of in-ecliptic trajectories for E-sail with constant pitch angle

NASA Astrophysics Data System (ADS)

Huo, Mingying; Mengali, Giovanni; Quarta, Alessandro A.

2018-05-01

Propellantless continuous-thrust propulsion systems, such as electric solar wind sails, may be successfully used for new space missions, especially those requiring high-energy orbit transfers. When the mass-to-thrust ratio is sufficiently large, the spacecraft trajectory is characterized by long flight times with a number of revolutions around the Sun. The corresponding mission analysis, especially when addressed within an optimal context, requires a significant amount of simulation effort. Analytical trajectories are therefore useful aids in a preliminary phase of mission design, even though exact solution are very difficult to obtain. The aim of this paper is to present an accurate, analytical, approximation of the spacecraft trajectory generated by an electric solar wind sail with a constant pitch angle, using the latest mathematical model of the thrust vector. Assuming a heliocentric circular parking orbit and a two-dimensional scenario, the simulation results show that the proposed equations are able to accurately describe the actual spacecraft trajectory for a long time interval when the propulsive acceleration magnitude is sufficiently small.

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.

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.

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.

Modeling low-thrust transfers between periodic orbits about five libration points: Manifolds and hierarchical design

NASA Astrophysics Data System (ADS)

Zeng, Hao; Zhang, Jingrui

2018-04-01

The low-thrust version of the fuel-optimal transfers between periodic orbits with different energies in the vicinity of five libration points is exploited deeply in the Circular Restricted Three-Body Problem. Indirect optimization technique incorporated with constraint gradients is employed to further improve the computational efficiency and accuracy of the algorithm. The required optimal thrust magnitude and direction can be determined to create the bridging trajectory that connects the invariant manifolds. A hierarchical design strategy dividing the constraint set is proposed to seek the optimal solution when the problem cannot be solved directly. Meanwhile, the solution procedure and the value ranges of used variables are summarized. To highlight the effectivity of the transfer scheme and aim at different types of libration point orbits, transfer trajectories between some sample orbits, including Lyapunov orbits, planar orbits, halo orbits, axial orbits, vertical orbits and butterfly orbits for collinear and triangular libration points, are investigated with various time of flight. Numerical results show that the fuel consumption varies from a few kilograms to tens of kilograms, related to the locations and the types of mission orbits as well as the corresponding invariant manifold structures, and indicates that the low-thrust transfers may be a beneficial option for the extended science missions around different libration points.

Combined high and low-thrust geostationary orbit insertion with radiation constraint

NASA Astrophysics Data System (ADS)

Macdonald, Malcolm; Owens, Steven Robert

2018-01-01

The sequential use of an electric propulsion system is considered in combination with a high-thrust propulsion system for application to the propellant-optimal Geostationary Orbit insertion problem, whilst considering both temporal and radiation flux constraints. Such usage is found to offer a combined propellant mass saving when compared with an equivalent high-thrust only transfer. This propellant mass saving is seen to increase as the allowable transfer duration is increased, and as the thrust from the low-thrust system is increased, assuming constant specific impulse. It was found that the required plane change maneuver is most propellant-efficiently performed by the high-thrust system. The propellant optimal trajectory incurs a significantly increased electron flux when compared to an equivalent high-thrust only transfer. However, the electron flux can be reduced to a similar order of magnitude by increasing the high-thrust propellant consumption, whilst still delivering an improved mass fraction.

Chasing a Comet with a Solar Sail

NASA Technical Reports Server (NTRS)

Stough, Robert W.; Heaton, Andrew F.; Whorton, Mark S.

2008-01-01

Solar sail propulsion systems enable a wide range of missions that require constant thrust or high delta-V over long mission times. One particularly challenging mission type is a comet rendezvous mission. This paper presents optimal low-thrust trajectory designs for a range of sailcraft performance metrics and mission transit times that enables a comet rendezvous mission. These optimal trajectory results provide a trade space which can be parameterized in terms of mission duration and sailcraft performance parameters such that a design space for a small satellite comet chaser mission is identified. These results show that a feasible space exists for a small satellite to perform a comet chaser mission in a reasonable mission time.

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.

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.

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.

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.

Trajectory optimization for the National Aerospace Plane

NASA Technical Reports Server (NTRS)

Lu, Ping

1993-01-01

The objective of this second phase research is to investigate the optimal ascent trajectory for the National Aerospace Plane (NASP) from runway take-off to orbital insertion and address the unique problems associated with the hypersonic flight trajectory optimization. The trajectory optimization problem for an aerospace plane is a highly challenging problem because of the complexity involved. Previous work has been successful in obtaining sub-optimal trajectories by using energy-state approximation and time-scale decomposition techniques. But it is known that the energy-state approximation is not valid in certain portions of the trajectory. This research aims at employing full dynamics of the aerospace plane and emphasizing direct trajectory optimization methods. The major accomplishments of this research include the first-time development of an inverse dynamics approach in trajectory optimization which enables us to generate optimal trajectories for the aerospace plane efficiently and reliably, and general analytical solutions to constrained hypersonic trajectories that has wide application in trajectory optimization as well as in guidance and flight dynamics. Optimal trajectories in abort landing and ascent augmented with rocket propulsion and thrust vectoring control were also investigated. Motivated by this study, a new global trajectory optimization tool using continuous simulated annealing and a nonlinear predictive feedback guidance law have been under investigation and some promising results have been obtained, which may well lead to more significant development and application in the near future.

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.

Low Thrust Mission Trajectories to Near Earth Asteroids

NASA Technical Reports Server (NTRS)

Saripalli, Pratik; Cardiff, Eric

2017-01-01

The discovery of 2016 HO3 and its classification as a quasi-satellite has sparked a stronger interest towards Near Earth Asteroids (NEAs). This work presents low-thrust low-power mission designs to various NEAs using an EELV Secondary Payload Adapter (ESPA). A global trajectory optimizer (EMTG) was used to generate mission solutions to a select 13 NEAs using a 200 watt BHT-200 thruster as a proof of concept. The missions presented here demonstrate that a low-cost electric propulsion ESPA mission to NEAs is a feasible concept for many asteroids.

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.

Trajectory optimization of spacecraft high-thrust orbit transfer using a modified evolutionary algorithm

NASA Astrophysics Data System (ADS)

Shirazi, Abolfazl

2016-10-01

This article introduces a new method to optimize finite-burn orbital manoeuvres based on a modified evolutionary algorithm. Optimization is carried out based on conversion of the orbital manoeuvre into a parameter optimization problem by assigning inverse tangential functions to the changes in direction angles of the thrust vector. The problem is analysed using boundary delimitation in a common optimization algorithm. A method is introduced to achieve acceptable values for optimization variables using nonlinear simulation, which results in an enlarged convergence domain. The presented algorithm benefits from high optimality and fast convergence time. A numerical example of a three-dimensional optimal orbital transfer is presented and the accuracy of the proposed algorithm is shown.

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.

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.

Trajectory optimization for lunar soft landing with complex constraints

NASA Astrophysics Data System (ADS)

Chu, Huiping; Ma, Lin; Wang, Kexin; Shao, Zhijiang; Song, Zhengyu

2017-11-01

A unified trajectory optimization framework with initialization strategies is proposed in this paper for lunar soft landing for various missions with specific requirements. Two main missions of interest are Apollo-like Landing from low lunar orbit and Vertical Takeoff Vertical Landing (a promising mobility method) on the lunar surface. The trajectory optimization is characterized by difficulties arising from discontinuous thrust, multi-phase connections, jump of attitude angle, and obstacles avoidance. Here R-function is applied to deal with the discontinuities of thrust, checkpoint constraints are introduced to connect multiple landing phases, attitude angular rate is designed to get rid of radical changes, and safeguards are imposed to avoid collision with obstacles. The resulting dynamic problems are generally with complex constraints. The unified framework based on Gauss Pseudospectral Method (GPM) and Nonlinear Programming (NLP) solver are designed to solve the problems efficiently. Advanced initialization strategies are developed to enhance both the convergence and computation efficiency. Numerical results demonstrate the adaptability of the framework for various landing missions, and the performance of successful solution of difficult dynamic problems.

Low-thrust trajectory analysis for the geosynchronous mission

NASA Technical Reports Server (NTRS)

Jasper, T. P.

1973-01-01

Methodology employed in development of a computer program designed to analyze optimal low-thrust trajectories is described, and application of the program to a Solar Electric Propulsion Stage (SEPS) geosynchronous mission is discussed. To avoid the zero inclination and eccentricity singularities which plague many small-force perturbation techniques, a special set of state variables (equinoctial) is used. Adjoint equations are derived for the minimum time problem and are also free from the singularities. Solutions to the state and adjoint equations are obtained by both orbit averaging and precision numerical integration; an evaluation of these approaches is made.

Influence of Structural Parameters on the Performance of Vortex Valve Variable-Thrust Solid Rocket Motor

NASA Astrophysics Data System (ADS)

Wei, Xianggeng; Li, Jiang; He, Guoqiang

2017-04-01

The vortex valve solid variable thrust motor is a new solid motor which can achieve Vehicle system trajectory optimization and motor energy management. Numerical calculation was performed to investigate the influence of vortex chamber diameter, vortex chamber shape, and vortex chamber height of the vortex valve solid variable thrust motor on modulation performance. The test results verified that the calculation results are consistent with laboratory results with a maximum error of 9.5%. The research drew the following major conclusions: the optimal modulation performance was achieved in a cylindrical vortex chamber, increasing the vortex chamber diameter improved the modulation performance of the vortex valve solid variable thrust motor, optimal modulation performance could be achieved when the height of the vortex chamber is half of the vortex chamber outlet diameter, and the hot gas control flow could result in an enhancement of modulation performance. The results can provide the basis for establishing the design method of the vortex valve solid variable thrust motor.

Heliocentric interplanetary low thrust trajectory optimization program, supplement 1, part 2

NASA Technical Reports Server (NTRS)

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

1978-01-01

The improvements made to the HILTOP electric propulsion trajectory computer program are described. A more realistic propulsion system model was implemented in which various thrust subsystem efficiencies and specific impulse are modeled as variable functions of power available to the propulsion system. The number of operating thrusters are staged, and the beam voltage is selected from a set of five (or less) constant voltages, based upon the application of variational calculus. The constant beam voltages may be optimized individually or collectively. The propulsion system logic is activated by a single program input key in such a manner as to preserve the HILTOP logic. An analysis describing these features, a complete description of program input quantities, and sample cases of computer output illustrating the program capabilities are presented.

Capture of near-Earth objects with low-thrust propulsion and invariant manifolds

NASA Astrophysics Data System (ADS)

Tang, Gao; Jiang, Fanghua

2016-01-01

In this paper, a mission incorporating low-thrust propulsion and invariant manifolds to capture near-Earth objects (NEOs) is investigated. The initial condition has the spacecraft rendezvousing with the NEO. The mission terminates once it is inserted into a libration point orbit (LPO). The spacecraft takes advantage of stable invariant manifolds for low-energy ballistic capture. Low-thrust propulsion is employed to retrieve the joint spacecraft-asteroid system. Global optimization methods are proposed for the preliminary design. Local direct and indirect methods are applied to optimize the two-impulse transfers. Indirect methods are implemented to optimize the low-thrust trajectory and estimate the largest retrievable mass. To overcome the difficulty that arises from bang-bang control, a homotopic approach is applied to find an approximate solution. By detecting the switching moments of the bang-bang control the efficiency and accuracy of numerical integration are guaranteed. By using the homotopic approach as the initial guess the shooting function is easy to solve. The relationship between the maximum thrust and the retrieval mass is investigated. We find that both numerically and theoretically a larger thrust is preferred.

A minimum propellant solution to an orbit-to-orbit transfer using a low thrust propulsion system

NASA Technical Reports Server (NTRS)

Cobb, Shannon S.

1991-01-01

The Space Exploration Initiative is considering the use of low thrust (nuclear electric, solar electric) and intermediate thrust (nuclear thermal) propulsion systems for transfer to Mars and back. Due to the duration of such a mission, a low thrust minimum-fuel solution is of interest; a savings of fuel can be substantial if the propulsion system is allowed to be turned off and back on. This switching of the propulsion system helps distinguish the minimal-fuel problem from the well-known minimum-time problem. Optimal orbit transfers are also of interest to the development of a guidance system for orbital maneuvering vehicles which will be needed, for example, to deliver cargoes to the Space Station Freedom. The problem of optimizing trajectories for an orbit-to-orbit transfer with minimum-fuel expenditure using a low thrust propulsion system is addressed.

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.

Tsien's method for generating non-Keplerian trajectories. Part 2: The question of thrust to orbit a sphere and the restricted three-body problem

NASA Technical Reports Server (NTRS)

Murad, P. A.

1993-01-01

Tsien's method is extended to treat the orbital motion of a body undergoing accelerations and decelerations. A generalized solution is discussed for the generalized case where a body undergoes azimuthal and radial thrust and the problem is further simplified for azimuthal thrust alone. Judicious selection of thrust could generate either an elliptic or hyperbolic trajectory. This is unexpected especially when the body has only enough energy for a lower state trajectory. The methodology is extended treating the problem of vehicle thrust for orbiting a sphere and vehicle thrust within the classical restricted three-body problem. Results for the latter situation can produce hyperbolic trajectories through eigen value decomposition. Since eigen values for no-thrust can be imaginary, thrust can generate real eigen values to describe hyperbolic trajectories. Keplerian dynamics appears to represent but a small subset of a much larger non-Keplerian domain especially when thrust effects are considered. The need for high thrust long duration space-based propulsion systems for changing a trajectory's canonical form is clearly demonstrated.

An Automated Solution of the Low-Thrust Interplanetary Trajectory Problem.

PubMed

Englander, Jacob A; Conway, Bruce A

2017-01-01

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, which 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 hypothetical missions to Mercury, the main asteroid belt, and Pluto.

An Automated Solution of the Low-Thrust Interplanetary Trajectory Problem

NASA Technical Reports Server (NTRS)

Englander, Jacob A.; Conway, Bruce

2016-01-01

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, which 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 hypothetical missions to Mercury, the main asteroid belt, and Pluto.

An Automated Solution of the Low-Thrust Interplanetary Trajectory Problem

PubMed Central

Englander, Jacob A.; Conway, Bruce A.

2017-01-01

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, which 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 hypothetical missions to Mercury, the main asteroid belt, and Pluto. PMID:29515289

Solution of the multiextreme optimization problem for low-thrust spacecraft flight to the asteroid apophis

NASA Astrophysics Data System (ADS)

Ivashkin, V. V.; Krylov, I. V.

2015-09-01

A method to optimize the flight trajectories to the asteroid Apophis that allows reliably to form a set of Pontryagin extremals for various boundary conditions of the flight, as well as effectively to search for a global problem optimum amongst its elements, is developed.

On the calculation of low-thrust fail-safe trajectories

NASA Technical Reports Server (NTRS)

Sauer, C. G., Jr.

1975-01-01

A guidance algorithm is developed for a low-thrust spacecraft such that target intercept is possible in spite of premature thrust termination along the trajectory. Such a trajectory is called a 'fail-safe' trajectory and the spacecraft thrust is utilized to minimize the relative target-spacecraft approach speed. The fail-safe guidance algorithm is solved using the concept of a critical thrust plane and a non-critical thrust direction. Several examples of fail-safe guidance are presented for a solar-electric propulsion flyby mission to the comet Encke.

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 adaptive guidance algorithm for an aerodynamically assisted orbital plane change maneuver. M.S. Thesis

NASA Technical Reports Server (NTRS)

Blissit, J. A.

1986-01-01

Using analysis results from the post trajectory optimization program, an adaptive guidance algorithm is developed to compensate for density, aerodynamic and thrust perturbations during an atmospheric orbital plane change maneuver. The maneuver offers increased mission flexibility along with potential fuel savings for future reentry vehicles. Although designed to guide a proposed NASA Entry Research Vehicle, the algorithm is sufficiently generic for a range of future entry vehicles. The plane change analysis provides insight suggesting a straight-forward algorithm based on an optimized nominal command profile. Bank angle, angle of attack, and engine thrust level, ignition and cutoff times are modulated to adjust the vehicle's trajectory to achieve the desired end-conditions. A performance evaluation of the scheme demonstrates a capability to guide to within 0.05 degrees of the desired plane change and five nautical miles of the desired apogee altitude while maintaining heating constraints. The algorithm is tested under off-nominal conditions of + or -30% density biases, two density profile models, + or -15% aerodynamic uncertainty, and a 33% thrust loss and for various combinations of these conditions.

CAMELOT: Computational-Analytical Multi-fidElity Low-thrust Optimisation Toolbox

NASA Astrophysics Data System (ADS)

Di Carlo, Marilena; Romero Martin, Juan Manuel; Vasile, Massimiliano

2018-03-01

Computational-Analytical Multi-fidElity Low-thrust Optimisation Toolbox (CAMELOT) is a toolbox for the fast preliminary design and optimisation of low-thrust trajectories. It solves highly complex combinatorial problems to plan multi-target missions characterised by long spirals including different perturbations. To do so, CAMELOT implements a novel multi-fidelity approach combining analytical surrogate modelling and accurate computational estimations of the mission cost. Decisions are then made using two optimisation engines included in the toolbox, a single-objective global optimiser, and a combinatorial optimisation algorithm. CAMELOT has been applied to a variety of case studies: from the design of interplanetary trajectories to the optimal de-orbiting of space debris and from the deployment of constellations to on-orbit servicing. In this paper, the main elements of CAMELOT are described and two examples, solved using the toolbox, are 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.

A globally nonsingular quaternion-based formulation for all-electric satellite trajectory optimization

NASA Astrophysics Data System (ADS)

Libraro, Paola

The general electric propulsion orbit-raising maneuver of a spacecraft must contend with four main limiting factors: the longer time of flight, multiple eclipses prohibiting continuous thrusting, long exposure to radiation from the Van Allen belt and high power requirement of the electric engines. In order to optimize a low-thrust transfer with respect to these challenges, the choice of coordinates and corresponding equations of motion used to describe the kinematical and dynamical behavior of the satellite is of critical importance. This choice can potentially affect the numerical optimization process as well as limit the set of mission scenarios that can be investigated. To increase the ability to determine the feasible set of mission scenarios able to address the challenges of an all-electric orbit-raising, a set of equations free of any singularities is required to consider a completely arbitrary injection orbit. For this purpose a new quaternion-based formulation of a spacecraft translational dynamics that is globally nonsingular has been developed. The minimum-time low-thrust problem has been solved using the new set of equations of motion inside a direct optimization scheme in order to investigate optimal low-thrust trajectories over the full range of injection orbit inclinations between 0 and 90 degrees with particular focus on high-inclinations. The numerical results consider a specific mission scenario in order to analyze three key aspects of the problem: the effect of the initial guess on the shape and duration of the transfer, the effect of Earth oblateness on transfer time and the role played by, radiation damage and power degradation in all-electric minimum-time transfers. Finally trade-offs between mass and cost savings are introduced through a test case.

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.

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.

Multiple burn fuel-optimal orbit transfers: Numerical trajectory computation and neighboring optimal feedback guidance

NASA Technical Reports Server (NTRS)

Chuang, C.-H.; Goodson, Troy D.; Ledsinger, Laura A.

1995-01-01

This report describes current work in the numerical computation of multiple burn, fuel-optimal orbit transfers and presents an analysis of the second variation for extremal multiple burn orbital transfers as well as a discussion of a guidance scheme which may be implemented for such transfers. The discussion of numerical computation focuses on the use of multivariate interpolation to aid the computation in the numerical optimization. The second variation analysis includes the development of the conditions for the examination of both fixed and free final time transfers. Evaluations for fixed final time are presented for extremal one, two, and three burn solutions of the first variation. The free final time problem is considered for an extremal two burn solution. In addition, corresponding changes of the second variation formulation over thrust arcs and coast arcs are included. The guidance scheme discussed is an implicit scheme which implements a neighboring optimal feedback guidance strategy to calculate both thrust direction and thrust on-off times.

Design and experiments of a linear piezoelectric motor driven by a single mode.

PubMed

Liu, Zhen; Yao, Zhiyuan; Li, Xiang; Fu, Qianwei

2016-11-01

In this contribution, we propose a novel linear piezoelectric motor with a compact stator that is driven by a single mode. The linear piezoelectric motor can realize bidirectional motion by changing the vibration modes of the stator. Finite element analysis is performed to determine the required vibration mode of the stator and obtain the optimal stator structure and dimensions. Furthermore, the trajectories of the driving foot are analyzed with and without consideration of the mechanical contact with the slider. It is shown that the trajectory of the driving foot is an oblique line when disregarding the contact, and the trajectory becomes an oblique ellipse while taking into account the contact. Finally, a prototype of the motor is fabricated based on the results of finite element analysis. The optimization results show that the motor reaches its maximum thrust force of 4.0 kg, maximum thrust-weight ratio of 33.3, maximum unloaded velocity of 385 mm/s under the excitation of Mode-B, and maximum unloaded velocity of 315 mm/s under the excitation of Mode-L.

Study to document low thrust trajectory optimization programs HILTOP and ASTOP

NASA Technical Reports Server (NTRS)

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

1974-01-01

Detailed documentation of the HILTOP and ASTOP computer programs is presented along with results of the analyses of the possible extension of the HILTOP program and results of an extra-ecliptic mission study performed with HILTOP.

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.

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.

Investigation of abort procedures for space shuttle-type vehicles

NASA Technical Reports Server (NTRS)

Powell, R. W.; Eide, D. G.

1974-01-01

An investigation has been made of abort procedures for space shuttle-type vehicles using a point mass trajectory optimization program known as POST. This study determined the minimum time gap between immediate and once-around safe return to the launch site from a baseline due-East launch trajectory for an alternate space shuttle concept which experiences an instantaneous loss of 25 percent of the total main engine thrust.

The cislunar low-thrust trajectories via the libration point

NASA Astrophysics Data System (ADS)

Qu, Qingyu; Xu, Ming; Peng, Kun

2017-05-01

The low-thrust propulsion will be one of the most important propulsion in the future due to its large specific impulse. Different from traditional low-thrust trajectories (LTTs) yielded by some optimization algorithms, the gradient-based design methodology is investigated for LTTs in this paper with the help of invariant manifolds of LL1 point and Halo orbit near the LL1 point. Their deformations under solar gravitational perturbation are also presented to design LTTs in the restricted four-body model. The perturbed manifolds of LL1 point and its Halo orbit serve as the free-flight phase to reduce the fuel consumptions as much as possible. An open-loop control law is proposed, which is used to guide the spacecraft escaping from Earth or captured by Moon. By using a two-dimensional search strategy, the ON/OFF time of the low-thrust engine in the Earth-escaping and Moon-captured phases can be obtained. The numerical implementations show that the LTTs achieved in this paper are consistent with the one adopted by the SMART-1 mission.

Fuel optimization for low-thrust Earth-Moon transfer via indirect optimal control

NASA Astrophysics Data System (ADS)

Pérez-Palau, Daniel; Epenoy, Richard

2018-02-01

The problem of designing low-energy transfers between the Earth and the Moon has attracted recently a major interest from the scientific community. In this paper, an indirect optimal control approach is used to determine minimum-fuel low-thrust transfers between a low Earth orbit and a Lunar orbit in the Sun-Earth-Moon Bicircular Restricted Four-Body Problem. First, the optimal control problem is formulated and its necessary optimality conditions are derived from Pontryagin's Maximum Principle. Then, two different solution methods are proposed to overcome the numerical difficulties arising from the huge sensitivity of the problem's state and costate equations. The first one consists in the use of continuation techniques. The second one is based on a massive exploration of the set of unknown variables appearing in the optimality conditions. The dimension of the search space is reduced by considering adapted variables leading to a reduction of the computational time. The trajectories found are classified in several families according to their shape, transfer duration and fuel expenditure. Finally, an analysis based on the dynamical structure provided by the invariant manifolds of the two underlying Circular Restricted Three-Body Problems, Earth-Moon and Sun-Earth is presented leading to a physical interpretation of the different families of trajectories.

Solar electric geocentric transfer with attitude constraints: Analysis

NASA Technical Reports Server (NTRS)

Sackett, L. L.; Malchow, H. L.; Delbaum, T. N.

1975-01-01

A time optimal or nearly time optimal trajectory program was developed for solar electric geocentric transfer with or without attitude constraints and with an optional initial high thrust stage. The method of averaging reduces computation time. A nonsingular set of orbital elements is used. The constraints, which are those of one of the SERT-C designs, introduce complexities into the analysis and the solution yields possible discontinuous changes in thrust direction. The power degradation due to VanAllen radiation is modeled analytically. A wide range of solar cell characteristics is assumed. Effects such as oblateness and shadowing are included. The analysis and the results of many example runs are included.

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.

Parametric Model of an Aerospike Rocket Engine

NASA Technical Reports Server (NTRS)

Korte, J. J.

2000-01-01

A suite of computer codes was assembled to simulate the performance of an aerospike engine and to generate the engine input for the Program to Optimize Simulated Trajectories. First an engine simulator module was developed that predicts the aerospike engine performance for a given mixture ratio, power level, thrust vectoring level, and altitude. This module was then used to rapidly generate the aerospike engine performance tables for axial thrust, normal thrust, pitching moment, and specific thrust. Parametric engine geometry was defined for use with the engine simulator module. The parametric model was also integrated into the iSIGHTI multidisciplinary framework so that alternate designs could be determined. The computer codes were used to support in-house conceptual studies of reusable launch vehicle designs.

Parametric Model of an Aerospike Rocket Engine

NASA Technical Reports Server (NTRS)

Korte, J. J.

2000-01-01

A suite of computer codes was assembled to simulate the performance of an aerospike engine and to generate the engine input for the Program to Optimize Simulated Trajectories. First an engine simulator module was developed that predicts the aerospike engine performance for a given mixture ratio, power level, thrust vectoring level, and altitude. This module was then used to rapidly generate the aerospike engine performance tables for axial thrust, normal thrust, pitching moment, and specific thrust. Parametric engine geometry was defined for use with the engine simulator module. The parametric model was also integrated into the iSIGHT multidisciplinary framework so that alternate designs could be determined. The computer codes were used to support in-house conceptual studies of reusable launch vehicle designs.

The Designing of the Mission to Mars for the Siol Delivery by the Electric Propulsion Spacecraft

NASA Astrophysics Data System (ADS)

Starinova, O. L.; Gao, Ch.; Kurochkin, D. V.; Yudong, H.

2018-04-01

The effectiveness of the mission to return soil from Mars depends on design and trajectory parameters.The problem of comprehensive optimization of the low-thrust mission Earth-Mars-Earth is formulated and solved in this paper.

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.

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.

A users manual for a computer program which calculates time optical geocentric transfers using solar or nuclear electric and high thrust propulsion

NASA Technical Reports Server (NTRS)

Sackett, L. L.; Edelbaum, T. N.; Malchow, H. L.

1974-01-01

This manual is a guide for using a computer program which calculates time optimal trajectories for high-and low-thrust geocentric transfers. Either SEP or NEP may be assumed and a one or two impulse, fixed total delta V, initial high thrust phase may be included. Also a single impulse of specified delta V may be included after the low thrust state. The low thrust phase utilizes equinoctial orbital elements to avoid the classical singularities and Kryloff-Boguliuboff averaging to help insure more rapid computation time. The program is written in FORTRAN 4 in double precision for use on an IBM 360 computer. The manual includes a description of the problem treated, input/output information, examples of runs, and source code listings.

A Numerical-Analytical Approach Based on Canonical Transformations for Computing Optimal Low-Thrust Transfers

NASA Astrophysics Data System (ADS)

da Silva Fernandes, S.; das Chagas Carvalho, F.; Bateli Romão, J. V.

2018-04-01

A numerical-analytical procedure based on infinitesimal canonical transformations is developed for computing optimal time-fixed low-thrust limited power transfers (no rendezvous) between coplanar orbits with small eccentricities in an inverse-square force field. The optimization problem is formulated as a Mayer problem with a set of non-singular orbital elements as state variables. Second order terms in eccentricity are considered in the development of the maximum Hamiltonian describing the optimal trajectories. The two-point boundary value problem of going from an initial orbit to a final orbit is solved by means of a two-stage Newton-Raphson algorithm which uses an infinitesimal canonical transformation. Numerical results are presented for some transfers between circular orbits with moderate radius ratio, including a preliminary analysis of Earth-Mars and Earth-Venus missions.

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.

Aeroassisted orbit transfer vehicle trajectory analysis

NASA Technical Reports Server (NTRS)

Braun, Robert D.; Suit, William T.

1988-01-01

The emphasis in this study was on the use of multiple pass trajectories for aerobraking. However, for comparison, single pass trajectories, trajectories using ballutes, and trajectories corrupted by atmospheric anomolies were run. A two-pass trajectory was chosen to determine the relation between sensitivity to errors and payload to orbit. Trajectories that used only aerodynamic forces for maneuvering could put more weight into the target orbits but were very sensitive to variations from the planned trajectors. Using some thrust control resulted in less payload to orbit, but greatly reduced the sensitivity to variations from nominal trajectories. When compared to the non-thrusting trajectories investigated, the judicious use of thrusting resulted in multiple pass trajectories that gave 97 percent of the payload to orbit with almost none of the sensitivity to variations from the nominal.

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.

Solar electric propulsion. [low thrust trajectory control

NASA Technical Reports Server (NTRS)

Barbieri, R. W.

1975-01-01

The major components of a solar electric propulsion system are discussed and some problems in low thrust mission analysis are detailed. Emphasis is placed on the development of a nominal low thrust trajectory and guidance and navigation aspects.

Simulator evaluation of optimal thrust management/fuel conservation strategies for airbus aircraft on short haul routes

NASA Technical Reports Server (NTRS)

Bochem, J. H.; Mossman, D. C.; Lanier, P. D.

1977-01-01

The feasibility of incorporating optimal concepts into a practical system was determined. Various earlier theoretical analyses were confirmed, and insight was gained into the sensitivity of fuel conservation strategies to nonlinear and second order aerodynamic and engine characteristics. In addition to the investigation of optimal trajectories the study ascertained combined fuel savings by utilizing various procedure-oriented improvements such as delayed flap/decelerating approaches and great circle navigation.

Sunmaster: An SEP cargo vehicle for Mars missions

NASA Technical Reports Server (NTRS)

Chiles, Aleasa; Fraser, Jennifer; Halsey, Andy; Honeycutt, David; Madden, Michael; Mcgough, Brian; Paulsen, David; Spear, Becky; Tarkenton, Lynne; Westley, Kevin

1991-01-01

Options are examined for an unmanned solar powered electric propulsion cargo vehicle for Mars missions. The 6 prime areas of study include: trajectory, propulsion system, power system, supporting structure, control system, and launch consideration. Optimization of the low thrust trajectory resulted in a total round trip mission time just under 4 years. The argon propelled electrostatic ion thruster system consists of seventeen 5 N engines and uses a specific impulse of 10,300 secs. At Earth, the system uses 13 engines to produce 60 N of thrust; at Mars, five engines are used, producing 25 N thrust. The thrust of the craft is varied between 60 N at Earth and 24 N at Mars due to reduced solar power available. Solar power is collected by a Fresnel lens concentrator system using a multistacked cell. This system provides 3.5 MW to the propulsion system after losses. Control and positioning to the craft are provided by a system of three double gimballed control moment gyros. Four shuttle 'C' launches will be used to transport the unassembled vehicle in modular units to low Earth orbit where it will be assembled using the Mobile Transporter of the Space Station Freedom.

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.

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.

Trajectory Optimization of a Bimodal Nuclear Powered Spacecraft to Mars

DTIC Science & Technology

1990-05-29

velocity M = initial mass of spacecraft o m= ion fuel expulsion rate (constant) 0 = thrust direction angle = gravitational constant of Sun AVto t...total velocity change possible for the impulsive engines AV1 = velocity change for Earth escape AV2 = velocity change for Mars capture AVto t = AV + AV

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.

Analytical investigations in aircraft and spacecraft trajectory optimization and optimal guidance

NASA Technical Reports Server (NTRS)

Markopoulos, Nikos; Calise, Anthony J.

1995-01-01

A collection of analytical studies is presented related to unconstrained and constrained aircraft (a/c) energy-state modeling and to spacecraft (s/c) motion under continuous thrust. With regard to a/c unconstrained energy-state modeling, the physical origin of the singular perturbation parameter that accounts for the observed 2-time-scale behavior of a/c during energy climbs is identified and explained. With regard to the constrained energy-state modeling, optimal control problems are studied involving active state-variable inequality constraints. Departing from the practical deficiencies of the control programs for such problems that result from the traditional formulations, a complete reformulation is proposed for these problems which, in contrast to the old formulation, will presumably lead to practically useful controllers that can track an inequality constraint boundary asymptotically, and even in the presence of 2-sided perturbations about it. Finally, with regard to s/c motion under continuous thrust, a thrust program is proposed for which the equations of 2-dimensional motion of a space vehicle in orbit, viewed as a point mass, afford an exact analytic solution. The thrust program arises under the assumption of tangential thrust from the costate system corresponding to minimum-fuel, power-limited, coplanar transfers between two arbitrary conics. The thrust program can be used not only with power-limited propulsion systems, but also with any propulsion system capable of generating continuous thrust of controllable magnitude, and, for propulsion types and classes of transfers for which it is sufficiently optimal the results of this report suggest a method of maneuvering during planetocentric or heliocentric orbital operations, requiring a minimum amount of computation; thus uniquely suitable for real-time feedback guidance implementations.

Multi-Objective Hybrid Optimal Control for Multiple-Flyby Interplanetary Mission Design using Chemical Propulsion

NASA Technical Reports Server (NTRS)

Englander, Jacob A.; Vavrina, Matthew A.

2015-01-01

Preliminary design of high-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys and the bodies at which those flybys are performed. For some missions, such as surveys of small bodies, the mission designer also contributes to target selection. In addition, real-valued decision variables, such as launch epoch, flight times, maneuver and flyby epochs, and flyby altitudes must be chosen. There are often many thousands 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 impulsive mission design problem as a multi-objective hybrid optimal control problem. The method is demonstrated on several real-world problems. Two assumptions are frequently made to simplify the modeling of an interplanetary high-thrust trajectory during the preliminary design phase. The first assumption is that because the available thrust is high, any maneuvers performed by the spacecraft can be modeled as discrete changes in velocity. This assumption removes the need to integrate the equations of motion governing the motion of a spacecraft under thrust and allows the change in velocity to be modeled as an impulse and the expenditure of propellant to be modeled using the time-independent solution to Tsiolkovsky's rocket equation [1]. The second assumption is that the spacecraft moves primarily under the influence of the central body, i.e. the sun, and all other perturbing forces may be neglected in preliminary design. The path of the spacecraft may then be modeled as a series of conic sections. When a spacecraft performs a close approach to a planet, the central body switches from the sun to that planet and the trajectory is modeled as a hyperbola with respect to the planet. This is known as the method of patched conics. The impulsive and patched-conic assumptions significantly simplify the preliminary design problem.

Optimal Electrodynamic Tether Phasing Maneuvers

NASA Technical Reports Server (NTRS)

Bitzer, Matthew S.; Hall, Christopher D.

2007-01-01

We study the minimum-time orbit phasing maneuver problem for a constant-current electrodynamic tether (EDT). The EDT is assumed to be a point mass and the electromagnetic forces acting on the tether are always perpendicular to the local magnetic field. After deriving and non-dimensionalizing the equations of motion, the only input parameters become current and the phase angle. Solution examples, including initial Lagrange costates, time of flight, thrust plots, and thrust angle profiles, are given for a wide range of current magnitudes and phase angles. The two-dimensional cases presented use a non-tilted magnetic dipole model, and the solutions are compared to existing literature. We are able to compare similar trajectories for a constant thrust phasing maneuver and we find that the time of flight is longer for the constant thrust case with similar initial thrust values and phase angles. Full three-dimensional solutions, which use a titled magnetic dipole model, are also analyzed for orbits with small inclinations.

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.

A trajectory generation and system characterization model for cislunar low-thrust spacecraft. Volume 2: Technical manual

NASA Technical Reports Server (NTRS)

Korsmeyer, David J.; Pinon, Elfego, III; Oconnor, Brendan M.; Bilby, Curt R.

1990-01-01

The documentation of the Trajectory Generation and System Characterization Model for the Cislunar Low-Thrust Spacecraft is presented in Technical and User's Manuals. The system characteristics and trajectories of low thrust nuclear electric propulsion spacecraft can be generated through the use of multiple system technology models coupled with a high fidelity trajectory generation routine. The Earth to Moon trajectories utilize near Earth orbital plane alignment, midcourse control dependent upon the spacecraft's Jacobian constant, and capture to target orbit utilizing velocity matching algorithms. The trajectory generation is performed in a perturbed two-body equinoctial formulation and the restricted three-body formulation. A single control is determined by the user for the interactive midcourse portion of the trajectory. The full spacecraft system characteristics and trajectory are provided as output.

Design of Launch Abort System Thrust Profile and Concept of Operations

NASA Technical Reports Server (NTRS)

Litton, Daniel; O'Keefe, Stephen A.; Winski, Richard G.; Davidson, John B.

2008-01-01

This paper describes how the Abort Motor thrust profile has been tailored and how optimizing the Concept of Operations on the Launch Abort System (LAS) of the Orion Crew Exploration Vehicle (CEV) aides in getting the crew safely away from a failed Crew Launch Vehicle (CLV). Unlike the passive nature of the Apollo system, the Orion Launch Abort Vehicle will be actively controlled, giving the program a more robust abort system with a higher probability of crew survival for an abort at all points throughout the CLV trajectory. By optimizing the concept of operations and thrust profile the Orion program will be able to take full advantage of the active Orion LAS. Discussion will involve an overview of the development of the abort motor thrust profile and the current abort concept of operations as well as their effects on the performance of LAS aborts. Pad Abort (for performance) and Maximum Drag (for separation from the Launch Vehicle) are the two points that dictate the required thrust and shape of the thrust profile. The results in this paper show that 95% success of all performance requirements is not currently met for Pad Abort. Future improvements to the current parachute sequence and other potential changes will mitigate the current problems, and meet abort performance requirements.

An unconditionally stable method for numerically solving solar sail spacecraft equations of motion

NASA Astrophysics Data System (ADS)

Karwas, Alex

Solar sails use the endless supply of the Sun's radiation to propel spacecraft through space. The sails use the momentum transfer from the impinging solar radiation to provide thrust to the spacecraft while expending zero fuel. Recently, the first solar sail spacecraft, or sailcraft, named IKAROS completed a successful mission to Venus and proved the concept of solar sail propulsion. Sailcraft experimental data is difficult to gather due to the large expenses of space travel, therefore, a reliable and accurate computational method is needed to make the process more efficient. Presented in this document is a new approach to simulating solar sail spacecraft trajectories. The new method provides unconditionally stable numerical solutions for trajectory propagation and includes an improved physical description over other methods. The unconditional stability of the new method means that a unique numerical solution is always determined. The improved physical description of the trajectory provides a numerical solution and time derivatives that are continuous throughout the entire trajectory. The error of the continuous numerical solution is also known for the entire trajectory. Optimal control for maximizing thrust is also provided within the framework of the new method. Verification of the new approach is presented through a mathematical description and through numerical simulations. The mathematical description provides details of the sailcraft equations of motion, the numerical method used to solve the equations, and the formulation for implementing the equations of motion into the numerical solver. Previous work in the field is summarized to show that the new approach can act as a replacement to previous trajectory propagation methods. A code was developed to perform the simulations and it is also described in this document. Results of the simulations are compared to the flight data from the IKAROS mission. Comparison of the two sets of data show that the new approach is capable of accurately simulating sailcraft motion. Sailcraft and spacecraft simulations are compared to flight data and to other numerical solution techniques. The new formulation shows an increase in accuracy over a widely used trajectory propagation technique. Simulations for two-dimensional, three-dimensional, and variable attitude trajectories are presented to show the multiple capabilities of the new technique. An element of optimal control is also part of the new technique. An additional equation is added to the sailcraft equations of motion that maximizes thrust in a specific direction. A technical description and results of an example optimization problem are presented. The spacecraft attitude dynamics equations take the simulation a step further by providing control torques using the angular rate and acceleration outputs of the numerical formulation.

Flight Management System Execution of Idle-Thrust Descents in Operations

NASA Technical Reports Server (NTRS)

Stell, Laurel L.

2011-01-01

To enable arriving aircraft to fly optimized descents computed by the flight management system (FMS) in congested airspace, ground automation must accurately predict descent trajectories. To support development of the trajectory predictor and its error models, commercial flights executed idle-thrust descents, and the recorded data includes the target speed profile and FMS intent trajectories. The FMS computes the intended descent path assuming idle thrust after top of descent (TOD), and any intervention by the controllers that alters the FMS execution of the descent is recorded so that such flights are discarded from the analysis. The horizontal flight path, cruise and meter fix altitudes, and actual TOD location are extracted from the radar data. Using more than 60 descents in Boeing 777 aircraft, the actual speeds are compared to the intended descent speed profile. In addition, three aspects of the accuracy of the FMS intent trajectory are analyzed: the meter fix crossing time, the TOD location, and the altitude at the meter fix. The actual TOD location is within 5 nmi of the intent location for over 95% of the descents. Roughly 90% of the time, the airspeed is within 0.01 of the target Mach number and within 10 KCAS of the target descent CAS, but the meter fix crossing time is only within 50 sec of the time computed by the FMS. Overall, the aircraft seem to be executing the descents as intended by the designers of the onboard automation.

Automated Design of Propellant-Optimal, End-to-End, Low-Thrust Trajectories for Trojan Asteroid Tours

NASA Technical Reports Server (NTRS)

Stuart, Jeffrey; Howell, Kathleen; Wilson, Roby

2013-01-01

The Sun-Jupiter Trojan asteroids are celestial bodies of great scientific interest as well as potential resources offering water and other mineral resources for longterm human exploration of the solar system. Previous investigations under this project have addressed the automated design of tours within the asteroid swarm. This investigation expands the current automation scheme by incorporating options for a complete trajectory design approach to the Trojan asteroids. Computational aspects of the design procedure are automated such that end-to-end trajectories are generated with a minimum of human interaction after key elements and constraints associated with a proposed mission concept are specified.

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.

Minimum-Cost Aircraft Descent Trajectories with a Constrained Altitude Profile

NASA Technical Reports Server (NTRS)

Wu, Minghong G.; Sadovsky, Alexander V.

2015-01-01

An analytical formula for solving the speed profile that accrues minimum cost during an aircraft descent with a constrained altitude profile is derived. The optimal speed profile first reaches a certain speed, called the minimum-cost speed, as quickly as possible using an appropriate extreme value of thrust. The speed profile then stays on the minimum-cost speed as long as possible, before switching to an extreme value of thrust for the rest of the descent. The formula is applied to an actual arrival route and its sensitivity to winds and airlines' business objectives is analyzed.

Automated Design of Multiphase Space Missions Using Hybrid Optimal Control

ERIC Educational Resources Information Center

Chilan, Christian Miguel

2009-01-01

A modern space mission is assembled from multiple phases or events such as impulsive maneuvers, coast arcs, thrust arcs and planetary flybys. Traditionally, a mission planner would resort to intuition and experience to develop a sequence of events for the multiphase mission and to find the space trajectory that minimizes propellant use by solving…

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.

Flapping Wings of an Inclined Stroke Angle: Experiments and Reduced-Order Models in Dual Aerial/Aquatic Flight

NASA Astrophysics Data System (ADS)

Izraelevitz, Jacob; Triantafyllou, Michael

2016-11-01

Flapping wings in nature demonstrate a large force actuation envelope, with capabilities beyond the limits of static airfoil section coefficients. Puffins, guillemots, and other auks particularly showcase this mechanism, as they are able to both generate both enough thrust to swim and lift to fly, using the same wing, by changing the wing motion trajectory. The wing trajectory is therefore an additional design criterion to be optimized along with traditional aircraft parameters, and could possibly enable dual aerial/aquatic flight. We showcase finite aspect-ratio flapping wing experiments, dynamic similarity arguments, and reduced-order models for predicting the performance of flapping wings that carry out complex motion trajectories.

Particle swarm optimization of ascent trajectories of multistage launch vehicles

NASA Astrophysics Data System (ADS)

Pontani, Mauro

2014-02-01

Multistage launch vehicles are commonly employed to place spacecraft and satellites in their operational orbits. If the rocket characteristics are specified, the optimization of its ascending trajectory consists of determining the optimal control law that leads to maximizing the final mass at orbit injection. The numerical solution of a similar problem is not trivial and has been pursued with different methods, for decades. This paper is concerned with an original approach based on the joint use of swarming theory and the necessary conditions for optimality. The particle swarm optimization technique represents a heuristic population-based optimization method inspired by the natural motion of bird flocks. Each individual (or particle) that composes the swarm corresponds to a solution of the problem and is associated with a position and a velocity vector. The formula for velocity updating is the core of the method and is composed of three terms with stochastic weights. As a result, the population migrates toward different regions of the search space taking advantage of the mechanism of information sharing that affects the overall swarm dynamics. At the end of the process the best particle is selected and corresponds to the optimal solution to the problem of interest. In this work the three-dimensional trajectory of the multistage rocket is assumed to be composed of four arcs: (i) first stage propulsion, (ii) second stage propulsion, (iii) coast arc (after release of the second stage), and (iv) third stage propulsion. The Euler-Lagrange equations and the Pontryagin minimum principle, in conjunction with the Weierstrass-Erdmann corner conditions, are employed to express the thrust angles as functions of the adjoint variables conjugate to the dynamics equations. The use of these analytical conditions coming from the calculus of variations leads to obtaining the overall rocket dynamics as a function of seven parameters only, namely the unknown values of the initial state and costate components, the coast duration, and the upper stage thrust duration. In addition, a simple approach is introduced and successfully applied with the purpose of satisfying exactly the path constraint related to the maximum dynamical pressure in the atmospheric phase. The basic version of the swarming technique, which is used in this research, is extremely simple and easy to program. Nevertheless, the algorithm proves to be capable of yielding the optimal rocket trajectory with a very satisfactory numerical accuracy.

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.

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 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.

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.

The role of invariant manifolds in lowthrust trajectory design (part III)

NASA Technical Reports Server (NTRS)

Lo, Martin W.; Anderson, Rodney L.; Lam, Try; Whiffen, Greg

2006-01-01

This paper is the third in a series to explore the role of invariant manifolds in the design of low thrust trajectories. In previous papers, we analyzed an impulsive thrust resonant gravity assist flyby trajectory to capture into Europa orbit using the invariant manifolds of unstable resonant periodic orbits and libration orbits. The energy savings provided by the gravity assist may be interpreted dynamically as the result of a finite number of intersecting invariant manifolds. In this paper we demonstrate that the same dynamics is at work for low thrust trajectories with resonant flybys and low energy capture. However, in this case, the flybys and capture are effected by continuous families of intersecting invariant manifolds.

Fuel-Efficient Descent and Landing Guidance Logic for a Safe Lunar Touchdown

NASA Technical Reports Server (NTRS)

Lee, Allan Y.

2011-01-01

The landing of a crewed lunar lander on the surface of the Moon will be the climax of any Moon mission. At touchdown, the landing mechanism must absorb the load imparted on the lander due to the vertical component of the lander's touchdown velocity. Also, a large horizontal velocity must be avoided because it could cause the lander to tip over, risking the life of the crew. To be conservative, the worst-case lander's touchdown velocity is always assumed in designing the landing mechanism, making it very heavy. Fuel-optimal guidance algorithms for soft planetary landing have been studied extensively. In most of these studies, the lander is constrained to touchdown with zero velocity. With bounds imposed on the magnitude of the engine thrust, the optimal control solutions typically have a "bang-bang" thrust profile: the thrust magnitude "bangs" instantaneously between its maximum and minimum magnitudes. But the descent engine might not be able to throttle between its extremes instantaneously. There is also a concern about the acceptability of "bang-bang" control to the crew. In our study, the optimal control of a lander is formulated with a cost function that penalizes both the touchdown velocity and the fuel cost of the descent engine. In this formulation, there is not a requirement to achieve a zero touchdown velocity. Only a touchdown velocity that is consistent with the capability of the landing gear design is required. Also, since the nominal throttle level for the terminal descent sub-phase is well below the peak engine thrust, no bound on the engine thrust is used in our formulated problem. Instead of bangbang type solution, the optimal thrust generated is a continuous function of time. With this formulation, we can easily derive analytical expressions for the optimal thrust vector, touchdown velocity components, and other system variables. These expressions provide insights into the "physics" of the optimal landing and terminal descent maneuver. These insights could help engineers to achieve a better "balance" between the conflicting needs of achieving a safe touchdown velocity, a low-weight landing mechanism, low engine fuel cost, and other design goals. In comparing the computed optimal control results with the preflight landing trajectory design of the Apollo-11 mission, we noted interesting similarities between the two missions.

Low-Thrust Transfers from Distant Retrograde Orbits to L2 Halo Orbits in the Earth-Moon System

NASA Technical Reports Server (NTRS)

Parrish, Nathan L.; Parker, Jeffrey S.; Hughes, Steven P.; Heiligers, Jeannette

2016-01-01

This paper presents a study of transfers between distant retrograde orbits (DROs) and L2 halo orbits in the Earth-Moon system that could be flown by a spacecraft with solar electric propulsion (SEP). Two collocation-based optimal control methods are used to optimize these highly-nonlinear transfers: Legendre pseudospectral and Hermite-Simpson. Transfers between DROs and halo orbits using low-thrust propulsion have not been studied previously. This paper offers a study of several families of trajectories, parameterized by the number of orbital revolutions in a synodic frame. Even with a poor initial guess, a method is described to reliably generate families of solutions. The circular restricted 3-body problem (CRTBP) is used throughout the paper so that the results are autonomous and simpler to understand.

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.

Fuel-optimal, low-thrust transfers between libration point orbits

NASA Astrophysics Data System (ADS)

Stuart, Jeffrey R.

Mission design requires the efficient management of spacecraft fuel to reduce mission cost, increase payload mass, and extend mission life. High efficiency, low-thrust propulsion devices potentially offer significant propellant reductions. Periodic orbits that exist in a multi-body regime and low-thrust transfers between these orbits can be applied in many potential mission scenarios, including scientific observation and communications missions as well as cargo transport. In light of the recent discovery of water ice in lunar craters, libration point orbits that support human missions within the Earth-Moon region are of particular interest. This investigation considers orbit transfer trajectories generated by a variable specific impulse, low-thrust engine with a primer-vector-based, fuel-optimizing transfer strategy. A multiple shooting procedure with analytical gradients yields rapid solutions and serves as the basis for an investigation into the trade space between flight time and consumption of fuel mass. Path and performance constraints can be included at node points along any thrust arc. Integration of invariant manifolds into the design strategy may also yield improved performance and greater fuel savings. The resultant transfers offer insight into the performance of the variable specific impulse engine and suggest novel implementations of conventional impulsive thrusters. Transfers incorporating invariant manifolds demonstrate the fuel savings and expand the mission design capabilities that are gained by exploiting system symmetry. A number of design applications are generated.

Trajectory design for a rendezvous mission to Earth's Trojan asteroid 2010 TK7

NASA Astrophysics Data System (ADS)

Lei, Hanlun; Xu, Bo; Zhang, Lei

2017-12-01

In this paper a rendezvous mission to the Earth's Trojan asteroid 2010 TK7 is proposed, and preliminary transfer trajectories are designed. Due to the high inclination (∼ 20.9°) of the target asteroid relative to the ecliptic plane, direct transfers usually require large amounts of fuel consumption, which is beyond the capacity of current technology. As gravity assist technique could effectively change the inclination of spacecraft's trajectory, it is adopted to reduce the launch energy and rendezvous velocity maneuver. In practical computation, impulsive and low-thrust, gravity-assisted trajectories are considered. Among all the trajectories computed, the low-thrust gravity-assisted trajectory with Venus-Earth-Venus (V-E-V) swingby sequence performs the best in terms of propellant mass. For a spacecraft with initial mass of 800 kg , propellant mass of the best trajectory is 36.74 kg . Numerical results indicate that both the impulsive and low-thrust, gravity-assisted trajectories corresponding to V-E-V sequence could satisfy mission constraints, and can be applied to practical rendezvous mission.

Optimization of the transfer trajectory of a low-thrust spacecraft for research of Jupiter using an Earth gravity-assist maneuver

NASA Astrophysics Data System (ADS)

Konstantinov, M. S.; Orlov, A. A.

2014-12-01

The paper analyzes the possibility of the use of a gravity-assist maneuver for flight to Jupiter. The advantage of the Earth gravity-assist maneuver in comparison with the direct transfer in terms of reduction of amount of energy required per transfer is considered. Quantitative and qualitative evaluations of two transfer profiles are given.

Designing capture trajectories to unstable periodic orbits around Europa

NASA Technical Reports Server (NTRS)

Russell, Ryan P.; Lam, Try

2006-01-01

The hostile environment of third body perturbations restricts a mission designer's ability to find well-behaved reproducible capture trajectories when dealing with limited control authority as is typical with low-thrust missions. The approach outlined in this paper confronts this shortcoming by utilizing dynamical systems theory and an extensive preexisting database of Restricted Three Body Problem (RTBP) periodic orbits. The stable manifolds of unstable periodic orbits are utilized to attract a spacecraft towards Europa. By selecting an appropriate periodic orbit, a mission designer can control important characteristics of the captured state including stability, minimum altitudes, characteristic inclinations, and characteristic radii among others. Several free parameters are optimized in the non-trivial mapping from the RTBP to a more realistic model. Although the ephemeris capture orbit is ballistic by design, low-thrust is used to target the state that leads to the capture orbit, control the spacecraft after arriving on the unstable quasi-periodic orbit, and begin the spiral down towards the science orbit. The approach allows a mission designer to directly target fuel efficient captures at Europa in an ephemeris model. Furthermore, it provides structure and controllability to the design of capture trajectories that reside in a chaotic environment.

Trajectory optimization and guidance for an aerospace plane

NASA Technical Reports Server (NTRS)

Mease, Kenneth D.; Vanburen, Mark A.

1989-01-01

The first step in the approach to developing guidance laws for a horizontal take-off, air breathing single-stage-to-orbit vehicle is to characterize the minimum-fuel ascent trajectories. The capability to generate constrained, minimum fuel ascent trajectories for a single-stage-to-orbit vehicle was developed. A key component of this capability is the general purpose trajectory optimization program OTIS. The pre-production version, OTIS 0.96 was installed and run on a Convex C-1. A propulsion model was developed covering the entire flight envelope of a single-stage-to-orbit vehicle. Three separate propulsion modes, corresponding to an after burning turbojet, a ramjet and a scramjet, are used in the air breathing propulsion phase. The Generic Hypersonic Aerodynamic Model Example aerodynamic model of a hypersonic air breathing single-stage-to-orbit vehicle was obtained and implemented. Preliminary results pertaining to the effects of variations in acceleration constraints, available thrust level and fuel specific impulse on the shape of the minimum-fuel ascent trajectories were obtained. The results show that, if the air breathing engines are sized for acceleration to orbital velocity, it is the acceleration constraint rather than the dynamic pressure constraint that is active during ascent.

Nonlinear feedback control for high alpha flight

NASA Technical Reports Server (NTRS)

Stalford, Harold

1990-01-01

Analytical aerodynamic models are derived from a high alpha 6 DOF wind tunnel model. One detail model requires some interpolation between nonlinear functions of alpha. One analytical model requires no interpolation and as such is a completely continuous model. Flight path optimization is conducted on the basic maneuvers: half-loop, 90 degree pitch-up, and level turn. The optimal control analysis uses the derived analytical model in the equations of motion and is based on both moment and force equations. The maximum principle solution for the half-loop is poststall trajectory performing the half-loop in 13.6 seconds. The agility induced by thrust vectoring capability provided a minimum effect on reducing the maneuver time. By means of thrust vectoring control the 90 degrees pitch-up maneuver can be executed in a small place over a short time interval. The agility capability of thrust vectoring is quite beneficial for pitch-up maneuvers. The level turn results are based currently on only outer layer solutions of singular perturbation. Poststall solutions provide high turn rates but generate higher losses of energy than that of classical sustained solutions.

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

NASA Technical Reports Server (NTRS)

Englander, Jacob

2016-01-01

This set of tutorial slides is an introduction to the Evolutionary Mission Trajectory Generator (EMTG), NASA Goddard Space Flight Center's autonomous tool for preliminary design of interplanetary missions. This slide set covers the basics of creating and post-processing simple interplanetary missions in EMTG using both high-thrust chemical and low-thrust electric propulsion along with a variety of operational constraints.

Multi-Objective Hybrid Optimal Control for Multiple-Flyby Interplanetary Mission Design Using Chemical Propulsion

NASA Technical Reports Server (NTRS)

Englander, Jacob A.; Vavrina, Matthew A.

2015-01-01

Preliminary design of high-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys and the bodies at which those flybys are performed. For some missions, such as surveys of small bodies, the mission designer also contributes to target selection. In addition, real-valued decision variables, such as launch epoch, flight times, maneuver and flyby epochs, and flyby altitudes must be chosen. There are often many thousands 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 impulsive mission design problem as a multiobjective hybrid optimal control problem. The method is demonstrated on several real-world problems.

Rapid near-optimal trajectory generation and guidance law development for single-stage-to-orbit airbreathing vehicles

NASA Technical Reports Server (NTRS)

Calise, A. J.; Flandro, G. A.; Corban, J. E.

1990-01-01

General problems associated with on-board trajectory optimization, propulsion system cycle selection, and with the synthesis of guidance laws were addressed for an ascent to low-earth-orbit of an air-breathing single-stage-to-orbit vehicle. The NASA Generic Hypersonic Aerodynamic Model Example and the Langley Accelerator aerodynamic sets were acquired and implemented. Work related to the development of purely analytic aerodynamic models was also performed at a low level. A generic model of a multi-mode propulsion system was developed that includes turbojet, ramjet, scramjet, and rocket engine cycles. Provisions were made in the dynamic model for a component of thrust normal to the flight path. Computational results, which characterize the nonlinear sensitivity of scramjet performance to changes in vehicle angle of attack, were obtained and incorporated into the engine model. Additional trajectory constraints were introduced: maximum dynamic pressure; maximum aerodynamic heating rate per unit area; angle of attack and lift limits; and limits on acceleration both along and normal to the flight path. The remainder of the effort focused on required modifications to a previously derived algorithm when the model complexity cited above was added. In particular, analytic switching conditions were derived which, under appropriate assumptions, govern optimal transition from one propulsion mode to another for two cases: the case in which engine cycle operations can overlap, and the case in which engine cycle operations are mutually exclusive. The resulting guidance algorithm was implemented in software and exercised extensively. It was found that the approximations associated with the assumed time scale separation employed in this work are reasonable except over the Mach range from roughly 5 to 8. This phenomenon is due to the very large thrust capability of scramjets in this Mach regime when sized to meet the requirement for ascent to orbit. By accounting for flight path angle and flight path angle rate in construction of the flight path over this Mach range, the resulting algorithm provides the means for rapid near-optimal trajectory generation and propulsion cycle selection over the entire Mach range from take-off to orbit.

Main braking phase for a soft moon landing as a form of trajectory correction

NASA Astrophysics Data System (ADS)

Likhachev, V. N.; Sikharulidze, Yu. G.; Fedotov, V. P.

2013-12-01

Rationale is given for the braking profile of a spacecraft making a soft landing on the Moon's surface, including the following four phases: main braking, free fall, repeated braking, and descent at a constant speed. Due to the large altitude differential over the braking path in near-polar regions of the Moon, main braking is proposed as a type of trajectory correction impulse using no altimeter. The boundary problem solution and statistical calculations are used to give the potential energy costs and characteristics of the dispersion characteristics for this phase and choose an optimal thrust-to-weight ratio for the phase.

Optimal three-dimensional reusable tug trajectories for planetary missions including correction for nodal precession

NASA Technical Reports Server (NTRS)

Borsody, J.

1976-01-01

Equations are derived by using the maximum principle to maximize the payload of a reusable tug for planetary missions. The analysis includes a correction for precession of the space shuttle orbit. The tug returns to this precessed orbit (within a specified time) and makes the required nodal correction. A sample case is analyzed that represents an inner planet mission as specified by a fixed declination and right ascension of the outgoing asymptote and the mission energy. The reusable stage performance corresponds to that of a typical cryogenic tug. Effects of space shuttle orbital inclination, several trajectory parameters, and tug thrust on payload are also investigated.

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

Predictability of Top of Descent Location for Operational Idle-Thrust Descents

NASA Technical Reports Server (NTRS)

Stell, Laurel L.

2010-01-01

To enable arriving aircraft to fly optimized descents computed by the flight management system (FMS) in congested airspace, ground automation must accurately predict descent trajectories. To support development of the trajectory predictor and its uncertainty models, commercial flights executed idle-thrust descents at a specified descent speed, and the recorded data included the specified descent speed profile, aircraft weight, and the winds entered into the FMS as well as the radar data. The FMS computed the intended descent path assuming idle thrust after top of descent (TOD), and the controllers and pilots then endeavored to allow the FMS to fly the descent to the meter fix with minimal human intervention. The horizontal flight path, cruise and meter fix altitudes, and actual TOD location were extracted from the radar data. Using approximately 70 descents each in Boeing 757 and Airbus 319/320 aircraft, multiple regression estimated TOD location as a linear function of the available predictive factors. The cruise and meter fix altitudes, descent speed, and wind clearly improve goodness of fit. The aircraft weight improves fit for the Airbus descents but not for the B757. Except for a few statistical outliers, the residuals have absolute value less than 5 nmi. Thus, these predictive factors adequately explain the TOD location, which indicates the data do not include excessive noise.

Potential applications of skip SMV with thrust engine

NASA Astrophysics Data System (ADS)

Wang, Weilin; Savvaris, Al

2016-11-01

This paper investigates the potential applications of Space Maneuver Vehicles (SMV) with skip trajectory. Due to soaring space operations over the past decades, the risk of space debris has considerably increased such as collision risks with space asset, human property on ground and even aviation. Many active debris removal methods have been investigated and in this paper, a debris remediation method is first proposed based on skip SMV. The key point is to perform controlled re-entry. These vehicles are expected to achieve a trans-atmospheric maneuver with thrust engine. If debris is released at altitude below 80 km, debris could be captured by the atmosphere drag force and re-entry interface prediction accuracy is improved. Moreover if the debris is released in a cargo at a much lower altitude, this technique protects high value space asset from break up by the atmosphere and improves landing accuracy. To demonstrate the feasibility of this concept, the present paper presents the simulation results for two specific mission profiles: (1) descent to predetermined altitude; (2) descent to predetermined point (altitude, longitude and latitude). The evolutionary collocation method is adopted for skip trajectory optimization due to its global optimality and high-accuracy. This method is actually a two-step optimization approach based on the heuristic algorithm and the collocation method. The optimal-control problem is transformed into a nonlinear programming problem (NLP) which can be efficiently and accurately solved by the sequential quadratic programming (SQP) procedure. However, such a method is sensitive to initial values. To reduce the sensitivity problem, genetic algorithm (GA) is adopted to refine the grids and provide near optimum initial values. By comparing the simulation data from different scenarios, it is found that skip SMV is feasible in active debris removal and the evolutionary collocation method gives a truthful re-entry trajectory that satisfies the path and boundary constraints.

Hybrid Differential Dynamic Programming with Stochastic Search

NASA Technical Reports Server (NTRS)

Aziz, Jonathan; Parker, Jeffrey; Englander, Jacob

2016-01-01

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASAs Dawn mission. The Dawn trajectory was designed with the DDP-based Static Dynamic Optimal Control algorithm used in the Mystic software. Another recently developed method, Hybrid Differential Dynamic Programming (HDDP) is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

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.

A feedback control for the advanced launch system

NASA Technical Reports Server (NTRS)

Seywald, Hans; Cliff, Eugene M.

1991-01-01

A robust feedback algorithm is presented for a near-minimum-fuel ascent of a two-stage launch vehicle operating in the equatorial plane. The development of the algorithm is based on the ideas of neighboring optimal control and can be derived into three phases. In phase 1, the formalism of optimal control is employed to calculate fuel-optimal ascent trajectories for a simple point-mass model. In phase 2, these trajectories are used to numerically calculate gain functions of time for the control(s), the total flight time, and possibly, for other variables of interest. In phase 3, these gains are used to determine feedback expressions for the controls associated with a more realistic model of a launch vehicle. With the Advanced Launch System in mind, all calculations are performed on a two-stage vehicle with fixed thrust history, but this restriction is by no means important for the approach taken. Performance and robustness of the algorithm is found to be excellent.

A guidance and navigation system for continuous low thrust vehicles. M.S. Thesis

NASA Technical Reports Server (NTRS)

Tse, C. J. C.

1973-01-01

A midcourse guidance and navigation system for continuous low thrust vehicles is described. A set of orbit elements, known as the equinoctial elements, are selected as the state variables. The uncertainties are modelled statistically by random vector and stochastic processes. The motion of the vehicle and the measurements are described by nonlinear stochastic differential and difference equations respectively. A minimum time nominal trajectory is defined and the equation of motion and the measurement equation are linearized about this nominal trajectory. An exponential cost criterion is constructed and a linear feedback guidance law is derived to control the thrusting direction of the engine. Using this guidance law, the vehicle will fly in a trajectory neighboring the nominal trajectory. The extended Kalman filter is used for state estimation. Finally a short mission using this system is simulated. The results indicate that this system is very efficient for short missions.

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.

Asteroid retrieval missions enabled by invariant manifold dynamics

NASA Astrophysics Data System (ADS)

Sánchez, Joan Pau; García Yárnoz, Daniel

2016-10-01

Near Earth Asteroids are attractive targets for new space missions; firstly, because of their scientific importance, but also because of their impact threat and prospective resources. The asteroid retrieval mission concept has thus arisen as a synergistic approach to tackle these three facets of interest in one single mission. This paper reviews the methodology used by the authors (2013) in a previous search for objects that could be transported from accessible heliocentric orbits into the Earth's neighbourhood at affordable costs (or Easily Retrievable Objects, a.k.a. EROs). This methodology consisted of a heuristic pruning and an impulsive manoeuvre trajectory optimisation. Low thrust propulsion on the other hand clearly enables the transportation of much larger objects due to its higher specific impulse. Hence, in this paper, low thrust retrieval transfers are sought using impulsive trajectories as first guesses to solve the optimal control problem. GPOPS-II is used to transcribe the continuous-time optimal control problem to a nonlinear programming problem (NLP). The latter is solved by IPOPT, an open source software package for large-scale NLPs. Finally, a natural continuation procedure that increases the asteroid mass allows to find out the largest objects that could be retrieved from a given asteroid orbit. If this retrievable mass is larger than the actual mass of the asteroid, the asteroid retrieval mission for this particular object is said to be feasible. The paper concludes with an updated list of 17 EROs, as of April 2016, with their maximum retrievable masses by means of low thrust propulsion. This ranges from 2000 tons for the easiest object to be retrieved to 300 tons for the least accessible of them.

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.

Hybrid Differential Dynamic Programming with Stochastic Search

NASA Technical Reports Server (NTRS)

Aziz, Jonathan; Parker, Jeffrey; Englander, Jacob A.

2016-01-01

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASA's Dawn mission. The Dawn trajectory was designed with the DDP-based Static/Dynamic Optimal Control algorithm used in the Mystic software.1 Another recently developed method, Hybrid Differential Dynamic Programming (HDDP),2, 3 is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

Unsteady Adjoint Approach for Design Optimization of Flapping Airfoils

NASA Technical Reports Server (NTRS)

Lee, Byung Joon; Liou, Meng-Sing

2012-01-01

This paper describes the work for optimizing the propulsive efficiency of flapping airfoils, i.e., improving the thrust under constraining aerodynamic work during the flapping flights by changing their shape and trajectory of motion with the unsteady discrete adjoint approach. For unsteady problems, it is essential to properly resolving time scales of motion under consideration and it must be compatible with the objective sought after. We include both the instantaneous and time-averaged (periodic) formulations in this study. For the design optimization with shape parameters or motion parameters, the time-averaged objective function is found to be more useful, while the instantaneous one is more suitable for flow control. The instantaneous objective function is operationally straightforward. On the other hand, the time-averaged objective function requires additional steps in the adjoint approach; the unsteady discrete adjoint equations for a periodic flow must be reformulated and the corresponding system of equations solved iteratively. We compare the design results from shape and trajectory optimizations and investigate the physical relevance of design variables to the flapping motion at on- and off-design conditions.

Optimum Climb to Cruise Noise Trajectories for the High Speed Civil Transport

NASA Technical Reports Server (NTRS)

Berton, Jeffrey J.

2003-01-01

By entraining large quantities of ambient air into advanced ejector nozzles, the jet noise of the proposed High Speed Civil Transport (HSCT) is expected to be reduced to levels acceptable for airport-vicinity noise certification. Away from the airport, however, this entrained air is shut off and the engines are powered up from their cutback levels to provide better thrust for the climb to cruise altitude. Unsuppressed jet noise levels propagating to the ground far from the airport are expected to be high. Complicating this problem is the HSCT's relative noise level with respect to the subsonic commercial fleet of 2010, which is expected to be much quieter than it is today after the retirement of older, louder, domestic stage II aircraft by the year 2000. In this study, the classic energy state approximation theory is extended to calculate trajectories that minimize the climb to cruise noise of the HSCT. The optimizer dynamically chooses the optimal altitude velocity trajectory, the engine power setting, and whether the ejector should be stowed or deployed with respect to practical aircraft climb constraints and noise limits.

MARS Gravity-Assist to Improve Missions towards Main-Belt Asteroids

NASA Astrophysics Data System (ADS)

Casalino, Lorenzo; Colasurdo, Guido

fain-belt asteroids are one of the keys to the investigation of the processes that lead to the solar electric propulsion (SEP) with ion thrusters is a mature technology for the exploration of the bolar system. NASA is currently planning the DAWN mission towards two asteroids of the main s with Vesta in 2010 and Ceres in 2014. A mission to an asteroid of the main belt requires a large velocity increment (V) and the use of high-specific-impulse thrusters, such as ion thrusters, p m ovides a large improvement of the payload and, consequently, of the scientific return of the of this kind of trajectory is a non-trivial task, since many local optima exist and performance can be improved by increasing the trip-time and the number of revolutions around the sun, in order to use t the propellant only in the most favorable positions (namely, perihelia, aphelia and nodes) along the Mars is midway between the Earth and the main belt; even though its gravity is quite small, a gravity assist from Mars can remarkably improve the trajectory performance and is considered in this paper. p he authors use an indirect optimization procedure based on the theory of optimal control. The Mars) spheres of influence is neglected; the equations of motion are therefore integrated only in the heliocentric reference frame, whereas the flyby is treated as a discontinuity of the spacecraft's velocity. The paper analyzes trajectories, which exploit chemical propulsion to escape from the E variable-power, constant-specific-impulse propulsion system is assumed. The optimization procedure provides departure, flyby and arrival dates, the hyperbolic excess velocity on leaving the t arth's sphere of influence, which must be provided by the chemical propulsion system, and the E e ass at rendezvous, when the trip time is assigned. As far as the thrust magnitude is concerned, m either full-thrust arcs or coast arcs are required, and the procedure provides the times to switch the g low and the spacecraft would pass too close to (or even inside) the planet's surface to obtain a is c A comparison of direct flight and Mars-Gravity-Assist trajectories is carried out in the paper. The oharacteristics and theoretical performance of the optimal trajectories are determined as a function Numerical results show that in many cases the energy and inclination increment, which is provided b f y Mars' gravity, can significantly reduce the propellant requirements and increase the spacecraft

Design of human missions to Mars and robotic missions to Jupiter

NASA Astrophysics Data System (ADS)

Okutsu, Masataka

We consider human missions to Mars and robotic missions to Jupiter for launch dates in the near- and far-future. For the near-future, we design trajectories for currently proposed space missions that have well-defined spacecraft and mission requirements. For example, for early human missions to Mars we assume that the constraints used in NASA's design reference missions are indicative of current and near-future technologies, which of course limit our capabilities to explore Mars--and these limits make the problem challenging. Similarly, in the case of robotic exploration of Jupiter, we consider that the technology levels assumed for the proposed Europa Orbiter mission represent reasonable limits. For the far-future (two to three decades from now), we take the best estimates from current literature about the capabilities that may be available in nuclear-powered electric propulsion. We consider hardware capabilities (in terms of specific mass, specific impulse, thrust, power, etc.) for low-thrust trajectories, which range froth near-term to far-future technologies. In designing such missions, several techniques are found useful. For example, the Tisserand Graph, which tracks the changes in orbital shapes and energies, provides insight in designing Jovian tours for the Europa Orbiter mission. The graph is also useful in analyzing abort trajectories for human missions to Mars. Furthermore, a patched-conic propagator, which can generate thousands of potential trajectories, plays a vital role in three of four chapters of this thesis. For launches in the next three decades, we discovered a class of Earth- Mars-Venus-Earth free returns (which appear only four times in the 100-year period), Jovian tours involving ten to twenty flybys of the Galilean satellites, and low-thrust trajectories to Jupiter via gravity assists from Venus, Earth, and Mars. In addition, our continuation method, in which a solution for a conic trajectory is gradually converted into that for a low- thrust trajectory, is found effective in design of some families of low-thrust trajectories. The method is applied, for example, in the design of a "one- vehicle cycler," an architecture requiring only one interplanetary vehicle for sustained human missions to Mars.

Enhancements on the Convex Programming Based Powered Descent Guidance Algorithm for Mars Landing

NASA Technical Reports Server (NTRS)

Acikmese, Behcet; Blackmore, Lars; Scharf, Daniel P.; Wolf, Aron

2008-01-01

In this paper, we present enhancements on the powered descent guidance algorithm developed for Mars pinpoint landing. The guidance algorithm solves the powered descent minimum fuel trajectory optimization problem via a direct numerical method. Our main contribution is to formulate the trajectory optimization problem, which has nonconvex control constraints, as a finite dimensional convex optimization problem, specifically as a finite dimensional second order cone programming (SOCP) problem. SOCP is a subclass of convex programming, and there are efficient SOCP solvers with deterministic convergence properties. Hence, the resulting guidance algorithm can potentially be implemented onboard a spacecraft for real-time applications. Particularly, this paper discusses the algorithmic improvements obtained by: (i) Using an efficient approach to choose the optimal time-of-flight; (ii) Using a computationally inexpensive way to detect the feasibility/ infeasibility of the problem due to the thrust-to-weight constraint; (iii) Incorporating the rotation rate of the planet into the problem formulation; (iv) Developing additional constraints on the position and velocity to guarantee no-subsurface flight between the time samples of the temporal discretization; (v) Developing a fuel-limited targeting algorithm; (vi) Initial result on developing an onboard table lookup method to obtain almost fuel optimal solutions in real-time.

Theory and Computation of Optimal Low- and Medium- Thrust Orbit Transfers

NASA Technical Reports Server (NTRS)

Goodson, Troy D.; Chuang, Jason C. H.; Ledsinger, Laura A.

1996-01-01

This report presents new theoretical results which lead to new algorithms for the computation of fuel-optimal multiple-burn orbit transfers of low and medium thrust. Theoretical results introduced herein show how to add burns to an optimal trajectory and show that the traditional set of necessary conditions may be replaced with a much simpler set of equations. Numerical results are presented to demonstrate the utility of the theoretical results and the new algorithms. Two indirect methods from the literature are shown to be effective for the optimal orbit transfer problem with relatively small numbers of burns. These methods are the Minimizing Boundary Condition Method (MBCM) and BOUNDSCO. Both of these methods make use of the first-order necessary conditions exactly as derived by optimal control theory. Perturbations due to Earth's oblateness and atmospheric drag are considered. These perturbations are of greatest interest for transfers that take place between low Earth orbit altitudes and geosynchronous orbit altitudes. Example extremal solutions including these effects and computed by the aforementioned methods are presented. An investigation is also made into a suboptimal multiple-burn guidance scheme. The FORTRAN code developed for this study has been collected together in a package named ORBPACK. ORBPACK's user manual is provided as an appendix to this report.

Lunar Cube Transfer Trajectory Options

NASA Technical Reports Server (NTRS)

Folta, David C.; Dichman, Don; Clark, Pamela; Haapala, Amanda; Howell, Kathleen

2014-01-01

Contingent upon the modification of an initial condition of the injected or deployed orbit. Additionally, these designs can be restricted by the selection of the Cubesat subsystem design such as propulsion or communication. Nonetheless, many trajectory options can be designed with have a wide range of transfer durations, fuel requirements, and final destinations. Our investigation of potential trajectories highlights several design options including deployment into low Earth orbit (LEO), geostationary transfer orbits (GTO), and higher energy direct lunar transfer orbits. In addition to direct transfer options from these initial orbits, we also investigate the use of longer duration Earth-Moon dynamical systems. For missions with an intended lunar orbit, much of the design process is spent optimizing a ballistic capture while other science locations such as Sun-Earth libration or heliocentric orbits may simply require a reduced Delta-V imparted at a convenient location along the trajectory. In this article we examine several design options that meet the above limited deployment and subsystem drivers. We study ways that both impulsive and low-thrust Solar Electric Propulsion (SEP) engines can be used to place the Cubesat first into a highly eccentric Earth orbit, enter the Moon's Sphere of Influence, and finally achieve a highly eccentric lunar orbit. We show that such low-thrust transfers are feasible with a realistic micro-thruster model, assuming that the Cubesat can generate sufficient power for the SEP. Two examples are shown here: (1) A Cubestat injected by Exploration Mission 1 (EM-1) then employing low thrust; and (2) a CubSat deployed in a GTO, then employing impulsive maneuvers. For the EM-1 injected initial design, we increase the EM-1 targeted lunar flyby distance to reduce the energy of the lunar flyby to match that of a typical lMoon system heteroclinic manifold. Figure 1 presents an option that encompasses the similar dynamics as that of the ARTEMIS mission design. Low-thrust maneuvers are used along the manifold trajectory to raise perigee to that of a lunar orbit, adjust the timing with respect to the Moon, rotate the line of apsides, and target a ballistic lunar encounter. In this design a second flyby decreases the orbital energy with respect to the Moon, so that C3 -0.1 km2s2. Another design, shown in Figure 2 emanates from a GTO then uses impulsive maneuvers to phase onto a local Earth-Moon manifold, which then transfers the CubeSat to a lunar encounter.

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.

A Hamiltonian approach to the planar optimization of mid-course corrections

NASA Astrophysics Data System (ADS)

Iorfida, E.; Palmer, P. L.; Roberts, M.

2016-04-01

Lawden's primer vector theory gives a set of necessary conditions that characterize the optimality of a transfer orbit, defined accordingly to the possibility of adding mid-course corrections. In this paper a novel approach is proposed where, through a polar coordinates transformation, the primer vector components decouple. Furthermore, the case when transfer, departure and arrival orbits are coplanar is analyzed using a Hamiltonian approach. This procedure leads to approximate analytic solutions for the in-plane components of the primer vector. Moreover, the solution for the circular transfer case is proven to be the Hill's solution. The novel procedure reduces the mathematical and computational complexity of the original case study. It is shown that the primer vector is independent of the semi-major axis of the transfer orbit. The case with a fixed transfer trajectory and variable initial and final thrust impulses is studied. The acquired related optimality maps are presented and analyzed and they express the likelihood of a set of trajectories to be optimal. Furthermore, it is presented which kind of requirements have to be fulfilled by a set of departure and arrival orbits to have the same profile of primer vector.

Explicit Low-Thrust Guidance for Reference Orbit Targeting

NASA Technical Reports Server (NTRS)

Lam, Try; Udwadia, Firdaus E.

2013-01-01

The problem of a low-thrust spacecraft controlled to a reference orbit is addressed in this paper. A simple and explicit low-thrust guidance scheme with constrained thrust magnitude is developed by combining the fundamental equations of motion for constrained systems from analytical dynamics with a Lyapunov-based method. Examples are given for a spacecraft controlled to a reference trajectory in the circular restricted three body problem.

Nonlinear maneuver autopilot for the F-15 aircraft

NASA Technical Reports Server (NTRS)

Menon, P. K. A.; Badgett, M. E.; Walker, R. A.

1989-01-01

A methodology is described for the development of flight test trajectory control laws based on singular perturbation methodology and nonlinear dynamic modeling. The control design methodology is applied to a detailed nonlinear six degree-of-freedom simulation of the F-15 and results for a level accelerations, pushover/pullup maneuver, zoom and pushover maneuver, excess thrust windup turn, constant thrust windup turn, and a constant dynamic pressure/constant load factor trajectory are presented.

Development of a unified guidance system for geocentric transfer. [for solar electric propulsion spacecraft

NASA Technical Reports Server (NTRS)

Cake, J. E.; Regetz, J. D., Jr.

1975-01-01

A method is presented for open loop guidance of a solar electric propulsion spacecraft to geosynchronous orbit. The method consists of determining the thrust vector profiles on the ground with an optimization computer program, and performing updates based on the difference between the actual trajectory and that predicted with a precision simulation computer program. The motivation for performing the guidance analysis during the mission planning phase is discussed, and a spacecraft design option that employs attitude orientation constraints is presented. The improvements required in both the optimization program and simulation program are set forth, together with the efforts to integrate the programs into the ground support software for the guidance system.

Development of a unified guidance system for geocentric transfer. [solar electric propulsion spacecraft

NASA Technical Reports Server (NTRS)

Cake, J. E.; Regetz, J. D., Jr.

1975-01-01

A method is presented for open loop guidance of a solar electric propulsion spacecraft to geosynchronsus orbit. The method consists of determining the thrust vector profiles on the ground with an optimization computer program, and performing updates based on the difference between the actual trajectory and that predicted with a precision simulation computer program. The motivation for performing the guidance analysis during the mission planning phase is discussed, and a spacecraft design option that employs attitude orientation constraints is presented. The improvements required in both the optimization program and simulation program are set forth, together with the efforts to integrate the programs into the ground support software for the guidance system.

Bimodal Nuclear Thermal Rocket Sizing and Trade Matrix for Lunar, Near Earth Asteroid and Mars Missions

NASA Astrophysics Data System (ADS)

McCurdy, David R.; Krivanek, Thomas M.; Roche, Joseph M.; Zinolabedini, Reza

2006-01-01

The concept of a human rated transport vehicle for various near earth missions is evaluated using a liquid hydrogen fueled Bimodal Nuclear Thermal Propulsion (BNTP) approach. In an effort to determine the preliminary sizing and optimal propulsion system configuration, as well as the key operating design points, an initial investigation into the main system level parameters was conducted. This assessment considered not only the performance variables but also the more subjective reliability, operability, and maintainability attributes. The SIZER preliminary sizing tool was used to facilitate rapid modeling of the trade studies, which included tank materials, propulsive versus an aero-capture trajectory, use of artificial gravity, reactor chamber operating pressure and temperature, fuel element scaling, engine thrust rating, engine thrust augmentation by adding oxygen to the flow in the nozzle for supersonic combustion, and the baseline turbopump configuration to address mission redundancy and safety requirements. A high level system perspective was maintained to avoid focusing solely on individual component optimization at the expense of system level performance, operability, and development cost.

The 1974 NASA-ASEE summer faculty fellowship aeronautics and space research program

NASA Technical Reports Server (NTRS)

Obrien, J. F., Jr.; Jones, C. O.; Barfield, B. F.

1974-01-01

Research activities by participants in the fellowship program are documented, and include such topics as: (1) multispectral imagery for detecting southern pine beetle infestations; (2) trajectory optimization techniques for low thrust vehicles; (3) concentration characteristics of a fresnel solar strip reflection concentrator; (4) calaboration and reduction of video camera data; (5) fracture mechanics of Cer-Vit glass-ceramic; (6) space shuttle external propellant tank prelaunch heat transfer; (7) holographic interferometric fringes; and (8) atmospheric wind and stress profiles in a two-dimensional internal boundary layer.

Estimation of energetic efficiency of heat supply in front of the aircraft at supersonic accelerated flight. Part II. Mathematical model of the trajectory boost part and computational results

NASA Astrophysics Data System (ADS)

Latypov, A. F.

2009-03-01

The fuel economy was estimated at boost trajectory of aerospace plane during energy supply to the free stream. Initial and final velocities of the flight were given. A model of planning flight above cold air in infinite isobaric thermal wake was used. The comparison of fuel consumption was done at optimal trajectories. The calculations were done using a combined power plant consisting of ramjet and liquid-propellant engine. An exergy model was constructed in the first part of the paper for estimating the ramjet thrust and specific impulse. To estimate the aerodynamic drag of aircraft a quadratic dependence on aerodynamic lift is used. The energy for flow heating is obtained at the sacrifice of an equivalent decrease of exergy of combustion products. The dependencies are obtained for increasing the range coefficient of cruise flight at different Mach numbers. In the second part of the paper, a mathematical model is presented for the boost part of the flight trajectory of the flying vehicle and computational results for reducing the fuel expenses at the boost trajectory at a given value of the energy supplied in front of the aircraft.

Control of asteroid retrieval trajectories to libration point orbits

NASA Astrophysics Data System (ADS)

Ceriotti, Matteo; Sanchez, Joan Pau

2016-09-01

The fascinating idea of shepherding asteroids for science and resource utilization is being considered as a credible concept in a not too distant future. Past studies identified asteroids which could be efficiently injected into manifolds which wind onto periodic orbits around collinear Lagrangian points of the Sun-Earth system. However, the trajectories are unstable, and errors in the capture maneuver would lead to complete mission failure, with potential danger of collision with the Earth, if uncontrolled. This paper investigates the controllability of some asteroids along the transfers and the periodic orbits, assuming the use of a solar-electric low-thrust system shepherding the asteroid. Firstly, an analytical approach is introduced to estimate the stability of the trajectories from a dynamical point of view; then, a numerical control scheme based on a linear quadratic regulator is proposed, where the gains are optimized for each trajectory through a genetic algorithm. A stochastic simulation with a Monte Carlo approach is used to account for different perturbed initial conditions and the epistemic uncertainty on the asteroid mass. Results show that only a small subset of the considered combinations of trajectories/asteroids are reliably controllable, and therefore controllability must be taken into account in the selection of potential targets.

Development of an analytical guidance algorithm for lunar descent

NASA Astrophysics Data System (ADS)

Chomel, Christina Tvrdik

In recent years, NASA has indicated a desire to return humans to the moon. With NASA planning manned missions within the next couple of decades, the concept development for these lunar vehicles has begun. The guidance, navigation, and control (GN&C) computer programs that will perform the function of safely landing a spacecraft on the moon are part of that development. The lunar descent guidance algorithm takes the horizontally oriented spacecraft from orbital speeds hundreds of kilometers from the desired landing point to the landing point at an almost vertical orientation and very low speed. Existing lunar descent GN&C algorithms date back to the Apollo era with little work available for implementation since then. Though these algorithms met the criteria of the 1960's, they are cumbersome today. At the basis of the lunar descent phase are two elements: the targeting, which generates a reference trajectory, and the real-time guidance, which forces the spacecraft to fly that trajectory. The Apollo algorithm utilizes a complex, iterative, numerical optimization scheme for developing the reference trajectory. The real-time guidance utilizes this reference trajectory in the form of a quartic rather than a more general format to force the real-time trajectory errors to converge to zero; however, there exist no guarantees under any conditions for this convergence. The proposed algorithm implements a purely analytical targeting algorithm used to generate two-dimensional trajectories "on-the-fly"' or to retarget the spacecraft to another landing site altogether. It is based on the analytical solutions to the equations for speed, downrange, and altitude as a function of flight path angle and assumes two constant thrust acceleration curves. The proposed real-time guidance algorithm has at its basis the three-dimensional non-linear equations of motion and a control law that is proven to converge under certain conditions through Lyapunov analysis to a reference trajectory formatted as a function of downrange, altitude, speed, and flight path angle. The two elements of the guidance algorithm are joined in Monte Carlo analysis to prove their robustness to initial state dispersions and mass and thrust errors. The robustness of the retargeting algorithm is also demonstrated.

Novel Approach on the Optimisation of Mid-Course Corrections Along Interplanetary Trajectories

NASA Astrophysics Data System (ADS)

Iorfida, Elisabetta; Palmer, Phil; Roberts, Mark

The primer vector theory, firstly proposed by Lawden, defines a set of necessary conditions to characterise whether an impulsive thrust trajectory is optimal with respect to propellant usage, within a two-body problem context. If the conditions are not satisfied, one or more potential intermediate impulses are performed along the transfer arc, in order to lower the overall cost. The method is based on the propagation of the state transition matrix and on the solution of a boundary value problem, which leads to a mathematical and computational complexity.In this paper, a different approach is introduced. It is based on a polar coordinates transformation of the primer vector which allows the decoupling between its in-plane and out-of-plane components. The out-of-plane component is solved analytically while for the in-plane ones a Hamiltonian approximation is made.The novel procedure reduces the mathematical complexity and the computational cost of Lawden's problem and gives also a different perspective about the optimisation of a transfer trajectory.

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.

Thrust Vector Control for Nuclear Thermal Rockets

NASA Technical Reports Server (NTRS)

Ensworth, Clinton B. F.

2013-01-01

Future space missions may use Nuclear Thermal Rocket (NTR) stages for human and cargo missions to Mars and other destinations. The vehicles are likely to require engine thrust vector control (TVC) to maintain desired flight trajectories. This paper explores requirements and concepts for TVC systems for representative NTR missions. Requirements for TVC systems were derived using 6 degree-of-freedom models of NTR vehicles. Various flight scenarios were evaluated to determine vehicle attitude control needs and to determine the applicability of TVC. Outputs from the models yielded key characteristics including engine gimbal angles, gimbal rates and gimbal actuator power. Additional factors such as engine thrust variability and engine thrust alignment errors were examined for impacts to gimbal requirements. Various technologies are surveyed for TVC systems for the NTR applications. A key factor in technology selection is the unique radiation environment present in NTR stages. Other considerations including mission duration and thermal environments influence the selection of optimal TVC technologies. Candidate technologies are compared to see which technologies, or combinations of technologies best fit the requirements for selected NTR missions. Representative TVC systems are proposed and key properties such as mass and power requirements are defined. The outputs from this effort can be used to refine NTR system sizing models, providing higher fidelity definition for TVC systems for future studies.

Low-thrust solar electric propulsion navigation simulation program

NASA Technical Reports Server (NTRS)

Hagar, H. J.; Eller, T. J.

1973-01-01

An interplanetary low-thrust, solar electric propulsion mission simulation program suitable for navigation studies is presented. The mathematical models for trajectory simulation, error compensation, and tracking motion are described. The languages, input-output procedures, and subroutines are included.

A rapid method for optimization of the rocket propulsion system for single-stage-to-orbit vehicles

NASA Technical Reports Server (NTRS)

Eldred, C. H.; Gordon, S. V.

1976-01-01

A rapid analytical method for the optimization of rocket propulsion systems is presented for a vertical take-off, horizontal landing, single-stage-to-orbit launch vehicle. This method utilizes trade-offs between propulsion characteristics affecting flight performance and engine system mass. The performance results from a point-mass trajectory optimization program are combined with a linearized sizing program to establish vehicle sizing trends caused by propulsion system variations. The linearized sizing technique was developed for the class of vehicle systems studied herein. The specific examples treated are the optimization of nozzle expansion ratio and lift-off thrust-to-weight ratio to achieve either minimum gross mass or minimum dry mass. Assumed propulsion system characteristics are high chamber pressure, liquid oxygen and liquid hydrogen propellants, conventional bell nozzles, and the same fixed nozzle expansion ratio for all engines on a vehicle.

A robust and high precision optimal explicit guidance scheme for solid motor propelled launch vehicles with thrust and drag uncertainty

NASA Astrophysics Data System (ADS)

Maity, Arnab; Padhi, Radhakant; Mallaram, Sanjeev; Mallikarjuna Rao, G.; Manickavasagam, M.

2016-10-01

A new nonlinear optimal and explicit guidance law is presented in this paper for launch vehicles propelled by solid motors. It can ensure very high terminal precision despite not having the exact knowledge of the thrust-time curve apriori. This was motivated from using it for a carrier launch vehicle in a hypersonic mission, which demands an extremely narrow terminal accuracy window for the launch vehicle for successful initiation of operation of the hypersonic vehicle. The proposed explicit guidance scheme, which computes the optimal guidance command online, ensures the required stringent final conditions with high precision at the injection point. A key feature of the proposed guidance law is an innovative extension of the recently developed model predictive static programming guidance with flexible final time. A penalty function approach is also followed to meet the input and output inequality constraints throughout the vehicle trajectory. In this paper, the guidance law has been successfully validated from nonlinear six degree-of-freedom simulation studies by designing an inner-loop autopilot as well, which enhances confidence of its usefulness significantly. In addition to excellent nominal results, the proposed guidance has been found to have good robustness for perturbed cases as well.

A guidance and navigation system for continuous low-thrust vehicles. M.S. Thesis

NASA Technical Reports Server (NTRS)

Jack-Chingtse, C.

1973-01-01

A midcourse guidance and navigation system for continuous low thrust vehicles was developed. The equinoctial elements are the state variables. Uncertainties are modelled statistically by random vector and stochastic processes. The motion of the vehicle and the measurements are described by nonlinear stochastic differential and difference equations respectively. A minimum time trajectory is defined; equations of motion and measurements are linearized about this trajectory. An exponential cost criterion is constructed and a linear feedback quidance law is derived. An extended Kalman filter is used for state estimation. A short mission using this system is simulated. It is indicated that this system is efficient for short missions, but longer missions require accurate trajectory and ground based measurements.

Aircraft Engine Thrust Estimator Design Based on GSA-LSSVM

NASA Astrophysics Data System (ADS)

Sheng, Hanlin; Zhang, Tianhong

2017-08-01

In view of the necessity of highly precise and reliable thrust estimator to achieve direct thrust control of aircraft engine, based on support vector regression (SVR), as well as least square support vector machine (LSSVM) and a new optimization algorithm - gravitational search algorithm (GSA), by performing integrated modelling and parameter optimization, a GSA-LSSVM-based thrust estimator design solution is proposed. The results show that compared to particle swarm optimization (PSO) algorithm, GSA can find unknown optimization parameter better and enables the model developed with better prediction and generalization ability. The model can better predict aircraft engine thrust and thus fulfills the need of direct thrust control of aircraft engine.

Estimation of energetic efficiency of heat supply in front of the aircraft at supersonic accelerated flight. Part 1. Mathematical models

NASA Astrophysics Data System (ADS)

Latypov, A. F.

2008-12-01

Fuel economy at boost trajectory of the aerospace plane was estimated during energy supply to the free stream. Initial and final flight velocities were specified. The model of a gliding flight above cold air in an infinite isobaric thermal wake was used. The fuel consumption rates were compared at optimal trajectory. The calculations were carried out using a combined power plant consisting of ramjet and liquid-propellant engine. An exergy model was built in the first part of the paper to estimate the ramjet thrust and specific impulse. A quadratic dependence on aerodynamic lift was used to estimate the aerodynamic drag of aircraft. The energy for flow heating was obtained at the expense of an equivalent reduction of the exergy of combustion products. The dependencies were obtained for increasing the range coefficient of cruise flight for different Mach numbers. The second part of the paper presents a mathematical model for the boost interval of the aircraft flight trajectory and the computational results for the reduction of fuel consumption at the boost trajectory for a given value of the energy supplied in front of the aircraft.

Improved Shaping Approach to the Preliminary Design of Low-Thrust Trajectories

NASA Astrophysics Data System (ADS)

Novak, D. M.; Vasile, M.

2011-01-01

This paper presents a general framework for the development of shape-based approaches to low-thrust trajectory design. A novel shaping method, based on a three-dimensional description of the trajectory in spherical coordinates, is developed within this general framework. Both the exponential sinusoid and the inverse polynomial shaping are demonstrated to be particular two-dimensional cases of the spherical one. The pseudoequinoctial shaping is revisited within the new framework, and the nonosculating nature of the pseudoequinoctial elements is analyzed. A two-step approach is introduced to solve the time of flight constraint, related to the design of low-thrust arcs with boundary constraints for both spherical and pseudoequinoctial shaping. The solution derived from the shaping approach is improved with a feedback linear-quadratic controller and compared against a direct collocation method based on finite elements in time. The new shaping approach and the combination of shaping and linear-quadratic controller are tested on three case studies: a mission to Mars, a mission to asteroid 1989ML, a mission to comet Tempel-1, and a mission to Neptune.

Performance trade studies of a solar electric orbit transfer mission

NASA Astrophysics Data System (ADS)

Sutton, D. M.; McLain, M. G.; Kechichian, J. A.

An analysis of several electric orbit transfer trade studies investigating the performance of a solar-powered electric orbit transfer vehicle (EOTV) is presented. One trade illustrates how the greatest payload capability for time-of-flight constrained transfers can be obtained by optimizing specific impulse. Various methods of reducing the accumulated fluence of charged particles during transit are evaluated in a second trade study. The reduction in fluence obtained by shaping the trajectory to avoid high radiation flux density regions is compared with reductions obtained by using a hybrid chemical/electric vehicle, by additional radiation-protective coverslide material added to the solar array, and by increasing the power of the vehicle. It is shown that a trajectory shaped to minimize fluence may be an advantage to the complete EOTV design. A final trade study shows how park orbit altitude influences the initial thrust-to-drag ratio of an EOTV.

Design of cycler trajectories and analysis of solar influences on radioactive decay rates during space missions

NASA Astrophysics Data System (ADS)

Rogers, Blake A.

This thesis investigates the design of interplanetary missions for the continual habitation of Mars via Earth-Mars cyclers and for the detection of variations in nuclear decay rates due to solar influences. Several cycler concepts have been proposed to provide safe and comfortable quarters for astronauts traveling between the Earth and Mars. However, no literature has appeared to show how these massive vehicles might be placed into their cycler trajectories. Trajectories are designed that use either Vinfinity leveraging or low thrust to establish cycler vehicles in their desired orbits. In the cycler trajectory cases considered, the use of Vinfinity leveraging or low thrust substantially reduces the total propellant needed to achieve the cycler orbit compared to direct orbit insertion. In the case of the classic Aldrin cycler, the propellant savings due to Vinfinity leveraging can be as large as a 24 metric ton reduction for a cycler vehicle with a dry mass of 75 metric tons, and an additional 111 metric ton reduction by instead using low thrust. The two-synodic period cyclers considered benefit less from Vinfinity leveraging, but have a smaller total propellant mass due to their lower approach velocities at Earth and Mars. It turns out that, for low-thrust establishment, the propellant required is approximately the same for each of the cycler trajectories. The Aldrin cycler has been proposed as a transportation system for human missions between Earth and Mars. However, the hyperbolic excess velocity values at the planetary encounters for these orbits are infeasibly large, especially at Mars. In a new version of the Aldrin cycler, low thrust is used in the interplanetary trajectories to reduce the encounter velocities. Reducing the encounter velocities at both planets reduces the propellant needed by the taxis (astronauts use these taxis to transfer between the planetary surfaces and the cycler vehicle) to perform hyperbolic rendezvous. While the propellant expenditure for the cycler vehicle increases, trade studies over seven synodic periods show that the low-thrust Aldrin cycler is effective in reducing the total (i.e., cycler plus taxi) initial mass in low-Earth orbit. A mission is proposed whose architecture is a series of stopovers, unlike conventional cycler trajectories that string series of flybys together. The vehicle would be captured into orbits about the Earth and Mars without landing on either planet. The zero hyperbolic-excess velocities with respect to the planets keep the mass of the taxis low. To allow a mission in every launch opportunity, the cycler vehicle is required to make a complete round trip in less than the synodic period of the two planets (i.e. 2 1/7 years). A high level of acceleration is required to satisfy the itinerary, which results in a large mass (90 metric tons) for the power generator. Fortuitously, the high (11 MWe) power level of the propulsion system would also be effective in hauling the cargo payload via a spiral trajectory about the Earth. Because one synodic period is not enough for the cycler vehicle to fly both the interplanetary trajectories and the Earth-spiral trajectories, it is suggested that two nuclear power generators be developed, which could alternate flying the interplanetary trajectories and the Earth-spiral trajectories. Once these power generators are launched and begin operating in space, the mass requirement in seven subsequent missions (over a period of 15 years beginning in 2022) would be modest at 254 to 296 metric tons to low-Earth orbit per mission. Two launches of NASA's Space Launch System for the cargo and one launch of the Falcon 9 Heavy for the crew would be more than adequate to maintain support for each consecutive mission. Previously, cycling trajectories have been constructed by finding the solution to Lambert's problem between two planetary encounters that occur some multiple of a synodic period apart. In this work, the relative equations of motion are investigated to determine if they can be used to find new cycler trajectories, as well as those previously discovered. First order approximations to the relative motion equations are unfruitful for Earth-Mars cyclers because the variation in radial distance from the Sun is too large. However, using optimization techniques, cycling trajectories are found for the Earth-Mars, Earth-Ceres, and Mars-Ceres systems. Experiments showing a seasonal variation of the nuclear decay rates of a number of different nuclei and decay anomalies--- apparently related to solar flares and solar rotation--- have suggested that the Sun may somehow be influencing nuclear decay processes. Recently, there have been searches for such an effect in 238Pu nuclei contained in the radioisotope thermoelectric generators on board the Cassini spacecraft. In this work, that analysis is modified and extended to obtain constraints on anomalous decays of 238Pu over a wider range of models, but these limits cannot be applied to other nuclei if the anomaly is composition-dependent. It is also shown that it may require very high sensitivity for terrestrial experiments to discriminate among some models if such a decay anomaly exists, motivating the consideration of future spacecraft experiments which would require less precision. A mission on which such an experiment could be run is proposed. The proposed mission will take various isotopes on a spacecraft that has a large variation in radial distance and return them to Earth. Two different types of trajectories are considered: one with intermediate Venus flybys and one that injects directly into an Earth-resonant orbit. It is shown that each of these types of trajectories have their relative merits with regards to the scientific objective. The suitability of the upcoming Solar Probe Plus and Solar Orbiter missions to perform this experiment is also investigated.

Alternative model of thrust-fault propagation

NASA Astrophysics Data System (ADS)

Eisenstadt, Gloria; de Paor, Declan G.

1987-07-01

A widely accepted explanation for the geometry of thrust faults is that initial failures occur on deeply buried planes of weak rock and that thrust faults propagate toward the surface along a staircase trajectory. We propose an alternative model that applies Gretener's beam-failure mechanism to a multilayered sequence. Invoking compatibility conditions, which demand that a thrust propagate both upsection and downsection, we suggest that ramps form first, at shallow levels, and are subsequently connected by flat faults. This hypothesis also explains the formation of many minor structures associated with thrusts, such as backthrusts, wedge structures, pop-ups, and duplexes, and provides a unified conceptual framework in which to evaluate field observations.

Power-limited low-thrust trajectory optimization with operation point detection

NASA Astrophysics Data System (ADS)

Chi, Zhemin; Li, Haiyang; Jiang, Fanghua; Li, Junfeng

2018-06-01

The power-limited solar electric propulsion system is considered more practical in mission design. An accurate mathematical model of the propulsion system, based on experimental data of the power generation system, is used in this paper. An indirect method is used to deal with the time-optimal and fuel-optimal control problems, in which the solar electric propulsion system is described using a finite number of operation points, which are characterized by different pairs of thruster input power. In order to guarantee the integral accuracy for the discrete power-limited problem, a power operation detection technique is embedded in the fourth-order Runge-Kutta algorithm with fixed step. Moreover, the logarithmic homotopy method and normalization technique are employed to overcome the difficulties caused by using indirect methods. Three numerical simulations with actual propulsion systems are given to substantiate the feasibility and efficiency of the proposed method.

Solving fuel-optimal low-thrust orbital transfers with bang-bang control using a novel continuation technique

NASA Astrophysics Data System (ADS)

Zhu, Zhengfan; Gan, Qingbo; Yang, Xin; Gao, Yang

2017-08-01

We have developed a novel continuation technique to solve optimal bang-bang control for low-thrust orbital transfers considering the first-order necessary optimality conditions derived from Lawden's primer vector theory. Continuation on the thrust amplitude is mainly described in this paper. Firstly, a finite-thrust transfer with an ;On-Off-On; thrusting sequence is modeled using a two-impulse transfer as initial solution, and then the thrust amplitude is decreased gradually to find an optimal solution with minimum thrust. Secondly, the thrust amplitude is continued from its minimum value to positive infinity to find the optimal bang-bang control, and a thrust switching principle is employed to determine the control structure by monitoring the variation of the switching function. In the continuation process, a bifurcation of bang-bang control is revealed and the concept of critical thrust is proposed to illustrate this phenomenon. The same thrust switching principle is also applicable to the continuation on other parameters, such as transfer time, orbital phase angle, etc. By this continuation technique, fuel-optimal orbital transfers with variable mission parameters can be found via an automated algorithm, and there is no need to provide an initial guess for the costate variables. Moreover, continuation is implemented in the solution space of bang-bang control that is either optimal or non-optimal, which shows that a desired solution of bang-bang control is obtained via continuation on a single parameter starting from an existing solution of bang-bang control. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed continuation technique. Specifically, this continuation technique provides an approach to find multiple solutions satisfying the first-order necessary optimality conditions to the same orbital transfer problem, and a continuation strategy is presented as a preliminary approach for solving the bang-bang control of many-revolution orbital transfers.

Minimum Climb to Cruise Noise Trajectories Modeled for the High Speed Civil Transport

NASA Technical Reports Server (NTRS)

Berton, Jeffrey J.

1998-01-01

The proposed U.S. High Speed Civil Transport (HSCT) will revolutionize commercial air travel by providing economical supersonic passenger service to destinations worldwide. Unlike the high-bypass turbofan engines that propel today's subsonic airliners, HSCT engines will have much higher jet exhaust speeds. Jet noise, caused by the turbulent mixing of high-speed exhaust with the surrounding air, poses a significant challenge for HSCT engine designers. To resolve this challenge, engineers have designed advanced mixer rejector nozzles that reduce HSCT jet noise to airport noise certification levels by entraining and mixing large quantities of ambient air with the engines' jet streams. Although this works well during the first several minutes of flight, far away from the airport, as the HSCT gains speed and climbs, poor ejector inlet recovery and ejector ram drag contribute to poor thrust, making it advantageous to turn off the ejector. Doing so prematurely, however, can cause unacceptable noise levels to propagate to the ground, even when the aircraft is many miles from the airport. This situation lends itself ideally to optimization, where the aircraft trajectory, throttle setting, and ejector setting can be varied (subject to practical aircraft constraints) to minimize the noise propagated to the ground. A method was developed at the NASA Lewis Research Center that employs a variation of the classic energy state approximation: a trajectory analysis technique historically used to minimize climb time or fuel burned in many aircraft problems. To minimize the noise on the ground at any given throttle setting, high aircraft altitudes are desirable; but the HSCT may either climb quickly to high altitudes using a high, noisy throttle setting or climb more slowly at a lower, quieter throttle setting. An optimizer has been programmed into NASA's existing aircraft and noise analysis codes to balance these options by dynamically choosing the best altitude-velocity path and throttle setting history. The noise level standard, or metric, used in the optimizer should be one that accurately reflects the subjective annoyance levels of ground-based observers under the flight path. A variety of noise metrics are available, many of which are practical for airport-vicinity noise certification. Unlike airport noise, however, the HSCT's climb noise will be characterized by relatively low noise levels, long durations, and low-frequency spectra. The noise metrics used in these calculations are based on the recommendations of researchers at the NASA Langley Research Center, who have correlated the flyover noise annoyance levels of actual laboratory subjects with a variety of measurements. Analysis of data from this optimizer has shown that significant reductions in noise may be obtained with trajectory optimization. And since throttling operations are performed in the subsonic portion of the climb path (where thrust is plentiful), only small penalties in HSCT range or fuel performance occur.

Tuning Monotonic Basin Hopping: Improving the Efficiency of Stochastic Search as Applied to Low-Thrust Trajectory Optimization

NASA Technical Reports Server (NTRS)

Englander, Jacob; Englander, Arnold

2014-01-01

Trajectory optimization methods using MBH have become well developed during the past decade. An essential component of MBH is a controlled random search through the multi-dimensional space of possible solutions. Historically, the randomness has been generated by drawing RVs from a uniform probability distribution. Here, we investigate the generating the randomness by drawing the RVs from Cauchy and Pareto distributions, chosen because of their characteristic long tails. We demonstrate that using Cauchy distributions (as first suggested by Englander significantly improves MBH performance, and that Pareto distributions provide even greater improvements. Improved performance is defined in terms of efficiency and robustness, where efficiency is finding better solutions in less time, and robustness is efficiency that is undiminished by (a) the boundary conditions and internal constraints of the optimization problem being solved, and (b) by variations in the parameters of the probability distribution. Robustness is important for achieving performance improvements that are not problem specific. In this work we show that the performance improvements are the result of how these long-tailed distributions enable MBH to search the solution space faster and more thoroughly. In developing this explanation, we use the concepts of sub-diffusive, normally-diffusive, and super-diffusive RWs originally developed in the field of statistical physics.

Spacecraft Mission Design for the Mitigation of the 2017 PDC Hypothetical Asteroid Threat

NASA Technical Reports Server (NTRS)

Barbee, Brent W.; Sarli, Bruno V.; Lyzhoft, Josh; Chodas, Paul W.; Englander, Jacob A.

2017-01-01

This paper presents a detailed mission design analysis results for the 2017 Planetary Defense Conference (PDC) Hypothetical Asteroid Impact Scenario, documented at https:cneos.jpl.nasa.govpdcspdc17. The mission design includes campaigns for both reconnaissance (flyby or rendezvous) of the asteroid (to characterize it and the nature of the threat it poses to Earth) and mitigation of the asteroid, via kinetic impactor deflection, nuclear explosive device (NED) deflection, or NED disruption. Relevant scenario parameters are varied to assess the sensitivity of the design outcome, such as asteroid bulk density, asteroid diameter, momentum enhancement factor, spacecraft launch vehicle, and mitigation system type. Different trajectory types are evaluated in the mission design process from purely ballistic to those involving optimal midcourse maneuvers, planetary gravity assists, and/or low-thrust solar electric propulsion. The trajectory optimization is targeted around peak deflection points that were found through a novel linear numerical technique method. The optimization process includes constrain parameters, such as Earth departure date, launch declination, spacecraft, asteroid relative velocity and solar phase angle, spacecraft dry mass, minimum/maximum spacecraft distances from Sun and Earth, and Earth-spacecraft communications line of sight. Results show that one of the best options for the 2017 PDC deflection is solar electric propelled rendezvous mission with a single spacecraft using NED for the deflection.

Logarithmic spiral trajectories generated by Solar sails

NASA Astrophysics Data System (ADS)

Bassetto, Marco; Niccolai, Lorenzo; Quarta, Alessandro A.; Mengali, Giovanni

2018-02-01

Analytic solutions to continuous thrust-propelled trajectories are available in a few cases only. An interesting case is offered by the logarithmic spiral, that is, a trajectory characterized by a constant flight path angle and a fixed thrust vector direction in an orbital reference frame. The logarithmic spiral is important from a practical point of view, because it may be passively maintained by a Solar sail-based spacecraft. The aim of this paper is to provide a systematic study concerning the possibility of inserting a Solar sail-based spacecraft into a heliocentric logarithmic spiral trajectory without using any impulsive maneuver. The required conditions to be met by the sail in terms of attitude angle, propulsive performance, parking orbit characteristics, and initial position are thoroughly investigated. The closed-form variations of the osculating orbital parameters are analyzed, and the obtained analytical results are used for investigating the phasing maneuver of a Solar sail along an elliptic heliocentric orbit. In this mission scenario, the phasing orbit is composed of two symmetric logarithmic spiral trajectories connected with a coasting arc.

Comet nucleus and asteroid sample return missions

NASA Technical Reports Server (NTRS)

Melton, Robert G.; Thompson, Roger C.; Starchville, Thomas F., Jr.; Adams, C.; Aldo, A.; Dobson, K.; Flotta, C.; Gagliardino, J.; Lear, M.; Mcmillan, C.

1992-01-01

During the 1991-92 academic year, the Pennsylvania State University has developed three sample return missions: one to the nucleus of comet Wild 2, one to the asteroid Eros, and one to three asteroids located in the Main Belt. The primary objective of the comet nucleus sample return mission is to rendezvous with a short period comet and acquire a 10 kg sample for return to Earth. Upon rendezvous with the comet, a tethered coring and sampler drill will contact the surface and extract a two-meter core sample from the target site. Before the spacecraft returns to Earth, a monitoring penetrator containing scientific instruments will be deployed for gathering long-term data about the comet. A single asteroid sample return mission to the asteroid 433 Eros (chosen for proximity and launch opportunities) will extract a sample from the asteroid surface for return to Earth. To limit overall mission cost, most of the mission design uses current technologies, except the sampler drill design. The multiple asteroid sample return mission could best be characterized through its use of future technology including an optical communications system, a nuclear power reactor, and a low-thrust propulsion system. A low-thrust trajectory optimization code (QuickTop 2) obtained from the NASA LeRC helped in planning the size of major subsystem components, as well as the trajectory between targets.

Construction of optimum controls and trajectories of motion of the center of masses of a spacecraft equipped with the solar sail and low-thrust engine, using quaternions and Kustaanheimo-Stiefel variables

NASA Astrophysics Data System (ADS)

Sapunkov, Ya. G.; Chelnokov, Yu. N.

2014-11-01

The problem of optimum rendezvous of a controllable spacecraft (SC) with an uncontrollable spacecraft, moving over a Keplerian elliptic orbit in the gravitational field of the Sun, is considered. Control of the SC is performed using a solar sail and low-thrust engine. For solving the problem, the regular quaternion equations of the two-body problem with the Kustaanheimo-Stiefel variables and the Pontryagin maximum principle are used. The combined integral quality functional, which characterizes energy consumption for controllable SC transition from an initial to final state and the time spent for this transition, is used as a minimized functional. The differential boundary-value optimization problems are formulated, and their first integrals are found. Examples of numerical solution of problems are presented. The paper develops the application [1-6] of quaternion regular equations with the Kustaanheimo-Stiefel variables in the space flight mechanics.

Guidance, navigation, and control study for a solar electric propulsion spacecraft

NASA Technical Reports Server (NTRS)

Kluever, Craig A.

1995-01-01

A preliminary investigation of a lunar-comet rendezvous mission using a solar electric propulsion (SEP) spacecraft was performed in two phases.The first phase involved exploration of the moon and the second involved rendezvous with a comet. The initial phase began with a chemical propulsion translunar injection and chemical insertion into a lunar orbit, followed by a low thrust SEP transfer to a circular, polar, low-lunar orbit. After collecting scientific data at the moon, the SEP spacecraft performed a spiral lunar escape maneuver to begin the interplanetary leg of the mission. After escape from the Earth-moon system, the SEP spacecraft maneuvered in interplanetary space and performed a rendezvous with a comet.The immediate goal of this study was to demonstrate the feasibility of using a low-thrust SEP spacecraft for orbit transfer to both the moon and a comet. Another primary goal was to develop a computer optimization code which would be robust enough to obtain minimum-fuel rendezvous trajectories for a wide range of comets.

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.

Thrust stand evaluation of engine performance improvement algorithms in an F-15 airplane

NASA Technical Reports Server (NTRS)

Conners, Timothy R.

1992-01-01

An investigation is underway to determine the benefits of a new propulsion system optimization algorithm in an F-15 airplane. The performance seeking control (PSC) algorithm optimizes the quasi-steady-state performance of an F100 derivative turbofan engine for several modes of operation. The PSC algorithm uses an onboard software engine model that calculates thrust, stall margin, and other unmeasured variables for use in the optimization. As part of the PSC test program, the F-15 aircraft was operated on a horizontal thrust stand. Thrust was measured with highly accurate load cells. The measured thrust was compared to onboard model estimates and to results from posttest performance programs. Thrust changes using the various PSC modes were recorded. Those results were compared to benefits using the less complex highly integrated digital electronic control (HIDEC) algorithm. The PSC maximum thrust mode increased intermediate power thrust by 10 percent. The PSC engine model did very well at estimating measured thrust and closely followed the transients during optimization. Quantitative results from the evaluation of the algorithms and performance calculation models are included with emphasis on measured thrust results. The report presents a description of the PSC system and a discussion of factors affecting the accuracy of the thrust stand load measurements.

Replacement of chemical rocket launchers by beamed energy propulsion.

PubMed

Fukunari, Masafumi; Arnault, Anthony; Yamaguchi, Toshikazu; Komurasaki, Kimiya

2014-11-01

Microwave Rocket is a beamed energy propulsion system that is expected to reach space at drastically lower cost. This cost reduction is estimated by replacing the first-stage engine and solid rocket boosters of the Japanese H-IIB rocket with Microwave Rocket, using a recently developed thrust model in which thrust is generated through repetitively pulsed microwave detonation with a reed-valve air-breathing system. Results show that Microwave Rocket trajectory, in terms of velocity versus altitude, can be designed similarly to the current H-IIB first stage trajectory. Moreover, the payload ratio can be increased by 450%, resulting in launch-cost reduction of 74%.

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.

A new method for optimization of low-thrust gravity-assist sequences

NASA Astrophysics Data System (ADS)

Maiwald, V.

2017-09-01

Recently missions like Hayabusa and Dawn have shown the relevance and benefits of low-thrust spacecraft concerning the exploration of our solar system. In general, the efficiency of low-thrust propulsion is one means of improving mission payload mass. At the same time, gravity-assist maneuvers can serve as mission enablers, as they have the capability to provide "free energy." A combination of both, gravity-assist and low-thrust propulsion, has the potential to generally improve mission performance, i.e. planning and optimization of gravity-assist sequences for low-thrust missions is a desirable asset. Currently no established methods exist to include the gravity-assist partners as optimization variable for low-thrust missions. The present paper explains how gravity-assists are planned and optimized, including the gravity-assist partners, for high-thrust missions and discusses the possibility to transfer the established method, based on the Tisserand Criterion, to low-thrust missions. It is shown how the Tisserand Criterion needs to be adapted using a correction term for the low-thrust situation. It is explained why this necessary correction term excludes an a priori evaluation of sequences and therefore their planning and an alternate approach is proposed. Preliminary results of this method, by application of a Differential Evolution optimization algorithm, are presented and discussed, showing that the method is valid but can be improved. Two constraints on the search space are briefly presented for that aim.

NASA Double Asteroid Redirection Test (Dart) Trajectory Validation and Robustness

NASA Technical Reports Server (NTRS)

Sarli, Bruno V.; Ozimek, Martin T.; Atchison, Justin A.; Englander, Jacob A.; Barbee, Brent W.

2017-01-01

The Double Asteroid Redirection Test (DART) mission will be the first to test the concept of a kinetic impactor. Several studies have been made on asteroid redirection and impact mitigation, however, to this date no mission tested the proposed concepts. An impact study on a representative body allows the measurement of the effects on the target's orbit and physical structure. With this goal, DART's objective is to verify the effectiveness of the kinetic impact concept for planetary defense. The spacecraft uses solar electric propulsion to escape Earth, flyby (138971) 2001 CB21 for impart rehearsal, and impact the secondary body of the (65803) Didymos system. This work focuses on the interplanetary trajectory design part of the mission with the validation of the baseline trajectory, performance comparison to other mission objectives, and assessment of the baseline robustness to missed thrust events. Results show a good performance of the selected trajectory for different mission objectives: latest possible escape date, maximum kinetic energy on impact, shortest possible time of flight, and use of an Earth swing-by. The baseline trajectory was shown to be robust to a missed thrust with 1% of fuel margin being enough to recover the mission for failures of more than 14 days.

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.

Tuning Monotonic Basin Hopping: Improving the Efficiency of Stochastic Search as Applied to Low-Thrust Trajectory Optimization

NASA Technical Reports Server (NTRS)

Englander, Jacob A.; Englander, Arnold C.

2014-01-01

Trajectory optimization methods using monotonic basin hopping (MBH) have become well developed during the past decade [1, 2, 3, 4, 5, 6]. An essential component of MBH is a controlled random search through the multi-dimensional space of possible solutions. Historically, the randomness has been generated by drawing random variable (RV)s from a uniform probability distribution. Here, we investigate the generating the randomness by drawing the RVs from Cauchy and Pareto distributions, chosen because of their characteristic long tails. We demonstrate that using Cauchy distributions (as first suggested by J. Englander [3, 6]) significantly improves monotonic basin hopping (MBH) performance, and that Pareto distributions provide even greater improvements. Improved performance is defined in terms of efficiency and robustness. Efficiency is finding better solutions in less time. Robustness is efficiency that is undiminished by (a) the boundary conditions and internal constraints of the optimization problem being solved, and (b) by variations in the parameters of the probability distribution. Robustness is important for achieving performance improvements that are not problem specific. In this work we show that the performance improvements are the result of how these long-tailed distributions enable MBH to search the solution space faster and more thoroughly. In developing this explanation, we use the concepts of sub-diffusive, normally-diffusive, and super-diffusive random walks (RWs) originally developed in the field of statistical physics.

A hybrid systems strategy for automated spacecraft tour design and optimization

NASA Astrophysics Data System (ADS)

Stuart, Jeffrey R.

As the number of operational spacecraft increases, autonomous operations is rapidly evolving into a critical necessity. Additionally, the capability to rapidly generate baseline trajectories greatly expands the range of options available to analysts as they explore the design space to meet mission demands. Thus, a general strategy is developed, one that is suitable for the construction of flight plans for both Earth-based and interplanetary spacecraft that encounter multiple objects, where these multiple encounters comprise a ``tour''. The proposed scheme is flexible in implementation and can readily be adjusted to a variety of mission architectures. Heuristic algorithms that autonomously generate baseline tour trajectories and, when appropriate, adjust reference solutions in the presence of rapidly changing environments are investigated. Furthermore, relative priorities for ranking the targets are explicitly accommodated during the construction of potential tour sequences. As a consequence, a priori, as well as newly acquired, knowledge concerning the target objects enhances the potential value of the ultimate encounter sequences. A variety of transfer options are incorporated, from rendezvous arcs enabled by low-thrust engines to more conventional impulsive orbit adjustments via chemical propulsion technologies. When advantageous, trajectories are optimized in terms of propellant consumption via a combination of indirect and direct methods; such a combination of available technologies is an example of hybrid optimization. Additionally, elements of hybrid systems theory, i.e., the blending of dynamical states, some discrete and some continuous, are integrated into the high-level tour generation scheme. For a preliminary investigation, this strategy is applied to mission design scenarios for a Sun-Jupiter Trojan asteroid tour as well as orbital debris removal for near-Earth applications.

Integrated Targeting and Guidance for Powered Planetary Descent

NASA Astrophysics Data System (ADS)

Azimov, Dilmurat M.; Bishop, Robert H.

2018-02-01

This paper presents an on-board guidance and targeting design that enables explicit state and thrust vector control and on-board targeting for planetary descent and landing. These capabilities are developed utilizing a new closed-form solution for the constant thrust arc of the braking phase of the powered descent trajectory. The key elements of proven targeting and guidance architectures, including braking and approach phase quartics, are employed. It is demonstrated that implementation of the proposed solution avoids numerical simulation iterations, thereby facilitating on-board execution of targeting procedures during the descent. It is shown that the shape of the braking phase constant thrust arc is highly dependent on initial mass and propulsion system parameters. The analytic solution process is explicit in terms of targeting and guidance parameters, while remaining generic with respect to planetary body and descent trajectory design. These features increase the feasibility of extending the proposed integrated targeting and guidance design to future cargo and robotic landing missions.

Integrated Targeting and Guidance for Powered Planetary Descent

NASA Astrophysics Data System (ADS)

Azimov, Dilmurat M.; Bishop, Robert H.

2018-06-01

This paper presents an on-board guidance and targeting design that enables explicit state and thrust vector control and on-board targeting for planetary descent and landing. These capabilities are developed utilizing a new closed-form solution for the constant thrust arc of the braking phase of the powered descent trajectory. The key elements of proven targeting and guidance architectures, including braking and approach phase quartics, are employed. It is demonstrated that implementation of the proposed solution avoids numerical simulation iterations, thereby facilitating on-board execution of targeting procedures during the descent. It is shown that the shape of the braking phase constant thrust arc is highly dependent on initial mass and propulsion system parameters. The analytic solution process is explicit in terms of targeting and guidance parameters, while remaining generic with respect to planetary body and descent trajectory design. These features increase the feasibility of extending the proposed integrated targeting and guidance design to future cargo and robotic landing missions.

Optimal Interception of a Maneuvering Long-range Missile

NASA Astrophysics Data System (ADS)

X. Vinh, Nguyen; T. Kabamba, Pierre; Takehira, Tetsuya

2001-01-01

In a Newtonian central force field, the minimum-fuel interception of a satellite, or a ballistic missile, in elliptic trajectory can be obtained via Lawden's theory of primer vector. To secure interception when the target performs evasive maneuvers, a new control law, with explicit solutions, is implemented. It is shown that by a rotation of coordinate system, the problem of three-dimensional interception is reduced to a planar problem. The general case of planar interception of a long-range ballistic missile is then studied. Examples of interception at a specified time, head-on interception and minimum-fuel interception are presented. In each case, the requirement for the thrust acceleration is expressed explicitly as a function of time.

Navigation and Guidance for Low-Thrust Trajectories, LOTNAV

NASA Astrophysics Data System (ADS)

Cano, J. L.; Bello, M.; Rodriguez-Canabal, J.

A number of interplanetary low-thrust missions have already been flown by many space agencies. Examples of already flown missions based on the use of electric propulsion are Deep Space 1, Hayabusa and SMART-1. Many others are already in the assessment phase or in the development phase itself. In such perspective, it is required by the space agencies the procurement and utilisation of assessment tools for fast prototyping in the areas of mission design and navigation. The Low-Thrust Interplanetary Navigation Tool, which is the subject of this paper, allows the mission analyst performing such type of quick assessment studies for the early phases in the development of low-thrust missions. A number of test cases on low-thrust missions are also presented along with the utilities composing the LOTNAV tool.

Subsystem Analysis/Optimization for the X-34 Main Propulsion System

NASA Technical Reports Server (NTRS)

McDonald, J. P.; Hedayat, A.; Brown, T. M.; Knight, K. C.; Champion, R. H., Jr.

1998-01-01

The Orbital Sciences Corporation X-34 vehicle demonstrates technologies and operations key to future reusable launch vehicles. The general flight performance goal of this unmanned rocket plane is Mach 8 flight at an altitude of 250,000 feet. The Main Propulsion System (MPS) supplies liquid propellants to the main engine, which provides the primary thrust for attaining mission goals. Major MPS design and operational goals are aircraft-like ground operations, quick turnaround between missions, and low initial/operational costs. Analyses related to optimal MPS subsystem design are reviewed in this paper. A pressurization system trade weighs maintenance/reliability concerns against those for safety in a comparison of designs using pressure regulators versus orifices to control pressurant flow. A propellant dump/feed system analysis weighs the issues of maximum allowable vehicle landing weight, trajectory, and MPS complexity to arrive at a final configuration for propellant dump/feed systems.

Thrust Direction Optimization: Satisfying Dawn's Attitude Agility Constraints

NASA Technical Reports Server (NTRS)

Whiffen, Gregory J.

2013-01-01

The science objective of NASA's Dawn Discovery mission is to explore the two largest members of the main asteroid belt, the giant asteroid Vesta and the dwarf planet Ceres. Dawn successfully completed its orbital mission at Vesta. The Dawn spacecraft has complex, difficult to quantify, and in some cases severe limitations on its attitude agility. The low-thrust transfers between science orbits at Vesta required very complex time varying thrust directions due to the strong and complex gravity and various science objectives. Traditional thrust design objectives (like minimum (Delta)V or minimum transfer time) often result in thrust direction time evolutions that can not be accommodated with the attitude control system available on Dawn. This paper presents several new optimal control objectives, collectively called thrust direction optimization that were developed and necessary to successfully navigate Dawn through all orbital transfers at Vesta.

Spacecraft Formation Flying Maneuvers Using Linear-Quadratic Regulation with No Radial Axis Inputs

NASA Technical Reports Server (NTRS)

Starin, Scott R.; Yedavalli, R. K.; Sparks, Andrew G.; Bauer, Frank H. (Technical Monitor)

2001-01-01

Regarding multiple spacecraft formation flying, the observation has been made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite (leader-follower) formation. A formulation of orbital dynamics using the state of one satellite relative to another is used. Without the need for thrust along the radial (zenith-nadir) axis of the relative reference frame ' propulsion system simplifications and weight reduction may be accomplished. Several linear-quadratic regulators (LQR) are explored and compared based on performance measures likely to be important to many missions, but not directly optimized in the LQR designs. Maneuver simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled leader. These short maneuver simulations demonstrate the capacity of the controller to perform changes from one formation geometry to another. This work focusses on formations in which the controlled satellite has a relative trajectory which projects onto the local horizon of the uncontrolled satellite as a circle. This formation has potential uses for distributed remote sensing systems.

High Power Electric Propulsion System for NEP: Propulsion and Trajectory Options

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

Koppel, Christophe R.; Duchemin, Olivier; Valentian, Dominique

Recent US initiatives in Nuclear Propulsion lend themselves naturally to raising the question of the assessment of various options and particularly to propose the High Power Electric Propulsion Subsystem (HPEPS) for the Nuclear Electric Propulsion (NEP). The purpose of this paper is to present the guidelines for the HPEPS with respect to the mission to Mars, for automatic probes as well as for manned missions. Among the various options, the technological options and the trajectory options are pointed out. The consequences of the increase of the electrical power of a thruster are first an increase of the thrust itself, butmore » also, as a general rule, an increase of the thruster performance due to its higher efficiency, particularly its specific impulse increase. The drawback is as a first parameter, the increase of the thruster's size, hence the so-called 'thrust density' shall be high enough or shall be drastically increased for ions thrusters. Due to the large mass of gas needed to perform the foreseen missions, the classical xenon rare gas is no more in competition, the total world production being limited to 20 -40 tons per year. Thus, the right selection of the propellant feeding the thruster is of prime importance. When choosing a propellant with lower molecular mass, the consequences at thruster level are an increase once more of the specific impulse, but at system level the dead mass may increase too, mainly because the increase of the mass of the propellant system tanks. Other alternatives, in rupture with respect to the current technologies, are presented in order to make the whole system more attractive. The paper presents a discussion on the thruster specific impulse increase that is sometime considered an increase of the main system performances parameter, but that induces for all electric propulsion systems drawbacks in the system power and mass design that are proportional to the thruster specific power increase (kW/N). The electric thruster specific impulse shall be optimized w.r.t. the mission. The trajectories taken into account in the paper are constrained by the allowable duration of the travel and the launcher size. The multi-arcs trajectories to Mars (using an optimized combination of chemical and Electric propulsion) are presented in detail. The compatibility with NEP systems that implies orbiting a sizeable nuclear reactor and a power generation system capable of converting thermal into electric power, with minimum mass and volumes fitting in with Ariane 5 or the Space Shuttle bay, is assessed.« less

Low-thrust orbit transfer optimization with refined Q-law and multi-objective genetic algorithm

NASA Technical Reports Server (NTRS)

Lee, Seungwon; Petropoulos, Anastassios E.; von Allmen, Paul

2005-01-01

An optimization method for low-thrust orbit transfers around a central body is developed using the Q-law and a multi-objective genetic algorithm. in the hybrid method, the Q-law generates candidate orbit transfers, and the multi-objective genetic algorithm optimizes the Q-law control parameters in order to simultaneously minimize both the consumed propellant mass and flight time of the orbit tranfer. This paper addresses the problem of finding optimal orbit transfers for low-thrust spacecraft.

Vehicle System Integration, Optimization, and Robustness

Science.gov Websites

Operations Technology Exchange Initiating Partnerships University Partners Government Partners Industry Contacts Researchers Thrust Area 5: Vehicle System Integration, Optimization, and Robustness Thrust Area only optimal design of the vehicle components, but also an optimization of the interactions between

A Conceptual Design of Omni-Directional Receiving Dual-Beam Laser Engine

NASA Astrophysics Data System (ADS)

Tang, Zhiping; Zhang, Qinghong

2010-05-01

The laser engine design is one of the key issues for laser propulsion technology. A concept of Omni-Directional Receiving Dual-Beam Laser Engine (ODLE) together with its configuration design is proposed in this paper. The ODLE is noted for its features as follows: First, the optical system is completely separated from the thrust system, the incident laser beams are reflected into the thrust chamber by the optics only twice, so the beam energy loss is small. Second, the optical system can be adjusted in all direction to track the incident laser beams, ensuring its wide applications in various kinds of launching trajectories. Third, the adoption of the dual-beam single-or double-engine configuration can reduce 50% of the power requirement for each laser, and a smooth laser relay can be carried out if needed during the launching process. The paper has proposed 2 launch plans into the LEO with the ODLE: the plane trajectory and the conic spiral trajectory. The simulated results indicate that the transmission distance of laser beams for the conic spiral trajectory is far less than that of the plane trajectory. As a result, it can reduce significantly the divergence and energy loss of laser beams, and is also of advantage for the measurement and control operation during the launch process.

DUKSUP: A Computer Program for High Thrust Launch Vehicle Trajectory Design and Optimization

NASA Technical Reports Server (NTRS)

Williams, C. H.; Spurlock, O. F.

2014-01-01

From the late 1960's through 1997, the leadership of NASA's Intermediate and Large class unmanned expendable launch vehicle projects resided at the NASA Lewis (now Glenn) Research Center (LeRC). One of LeRC's primary responsibilities --- trajectory design and performance analysis --- was accomplished by an internally-developed analytic three dimensional computer program called DUKSUP. Because of its Calculus of Variations-based optimization routine, this code was generally more capable of finding optimal solutions than its contemporaries. A derivation of optimal control using the Calculus of Variations is summarized including transversality, intermediate, and final conditions. The two point boundary value problem is explained. A brief summary of the code's operation is provided, including iteration via the Newton-Raphson scheme and integration of variational and motion equations via a 4th order Runge-Kutta scheme. Main subroutines are discussed. The history of the LeRC trajectory design efforts in the early 1960's is explained within the context of supporting the Centaur upper stage program. How the code was constructed based on the operation of the Atlas/Centaur launch vehicle, the limits of the computers of that era, the limits of the computer programming languages, and the missions it supported are discussed. The vehicles DUKSUP supported (Atlas/Centaur, Titan/Centaur, and Shuttle/Centaur) are briefly described. The types of missions, including Earth orbital and interplanetary, are described. The roles of flight constraints and their impact on launch operations are detailed (such as jettisoning hardware on heating, Range Safety, ground station tracking, and elliptical parking orbits). The computer main frames on which the code was hosted are described. The applications of the code are detailed, including independent check of contractor analysis, benchmarking, leading edge analysis, and vehicle performance improvement assessments. Several of DUKSUP's many major impacts on launches are discussed including Intelsat, Voyager, Pioneer Venus, HEAO, Galileo, and Cassini.

DUKSUP: A Computer Program for High Thrust Launch Vehicle Trajectory Design and Optimization

NASA Technical Reports Server (NTRS)

Spurlock, O. Frank; Williams, Craig H.

2015-01-01

From the late 1960s through 1997, the leadership of NASAs Intermediate and Large class unmanned expendable launch vehicle projects resided at the NASA Lewis (now Glenn) Research Center (LeRC). One of LeRCs primary responsibilities --- trajectory design and performance analysis --- was accomplished by an internally-developed analytic three dimensional computer program called DUKSUP. Because of its Calculus of Variations-based optimization routine, this code was generally more capable of finding optimal solutions than its contemporaries. A derivation of optimal control using the Calculus of Variations is summarized including transversality, intermediate, and final conditions. The two point boundary value problem is explained. A brief summary of the codes operation is provided, including iteration via the Newton-Raphson scheme and integration of variational and motion equations via a 4th order Runge-Kutta scheme. Main subroutines are discussed. The history of the LeRC trajectory design efforts in the early 1960s is explained within the context of supporting the Centaur upper stage program. How the code was constructed based on the operation of the AtlasCentaur launch vehicle, the limits of the computers of that era, the limits of the computer programming languages, and the missions it supported are discussed. The vehicles DUKSUP supported (AtlasCentaur, TitanCentaur, and ShuttleCentaur) are briefly described. The types of missions, including Earth orbital and interplanetary, are described. The roles of flight constraints and their impact on launch operations are detailed (such as jettisoning hardware on heating, Range Safety, ground station tracking, and elliptical parking orbits). The computer main frames on which the code was hosted are described. The applications of the code are detailed, including independent check of contractor analysis, benchmarking, leading edge analysis, and vehicle performance improvement assessments. Several of DUKSUPs many major impacts on launches are discussed including Intelsat, Voyager, Pioneer Venus, HEAO, Galileo, and Cassini.

Fuel-Optimal Altitude Maintenance of Low-Earth-Orbit Spacecrafts by Combined Direct/Indirect Optimization

NASA Astrophysics Data System (ADS)

Kim, Kyung-Ha; Park, Chandeok; Park, Sang-Young

2015-12-01

This work presents fuel-optimal altitude maintenance of Low-Earth-Orbit (LEO) spacecrafts experiencing non-negligible air drag and J2 perturbation. A pseudospectral (direct) method is first applied to roughly estimate an optimal fuel consumption strategy, which is employed as an initial guess to precisely determine itself. Based on the physical specifications of KOrea Multi-Purpose SATellite-2 (KOMPSAT-2), a Korean artificial satellite, numerical simulations show that a satellite ascends with full thrust at the early stage of the maneuver period and then descends with null thrust. While the thrust profile is presumably bang-off, it is difficult to precisely determine the switching time by using a pseudospectral method only. This is expected, since the optimal switching epoch does not coincide with one of the collocation points prescribed by the pseudospectral method, in general. As an attempt to precisely determine the switching time and the associated optimal thrust history, a shooting (indirect) method is then employed with the initial guess being obtained through the pseudospectral method. This hybrid process allows the determination of the optimal fuel consumption for LEO spacecrafts and their thrust profiles efficiently and precisely.

Thrust Direction Optimization: Satisfying Dawn's Attitude Agility Constraints

NASA Technical Reports Server (NTRS)

Whiffen, Gregory J.

2013-01-01

The science objective of NASA's Dawn Discovery mission is to explore the giant asteroid Vesta and the dwarf planet Ceres, the two largest members of the main asteroid belt. Dawn successfully completed its orbital mission at Vesta. The Dawn spacecraft has complex, difficult to quantify, and in some cases severe limitations on its attitude agility. The low-thrust transfers between science orbits at Vesta required very complex time varying thrust directions due to the strong and complex gravity and various science objectives. Traditional low-thrust design objectives (like minimum change in velocity or minimum transfer time) often result in thrust direction time evolutions that cannot be accommodated with the attitude control system available on Dawn. This paper presents several new optimal control objectives, collectively called thrust direction optimization that were developed and turned out to be essential to the successful navigation of Dawn at Vesta.

New numerical methods for open-loop and feedback solutions to dynamic optimization problems

NASA Astrophysics Data System (ADS)

Ghosh, Pradipto

The topic of the first part of this research is trajectory optimization of dynamical systems via computational swarm intelligence. Particle swarm optimization is a nature-inspired heuristic search method that relies on a group of potential solutions to explore the fitness landscape. Conceptually, each particle in the swarm uses its own memory as well as the knowledge accumulated by the entire swarm to iteratively converge on an optimal or near-optimal solution. It is relatively straightforward to implement and unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, is still relatively new. In the first half of this thesis particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems including thrust programming for minimum fuel, multi-burn spacecraft orbit transfer, and computing minimum-time rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of constrained nonlinear mixed-integer programming problems with the swarming technique. For each solved optimal programming problem, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy. The second half of this research develops a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general nonlinear differential equations. A notable revelation from this development is that the resulting control law has an algebraic closed-form structure. The proposed method uses an optimal spatial statistical predictor called universal kriging to construct the surrogate model of a feedback controller, which is capable of quickly predicting an optimal control estimate based on current state (and time) information. With universal kriging, an approximation to the optimal feedback map is computed by conceptualizing a set of state-control samples from pre-computed extremals to be a particular realization of a jointly Gaussian spatial process. Feedback policies are computed for a variety of example dynamic optimization problems in order to evaluate the effectiveness of this methodology. This feedback synthesis approach is found to combine good numerical accuracy with low computational overhead, making it a suitable candidate for real-time applications. Particle swarm and universal kriging are combined for a capstone example, a near optimal, near-admissible, full-state feedback control law is computed and tested for the heat-load-limited atmospheric-turn guidance of an aeroassisted transfer vehicle. The performance of this explicit guidance scheme is found to be very promising; initial errors in atmospheric entry due to simulated thruster misfirings are found to be accurately corrected while closely respecting the algebraic state-inequality constraint.

The DTIC Review. Hybrid and Electronic Vehicles. Volume 4. Number 1, June 1998.

DTIC Science & Technology

1998-06-01

ARGONNE NATIONAL LAB KIRTLAND AFB, NM IL (U) Constant-Thrust Orbit-Raising Transfer Charts. • (U) Dynamics and Controls in Maglev Systems DESCRIPTIVE...method to levitated ( MAGLEV ) ground transportation systems has generate minimum-fuel trajectories between coplanar important consequences for safety...satellite designers to control systems must be considered if MAGLEV systems assess preliminary fuel requirements for constant-thrust are to be economically

Powered Descent Guidance with General Thrust-Pointing Constraints

NASA Technical Reports Server (NTRS)

Carson, John M., III; Acikmese, Behcet; Blackmore, Lars

2013-01-01

The Powered Descent Guidance (PDG) algorithm and software for generating Mars pinpoint or precision landing guidance profiles has been enhanced to incorporate thrust-pointing constraints. Pointing constraints would typically be needed for onboard sensor and navigation systems that have specific field-of-view requirements to generate valid ground proximity and terrain-relative state measurements. The original PDG algorithm was designed to enforce both control and state constraints, including maximum and minimum thrust bounds, avoidance of the ground or descent within a glide slope cone, and maximum speed limits. The thrust-bound and thrust-pointing constraints within PDG are non-convex, which in general requires nonlinear optimization methods to generate solutions. The short duration of Mars powered descent requires guaranteed PDG convergence to a solution within a finite time; however, nonlinear optimization methods have no guarantees of convergence to the global optimal or convergence within finite computation time. A lossless convexification developed for the original PDG algorithm relaxed the non-convex thrust bound constraints. This relaxation was theoretically proven to provide valid and optimal solutions for the original, non-convex problem within a convex framework. As with the thrust bound constraint, a relaxation of the thrust-pointing constraint also provides a lossless convexification that ensures the enhanced relaxed PDG algorithm remains convex and retains validity for the original nonconvex problem. The enhanced PDG algorithm provides guidance profiles for pinpoint and precision landing that minimize fuel usage, minimize landing error to the target, and ensure satisfaction of all position and control constraints, including thrust bounds and now thrust-pointing constraints.

Electric Solar Wind Sail Kinetic Energy Impactor for Asteroid Deflection Missions

NASA Astrophysics Data System (ADS)

Yamaguchi, Kouhei; Yamakawa, Hiroshi

2016-03-01

An electric solar wind sail uses the natural solar wind stream to produce low but continuous thrust by interacting with a number of long thin charged tethers. It allows a spacecraft to generate a thrust without consuming any reaction mass. The aim of this paper is to investigate the use of a spacecraft with such a propulsion system to deflect an asteroid with a high relative velocity away from an Earth collision trajectory. To this end, we formulate a simulation model for the electric solar wind sail. By summing thrust vectors exerted on each tether, a dynamic model which gives the relation between the thrust and sail attitude is proposed. Orbital maneuvering by fixing the sail's attitude and changing tether voltage is considered. A detailed study of the deflection of fictional asteroids, which are assumed to be identified 15 years before Earth impact, is also presented. Assuming a spacecraft characteristic acceleration of 0.5 mm/s 2, and a projectile mass of 1,000 kg, we show that the trajectory of asteroids with one million tons can be changed enough to avoid a collision with the Earth. Finally, the effectiveness of using this method of propulsion in an asteroid deflection mission is evaluated in comparison with using flat photonic solar sails.

Highly efficient, very low-thrust transfer to geosynchronous orbit - Exact and approximate solutions

NASA Astrophysics Data System (ADS)

Redding, D. C.

1984-04-01

An overview is provided of the preflight, postflight, and accuracy analysis of the Titan IIIC launch vehicle that injects payloads into geosynchronous orbits. The postflight trajectory reconstruction plays an important role in determining payload injection accuracy. Furthermore, the postflight analysis provides useful information about the characteristics of measuring instruments subjected to a flight environment. Suitable approaches for meeting mission specifications, trajectory requirements, and instrument constraints are considered, taking into account the importance of preflight trajectory analysis activities. Gimbal flip avoidance algorithms in the flight software, and considerable beta gimbal analysis ensures a singularity-free trajectory.

Research on the transfers to Halo orbits from the view of invariant manifolds

NASA Astrophysics Data System (ADS)

Xu, Ming; Tan, Tian; Xu, ShiJie

2012-04-01

This paper discusses the evolutions of invariant manifolds of Halo orbits by low-thrust and lunar gravity. The possibility of applying all these manifolds in designing low-thrust transfer, and the presence of single-impulse trajectories under lunar gravity are also explained. The relationship between invariant manifolds and the altitude of the perigee is investigated using a Poincaré map. Six types of single-impulse transfer trajectories are then attained from the geometry of the invariant manifolds. The evolutions of controlled manifolds are surveyed by the gradient law of Jacobi energy, and the following conclusions are drawn. First, the low thrust (acceleration or deceleration) near the libration point is very inefficient that the spacecraft free-flies along the invariant manifolds. The purpose is to increase its velocity and avoid stagnation near the libration point. Second, all controlled manifolds are captured because they lie inside the boundary of Earth's gravity trap in the configuration space. The evolutions of invariant manifolds under lunar gravity are indicated from the relationship between the lunar phasic angle and the altitude of the perigee. Third and last, most of the manifolds have preserved their topologies in the circular restricted three-body problem. However, the altitudes of the perigee of few manifolds are quite non-continuous, which can be used to generate single- impulse flyby trajectories.

Determination of optimal trajectories for an aircraft returning to the runway following a complete loss of thrust after takeoff

NASA Astrophysics Data System (ADS)

Gordon, Craig A.

This thesis examines the ability of a small, single-engine airplane to return to the runway following an engine failure shortly after takeoff. Two sets of trajectories are examined. One set of trajectories has the airplane fly a straight climb on the runway heading until engine failure. The other set of trajectories has the airplane perform a 90° turn at an altitude of 500 feet and continue until engine failure. Various combinations of wind speed, wind direction, and engine failure times are examined. The runway length required to complete the entire flight from the beginning of the takeoff roll to wheels stop following the return to the runway after engine failure is calculated for each case. The optimal trajectories following engine failure consist of three distinct segments: a turn back toward the runway using a large bank angle and angle of attack; a straight glide; and a reversal turn to align the airplane with the runway. The 90° turn results in much shorter required runway lengths at lower headwind speeds. At higher headwind speeds, both sets of trajectories are limited by the length of runway required for the landing rollout, but the straight climb cases generally require a lower angle of attack to complete the flight. The glide back to the runway is performed at an airspeed below the best glide speed of the airplane due to the need to conserve potential energy after the completion of the turn back toward the runway. The results are highly dependent on the rate of climb of the airplane during powered flight. The results of this study can aid the pilot in determining whether or not a return to the runway could be performed in the event of an engine failure given the specific wind conditions and runway length at the time of takeoff. The results can also guide the pilot in determining the takeoff profile that would offer the greatest advantage in returning to the runway.

A Method of Efficient Inclination Changes for Low-thrust Spacecraft

NASA Technical Reports Server (NTRS)

Falck, Robert; Gefert, Leon

2002-01-01

The evolution of low-thrust propulsion technologies has reached a point where such systems have become an economical option for many space missions. The development of efficient, low trip time control laws has received an increasing amount of attention in recent years, though few studies have examined the subject of inclination changing maneuvers in detail. A method for performing economical inclination changes through the use of an efficiency factor is derived front Lagrange's planetary equations. The efficiency factor can be used to regulate propellant expenditure at the expense of trip time. Such a method can be used for discontinuous-thrust transfers that offer reduced propellant masses and trip-times in comparison to continuous thrust transfers, while utilizing thrusters that operate at a lower specific impulse. Performance comparisons of transfers utilizing this approach with continuous-thrust transfers are generated through trajectory simulation and are presented in this paper.

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.

Influence of Thrust Level on the Architecture and Optimal Working Process Parameters of a Small-scale Turbojet for UAV

NASA Astrophysics Data System (ADS)

Kuz`michev, V. S.; Filinov, E. P.; Ostapyuk, Ya A.

2018-01-01

This article describes how the thrust level influences the turbojet architecture (types of turbomachines that provide the maximum efficiency) and its working process parameters (turbine inlet temperature (TIT) and overall pressure ratio (OPR)). Functional gasdynamic and strength constraints were included, total mass of fuel and the engine required for mission and the specific fuel consumption (SFC) were considered optimization criteria. Radial and axial turbines and compressors were considered. The results show that as the engine thrust decreases, optimal values of working process parameters decrease too, and the regions of compromise shrink. Optimal engine architecture and values of working process parameters are suggested for turbojets with thrust varying from 100N to 100kN. The results show that for the thrust below 25kN the engine scale factor should be taken into the account, as the low flow rates begin to influence the efficiency of engine elements substantially.

Simple control laws for low-thrust orbit transfers

NASA Technical Reports Server (NTRS)

Petropoulos, Anastassios E.

2003-01-01

Two methods are presented by which to determine both a thrust direction and when to apply thrust to effect specified changes in any of the orbit elements except for true anomaly, which is assumed free. The central body is assumed to be a point mass, and the initial and final orbits are assumed closed. Thrust, when on, is of a constant value, and specific impulse is constant. The thrust profiles derived from the two methods are not propellant-optimal, but are based firstly on the optimal thrust directions and location on the osculating orbit for changing each of the orbit elements and secondly on the desired changes in the orbit elements. Two examples of transfers are presented, one in semimajor axis and inclination, and one in semimajor axis and eccentricity. The latter compares favourably with a propellant-optimized transfer between the same orbits. The control laws have few input parameters, but can still capture the complexity of a wide variety of orbit transfers.

SEP thrust subsystem performance sensitivity analysis

NASA Technical Reports Server (NTRS)

Atkins, K. L.; Sauer, C. G., Jr.; Kerrisk, D. J.

1973-01-01

This is a two-part report on solar electric propulsion (SEP) performance sensitivity analysis. The first part describes the preliminary analysis of the SEP thrust system performance for an Encke rendezvous mission. A detailed description of thrust subsystem hardware tolerances on mission performance is included together with nominal spacecraft parameters based on these tolerances. The second part describes the method of analysis and graphical techniques used in generating the data for Part 1. Included is a description of both the trajectory program used and the additional software developed for this analysis. Part 2 also includes a comprehensive description of the use of the graphical techniques employed in this performance analysis.

14 CFR 417.207 - Trajectory analysis.

Code of Federal Regulations, 2013 CFR

2013-01-01

... any stage that has the potential to impact the Earth and does not burn to propellant depletion before a programmed thrust termination. (3) For launch vehicles flown with a flight safety system, a...

14 CFR 417.207 - Trajectory analysis.

Code of Federal Regulations, 2012 CFR

2012-01-01

... any stage that has the potential to impact the Earth and does not burn to propellant depletion before a programmed thrust termination. (3) For launch vehicles flown with a flight safety system, a...

14 CFR 417.207 - Trajectory analysis.

Code of Federal Regulations, 2014 CFR

2014-01-01

... any stage that has the potential to impact the Earth and does not burn to propellant depletion before a programmed thrust termination. (3) For launch vehicles flown with a flight safety system, a...

Orbital Disturbance Analysis due to the Lunar Gravitational Potential and Deviation Minimization through the Trajectory Control in Closed Loop

NASA Astrophysics Data System (ADS)

Gonçalves, L. D.; Rocco, E. M.; de Moraes, R. V.

2013-10-01

A study evaluating the influence due to the lunar gravitational potential, modeled by spherical harmonics, on the gravity acceleration is accomplished according to the model presented in Konopliv (2001). This model provides the components x, y and z for the gravity acceleration at each moment of time along the artificial satellite orbit and it enables to consider the spherical harmonic degree and order up to100. Through a comparison between the gravity acceleration from a central field and the gravity acceleration provided by Konopliv's model, it is obtained the disturbing velocity increment applied to the vehicle. Then, through the inverse problem, the Keplerian elements of perturbed orbit of the satellite are calculated allowing the orbital motion analysis. Transfer maneuvers and orbital correction of lunar satellites are simulated considering the disturbance due to non-uniform gravitational potential of the Moon, utilizing continuous thrust and trajectory control in closed loop. The simulations are performed using the Spacecraft Trajectory Simulator-STRS, Rocco (2008), which evaluate the behavior of the orbital elements, fuel consumption and thrust applied to the satellite over the time.

TRAGEN: Computer program to simulate an aircraft steered to follow a specified verticle profile. User's guide

NASA Technical Reports Server (NTRS)

1983-01-01

The longitudinal dynamics of a medium range twin-jet or tri-jet transport aircraft are simulated. For the climbing trajectory, the thrust is constrained to maximum value, and for descent, the thrust is set at idle. For cruise, the aircraft is held in the trim condition. For climb or descent, the aircraft is steered to follow either (a) a fixed profile which is input to the program or (b) a profile computed at the beginning of that segment of the run. For climb, the aircraft is steered to maintain the given airspeed as a function of altitude. For descent, the aircraft is steered to maintain the given altitude as a function of range-to-go. In both cases, the control variable is angle-of-attack. The given output trajectory is presented and compared with the input trajectory. Step climb is treated just as climb. For cruise, the Breguet equations are used to compute the fuel burned to achieve a given range and to connect given initial and final values of altitude and Mach number.

Space shuttle vehicle rocket plume impingement study for separation analysis. Tasks 2 and 3: Definition and preliminary plume impingement analysis for the MSC booster

NASA Technical Reports Server (NTRS)

Wojciechowski, C. J.; Penny, M. M.; Prozan, R. J.

1970-01-01

The results are presented of a space shuttle plume impingement study for the Manned Spacecraft Center configuration. This study was conducted as two tasks which were to (1) define the orbiter main stage engine exhaust plume flow field, and (2) define the plume impingement heating, force and resulting moment environments on the booster during the staging maneuver. To adequately define these environments during the staging maneuver and allow for deviation from the nominal separation trajectory, a multitude of relative orbiter/booster positions are analyzed which map the region that contains the separation trajectories. The data presented can be used to determine a separation trajectory which will result in acceptable impingement heating rates, forces, and the resulting moments. The data, presented in graphical form, include the effect of roll, pitch and yaw maneuvers for the booster. Quasi-steady state analysis methods were used with the orbiter engine operating at full thrust. To obtain partial thrust results, simple ratio equations are presented.

Optimal high- and low-thrust geocentric transfer

NASA Technical Reports Server (NTRS)

Sackett, L. L.; Edelbaum, T. N.

1974-01-01

A computer code which rapidly calculates time optimal combined high- and low-thrust transfers between two geocentric orbits in the presence of a strong gravitational field has been developed as a mission analysis tool. The low-thrust portion of the transfer can be between any two arbitrary ellipses. There is an option for including the effect of two initial high-thrust impulses which would raise the spacecraft from a low, initially circular orbit to the initial orbit for the low-thrust portion of the transfer. In addition, the effect of a single final impulse after the low-thrust portion of the transfer may be included. The total Delta V for the initial two impulses must be specified as well as the Delta V for the final impulse. Either solar electric or nuclear electric propulsion can be assumed for the low-thrust phase of the transfer.

Propulsion Technology Assessment: Science and Enabling Technologies to Explore the Interstellar Medium

NASA Technical Reports Server (NTRS)

Hopkins, Randall C.; Thomas, Herbert D.; Wiegmann, Bruce M.; Heaton, Andrew F.; Johnson, Les; Beers, Benjamin R.

2015-01-01

The Advanced Concepts Office at NASA’s George C. Marshall Space Flight Center conducted a study to assess what low-thrust advanced propulsion system candidates, existing and near term, could deliver a small, Voyager-like satellite to our solar system’s heliopause, approximately 100 AU from the sun, within 10 years. The advanced propulsion system trade study consisted of three candidates, including a Magnetically Shielded Miniature Hall thruster, a solar sail and an electric sail. A second analysis was conducted to determine which solid rocket motor kick stage(s) would be required to provide additional thrust at various points in the trajectory, assuming a characteristic energy capability provided by a Space Launch System Block 1B vehicle architecture carrying an 8.4 meter payload fairing. Two trajectory profiles were considered, including an escape trajectory using a Jupiter gravity assist and an escape trajectory first performing a Jupiter gravity assist followed by an Oberth maneuver around the sun and an optional Saturn gravity assist. Results indicated that if the Technology Readiness Level of an electric sail could be increased in time, this technology could not only enable a satellite to reach 100 AU in 10 years but it could potentially do so in even less time.

NASA Double Asteroid Redirection Test (DART) Trajectory Validation and Robutness

NASA Technical Reports Server (NTRS)

Sarli, Bruno V.; Ozimek, Martin T.; Atchison, Justin A.; Englander, Jacob A.; Barbee, Brent W.

2017-01-01

The Double Asteroid Redirection Test (DART) mission will be the first to test the concept of a kinetic impactor. Several studies have been made on asteroid redirection and impact mitigation, however, to this date no mission tested the proposed concepts. An impact study on a representative body allows the measurement of the effects on the target's orbit and physical structure. With this goal, DART's objective is to verify the effectiveness of the kinetic impact concept for planetary defense. The spacecraft uses solar electric propulsion to escape Earth, fly by (138971) 2001 CB21 for impact rehearsal, and impact Didymos-B, the secondary body of the binary (65803) Didymos system. This work focuses on the heliocentric transfer design part of the mission with the validation of the baseline trajectory, performance comparison to other mission objectives, and assessment of the baseline robustness to missed thrust events. Results show a good performance of the selected trajectory for different mission objectives: latest possible escape date, maximum kinetic energy on impact, shortest possible time of flight, and use of an Earth swing-by. The baseline trajectory was shown to be robust to a missed thrust with 1% of fuel margin being enough to recover the mission for failures of more than 14 days.

Optimization and Analysis of a U-Shaped Linear Piezoelectric Ultrasonic Motor Using Longitudinal Transducers

PubMed Central

Yu, Hongpeng; Quan, Qiquan; Tian, Xinqi; Li, He

2018-01-01

A novel U-shaped piezoelectric ultrasonic motor that mainly focused on miniaturization and high power density was proposed, fabricated, and tested in this work. The longitudinal vibrations of the transducers were excited to form the elliptical movements on the driving feet. Finite element method (FEM) was used for design and analysis. The resonance frequencies of the selected vibration modes were tuned to be very close to each other with modal analysis and the movement trajectories of the driving feet were gained with transient simulation. The vibration modes and the mechanical output abilities were tested to evaluate the proposed motor further by a prototype. The maximum output speed was tested to be 416 mm/s, the maximum thrust force was 21 N, and the maximum output power was 5.453 W under frequency of 29.52 kHz and voltage of 100 Vrms. The maximum output power density of the prototype reached 7.59 W/kg, which was even greater than a previous similar motor under the exciting voltage of 200 Vrms. The proposed motor showed great potential for linear driving of large thrust force and high power density. PMID:29518963

Optimization and Analysis of a U-Shaped Linear Piezoelectric Ultrasonic Motor Using Longitudinal Transducers.

PubMed

Yu, Hongpeng; Quan, Qiquan; Tian, Xinqi; Li, He

2018-03-07

A novel U-shaped piezoelectric ultrasonic motor that mainly focused on miniaturization and high power density was proposed, fabricated, and tested in this work. The longitudinal vibrations of the transducers were excited to form the elliptical movements on the driving feet. Finite element method (FEM) was used for design and analysis. The resonance frequencies of the selected vibration modes were tuned to be very close to each other with modal analysis and the movement trajectories of the driving feet were gained with transient simulation. The vibration modes and the mechanical output abilities were tested to evaluate the proposed motor further by a prototype. The maximum output speed was tested to be 416 mm/s, the maximum thrust force was 21 N, and the maximum output power was 5.453 W under frequency of 29.52 kHz and voltage of 100 V rms . The maximum output power density of the prototype reached 7.59 W/kg, which was even greater than a previous similar motor under the exciting voltage of 200 V rms . The proposed motor showed great potential for linear driving of large thrust force and high power density.

A Flight Demonstration of Plasma Rocket Propulsion

NASA Technical Reports Server (NTRS)

Petro, Andrew; Chang-Diaz, Franklin; Schwenterly, WIlliam; Hitt, Michael; Lepore, Joseph

2000-01-01

The Advanced Space Propulsion Laboratory at the NASA Johnson Space Center has been engaged in the development of a variable specific impulse magnetoplasma rocket (V ASIMR) for several years. This type of rocket could be used in the future to propel interplanetary spacecraft and has the potential to open the entire solar system to human exploration. One feature of this propulsion technology is the ability to vary its specific impulse so that it can be operated in a mode that maximizes propellant efficiency or a mode that maximizes thrust. Variation of specific impulse and thrust enhances the ability to optimize interplanetary trajectories and results in shorter trip times and lower propellant requirements than with a fixed specific impulse. In its ultimate application for interplanetary travel, the VASIMR would be a multi-megawatt device. A much lower power system is being designed for demonstration in the 2004 timeframe. This first space demonstration would employ a lO-kilowatt thruster aboard a solar powered spacecraft in Earth orbit. The 1O-kilowatt V ASIMR demonstration unit would operate for a period of several months with hydrogen or deuterium propellant with a specific impulse of 10,000 seconds.

Feasibility of Reusable Continuous Thrust Spacecraft for Cargo Resupply Missions to Mars

NASA Astrophysics Data System (ADS)

Rabotin, C. B.

Continuous thrust propulsion systems benefit from a much greater efficiency in vacuum than chemical rockets, at the expense of lower instantaneous thrust and high power requirements. The satellite telecommunications industry, known for greatly emphasizing heritage over innovation, now uses electric propulsion for station keeping on a number of spacecraft, and for orbit raising for some smaller satellites, such as the Boeing 702SP platform. Only a few interplanetary missions have relied on continuous thrust for most of their mission, such as ESA's 367 kg SMART-1 and NASA's 1217 kg Dawn mission. The high specific impulse of these continuous thrust engines should make them suitable for transportation of heavy payloads to inner solar system destinations in such a way to limit the dependency on heavy rocket launches. Additionally, such spacecraft should be able to perform orbital insertions at destination in order to deliver the cargo directly in a desired orbit. An example application is designing round-trip missions to Mars to support exploration and eventually colonization. This research investigates the feasibility of return journeys to Mars based on the performance of existing or in-development continuous thrust propulsion systems. In order to determine the business viability of such missions, an emphasis is made on the time of flight during different parts of the mission, the relative velocity with respect to the destination planet, and the fuel requirements. The study looks at the applicability for interplanetary mission design of simple control laws for efficient correction of orbital elements, and of thrusting purely in velocity or anti-velocity direction. The simulations explore different configurations of continuous thrusting technologies using a patched-conics approach. In addition, all simulation scenarios facilitate escape from planetary gravity wells as the initial spacecraft orbit is highly elliptical, both around the Earth and around Mars. This work does not include any optimal trajectory design. For this research, a highly configurable orbit propagation software with SPICE ephemerides was developed from scratch in Go, a modern compiled computer language. The outcome of this research is that simple orbital element control laws do not lead to more efficient or faster interplanetary transfers. In addition, spiraling out of Earth's gravity wells requires a substantial amount of time despite starting from a highly elliptical orbit, and even with clustered high thrust engines like the VASIMR VX-200. Further investigation should look into hybrid solutions with a chemical engine for departing Earth; outbound spirals from Mars take a more reasonable amount of time.

Low thrust optimal orbital transfers

NASA Technical Reports Server (NTRS)

Cobb, Shannon S.

1994-01-01

For many optimal transfer problems it is reasonable to expect that the minimum time solution is also the minimum fuel solution. However, if one allows the propulsion system to be turned off and back on, it is clear that these two solutions may differ. In general, high thrust transfers resemble the well known impulsive transfers where the burn arcs are of very short duration. The low and medium thrust transfers differ in that their thrust acceleration levels yield longer burn arcs and thus will require more revolutions. In this research, we considered two approaches for solving this problem: a powered flight guidance algorithm previously developed for higher thrust transfers was modified and an 'averaging technique' was investigated.

Engine performance analysis and optimization of a dual-mode scramjet with varied inlet conditions

NASA Astrophysics Data System (ADS)

Tian, Lu; Chen, Li-Hong; Chen, Qiang; Zhong, Feng-Quan; Chang, Xin-Yu

2016-02-01

A dual-mode scramjet can operate in a wide range of flight conditions. Higher thrust can be generated by adopting suitable combustion modes. Based on the net thrust, an analysis and preliminary optimal design of a kerosene-fueled parameterized dual-mode scramjet at a crucial flight Mach number of 6 were investigated by using a modified quasi-one-dimensional method and simulated annealing strategy. Engine structure and heat release distributions, affecting the engine thrust, were chosen as analytical parameters for varied inlet conditions (isolator entrance Mach number: 1.5-3.5). Results show that different optimal heat release distributions and structural conditions can be obtained at five different inlet conditions. The highest net thrust of the parameterized dual-mode engine can be achieved by a subsonic combustion mode at an isolator entrance Mach number of 2.5. Additionally, the effects of heat release and scramjet structure on net thrust have been discussed. The present results and the developed analytical method can provide guidance for the design and optimization of high-performance dual-mode scramjets.

Characterization of Space Shuttle Reusable Rocket Motor Static Test Stand Thrust Measurements

NASA Technical Reports Server (NTRS)

Cook, Mart L.; Gruet, Laurent; Cash, Stephen F. (Technical Monitor)

2003-01-01

Space Shuttle Reusable Solid Rocket Motors (RSRM) are static tested at two ATK Thiokol Propulsion facilities in Utah, T-24 and T-97. The newer T-97 static test facility was recently upgraded to allow thrust measurement capability. All previous static test motor thrust measurements have been taken at T-24; data from these tests were used to characterize thrust parameters and requirement limits for flight motors. Validation of the new T-97 thrust measurement system is required prior to use for official RSRM performance assessments. Since thrust cannot be measured on RSRM flight motors, flight motor measured chamber pressure and a nominal thrust-to-pressure relationship (based on static test motor thrust and pressure measurements) are used to reconstruct flight motor performance. Historical static test and flight motor performance data are used in conjunction with production subscale test data to predict RSRM performance. The predicted motor performance is provided to support Space Shuttle trajectory and system loads analyses. Therefore, an accurate nominal thrust-to-pressure (F/P) relationship is critical for accurate RSRM flight motor performance and Space Shuttle analyses. Flight Support Motors (FSM) 7, 8, and 9 provided thrust data for the validation of the T-97 thrust measurement system. The T-97 thrust data were analyzed and compared to thrust previously measured at T-24 to verify measured thrust data and identify any test-stand bias. The T-97 FIP data were consistent and within the T-24 static test statistical family expectation. The FSMs 7-9 thrust data met all NASA contract requirements, and the test stand is now verified for future thrust measurements.

ADMAP (automatic data manipulation program)

NASA Technical Reports Server (NTRS)

Mann, F. I.

1971-01-01

Instructions are presented on the use of ADMAP, (automatic data manipulation program) an aerospace data manipulation computer program. The program was developed to aid in processing, reducing, plotting, and publishing electric propulsion trajectory data generated by the low thrust optimization program, HILTOP. The program has the option of generating SC4020 electric plots, and therefore requires the SC4020 routines to be available at excution time (even if not used). Several general routines are present, including a cubic spline interpolation routine, electric plotter dash line drawing routine, and single parameter and double parameter sorting routines. Many routines are tailored for the manipulation and plotting of electric propulsion data, including an automatic scale selection routine, an automatic curve labelling routine, and an automatic graph titling routine. Data are accepted from either punched cards or magnetic tape.

Crew Exploration Vehicle Ascent Abort Trajectory Analysis and Optimization

NASA Technical Reports Server (NTRS)

Falck, Robert D.; Gefert, Leon P.

2007-01-01

The Orion Crew Exploration Vehicle is the first crewed capsule design to be developed by NASA since Project Apollo. Unlike Apollo, however, the CEV is being designed for service in both Lunar and International Space Station missions. Ascent aborts pose some issues that were not present for Apollo, due to its launch azimuth, nor Space Shuttle, due to its cross range capability. The requirement that a North Atlantic splashdown following an abort be avoidable, in conjunction with the requirement for overlapping abort modes to maximize crew survivability, drives the thrust level of the service module main engine. This paper summarizes 3DOF analysis conducted by NASA to aid in the determination of the appropriate propulsion system for the service module, and the appropriate propellant loading for ISS missions such that crew survivability is maximized.

The Lunar IceCube Mission Design: Construction of Feasible Transfer Trajectories with a Constrained Departure

NASA Technical Reports Server (NTRS)

Folta, David C.; Bosanac, Natasha; Cox, Andrew; Howell, Kathleen C.

2016-01-01

Lunar IceCube, a 6U CubeSat, will prospect for water and other volatiles from a low-periapsis, highly inclined elliptical lunar orbit. Injected from Exploration Mission-1, a lunar gravity assisted multi-body transfer trajectory will capture into a lunar science orbit. The constrained departure asymptote and value of trans-lunar energy limit transfer trajectory types that re-encounter the Moon with the necessary energy and flight duration. Purdue University and Goddard Space Flight Center's Adaptive Trajectory Design tool and dynamical system research is applied to uncover cislunar spatial regions permitting viable transfer arcs. Numerically integrated transfer designs applying low-thrust and a design framework are described.

Analysis of a flare-director concept for an externally blown flap STOL aircraft

NASA Technical Reports Server (NTRS)

Middleton, D. B.

1974-01-01

A flare-director concept involving a thrust-required flare-guidance equation was developed and tested on a moving-base simulator. The equation gives a signal to command thrust as a linear function of the errors between the variables thrust, altitude, and altitude rate and corresponding values on a desired reference flare trajectory. During the simulator landing tests this signal drove either the horizontal command bar of the aircraft's flight director or a thrust-command dot on a head-up virtual-image display of a flare director. It was also used as the input to a simple autoflare system. An externally blown flap STOL (short take-off and landing) aircraft (with considerable stability and control augmentation) was modeled for the landing tests. The pilots considered the flare director a valuable guide for executing a proper flare-thrust program under instrument-landing conditions, but were reluctant to make any use of the head-up display when they were performing the landings visually.

Low-thrust roundtrip trajectories to Mars with one-synodic-period repeat time

NASA Astrophysics Data System (ADS)

Okutsu, Masataka; Landau, Damon F.; Rogers, Blake A.; Longuski, James M.

2015-05-01

Cycler trajectories-both ballistic and powered-are reported in the literature in which there are two-vehicle, three-vehicle, and four-vehicle cases. Such trajectories permit the installation of cycler vehicles which provide safe and comfortable living conditions for human space travel between Earth and Mars during every synodic opportunity. The question the present paper answers is a logical, obvious one: Does a single-vehicle, one-synodic-period cycler exist? The answer is yes: such a trajectory can be flown-but only with a high-power electric propulsion system. In our example, it is found that "stopover" trajectories that spend 30 days in orbit about Earth and 30 days about Mars, and return astronauts to Earth in one synodic period require a 90-t power generator with a power level of 11 MWe. Fortuitously, and in lieu of using chemical propulsion, the high power level of the electric propulsion system would also be effective in hauling the cargo payload via a spiral trajectory about the Earth. But because one synodic period is not enough for the cycler vehicle to fly both the interplanetary trajectories and the Earth-spiral trajectories, we suggest developing two nuclear power generators, which could alternate flying the interplanetary trajectories and the Earth-spiral trajectories. Once these power generators are launched and begin operating in space, the mass requirement in seven subsequent missions (over a period of 15 years beginning in 2022) would be modest at 250-300 metric tons to low-Earth orbit per mission. Thus two cargo launches of NASA's Space Launch System and one crew launch of the Falcon Heavy, for example, would be adequate to maintain support for each consecutive mission. Although we propose developing two sets of electric propulsion systems to account for the Earth-spiral phases, only one vehicle is flown on a heliocentric trajectory at any given time. Thus, our low-thrust stopover cycler with zero encounter velocities falls into a category of a "one-vehicle cycler," which completes the gap in the literature, where we have already seen multiple-vehicle cycler concepts.

OPTRAN- OPTIMAL LOW THRUST ORBIT TRANSFERS

NASA Technical Reports Server (NTRS)

Breakwell, J. V.

1994-01-01

OPTRAN is a collection of programs that solve the problem of optimal low thrust orbit transfers between non-coplanar circular orbits for spacecraft with chemical propulsion systems. The programs are set up to find Hohmann-type solutions, with burns near the perigee and apogee of the transfer orbit. They will solve both fairly long burn-arc transfers and "divided-burn" transfers. Program modeling includes a spherical earth gravity model and propulsion system models for either constant thrust or constant acceleration. The solutions obtained are optimal with respect to fuel use: i.e., final mass of the spacecraft is maximized with respect to the controls. The controls are the direction of thrust and the thrust on/off times. Two basic types of programs are provided in OPTRAN. The first type is for "exact solution" which results in complete, exact tkme-histories. The exact spacecraft position, velocity, and optimal thrust direction are given throughout the maneuver, as are the optimal thrust switch points, the transfer time, and the fuel costs. Exact solution programs are provided in two versions for non-coplanar transfers and in a fast version for coplanar transfers. The second basic type is for "approximate solutions" which results in approximate information on the transfer time and fuel costs. The approximate solution is used to estimate initial conditions for the exact solution. It can be used in divided-burn transfers to find the best number of burns with respect to time. The approximate solution is useful by itself in relatively efficient, short burn-arc transfers. These programs are written in FORTRAN 77 for batch execution and have been implemented on a DEC VAX series computer with the largest program having a central memory requirement of approximately 54K of 8 bit bytes. The OPTRAN program were developed in 1983.

DESTINY+ Trajectory Design to (3200) Phaethon

NASA Astrophysics Data System (ADS)

Sarli, Bruno Victorino; Horikawa, Makoto; Yam, Chit Hong; Kawakatsu, Yasuhiro; Yamamoto, Takayuki

2018-03-01

This work explores the target selection and trajectory design of the mission candidate for ISAS/JAXA's small science satellite series, DESTINY PLUS or DESTINY+. This mission combines unique aspects of the latest satellite technology and exploration of transition bodies to fill a technical and scientific gap in the Japanese space science program. The spacecraft is targeted to study the comet-asteroid transition body (3200) Phaethon through a combination of low-thrust propulsion and Earth Gravity Assist. The trajectory design concept is presented in details together with the launch window and flyby date analysis. Alternative targets for a possible mission extension scenario are also explored.

Multi-Objective Optimization of Moving-magnet Linear Oscillatory Motor Using Response Surface Methodology with Quantum-Behaved PSO Operator

NASA Astrophysics Data System (ADS)

Lei, Meizhen; Wang, Liqiang

2018-01-01

To reduce the difficulty of manufacturing and increase the magnetic thrust density, a moving-magnet linear oscillatory motor (MMLOM) without inner-stators was Proposed. To get the optimal design of maximum electromagnetic thrust with minimal permanent magnetic material, firstly, the 3D finite element analysis (FEA) model of the MMLOM was built and verified by comparison with prototype experiment result. Then the influence of design parameters of permanent magnet (PM) on the electromagnetic thrust was systematically analyzed by the 3D FEA to get the design parameters. Secondly, response surface methodology (RSM) was employed to build the response surface model of the new MMLOM, which can obtain an analytical model of the PM volume and thrust. Then a multi-objective optimization methods for design parameters of PM, using response surface methodology (RSM) with a quantum-behaved PSO (QPSO) operator, was proposed. Then the way to choose the best design parameters of PM among the multi-objective optimization solution sets was proposed. Then the 3D FEA of the optimal design candidates was compared. The comparison results showed that the proposed method can obtain the best combination of the geometric parameters of reducing the PM volume and increasing the thrust.

Thrust Measurements in Ballistic Pendulum Ablative Laser Propulsion Experiments

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

Brazolin, H.; Rodrigues, N. A. S.; Minucci, M. A. S.

This paper describes a setup for thrust measurement in ablative laser propulsion experiments, based on a simple ballistic pendulum associated to an imaging system, which is being assembled at IEAv. A light aluminium pendulum holding samples is placed inside a 100 liters vacuum chamber with two optical windows: the first (in ZnSe) for the laser beam and the second (in fused quartz) for the pendulum visualization. A TEA-CO{sub 2} laser beam is focused to the samples providing ablation and transferring linear moment to the pendulum as a whole. A CCD video camera captures the oscillatory movement of the pendulum andmore » the its trajectory is obtained by image processing. By fitting the trajectory of the pendulum to a dumped sinusoidal curve is possible to obtain the amplitude of the movement which is directly related to the momentum transfered to the sample.« less

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.

Space Trajectory Error Analysis Program (STEAP) for halo orbit missions. Volume 2: Programmer's manual

NASA Technical Reports Server (NTRS)

Byrnes, D. V.; Carney, P. C.; Underwood, J. W.; Vogt, E. D.

1974-01-01

The six month effort was responsible for the development, test, conversion, and documentation of computer software for the mission analysis of missions to halo orbits about libration points in the earth-sun system. The software consisting of two programs called NOMNAL and ERRAN is part of the Space Trajectories Error Analysis Programs. The program NOMNAL targets a transfer trajectory from earth on a given launch date to a specified halo orbit on a required arrival date. Either impulsive or finite thrust insertion maneuvers into halo orbit are permitted by the program. The transfer trajectory is consistent with a realistic launch profile input by the user. The second program ERRAN conducts error analyses of the targeted transfer trajectory. Measurements including range, doppler, star-planet angles, and apparent planet diameter are processed in a Kalman-Schmidt filter to determine the trajectory knowledge uncertainty.

Low-thrust mission risk analysis, with application to a 1980 rendezvous with the comet Encke

NASA Technical Reports Server (NTRS)

Yen, C. L.; Smith, D. B.

1973-01-01

A computerized failure process simulation procedure is used to evaluate the risk in a solar electric space mission. The procedure uses currently available thrust-subsystem reliability data and performs approximate simulations of the thrust sybsystem burn operation, the system failure processes, and the retargeting operations. The method is applied to assess the risks in carrying out a 1980 rendezvous mission to the comet Encke. Analysis of the results and evaluation of the effects of various risk factors on the mission show that system component failure rates are the limiting factors in attaining a high mission relability. It is also shown that a well-designed trajectory and system operation mode can be used effectively to partially compensate for unreliable thruster performance.

Orbital and angular motion construction for low thrust interplanetary flight

NASA Astrophysics Data System (ADS)

Yelnikov, R. V.; Mashtakov, Y. V.; Ovchinnikov, M. Yu.; Tkachev, S. S.

2016-11-01

Low thrust interplanetary flight is considered. Firstly, the fuel-optimal control is found. Then the angular motion is synthesized. This motion provides the thruster tracking of the required by optimal control direction. And, finally, reaction wheel control law for tracking this angular motion is proposed and implemented. The numerical example is given and total operation time for thrusters is found. Disturbances from solar pressure, thrust eccentricity, inaccuracy of reaction wheels installation and errors of inertia tensor are taken into account.

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

General view of a Solid Rocket Motor Nozzle in the ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

General view of a Solid Rocket Motor Nozzle in the Solid Rocket Booster (SRB) Assembly and Refurbishment Facility at Kennedy Space Center, being prepared to be mated with the Aft Skirt. In this view you can see the attach brackets where the Thrust Vector Control System actuators connect to the nozzle which can swivel the nozzle up to 3.5 degrees to redirect the thrust to steer and maintain the Shuttle's programmed trajectory. - Space Transportation System, Solid Rocket Boosters, Lyndon B. Johnson Space Center, 2101 NASA Parkway, Houston, Harris County, TX

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.

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.

Direct Method Transcription for a Human-Class Translunar Injection Trajectory Optimization

NASA Technical Reports Server (NTRS)

Witzberger, Kevin E.; Zeiler, Tom

2012-01-01

This paper presents a new trajectory optimization software package developed in the framework of a low-to-high fidelity 3 degrees-of-freedom (DOF)/6-DOF vehicle simulation program named Mission Analysis Simulation Tool in Fortran (MASTIF) and its application to a translunar trajectory optimization problem. The functionality of the developed optimization package is implemented as a new "mode" in generalized settings to make it applicable for a general trajectory optimization problem. In doing so, a direct optimization method using collocation is employed for solving the problem. Trajectory optimization problems in MASTIF are transcribed to a constrained nonlinear programming (NLP) problem and solved with SNOPT, a commercially available NLP solver. A detailed description of the optimization software developed is provided as well as the transcription specifics for the translunar injection (TLI) problem. The analysis includes a 3-DOF trajectory TLI optimization and a 3-DOF vehicle TLI simulation using closed-loop guidance.

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.

Optimal design and installation of ultra high bypass ratio turbofan nacelle

NASA Astrophysics Data System (ADS)

Savelyev, Andrey; Zlenko, Nikolay; Matyash, Evgeniy; Mikhaylov, Sergey; Shenkin, Andrey

2016-10-01

The paper is devoted to the problem of designing and optimizing the nacelle of turbojet bypass engine with high bypass ratio and high thrust. An optimization algorithm EGO based on development of surrogate models and the method for maximizing the probability of improving the objective function has been used. The designing methodology has been based on the numerical solution of the Reynolds equations system. Spalart-Allmaras turbulence model has been chosen for RANS closure. The effective thrust losses has been uses as an objective function in optimizing the engine nacelle. As a result of optimization, effective thrust has been increased by 1.5 %. The Blended wing body aircraft configuration has been studied as a possible application. Two variants of the engine layout arrangement have been considered. It has been shown that the power plant changes the pressure distribution on the aircraft surface. It results in essential diminishing the configuration lift-drag ratio.

Optimization of supersonic axisymmetric nozzles with a center body for aerospace propulsion

NASA Astrophysics Data System (ADS)

Davidenko, D. M.; Eude, Y.; Falempin, F.

2011-10-01

This study is aimed at optimization of axisymmetric nozzles with a center body, which are suitable for thrust engines having an annular duct. To determine the flow conditions and nozzle dimensions, the Vinci rocket engine is chosen as a prototype. The nozzle contours are described by 2nd and 3rd order analytical functions and specified by a set of geometrical parameters. A direct optimization method is used to design maximum thrust nozzle contours. During optimization, the flow of multispecies reactive gas is simulated by an Euler code. Several optimized contours have been obtained for the center body diameter ranging from 0.2 to 0.4 m. For these contours, Navier-Stokes (NS) simulations have been performed to take into account viscous effects assuming adiabatic and cooled wall conditions. The paper presents an analysis of factors influencing the nozzle thrust.

Research on design method of the full form ship with minimum thrust deduction factor

NASA Astrophysics Data System (ADS)

Zhang, Bao-ji; Miao, Ai-qin; Zhang, Zhu-xin

2015-04-01

In the preliminary design stage of the full form ships, in order to obtain a hull form with low resistance and maximum propulsion efficiency, an optimization design program for a full form ship with the minimum thrust deduction factor has been developed, which combined the potential flow theory and boundary layer theory with the optimization technique. In the optimization process, the Sequential Unconstrained Minimization Technique (SUMT) interior point method of Nonlinear Programming (NLP) was proposed with the minimum thrust deduction factor as the objective function. An appropriate displacement is a basic constraint condition, and the boundary layer separation is an additional one. The parameters of the hull form modification function are used as design variables. At last, the numerical optimization example for lines of after-body of 50000 DWT product oil tanker was provided, which indicated that the propulsion efficiency was improved distinctly by this optimal design method.

Thrust stand evaluation of engine performance improvement algorithms in an F-15 airplane

NASA Technical Reports Server (NTRS)

Conners, Timothy R.

1992-01-01

Results are presented from the evaluation of the performance seeking control (PSC) optimization algorithm developed by Smith et al. (1990) for F-15 aircraft, which optimizes the quasi-steady-state performance of an F100 derivative turbofan engine for several modes of operation. The PSC algorithm uses onboard software engine model that calculates thrust, stall margin, and other unmeasured variables for use in the optimization. Comparisons are presented between the load cell measurements, PSC onboard model thrust calculations, and posttest state variable model computations. Actual performance improvements using the PSC algorithm are presented for its various modes. The results of using PSC algorithm are compared with similar test case results using the HIDEC algorithm.

Optimal Pitch Thrust-Vector Angle and Benefits for all Flight Regimes

NASA Technical Reports Server (NTRS)

Gilyard, Glenn B.; Bolonkin, Alexander

2000-01-01

The NASA Dryden Flight Research Center is exploring the optimum thrust-vector angle on aircraft. Simple aerodynamic performance models for various phases of aircraft flight are developed and optimization equations and algorithms are presented in this report. Results of optimal angles of thrust vectors and associated benefits for various flight regimes of aircraft (takeoff, climb, cruise, descent, final approach, and landing) are given. Results for a typical wide-body transport aircraft are also given. The benefits accruable for this class of aircraft are small, but the technique can be applied to other conventionally configured aircraft. The lower L/D aerodynamic characteristics of fighters generally would produce larger benefits than those produced for transport aircraft.

Saturn Apollo Program

NASA Image and Video Library

1963-01-01

J-2 engines for the Saturn IB/Saturn V launch vehicles are lined up in the assembly area at Rocketdyne's manufacturing plant in Canoga Park, California. Five J-2 engines provided more than 1,000,000 pounds of thrust to accelerate the second stage toward a Moon trajectory.

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.

Optimal Low-Thrust Limited-Power Transfers between Arbitrary Elliptic Coplanar Orbits

NASA Technical Reports Server (NTRS)

daSilvaFernandes, Sandro; dasChagasCarvalho, Francisco

2007-01-01

In this work, a complete first order analytical solution, which includes the short periodic terms, for the problem of optimal low-thrust limited-power transfers between arbitrary elliptic coplanar orbits in a Newtonian central gravity field is obtained through Hamilton-Jacobi theory and a perturbation method based on Lie series.

Preliminary supersonic flight test evaluation of performance seeking control

NASA Technical Reports Server (NTRS)

Orme, John S.; Gilyard, Glenn B.

1993-01-01

Digital flight and engine control, powerful onboard computers, and sophisticated controls techniques may improve aircraft performance by maximizing fuel efficiency, maximizing thrust, and extending engine life. An adaptive performance seeking control system for optimizing the quasi-steady state performance of an F-15 aircraft was developed and flight tested. This system has three optimization modes: minimum fuel, maximum thrust, and minimum fan turbine inlet temperature. Tests of the minimum fuel and fan turbine inlet temperature modes were performed at a constant thrust. Supersonic single-engine flight tests of the three modes were conducted using varied after burning power settings. At supersonic conditions, the performance seeking control law optimizes the integrated airframe, inlet, and engine. At subsonic conditions, only the engine is optimized. Supersonic flight tests showed improvements in thrust of 9 percent, increases in fuel savings of 8 percent, and reductions of up to 85 deg R in turbine temperatures for all three modes. The supersonic performance seeking control structure is described and preliminary results of supersonic performance seeking control tests are given. These findings have implications for improving performance of civilian and military aircraft.

Human Outer Solar System Exploration via Q-Thruster Technology

NASA Technical Reports Server (NTRS)

Joosten, B. Kent; White, Harold G.

2014-01-01

Propulsion technology development efforts at the NASA Johnson Space Center continue to advance the understanding of the quantum vacuum plasma thruster (QThruster), a form of electric propulsion. Through the use of electric and magnetic fields, a Q-thruster pushes quantum particles (electrons/positrons) in one direction, while the Qthruster recoils to conserve momentum. This principle is similar to how a submarine uses its propeller to push water in one direction, while the submarine recoils to conserve momentum. Based on laboratory results, it appears that continuous specific thrust levels of 0.4 - 4.0 N/kWe are achievable with essentially no onboard propellant consumption. To evaluate the potential of this technology, a mission analysis tool was developed utilizing the Generalized Reduced Gradient non-linear parameter optimization engine contained in the Microsoft Excel® platform. This tool allowed very rapid assessments of "Q-Ship" minimum time transfers from earth to the outer planets and back utilizing parametric variations in thrust acceleration while enforcing constraints on planetary phase angles and minimum heliocentric distances. A conservative Q-Thruster specific thrust assumption (0.4 N/kWe) combined with "moderate" levels of space nuclear power (1 - 2 MWe) and vehicle specific mass (45 - 55 kg/kWe) results in continuous milli-g thrust acceleration, opening up realms of human spaceflight performance completely unattainable by any current systems or near-term proposed technologies. Minimum flight times to Mars are predicted to be as low as 75 days, but perhaps more importantly new "retro-phase" and "gravity-augmented" trajectory shaping techniques were revealed which overcome adverse planetary phasing and allow virtually unrestricted departure and return opportunities. Even more impressively, the Jovian and Saturnian systems would be opened up to human exploration with round-trip times of 21 and 32 months respectively including 6 to 12 months of exploration at the destinations. Finally, interstellar trip times are assessed at milli-g acceleration levels.

Variational differential equations for engineering type trajectories close to a planet with an atmosphere

NASA Technical Reports Server (NTRS)

Dickmanns, E. D.

1972-01-01

The differential equations for the adjoint variables are derived and coded in FORTRAN. The program is written in a form to either take into account or neglect thrust, aerodynamic forces, planet rotation and oblateness, and altitude dependent winds.

A graphical approach to electric sail mission design with radial thrust

NASA Astrophysics Data System (ADS)

Mengali, Giovanni; Quarta, Alessandro A.; Aliasi, Generoso

2013-02-01

This paper describes a semi-analytical approach to electric sail mission analysis under the assumption that the spacecraft experiences a purely radial, outward, propulsive acceleration. The problem is tackled by means of the potential well concept, a very effective idea that was originally introduced by Prussing and Coverstone in 1998. Unlike a classical procedure that requires the numerical integration of the equations of motion, the proposed method provides an estimate of the main spacecraft trajectory parameters, as its maximum and minimum attainable distance from the Sun, with the simple use of analytical relationships and elementary graphs. A number of mission scenarios clearly show the effectiveness of the proposed approach. In particular, when the spacecraft parking orbit is either circular or elliptic it is possible to find the optimal performances required to reach an escape condition or a given distance from the Sun. Another example is given by the optimal strategy required to reach a heliocentric Keplerian orbit of prescribed orbital period. Finally the graphical approach is applied to the preliminary design of a nodal mission towards a Near Earth Asteroid.

Longitudinal long-period dynamics of aerospace craft

NASA Technical Reports Server (NTRS)

Berry, Donald T.

1988-01-01

Linear analyses are performed to examine the generic aspects of aerospace vehicle longitudinal long-period or trajectory modes of motion. The influence of Mach number, dynamic pressure, thrust-to-drag ratio, and propulsion system thrust laws on the longitudinal trajectory modes is presented in terms of phugoid frequency and damping and height mode stability. The results of these analyses are compared to flying qualities requirements where possible, and potential deficiencies in both the vehicle and the criteria are noted. A preliminary look at possible augmentation schemes to improve potential deficiencies is also presented. Interpretation of the practical consequences of the results is aided by typical time histories. Results indicate that propulsion system characteristics are the dominant influence on the longitudinal long-period flight dynamics of hypersonic aerospace craft. However, straightforward augmentation systems demonstrated the potential to accommodate these influences if the effects are included in the design process. These efforts may be hampered by a lack of design criteria for hypersonic aircraft.

Mission Analysis Program for Solar Electric Propulsion (MAPSEP). Volume 1: Analytical manual for earth orbital MAPSEP

NASA Technical Reports Server (NTRS)

1975-01-01

An introduction to the MAPSEP organization and a detailed analytical description of all models and algorithms are given. These include trajectory and error covariance propagation methods, orbit determination processes, thrust modeling, and trajectory correction (guidance) schemes. Earth orbital MAPSEP contains the capability of analyzing almost any currently projected low thrust mission from low earth orbit to super synchronous altitudes. Furthermore, MAPSEP is sufficiently flexible to incorporate extended dynamic models, alternate mission strategies, and almost any other system requirement imposed by the user. As in the interplanetary version, earth orbital MAPSEP represents a trade-off between precision modeling and computational speed consistent with defining necessary system requirements. It can be used in feasibility studies as well as in flight operational support. Pertinent operational constraints are available both implicitly and explicitly. However, the reader should be warned that because of program complexity, MAPSEP is only as good as the user and will quickly succumb to faulty user inputs.

Axial Surface Mapping of Wrinkle Ridges on Solis Planum, Mars from MOLA Topography: Constraints on Subsurface Blind Thrust Geometry

NASA Technical Reports Server (NTRS)

Vidal, A.; Mueller, K.; Golombek, M. P.

2003-01-01

We undertook axial surface mapping of selected wrinkle ridges on Solis Planum, Mars in order to assess the subsurface geometry of blind thrusts proposed to exist beneath them. This work builds on previous work that defined structural families of wrinkle ridges based on their surface morphology in this region. Although a growing consensus exists for models of wrinkle ridge kinematics and mechanics, a number of current problems remain. These include the origin of topographic offset across the edges of wrinkle ridges, the relationship between broad arches and superposed ridges, the origin of smaller wrinkles, and perhaps most importantly, the trajectory of blind thrusts that underlie wrinkle ridges and accommodate shortening at deeper crustal levels. We are particularly interested in defining the depths at which blind thrusts flatten under wrinkle ridges in order to provide constraints on the brittle-ductile transition during Early Hesperian time. We also seek to test whether wrinkle ridges on Solis Planum develop above reactivated faults or newly formed ones.

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.

Chaotic Dynamics in a Low-Energy Transfer Strategy to the Equilateral Equilibrium Points in the Earth-Moon System

NASA Astrophysics Data System (ADS)

Salazar, F. J. T.; Macau, E. E. N.; Winter, O. C.

In the frame of the equilateral equilibrium points exploration, numerous future space missions will require maximization of payload mass, simultaneously achieving reasonable transfer times. To fulfill this request, low-energy non-Keplerian orbits could be used to reach L4 and L5 in the Earth-Moon system instead of high energetic transfers. Previous studies have shown that chaos in physical systems like the restricted three-body Earth-Moon-particle problem can be used to direct a chaotic trajectory to a target that has been previously considered. In this work, we propose to transfer a spacecraft from a circular Earth Orbit in the chaotic region to the equilateral equilibrium points L4 and L5 in the Earth-Moon system, exploiting the chaotic region that connects the Earth with the Moon and changing the trajectory of the spacecraft (relative to the Earth) by using a gravity assist maneuver with the Moon. Choosing a sequence of small perturbations, the time of flight is reduced and the spacecraft is guided to a proper trajectory so that it uses the Moon's gravitational force to finally arrive at a desired target. In this study, the desired target will be an orbit about the Lagrangian equilibrium points L4 or L5. This strategy is not only more efficient with respect to thrust requirement, but also its time transfer is comparable to other known transfer techniques based on time optimization.

A model for helicopter guidance on spiral trajectories

NASA Technical Reports Server (NTRS)

Mendenhall, S.; Slater, G. L.

1980-01-01

A point mass model is developed for helicopter guidance on spiral trajectories. A fully coupled set of state equations is developed and perturbation equations suitable for 3-D and 4-D guidance are derived and shown to be amenable to conventional state variable feedback methods. Control variables are chosen to be the magnitude and orientation of the net rotor thrust. Using these variables reference controls for nonlevel accelerating trajectories are easily determined. The effects of constant wind are shown to require significant feedforward correction to some of the reference controls and to the time. Although not easily measured themselves, the controls variables chosen are shown to be easily related to the physical variables available in the cockpit.

Gravity-assist trajectories to Venus, Mars, and the ice giants: Mission design with human and robotic applications

NASA Astrophysics Data System (ADS)

Hughes, Kyle M.

Gravity-assist trajectories to Uranus and Neptune are found (with the allowance of impulsive maneuvers using chemical propulsion) for launch dates ranging from 2024 to 2038 for Uranus and 2020 to 2070 for Neptune. Solutions are found using a patched conic model with analytical ephemeris via the Satellite Tour Design Program (STOUR), originally developed at the Jet Propulsion Laboratory (JPL). Delivered payload mass is computed for all solutions for select launch vehicles, and attractive solutions are identified as those that deliver a specified amount of payload mass into orbit at the target body in minimum time. The best cases for each launch year are cataloged for orbiter missions to Uranus and Neptune. Solutions with sufficient delivered payload for a multi-planet mission (e.g. sending a probe to Saturn on the way to delivering an orbiter at Uranus) become available when the Space Launch System (SLS) launch vehicle is employed. A set of possible approach trajectories are modeled at the target planet to assess what (if any) adjustments are needed for ring avoidance, and to determine the probe entry conditions. Mars free-return trajectories are found with an emphasis on short flight times for application to near-term human flyby missions (similar to that of Inspiration Mars). Venus free-returns are also investigated and proposed as an alternative to a human Mars flyby mission. Attractive Earth-Mars free-return opportunities are identified that use an intermediate Venus flyby. One such opportunity, in 2021, has been adopted by the Inspiration Mars Foundation as a backup to the currently considered 2018 Mars free-return opportunity. Methods to establish spacecraft into Earth-Mars cycler trajectories are also investigated to reduce the propellant cost required to inject a 95-metric ton spacecraft into a cycler orbit. The establishment trajectories considered use either a V-infinity leveraging maneuver or low thrust. The V-infinity leveraging establishment trajectories are validated using patched conics via the STOUR program. Establishment trajectories that use low-thrust were investigated with particular focus on validating the patched-conic based solutions at instances where Earth encounter times are not negligible.

NASA/USRA advanced space design program: The laser powered interorbital vehicle

NASA Technical Reports Server (NTRS)

1989-01-01

A preliminary design is presented for a low-thrust Laser Powered Interorbital Vehicle (LPIV) intended for cargo transportation between an earth space station and a lunar base. The LPIV receives its power from two iodide laser stations, one orbiting the earth and the other located on the surface of the moon. The selected mission utilizes a spiral trajectory, characteristic of a low-thrust spacecraft, requiring 8 days for a lunar rendezvous and an additional 9 days for return. The ship's configuration consists primarily of an optical train, two hydrogen plasma engines, a 37.1 m box beam truss, a payload module, and fuel tanks. The total mass of the vehicle fully loaded is 63300 kg. A single plasma, regeneratively cooled engine design is incorporated into the two 500 N engines. These are connected to the spacecraft by turntables which allow the vehicle to thrust tangentially to the flight path. Proper collection and transmission of the laser beam to the thrust chambers is provided through the optical train. This system consists of the 23 m diameter primary mirror, a convex parabolic secondary mirror, a beam splitter and two concave parabolic tertiary mirrors. The payload bay is capable of carrying 18000 kg of cargo. The module is located opposite the primary mirror on the main truss. Fuel tanks carrying a maximum of 35000 kg of liquid hydrogen are fastened to tracks which allow the tanks to be moved perpendicular to the main truss. This capability is required to prevent the center of mass from moving out of the thrust vector line. The laser beam is located and tracked by means of an acquisition, pointing and tracking system which can be locked onto the space-based laser station. Correct orientation of the spacecraft with the laser beam is maintained by control moment gyros and reaction control rockets. Additionally an aerobrake configuration was designed to provide the option of using the atmospheric drag in place of propulsion for a return trajectory.

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.

Low Thrust Cis-Lunar Transfers Using a 40 kW-Class Solar Electric Propulsion Spacecraft

NASA Technical Reports Server (NTRS)

Mcguire, Melissa L.; Burke, Laura M.; Mccarty, Steven L.; Hack, Kurt J.; Whitley, Ryan J.; Davis, Diane C.; Ocampo, Cesar

2017-01-01

This paper captures trajectory analysis of a representative low thrust, high power Solar Electric Propulsion (SEP) vehicle to move a mass around cis-lunar space in the range of 20 to 40 kW power to the Electric Propulsion (EP) system. These cis-lunar transfers depart from a selected Near Rectilinear Halo Orbit (NRHO) and target other cis-lunar orbits. The NRHO cannot be characterized in the classical two-body dynamics more familiar in the human spaceflight community, and the use of low thrust orbit transfers provides unique analysis challenges. Among the target orbit destinations documented in this paper are transfers between a Southern and Northern NRHO, transfers between the NRHO and a Distant Retrograde Orbit (DRO) and a transfer between the NRHO and two different Earth Moon Lagrange Point 2 (EML2) Halo orbits. Because many different NRHOs and EML2 halo orbits exist, simplifying assumptions rely on previous analysis of orbits that meet current abort and communication requirements for human mission planning. Investigation is done into the sensitivities of these low thrust transfers to EP system power. Additionally, the impact of the Thrust to Weight ratio of these low thrust SEP systems and the ability to transit between these unique orbits are investigated.

Thrust generation by a heaving flexible foil: Resonance, nonlinearities, and optimality

NASA Astrophysics Data System (ADS)

Paraz, Florine; Schouveiler, Lionel; Eloy, Christophe

2016-01-01

Flexibility of marine animal fins has been thought to enhance swimming performance. However, despite numerous experimental and numerical studies on flapping flexible foils, there is still no clear understanding of the effect of flexibility and flapping amplitude on thrust generation and swimming efficiency. Here, to address this question, we combine experiments on a model system and a weakly nonlinear analysis. Experiments consist in immersing a flexible rectangular plate in a uniform flow and forcing this plate into a heaving motion at its leading edge. A complementary theoretical model is developed assuming a two-dimensional inviscid problem. In this model, nonlinear effects are taken into account by considering a transverse resistive drag. Under these hypotheses, a modal decomposition of the system motion allows us to predict the plate response amplitude and the generated thrust, as a function of the forcing amplitude and frequency. We show that this model can correctly predict the experimental data on plate kinematic response and thrust generation, as well as other data found in the literature. We also discuss the question of efficiency in the context of bio-inspired propulsion. Using the proposed model, we show that the optimal propeller for a given thrust and a given swimming speed is achieved when the actuating frequency is tuned to a resonance of the system, and when the optimal forcing amplitude scales as the square root of the required thrust.

Preliminary flight evaluation of an engine performance optimization algorithm

NASA Technical Reports Server (NTRS)

Lambert, H. H.; Gilyard, G. B.; Chisholm, J. D.; Kerr, L. J.

1991-01-01

A performance seeking control (PSC) algorithm has undergone initial flight test evaluation in subsonic operation of a PW 1128 engined F-15. This algorithm is designed to optimize the quasi-steady performance of an engine for three primary modes: (1) minimum fuel consumption; (2) minimum fan turbine inlet temperature (FTIT); and (3) maximum thrust. The flight test results have verified a thrust specific fuel consumption reduction of 1 pct., up to 100 R decreases in FTIT, and increases of as much as 12 pct. in maximum thrust. PSC technology promises to be of value in next generation tactical and transport aircraft.

An Analytic Approximation to Very High Specific Impulse and Specific Power Interplanetary Space Mission Analysis

NASA Technical Reports Server (NTRS)

Williams, Craig Hamilton

1995-01-01

A simple, analytic approximation is derived to calculate trip time and performance for propulsion systems of very high specific impulse (50,000 to 200,000 seconds) and very high specific power (10 to 1000 kW/kg) for human interplanetary space missions. The approach assumed field-free space, constant thrust/constant specific power, and near straight line (radial) trajectories between the planets. Closed form, one dimensional equations of motion for two-burn rendezvous and four-burn round trip missions are derived as a function of specific impulse, specific power, and propellant mass ratio. The equations are coupled to an optimizing parameter that maximizes performance and minimizes trip time. Data generated for hypothetical one-way and round trip human missions to Jupiter were found to be within 1% and 6% accuracy of integrated solutions respectively, verifying that for these systems, credible analysis does not require computationally intensive numerical techniques.

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.

Reentry trajectory optimization based on a multistage pseudospectral method.

PubMed

Zhao, Jiang; Zhou, Rui; Jin, Xuelian

2014-01-01

Of the many direct numerical methods, the pseudospectral method serves as an effective tool to solve the reentry trajectory optimization for hypersonic vehicles. However, the traditional pseudospectral method is time-consuming due to large number of discretization points. For the purpose of autonomous and adaptive reentry guidance, the research herein presents a multistage trajectory control strategy based on the pseudospectral method, capable of dealing with the unexpected situations in reentry flight. The strategy typically includes two subproblems: the trajectory estimation and trajectory refining. In each processing stage, the proposed method generates a specified range of trajectory with the transition of the flight state. The full glide trajectory consists of several optimal trajectory sequences. The newly focused geographic constraints in actual flight are discussed thereafter. Numerical examples of free-space flight, target transition flight, and threat avoidance flight are used to show the feasible application of multistage pseudospectral method in reentry trajectory optimization.

Reentry Trajectory Optimization Based on a Multistage Pseudospectral Method

PubMed Central

Zhou, Rui; Jin, Xuelian

2014-01-01

Of the many direct numerical methods, the pseudospectral method serves as an effective tool to solve the reentry trajectory optimization for hypersonic vehicles. However, the traditional pseudospectral method is time-consuming due to large number of discretization points. For the purpose of autonomous and adaptive reentry guidance, the research herein presents a multistage trajectory control strategy based on the pseudospectral method, capable of dealing with the unexpected situations in reentry flight. The strategy typically includes two subproblems: the trajectory estimation and trajectory refining. In each processing stage, the proposed method generates a specified range of trajectory with the transition of the flight state. The full glide trajectory consists of several optimal trajectory sequences. The newly focused geographic constraints in actual flight are discussed thereafter. Numerical examples of free-space flight, target transition flight, and threat avoidance flight are used to show the feasible application of multistage pseudospectral method in reentry trajectory optimization. PMID:24574929

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.

A Quick Method for Estimating Vehicle Characteristics Appropriate for Continuous Thrust Round Trip Missions Within the Solar System

NASA Technical Reports Server (NTRS)

Emrich, Bill

2006-01-01

A simple method of estimating vehicle parameters appropriate for interplanetary travel can provide a useful tool for evaluating the suitability of particular propulsion systems to various space missions. Although detailed mission analyses for interplanetary travel can be quite complex, it is possible to derive hirly simple correlations which will provide reasonable trip time estimates to the planets. In the present work, it is assumed that a constant thrust propulsion system propels a spacecraft on a round trip mission having equidistant outbound and inbound legs in which the spacecraft accelerates during the first portion of each leg of the journey and decelerates during the last portion of each leg of the journey. Comparisons are made with numerical calculations from low thrust trajectory codes to estimate the range of applicability of the simplified correlations.

Space Trajectory Error Analysis Program (STEAP) for halo orbit missions. Volume 1: Analytic and user's manual

NASA Technical Reports Server (NTRS)

Byrnes, D. V.; Carney, P. C.; Underwood, J. W.; Vogt, E. D.

1974-01-01

Development, test, conversion, and documentation of computer software for the mission analysis of missions to halo orbits about libration points in the earth-sun system is reported. The software consisting of two programs called NOMNAL and ERRAN is part of the Space Trajectories Error Analysis Programs (STEAP). The program NOMNAL targets a transfer trajectory from Earth on a given launch date to a specified halo orbit on a required arrival date. Either impulsive or finite thrust insertion maneuvers into halo orbit are permitted by the program. The transfer trajectory is consistent with a realistic launch profile input by the user. The second program ERRAN conducts error analyses of the targeted transfer trajectory. Measurements including range, doppler, star-planet angles, and apparent planet diameter are processed in a Kalman-Schmidt filter to determine the trajectory knowledge uncertainty. Execution errors at injection, midcourse correction and orbit insertion maneuvers are analyzed along with the navigation uncertainty to determine trajectory control uncertainties and fuel-sizing requirements. The program is also capable of generalized covariance analyses.

Lessons for Interstellar Travel from the G&C Design of the NEA Scout Solar Sail Mission

NASA Technical Reports Server (NTRS)

Heaton, Andrew; Diedrich, Benjamin

2017-01-01

NASA is developing the Near Earth Asteroid (NEA) Scout mission that will use a solar sail to travel to an asteroid where it will perform a slow flyby to acquire science imagery. A guidance and control system was developed to meet the science and trajectory requirements. The NEA Scout design process can be applied to an interstellar or precursor mission that uses a beam-propelled sail. The scientific objectives are met by accurately targeting the destination trajectory position and velocity. The destination is targeted by understanding the force on the sail from the beam (or sunlight in the case of NEA Scout) over the duration of the thrust maneuver. The propulsive maneuver is maintained by accurate understanding of the torque on the sail, which is a function of sail shape, optical properties, and mass properties, all of which apply to NEA Scout and beam propelled sails. NEA Scout uses active control of the sail attitude while trimming the solar torque, which could be used on a beamed propulsion sail if necessary. The biggest difference is that NEA Scout can correct for uncertainties in sail thrust modeling, spacecraft orbit, and target orbit throughout the flight to the target, while beamed propulsion needs accurate operation for the short duration of the beamed propulsion maneuver, making accurate understanding of the sail thrust and orbits much more critical.

Lessons for Interstellar Travel from the Guidance and Control Design of the Near Earth Asteroid Scout Solar Sail Mission

NASA Technical Reports Server (NTRS)

Diedrich, Benjamin; Heaton, Andrew

2017-01-01

NASA is developing the Near Earth Asteroid (NEA) Scout mission that will use a solar sail to travel to an asteroid where it will perform a slow flyby to acquire science imagery. A guidance and control system was developed to meet the science and trajectory requirements. The NEA Scout design process can be applied to an interstellar or precursor mission that uses a beam propelled sail. The scientific objectives are met by accurately targeting the destination trajectory position and velocity. The destination is targeted by understanding the force on the sail from the beam (or sunlight in the case of NEA Scout) over the duration of the thrust maneuver. The propulsive maneuver is maintained by accurate understanding of the torque on the sail, which is a function of sail shape, optical properties, and mass properties, all of which apply to NEA Scout and beam propelled sails. NEA Scout uses active control of the sail attitude while trimming the solar torque, which could be used on a beamed propulsion sail if necessary. The biggest difference is that NEA Scout can correct for uncertainties in sail thrust modeling, spacecraft orbit, and target orbit throughout the flight to the target, while beamed propulsion needs accurate operation for the short duration of the beamed propulsion maneuver, making accurate understanding of the sail thrust and orbits much more critical.

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.

Attitude Control for an Aero-Vehicle Using Vector Thrusting and Variable Speed Control Moment Gyros

NASA Technical Reports Server (NTRS)

Shin, Jong-Yeob; Lim, K. B.; Moerder, D. D.

2005-01-01

Stabilization of passively unstable thrust-levitated vehicles can require significant control inputs. Although thrust vectoring is a straightforward choice for realizing these inputs, this may lead to difficulties discussed in the paper. This paper examines supplementing thrust vectoring with Variable-Speed Control Moment Gyroscopes (VSCMGs). The paper describes how to allocate VSCMGs and the vectored thrust mechanism for attitude stabilization in frequency domain and also shows trade-off between vectored thrust and VSCMGs. Using an H2 control synthesis methodology in LMI optimization, a feedback control law is designed for a thrust-levitated research vehicle and is simulated with the full nonlinear model. It is demonstrated that VSCMGs can reduce the use of vectored thrust variation for stabilizing the hovering platform in the presence of strong wind gusts.

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 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.

Mass breakdown model of solar-photon sail shuttle: The case for Mars

NASA Astrophysics Data System (ADS)

Vulpetti, Giovanni; Circi, Christian

2016-02-01

The main aim of this paper is to set up a many-parameter model of mass breakdown to be applied to a reusable Earth-Mars-Earth solar-photon sail shuttle, and analyze the system behavior in two sub-problems: (1) the zero-payload shuttle, and (2) given the sailcraft sail loading and the gross payload mass, find the sail area of the shuttle. The solution to the subproblem-1 is of technological and programmatic importance. The general analysis of subproblem-2 is presented as a function of the sail side length, system mass, sail loading and thickness. In addition to the behaviors of the main system masses, useful information for future work on the sailcraft trajectory optimization is obtained via (a) a detailed mass model for the descent/ascent Martian Excursion Module, and (b) the fifty-fifty solution to the sailcraft sail loading breakdown equation. Of considerable importance is the evaluation of the minimum altitude for the rendezvous between the ascent rocket vehicle and the solar-photon sail propulsion module, a task performed via the Mars Climate Database 2014-2015. The analysis shows that such altitude is 300 km; below it, the atmospheric drag prevails over the solar-radiation thrust. By this value, an example of excursion module of 1500 kg in total mass is built, and the sailcraft sail loading and the return payload are calculated. Finally, the concept of launch opportunity-wide for a shuttle driven by solar-photon sail is introduced. The previous fifty-fifty solution may be a good initial guess for the trajectory optimization of this type of shuttle.

Fuel optimal maneuvers of spacecraft about a circular orbit

NASA Technical Reports Server (NTRS)

Carter, T. E.

1982-01-01

Fuel optimal maneuvers of spacecraft relative to a body in circular orbit are investigated using a point mass model in which the magnitude of the thrust vector is bounded. All nonsingular optimal maneuvers consist of intervals of full thrust and coast and are found to contain at most seven such intervals in one period. Only four boundary conditions where singular solutions occur are possible. Computer simulation of optimal flight path shapes and switching functions are found for various boundary conditions. Emphasis is placed on the problem of soft rendezvous with a body in circular orbit.

Trajectory Design for the Lunar Polar Hydrogen Mapper Mission

NASA Technical Reports Server (NTRS)

Genova, Anthony L.; Dunham, David W.

2017-01-01

The presented trajectory was designed for the Lunar Polar Hydrogen Mapper (LunaH-Map) 6U CubeSat, which was awarded a ride on NASAs Space Launch System (SLS) with Exploration Mission 1 (EM-1) via NASAs 2015 SIMPLEX proposal call. After deployment from EM-1s upper stage (which is planned to enter heliocentric space via a lunar flyby), the LunaH-Map CubeSat will alter its trajectory via its low-thrust ion engine to target a lunar flyby that yields a Sun-Earth-Moon weak stability boundary transfer to set up a ballistic lunar capture. Finally, the orbit energy is lowered to reach the required quasi-frozen science orbit with periselene above the lunar south pole.

Performance seeking control: Program overview and future directions

NASA Technical Reports Server (NTRS)

Gilyard, Glenn B.; Orme, John S.

1993-01-01

A flight test evaluation of the performance-seeking control (PSC) algorithm on the NASA F-15 highly integrated digital electronic control research aircraft was conducted for single-engine operation at subsonic and supersonic speeds. The model-based PSC system was developed with three optimization modes: minimum fuel flow at constant thrust, minimum turbine temperature at constant thrust, and maximum thrust at maximum dry and full afterburner throttle settings. Subsonic and supersonic flight testing were conducted at the NASA Dryden Flight Research Facility covering the three PSC optimization modes and over the full throttle range. Flight results show substantial benefits. In the maximum thrust mode, thrust increased up to 15 percent at subsonic and 10 percent at supersonic flight conditions. The minimum fan turbine inlet temperature mode reduced temperatures by more than 100 F at high altitudes. The minimum fuel flow mode results decreased fuel consumption up to 2 percent in the subsonic regime and almost 10 percent supersonically. These results demonstrate that PSC technology can benefit the next generation of fighter or transport aircraft. NASA Dryden is developing an adaptive aircraft performance technology system that is measurement based and uses feedback to ensure optimality. This program will address the technical weaknesses identified in the PSC program and will increase performance gains.

Optimal orbit transfer suitable for large flexible structures

NASA Technical Reports Server (NTRS)

Chatterjee, Alok K.

1989-01-01

The problem of continuous low-thrust planar orbit transfer of large flexible structures is formulated as an optimal control problem with terminal state constraints. The dynamics of the spacecraft motion are treated as a point-mass central force field problem; the thrust-acceleration magnitude is treated as an additional state variable; and the rate of change of thrust-acceleration is treated as a control variable. To ensure smooth transfer, essential for flexible structures, an additional quadratic term is appended to the time cost functional. This term penalizes any abrupt change in acceleration. Numerical results are presented for the special case of a planar transfer.

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

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.

Modeling, Simulation, and Control of a Solar Electric Propulsion Vehicle in Near-Earth Vicinity Including Solar Array Degradation

NASA Technical Reports Server (NTRS)

Witzberger, Kevin (Inventor); Hojnicki, Jeffery (Inventor); Manzella, David (Inventor)

2016-01-01

Modeling and control software that integrates the complexities of solar array models, a space environment, and an electric propulsion system into a rigid body vehicle simulation and control model is provided. A rigid body vehicle simulation of a solar electric propulsion (SEP) vehicle may be created using at least one solar array model, at least one model of a space environment, and at least one model of a SEP propulsion system. Power availability and thrust profiles may be determined based on the rigid body vehicle simulation as the SEP vehicle transitions from a low Earth orbit (LEO) to a higher orbit or trajectory. The power availability and thrust profiles may be displayed such that a user can use the displayed power availability and thrust profiles to determine design parameters for an SEP vehicle mission.

Evaluation and modeling of autonomous attitude thrust control for the Geostation Operational Environmental Satellite (GOES)-8 orbit determination

NASA Technical Reports Server (NTRS)

Forcey, W.; Minnie, C. R.; Defazio, R. L.

1995-01-01

The Geostationary Operational Environmental Satellite (GOES)-8 experienced a series of orbital perturbations from autonomous attitude control thrusting before perigee raising maneuvers. These perturbations influenced differential correction orbital state solutions determined by the Goddard Space Flight Center (GSFC) Goddard Trajectory Determination System (GTDS). The maneuvers induced significant variations in the converged state vector for solutions using increasingly longer tracking data spans. These solutions were used for planning perigee maneuvers as well as initial estimates for orbit solutions used to evaluate the effectiveness of the perigee raising maneuvers. This paper discusses models for the incorporation of attitude thrust effects into the orbit determination process. Results from definitive attitude solutions are modeled as impulsive thrusts in orbit determination solutions created for GOES-8 mission support. Due to the attitude orientation of GOES-8, analysis results are presented that attempt to absorb the effects of attitude thrusting by including a solution for the coefficient of reflectivity, C(R). Models to represent the attitude maneuvers are tested against orbit determination solutions generated during real-time support of the GOES-8 mission. The modeling techniques discussed in this investigation offer benefits to the remaining missions in the GOES NEXT series. Similar missions with large autonomous attitude control thrusting, such as the Solar and Heliospheric Observatory (SOHO) spacecraft and the INTELSAT series, may also benefit from these results.

Optimization of self-acting step thrust bearings for load capacity and stiffness.

NASA Technical Reports Server (NTRS)

Hamrock, B. J.

1972-01-01

Linearized analysis of a finite-width rectangular step thrust bearing. Dimensionless load capacity and stiffness are expressed in terms of a Fourier cosine series. The dimensionless load capacity and stiffness were found to be a function of the dimensionless bearing number, the pad length-to-width ratio, the film thickness ratio, the step location parameter, and the feed groove parameter. The equations obtained in the analysis were verified. The assumptions imposed were substantiated by comparing the results with an existing exact solution for the infinite width bearing. A digital computer program was developed which determines optimal bearing configuration for maximum load capacity or stiffness. Simple design curves are presented. Results are shown for both compressible and incompressible lubrication. Through a parameter transformation the results are directly usable in designing optimal step sector thrust bearings.

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.

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.

Two-Dimensional Motions of Rockets

ERIC Educational Resources Information Center

Kang, Yoonhwan; Bae, Saebyok

2007-01-01

We analyse the two-dimensional motions of the rockets for various types of rocket thrusts, the air friction and the gravitation by using a suitable representation of the rocket equation and the numerical calculation. The slope shapes of the rocket trajectories are discussed for the three types of rocket engines. Unlike the projectile motions, the…

Program documentation. Program description and user information for the hydraulics/auxiliary power unit (HYDRA) computer program. [for the space shuttle orbiter

NASA Technical Reports Server (NTRS)

Redwine, W. J.

1979-01-01

A timeline containing altitude, control surface deflection rates and angles, hinge moment loads, thrust vector control gimbal rates, and main throttle settings is used to derive the model. The timeline is constructed from the output of one or more trajectory simulation programs.

Maximum thrust mode evaluation

NASA Technical Reports Server (NTRS)

Orme, John S.; Nobbs, Steven G.

1995-01-01

Measured reductions in acceleration times which resulted from the application of the F-15 performance seeking control (PSC) maximum thrust mode during the dual-engine test phase is presented as a function of power setting and flight condition. Data were collected at altitudes of 30,000 and 45,000 feet at military and maximum afterburning power settings. The time savings for the supersonic acceleration is less than at subsonic Mach numbers because of the increased modeling and control complexity. In addition, the propulsion system was designed to be optimized at the mid supersonic Mach number range. Recall that even though the engine is at maximum afterburner, PSC does not trim the afterburner for the maximum thrust mode. Subsonically at military power, time to accelerate from Mach 0.6 to 0.95 was cut by between 6 and 8 percent with a single engine application of PSC, and over 14 percent when both engines were optimized. At maximum afterburner, the level of thrust increases were similar in magnitude to the military power results, but because of higher thrust levels at maximum afterburner and higher aircraft drag at supersonic Mach numbers the percentage thrust increase and time to accelerate was less than for the supersonic accelerations. Savings in time to accelerate supersonically at maximum afterburner ranged from 4 to 7 percent. In general, the maximum thrust mode has performed well, demonstrating significant thrust increases at military and maximum afterburner power. Increases of up to 15 percent at typical combat-type flight conditions were identified. Thrust increases of this magnitude could be useful in a combat situation.

Orbit Transfer Vehicle Engine Study. Phase A, extension 1: Advanced expander cycle engine optimization

NASA Technical Reports Server (NTRS)

Mellish, J. A.

1979-01-01

The performance optimization of expander cycle engines at vacuum thrust levels of 10K, 15K, and 20K lb is discussed. The optimization is conducted for a maximum engine length with an extendible nozzle in the retracted position of 60 inches and an engine mixture ratio of 6.0:1. The thrust chamber geometry and cycle analyses are documented. In addition, the sensitivity of a recommended baseline expander cycle to component performance variations is determined and chilldown/start propellant consumptions are estimated.

Orbit transfer vehicle engine study, phase A, extension 1: Volume 2: Study results

NASA Technical Reports Server (NTRS)

Mellish, J. A.

1981-01-01

Because of the advantage of the Advanced Expander Cycle Engine brought out in initial studies, further design optimization and comparative analyses were undertaken. The major results and conclusion derived are summarized. The primary areas covered are (1) thrust chamber geometry optimization, (2) expander cycle optimization, (3) alternate low thrust capability, (4) safety and reliability, (5) development risk comparison, and (6) cost comparisons. All of the results obtained were used to baseline the initial design concept for the OTV Advanced Expander Cycle Engine Point Design Study.

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.

Inflight thermodynamic properties

NASA Technical Reports Server (NTRS)

Brown, S. C.; Daniels, G. E.; Johnson, D. L.; Smith, O. E.

1973-01-01

The inflight thermodynamic parameters (temperature, pressure, and density) of the atmosphere are presented. Mean and extreme values of the thermodynamic parameters given here can be used in application of many aerospace problems, such as: (1) research and planning and engineering design of remote earth sensing systems; (2) vehicle design and development; and (3) vehicle trajectory analysis, dealing with vehicle thrust, dynamic pressure, aerodynamic drag, aerodynamic heating, vibration, structural and guidance limitations, and reentry analysis. Atmospheric density plays a very important role in most of the above problems. A subsection on reentry is presented, giving atmospheric models to be used for reentry heating, trajectory, etc., analysis.

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.

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.

A zonal computational procedure adapted to the optimization of two-dimensional thrust augmentor inlets

NASA Technical Reports Server (NTRS)

Lund, T. S.; Tavella, D. A.; Roberts, L.

1985-01-01

A viscous-inviscid interaction methodology based on a zonal description of the flowfield is developed as a mean of predicting the performance of two-dimensional thrust augmenting ejectors. An inviscid zone comprising the irrotational flow about the device is patched together with a viscous zone containing the turbulent mixing flow. The inviscid region is computed by a higher order panel method, while an integral method is used for the description of the viscous part. A non-linear, constrained optimization study is undertaken for the design of the inlet region. In this study, the viscous-inviscid analysis is complemented with a boundary layer calculation to account for flow separation from the walls of the inlet region. The thrust-based Reynolds number as well as the free stream velocity are shown to be important parameters in the design of a thrust augmentor inlet.

Theory and computation of optimal low- and medium-thrust transfers

NASA Technical Reports Server (NTRS)

Chuang, C.-H.

1994-01-01

This report presents two numerical methods considered for the computation of fuel-optimal, low-thrust orbit transfers in large numbers of burns. The origins of these methods are observations made with the extremal solutions of transfers in small numbers of burns; there seems to exist a trend such that the longer the time allowed to perform an optimal transfer the less fuel that is used. These longer transfers are obviously of interest since they require a motor of low thrust; however, we also find a trend that the longer the time allowed to perform the optimal transfer the more burns are required to satisfy optimality. Unfortunately, this usually increases the difficulty of computation. Both of the methods described use small-numbered burn solutions to determine solutions in large numbers of burns. One method is a homotopy method that corrects for problems that arise when a solution requires a new burn or coast arc for optimality. The other method is to simply patch together long transfers from smaller ones. An orbit correction problem is solved to develop this method. This method may also lead to a good guidance law for transfer orbits with long transfer times.

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.

Work Optimization Predicts Accretionary Faulting: An Integration of Physical and Numerical Experiments

NASA Astrophysics Data System (ADS)

McBeck, Jessica A.; Cooke, Michele L.; Herbert, Justin W.; Maillot, Bertrand; Souloumiac, Pauline

2017-09-01

We employ work optimization to predict the geometry of frontal thrusts at two stages of an evolving physical accretion experiment. Faults that produce the largest gains in efficiency, or change in external work per new fault area, ΔWext/ΔA, are considered most likely to develop. The predicted thrust geometry matches within 1 mm of the observed position and within a few degrees of the observed fault dip, for both the first forethrust and backthrust when the observed forethrust is active. The positions of the second backthrust and forethrust that produce >90% of the maximum ΔWext/ΔA also overlap the observed thrusts. The work optimal fault dips are within a few degrees of the fault dips that maximize the average Coulomb stress. Slip gradients along the detachment produce local elevated shear stresses and high strain energy density regions that promote thrust initiation near the detachment. The mechanical efficiency (Wext) of the system decreases at each of the two simulated stages of faulting and resembles the evolution of experimental force. The higher ΔWext/ΔA due to the development of the first pair relative to the second pair indicates that the development of new thrusts may lead to diminishing efficiency gains as the wedge evolves. The numerical estimates of work consumed by fault propagation overlap the range calculated from experimental force data and crustal faults. The integration of numerical and physical experiments provides a powerful approach that demonstrates the utility of work optimization to predict the development of faults.

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.

Ultrasail

NASA Technical Reports Server (NTRS)

Burton, R.; Benavides, G.; Coverston, V.; Hartmann, W.; Hargens, J.; Westerhoff, J.; Jones, Jonathan (Technical Monitor)

2003-01-01

Ultrasail is a complete sail system for the launch, deployment, stabilization and control of very large solar sails enabling reduced mission times for interplanetary and deep space spacecraft. Ultrasail is an innovative, non-traditional approach to propulsion technology achieved by combining propulsion and control systems developed for formation-flying microsatellites with an innovative solar sail architecture to achieve sq km-class controllable sail areas, sail subsystem area densities of 1 gm per sq m, and thrust levels equivalent to 400 kW ion thruster systems used for comparable deep space missions. Ultrasail can conceivably even achieve outer planetary rendezvous, a deep space capability now reserved for high-mass nuclear and chemical systems. Ultrasail is a Delta IV-launched multi-blade spin-stabilized system with blade lengths as long as 50 km, reminiscent of the MacNeal Heliogyro. The primary innovation is the near-elimination of sail supporting structures by attaching the sail tip to a rigid formation-flying microsatellite truss which deploys the sail blade, and which then articulates the blade to provide attitude control, including spin stabilization and precession of the spin axis. These tip microsatellites are controlled by a solar-powered 3-axis microthruster system (electric or cold gas) to maintain proper sail film tension during deployment and spin-up. The satellite mass also provides a stabilizing centrifugal force on the blade while in rotation. Understanding the dynamics of individual blades is key to the overall dynamics of Ultrasail. Forces and torques that must be modeled include those due to solar pressure, those generated by the microsatellite at the blade tip and by torques applied at the blade root. Centrifugal forces also play a significant role in the deployment and maintenance of the sail configuration. To capture the dynamics of the overall system, the equations of motion for the blades have been derived. Using these differential equations, a control law will be derived to maneuver Ultrasail. This law involves the pitching of the individual blades thereby moving the distribution of the radiation pressure on each individual blade and inducing a resultant torque on the system. The direction of the angular momentum vector and its rate of precession can be controlled through the pitch angle of the blades. The Ultrasail trajectory is also being studied. Optimal or near-optimal trajectories are being generated to showcase Ultrasail performance. Various missions, e.g. outer planet and solar polar missions for observation of the Sun, are currently being investigated to demonstrate the performance enhancements generated by Ultrasail technology. Calculus-of-variations-based optimization software is used to produce optimal Ultrasail trajectories. The performance of these trajectories is being compared to optimal results generated with other propulsion models, including chemical propulsion, ion propulsion, and competing solar sail concepts. Results of these studies will quantify the performance of Ultrasail compared to existing solar sail concepts for high energy missions.

Thrust Production and Wake Structure of a Batoid-Inspired Oscillating Fin

NASA Astrophysics Data System (ADS)

Clark, Richard

2005-11-01

Experiments are reported on the hydrodynamic performance of a flexible fin. The fin replicates some features of the pectoral fin of a batoid fish (such as a ray or skate) in that it is actuated in a traveling wave motion, with the amplitude of the motion increasing linearly along the span from root to tip. Thrust is found to increase with non-dimensional frequency, and an optimal oscillatory gait is identified. Power consumption measurements lead to the computation of Froude efficiency, and an optimal efficiency condition is evaluated. Wake visualizations are presented, and a vortex model of the wake near zero net thrust is suggested. Strouhal number effects on the wake topology are also illustrated.

Thrust production and wake structure of a batoid-inspired oscillating fin

NASA Astrophysics Data System (ADS)

Clark, R. P.; Smits, A. J.

2006-09-01

Experiments are reported on the hydrodynamic performance of a flexible fin. The fin replicates some features of the pectoral fin of a batoid fish (such as a ray or skate) in that it is actuated in a travelling wave motion, with the amplitude of the motion increasing linearly along the span from root to tip. Thrust is found to increase with non-dimensional frequency, and an optimal oscillatory gait is identified. Power consumption measurements lead to the computation of propulsive efficiency, and an optimal efficiency condition is evaluated. Wake visualizations are presented, and a vortex model of the wake near zero net thrust is suggested. Strouhal number effects on the wake topology are also illustrated.

Flowfield analysis of modern helicopter rotors in hover by Navier-Stokes method

NASA Technical Reports Server (NTRS)

Srinivasan, G. R.; Raghavan, V.; Duque, E. P. N.

1991-01-01

The viscous, three-dimensional, flowfields of UH60 and BERP rotors are calculated for lifting hover configurations using a Navier-Stokes computational fluid dynamics method with a view to understand the importance of planform effects on the airloads. In this method, the induced effects of the wake, including the interaction of tip vortices with successive blades, are captured as a part of the overall flowfield solution without prescribing any wake models. Numerical results in the form of surface pressures, hover performance parameters, surface skin friction and tip vortex patterns, and vortex wake trajectory are presented at two thrust conditions for UH60 and BERP rotors. Comparison of results for the UH60 model rotor show good agreement with experiments at moderate thrust conditions. Comparison of results with equivalent rectangular UH60 blade and BERP blade indicates that the BERP blade, with an unconventional planform, gives more thrust at the cost of more power and a reduced figure of merit. The high thrust conditions considered produce severe shock-induced flow separation for UH60 blade, while the BERP blade develops more thrust and minimal separation. The BERP blade produces a tighter tip vortex structure compared with the UH60 blade. These results and the discussion presented bring out the similarities and differences between the two rotors.

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.

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.

Trajectory Control of Rendezvous with Maneuver Target Spacecraft

NASA Technical Reports Server (NTRS)

Zhou, Zhinqiang

2012-01-01

In this paper, a nonlinear trajectory control algorithm of rendezvous with maneuvering target spacecraft is presented. The disturbance forces on the chaser and target spacecraft and the thrust forces on the chaser spacecraft are considered in the analysis. The control algorithm developed in this paper uses the relative distance and relative velocity between the target and chaser spacecraft as the inputs. A general formula of reference relative trajectory of the chaser spacecraft to the target spacecraft is developed and applied to four different proximity maneuvers, which are in-track circling, cross-track circling, in-track spiral rendezvous and cross-track spiral rendezvous. The closed-loop differential equations of the proximity relative motion with the control algorithm are derived. It is proven in the paper that the tracking errors between the commanded relative trajectory and the actual relative trajectory are bounded within a constant region determined by the control gains. The prediction of the tracking errors is obtained. Design examples are provided to show the implementation of the control algorithm. The simulation results show that the actual relative trajectory tracks the commanded relative trajectory tightly. The predicted tracking errors match those calculated in the simulation results. The control algorithm developed in this paper can also be applied to interception of maneuver target spacecraft and relative trajectory control of spacecraft formation flying.

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.

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.

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.

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.

Geological mapping of the Schuppen belt of north-east India using geospatial technology

NASA Astrophysics Data System (ADS)

Ghosh, Tanaya; Basu, Surajit; Hazra, Sugata

2014-01-01

A revised geologic map of the Schuppen belt of northeast India has been prepared based on interpretation of digitally enhanced satellite images. The satellite image interpretation is supported by limited field work and existing geologic maps. Available geological maps of this fold thrust belt are discontinuous and multi-scaled. The authors are of multiple opinions regarding the trajectory of formation boundaries and fault contacts. Digital image processing of satellite images and limited field surveys have been used to reinterpret and modify the existing geological maps of this fold thrust belt. Optical data of Landsat Thematic Mapper, Enhanced Thematic Mapper and elevation data of ASTER have been used to prepare this revised geological map. The study area extends from Hajadisa in south to Digboi oilfield in north, bounded by Naga thrust in the west and Disang thrust in the east. PCA, Image fusion, Linear Contrast stretch, Histogram Equalization and Painted relief algorithms have been used for the delineation of major geological lineaments like lithological boundary, thrust and strike slip faults. Digital elevation maps have enabled in the discrimination between thrust contacts and lithological boundaries, with the former being located mostly in the valleys. Textural enhancements of PCA, colour composites and Painted relief algorithm have been used to discriminate between different rock types. Few geological concepts about the terrain have been revisited and modified. It is assumed that this revised map should be of practical use as this terrain promises unexploited hydrocarbon reserves.

Low thrust vehicle concept study

NASA Technical Reports Server (NTRS)

1980-01-01

Low thrust chemical (hydrogen-oxygen) propulsion systems configured specifically for low acceleration orbit transfer of large space systems were defined. Results indicate that it is cost effective and least risk to combine the OTV and stowed spacecraft in a single 65 K Shuttle. The study shows that the engine for an optimized low thrust stage (1) does not require very low thrust; (2) 1-3 K thrust range appears optimum; (3) thrust transient is not a concern; (4) throttling probably not worthwhile; and (5) multiple thrusters complicate OTV/LSS design and aggravate LSS loads. Regarding the optimum vehicle for low acceleration missions, the single shuttle launch (LSS and expendable OTV) is most cost effective and least risky. Multiple shuttles increase diameter 20%. The space based radar structure short OTV (which maximizes space available for packaged LSS) favors use of torus tank. Propellant tank pressures/vapor residuals are little affected by engine thrust level or number of burns.

Structural optimization of the Halbach array PM rim thrust motor

NASA Astrophysics Data System (ADS)

Cao, Haichuan; Chen, Weihu

2018-05-01

The Rim-driven Thruster (RDT) integrates the thrust motor and the propeller, which can effectively reduce the space occupied by the propulsion system, improve the propulsion efficiency, and thus has important research value and broad market prospects. The Halbach Permanent Magnet Rim Thrust Motor (HPMRTM) can improve the torque density of the propulsion motor by utilizing the unilateral magnetic field of the Halbach array. In this paper, the numerical method is used to study the electromagnetic performance of the motor under different Halbach array parameters. The relationship between motor parameters such as air-gap flux density, electromagnetic torque and Halbach array parameters is obtained, and then the motor structure is optimized. By comparing with Common Permanent Magnet RTM, the advantages of HPMRTM are verified.

Optimal low thrust geocentric transfer. [mission analysis computer program

NASA Technical Reports Server (NTRS)

Edelbaum, T. N.; Sackett, L. L.; Malchow, H. L.

1973-01-01

A computer code which will rapidly calculate time-optimal low thrust transfers is being developed as a mission analysis tool. The final program will apply to NEP or SEP missions and will include a variety of environmental effects. The current program assumes constant acceleration. The oblateness effect and shadowing may be included. Detailed state and costate equations are given for the thrust effect, oblateness effect, and shadowing. A simple but adequate model yields analytical formulas for power degradation due to the Van Allen radiation belts for SEP missions. The program avoids the classical singularities by the use of equinoctial orbital elements. Kryloff-Bogoliuboff averaging is used to facilitate rapid calculation. Results for selected cases using the current program are given.

Thrust production and wake structure of a batoid-inspired oscillating fin

PubMed Central

CLARK, R. P.; SMITS, A. J.

2009-01-01

Experiments are reported on the hydrodynamic performance of a flexible fin. The fin replicates some features of the pectoral fin of a batoid fish (such as a ray or skate) in that it is actuated in a travelling wave motion, with the amplitude of the motion increasing linearly along the span from root to tip. Thrust is found to increase with non-dimensional frequency, and an optimal oscillatory gait is identified. Power consumption measurements lead to the computation of propulsive efficiency, and an optimal efficiency condition is evaluated. Wake visualizations are presented, and a vortex model of the wake near zero net thrust is suggested. Strouhal number effects on the wake topology are also illustrated. PMID:19746188

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.

Nozzle design study for a quasi-axisymmetric scramjet-powered vehicle at Mach 7.9 flight conditions

NASA Astrophysics Data System (ADS)

Tanimizu, Katsuyoshi; Mee, David J.; Stalker, Raymond J.; Jacobs, Peter A.

2013-09-01

A nozzle shape optimization study for a quasi-axisymmetric scramjet has been performed for a Mach 7.9 operating condition with hydrogen fuel, aiming at the application of a hypersonic airbreathing vehicle. In this study, the nozzle geometry which is parameterized by a set of design variables, is optimized for the single objective of maximum net thrust using an in-house CFD solver for inviscid flowfields with a simple force prediction methodology. The combustion is modelled using a simple chemical reaction code. The effects of the nozzle design on the overall vehicle performance are discussed. For the present geometry, net thrust is achieved for the optimized vehicle design. The results of the nozzle-optimization study show that performance is limited by the nozzle area ratio that can be incorporated into the vehicle without leading to too large a base diameter of the vehicle and increasing the external drag of the vehicle. This study indicates that it is very difficult to achieve positive thrust at Mach 7.9 using the basic geometry investigated.

Trajectory Design for a Cislunar Cubesat Leveraging Dynamical Systems Techniques: The Lunar Icecube Mission

NASA Technical Reports Server (NTRS)

Bosanac, Natasha; Cox, Andrew; Howell, Kathleen C.; Folta, David C.

2017-01-01

Lunar IceCube is a 6U CubeSat that is designed to detect and observe lunar volatiles from a highly inclined orbit. This spacecraft, equipped with a low-thrust engine, will be deployed from the upcoming Exploration Mission-1 vehicle in late 2018. However, significant uncertainty in the deployment conditions for secondary payloads impacts both the availability and geometry of transfers that deliver the spacecraft to the lunar vicinity. A framework that leverages dynamical systems techniques is applied to a recently updated set of deployment conditions and spacecraft parameter values for the Lunar IceCube mission, demonstrating the capability for rapid trajectory design.

Hypersonic trajectory control of aerospace plane with integrated SCRAMJET engine

NASA Astrophysics Data System (ADS)

Yonemoto, Koichi

The aerospace plane is an airbreathing 'propulsion configured' vehicle having proper forebody contour for inflow pre-compression to the inlet and afterbody that operates as an external expansion nozzle. Since the whole lower side of the body acts as important compression and expansion elements for the airbreathing engine, the flight attitude influences its performance such as specific impulse and thrust coefficient considerably. The stability of ascent trajectory controlling dynamic pressure or heat-input rate is analyzed considering the performance change due to attitude fluctuation. The performance of scramjet engine, a typical hypersonic airbreathing engine, is estimated by a rapid prediction methodology of the combustor proposed by Ikawa.

Trajectory design for a cislunar CubeSat leveraging dynamical systems techniques: The Lunar IceCube mission

NASA Astrophysics Data System (ADS)

Bosanac, Natasha; Cox, Andrew D.; Howell, Kathleen C.; Folta, David C.

2018-03-01

Lunar IceCube is a 6U CubeSat that is designed to detect and observe lunar volatiles from a highly inclined orbit. This spacecraft, equipped with a low-thrust engine, is expected to be deployed from the upcoming Exploration Mission-1 vehicle. However, significant uncertainty in the deployment conditions for secondary payloads impacts both the availability and geometry of transfers that deliver the spacecraft to the lunar vicinity. A framework that leverages dynamical systems techniques is applied to a recently updated set of deployment conditions and spacecraft parameter values for the Lunar IceCube mission, demonstrating the capability for rapid trajectory design.

Liquid-Propellant Rocket Engine Throttling: A Comprehensive Review

NASA Technical Reports Server (NTRS)

Casiano, Matthew; Hulka, James; Yang, Virog

2009-01-01

Liquid-Propellant Rocket Engines (LREs) are capable of on-command variable thrust or thrust modulation, an operability advantage that has been studied intermittently since the late 1930s. Throttleable LREs can be used for planetary entry and descent, space rendezvous, orbital maneuvering including orientation and stabilization in space, and hovering and hazard avoidance during planetary landing. Other applications have included control of aircraft rocket engines, limiting of vehicle acceleration or velocity using retrograde rockets, and ballistic missile defense trajectory control. Throttleable LREs can also continuously follow the most economical thrust curve in a given situation, compared to discrete throttling changes over a few select operating points. The effects of variable thrust on the mechanics and dynamics of an LRE as well as difficulties and issues surrounding the throttling process are important aspects of throttling behavior. This review provides a detailed survey of LRE throttling centered around engines from the United States. Several LRE throttling methods are discussed, including high-pressure-drop systems, dual-injector manifolds, gas injection, multiple chambers, pulse modulation, throat throttling, movable injector components, and hydrodynamically dissipative injectors. Concerns and issues surrounding each method are examined, and the advantages and shortcomings compared.

Turbine Performance Optimization Task Status

NASA Technical Reports Server (NTRS)

Griffin, Lisa W.; Turner, James E. (Technical Monitor)

2001-01-01

Capability to optimize for turbine performance and accurately predict unsteady loads will allow for increased reliability, Isp, and thrust-to-weight. The development of a fast, accurate aerodynamic design, analysis, and optimization system is required.

Solar Sail Roadmap Mission GN and C Challenges

NASA Technical Reports Server (NTRS)

Heaton, Andrew F.

2005-01-01

The NASA In-Space Propulsion program is funding development work for solar sails to enhance future scientific opportunities. Key to this effort are scientific solar sail roadmap missions identified by peer review. The two near-term missions of interest are L1 Diamond and Solar Polar Imager. Additionally, the New Millennium Program is sponsoring the Space Technology 9 (ST9) demonstration mission. Solar sails are one of five technologies competing for the ST9 flight demonstration. Two candidate solar sail missions have been identified for a potential ST9 flight. All the roadmap missions and candidate flight demonstration missions face various GN&C challenges. A variety of efforts are underway to address these challenges. These include control actuator design and testing, low thrust optimization studies, attitude control system design and modeling, control-structure interaction studies, trajectory control design, and solar radiation pressure model development. Here we survey the various efforts underway and identify a few of specific recent interest and focus.

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.

Trajectory optimization for the National Aerospace Plane

NASA Technical Reports Server (NTRS)

Lu, Ping

1992-01-01

The primary objective of this research is to develop an efficient and robust trajectory optimization tool for the optimal ascent problem of the National Aerospace Plane (NASP). This report is organized in the following order to summarize the complete work: Section two states the formulation and models of the trajectory optimization problem. An inverse dynamics approach to the problem is introduced in Section three. Optimal trajectories corresponding to various conditions and performance parameters are presented in Section four. A midcourse nonlinear feedback controller is developed in Section five. Section six demonstrates the performance of the inverse dynamics approach and midcourse controller during disturbances. Section seven discusses rocket assisted ascent which may be beneficial when orbital altitude is high. Finally, Section eight recommends areas of future research.

Optimization design of energy deposition on single expansion ramp nozzle

NASA Astrophysics Data System (ADS)

Ju, Shengjun; Yan, Chao; Wang, Xiaoyong; Qin, Yupei; Ye, Zhifei

2017-11-01

Optimization design has been widely used in the aerodynamic design process of scramjets. The single expansion ramp nozzle is an important component for scramjets to produces most of thrust force. A new concept of increasing the aerodynamics of the scramjet nozzle with energy deposition is presented. The essence of the method is to create a heated region in the inner flow field of the scramjet nozzle. In the current study, the two-dimensional coupled implicit compressible Reynolds Averaged Navier-Stokes and Menter's shear stress transport turbulence model have been applied to numerically simulate the flow fields of the single expansion ramp nozzle with and without energy deposition. The numerical results show that the proposal of energy deposition can be an effective method to increase force characteristics of the scramjet nozzle, the thrust coefficient CT increase by 6.94% and lift coefficient CN decrease by 26.89%. Further, the non-dominated sorting genetic algorithm coupled with the Radial Basis Function neural network surrogate model has been employed to determine optimum location and density of the energy deposition. The thrust coefficient CT and lift coefficient CN are selected as objective functions, and the sampling points are obtained numerically by using a Latin hypercube design method. The optimized thrust coefficient CT further increase by 1.94%, meanwhile, the optimized lift coefficient CN further decrease by 15.02% respectively. At the same time, the optimized performances are in good and reasonable agreement with the numerical predictions. The findings suggest that scramjet nozzle design and performance can benefit from the application of energy deposition.

Propeller noise minimization without thrust loss due to asymmetric blade distribution

NASA Astrophysics Data System (ADS)

Dobrzynski, Werner

1990-11-01

Measures which can be taken to minimize propeller noise caused by asymmetric blade distribution, without loss of thrust, are discussed. The theoretical optimization of angular separation and its relation to the minimization of noise is reviewed. Experimental results on various propellers are discussed.

FLORIS 2017

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

2017-08-04

This code is an enhancement to the existing FLORIS code, SWR 14-20. In particular, this enhancement computes overall thrust and turbulence intensity throughout a wind plant. This information is used to form a description of the fatigue loads experienced throughtout the wind plant. FLORIS has been updated to include an optimization routine that optimizes FLORIS to minimize thrust and turbulence intensity (and therefore loads) across the wind plant. Previously, FLORIS had been designed to optimize power out of a wind plant. However, as turbines age, more wind plant owner/operators are looking for ways to reduce their fatigue loads without sacrificingmore » too much power.« less

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.

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.

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.

Optimal specific wavelength for maximum thrust production in undulatory propulsion

PubMed Central

Nangia, Nishant; Bale, Rahul; Chen, Nelson; Hanna, Yohanna; Patankar, Neelesh A.

2017-01-01

What wavelengths do undulatory swimmers use during propulsion? In this work we find that a wide range of body/caudal fin (BCF) swimmers, from larval zebrafish and herring to fully–grown eels, use specific wavelength (ratio of wavelength to tail amplitude of undulation) values that fall within a relatively narrow range. The possible emergence of this constraint is interrogated using numerical simulations of fluid–structure interaction. Based on these, it was found that there is an optimal specific wavelength (OSW) that maximizes the swimming speed and thrust generated by an undulatory swimmer. The observed values of specific wavelength for BCF animals are relatively close to this OSW. The mechanisms underlying the maximum propulsive thrust for BCF swimmers are quantified and are found to be consistent with the mechanisms hypothesized in prior work. The adherence to an optimal value of specific wavelength in most natural hydrodynamic propulsors gives rise to empirical design criteria for man–made propulsors. PMID:28654649

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.

Closeup view of the interior of an Aft Skirt being ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

Close-up view of the interior of an Aft Skirt being tested and prepared for mating with sub assemblies in the Solid Rocket Booster (SRB) Assembly and Refurbishment Facility at Kennedy Space Center. This view is showing the SRB Thrust Vector Control (TVC) System which includes independent auxiliary power units for each actuator to pressurize their respective hydraulic systems. When the Nozzle is mated with the Aft Skirt the two actuators, located on the left and right side of the TVC System in this view, can swivel it up to 3.5 degrees to redirect the thrust to steer and maintain the Shuttle's programmed trajectory. - Space Transportation System, Solid Rocket Boosters, Lyndon B. Johnson Space Center, 2101 NASA Parkway, Houston, Harris County, TX

Conceptual Design of a Z-Pinch Fusion Propulsion System

NASA Technical Reports Server (NTRS)

Adams, Robert; Polsgrove, Tara; Fincher, Sharon; Fabinski, Leo; Maples, Charlotte; Miernik, Janie; Stratham, Geoffrey; Cassibry, Jason; Cortez, Ross; Turner, Matthew;

Design and optimization of a modal- independent linear ultrasonic motor.

PubMed

Zhou, Shengli; Yao, Zhiyuan

2014-03-01

To simplify the design of the linear ultrasonic motor (LUSM) and improve its output performance, a method of modal decoupling for LUSMs is proposed in this paper. The specific embodiment of this method is decoupling of the traditional LUSM stator's complex vibration into two simple vibrations, with each vibration implemented by one vibrator. Because the two vibrators are designed independently, their frequencies can be tuned independently and frequency consistency is easy to achieve. Thus, the method can simplify the design of the LUSM. Based on this method, a prototype modal- independent LUSM is designed and fabricated. The motor reaches its maximum thrust force of 47 N, maximum unloaded speed of 0.43 m/s, and maximum power of 7.85 W at applied voltage of 200 Vpp. The motor's structure is then optimized by controlling the difference between the two vibrators' resonance frequencies to reach larger output speed, thrust, and power. The optimized results show that when the frequency difference is 73 Hz, the output force, speed, and power reach their maximum values. At the input voltage of 200 Vpp, the motor reaches its maximum thrust force of 64.2 N, maximum unloaded speed of 0.76 m/s, maximum power of 17.4 W, maximum thrust-weight ratio of 23.7, and maximum efficiency of 39.6%.

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.

Performance seeking control program overview

NASA Technical Reports Server (NTRS)

Orme, John S.

1995-01-01

The Performance Seeking Control (PSC) program evolved from a series of integrated propulsion-flight control research programs flown at NASA Dryden Flight Research Center (DFRC) on an F-15. The first of these was the Digital Electronic Engine Control (DEEC) program and provided digital engine controls suitable for integration. The DEEC and digital electronic flight control system of the NASA F-15 were ideally suited for integrated controls research. The Advanced Engine Control System (ADECS) program proved that integrated engine and aircraft control could improve overall system performance. The objective of the PSC program was to advance the technology for a fully integrated propulsion flight control system. Whereas ADECS provided single variable control for an average engine, PSC controlled multiple propulsion system variables while adapting to the measured engine performance. PSC was developed as a model-based, adaptive control algorithm and included four optimization modes: minimum fuel flow at constant thrust, minimum turbine temperature at constant thrust, maximum thrust, and minimum thrust. Subsonic and supersonic flight testing were conducted at NASA Dryden covering the four PSC optimization modes and over the full throttle range. Flight testing of the PSC algorithm, conducted in a series of five flight test phases, has been concluded at NASA Dryden covering all four of the PSC optimization modes. Over a three year period and five flight test phases 72 research flights were conducted. The primary objective of flight testing was to exercise each PSC optimization mode and quantify the resulting performance improvements.

Orbit Modification of Earth-Crossing Asteroids/Comets Using Rendezvous Spacecraft and Laser Ablation

NASA Technical Reports Server (NTRS)

Park, Sang-Young; Mazanek, Daniel D.

2005-01-01

This report describes the approach and results of an end-to-end simulation to deflect a long-period comet (LPC) by using a rapid rendezvous spacecraft and laser ablation system. The laser energy required for providing sufficient deflection DELTA V and an analysis of possible intercept/rendezvous spacecraft trajectories are studied in this analysis. These problems minimize a weighted sum of the flight time and required propellant by using an advanced propulsion system. The optimal thrust-vector history and propellant mass to use are found in order to transfer a spacecraft from the Earth to a targeted celestial object. One goal of this analysis is to formulate an optimization problem for intercept/rendezvous spacecraft trajectories. One approach to alter the trajectory of the object in a highly controlled manner is to use pulsed laser ablative propulsion. A sufficiently intense laser pulse ablates the surface of a near-Earth object (NEO) by causing plasma blowoff. The momentum change from a single laser pulse is very small. However, the cumulative effect is very effective because the laser can interact with the object over long periods of time. The laser ablation technique can overcome the mass penalties associated with other nondisruptive approaches because no propellant is required to generate the DELTA V (the material of the celestial object is the propellant source). Additionally, laser ablation is effective against a wide range of surface materials and does not require any landing or physical attachment to the object. For diverting distant asteroids and comets, the power and optical requirements of a laser ablation system on or near the Earth may be too extreme to contemplate in the next few decades. A hybrid solution would be for a spacecraft to carry a laser as a payload to a particular celestial body. The spacecraft would require an advanced propulsion system capable of rapid rendezvous with the object and an extremely powerful electrical generator, which is likely needed for the propulsion system as well. The spacecraft would station-keep with the object at a small standoff distance while the laser ablation is performed.

Analysis of Flight Management System Predictions of Idle-Thrust Descents

NASA Technical Reports Server (NTRS)

Stell, Laurel

2010-01-01

To enable arriving aircraft to fly optimized descents computed by the flight management system (FMS) in congested airspace, ground automation must accurately predict descent trajectories. To support development of the predictor and its uncertainty models, descents from cruise to the meter fix were executed using vertical navigation in a B737-700 simulator and a B777-200 simulator, both with commercial FMSs. For both aircraft types, the FMS computed the intended descent path for a specified speed profile assuming idle thrust after top of descent (TOD), and then it controlled the avionics without human intervention. The test matrix varied aircraft weight, descent speed, and wind conditions. The first analysis in this paper determined the effect of the test matrix parameters on the FMS computation of TOD location, and it compared the results to those for the current ground predictor in the Efficient Descent Advisor (EDA). The second analysis was similar but considered the time to fly a specified distance to the meter fix. The effects of the test matrix variables together with the accuracy requirements for the predictor will determine the allowable error for the predictor inputs. For the B737, the EDA prediction of meter fix crossing time agreed well with the FMS; but its prediction of TOD location probably was not sufficiently accurate to enable idle-thrust descents in congested airspace, even though the FMS and EDA gave similar shapes for TOD location as a function of the test matrix variables. For the B777, the FMS and EDA gave different shapes for the TOD location function, and the EDA prediction of the TOD location is not accurate enough to fully enable the concept. Furthermore, the differences between the FMS and EDA predictions of meter fix crossing time for the B777 indicated that at least one of them was not sufficiently accurate.

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

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

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.

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.

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.

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

Problems of millipound thrust measurement. The "Hansen Suspension"

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

Carta, David G.

Considered in detail are problems which led to the need and use of the 'Hansen Suspension'. Also discussed are problems which are likely to be encountered in any low level thrust measuring system. The methods of calibration and the accuracies involved are given careful attention. With all parameters optimized and calibration techniques perfected, the system was found capable of a resolution of 10 {mu} lbs. A comparison of thrust measurements made by the 'Hansen Suspension' with measurements of a less sophisticated device leads to some surprising results.

Experimental study on thrust and power of flapping-wing system based on rack-pinion mechanism.

PubMed

Nguyen, Tuan Anh; Vu Phan, Hoang; Au, Thi Kim Loan; Park, Hoon Cheol

2016-06-20

This experimental study investigates the effect of three parameters: wing aspect ratio (AR), wing offset, and flapping frequency, on thrust generation and power consumption of a flapping-wing system based on a rack-pinion mechanism. The new flapping-wing system is simple but robust, and is able to create a large flapping amplitude. The thrust measured by a load cell reveals that for a given power, the flapping-wing system using a higher wing AR produces larger thrust and higher flapping frequency at the wing offset of 0.15[Formula: see text] or 0.20[Formula: see text] ([Formula: see text] is the mean chord) than other wing offsets. Of the three parameters, the flapping frequency plays a more significant role on thrust generation than either the wing AR or the wing offset. Based on the measured thrusts, an empirical equation for thrust prediction is suggested, as a function of wing area, flapping frequency, flapping angle, and wing AR. The difference between the predicted and measured thrusts was less than 7%, which proved that the empirical equation for thrust prediction is reasonable. On average, the measured power consumption to flap the wings shows that 46.5% of the input power is spent to produce aerodynamic forces, 14.0% to overcome inertia force, 9.5% to drive the rack-pinion-based flapping mechanism, and 30.0% is wasted as the power loss of the installed motor. From the power analysis, it is found that the wing with an AR of 2.25 using a wing offset of 0.20[Formula: see text] showed the optimal power loading in the flapping-wing system. In addition, the flapping frequency of 25 Hz is recommended as the optimal frequency of the current flapping-wing system for high efficiency, which was 48.3%, using a wing with an AR of 2.25 and a wing offset of 0.20[Formula: see text] in the proposed design.

Fuel optimal maneuvers for spacecraft with fixed thrusters

NASA Technical Reports Server (NTRS)

Carter, T. C.

1982-01-01

Several mathematical models, including a minimum integral square criterion problem, were used for the qualitative investigation of fuel optimal maneuvers for spacecraft with fixed thrusters. The solutions consist of intervals of "full thrust" and "coast" indicating that thrusters do not need to be designed as "throttleable" for fuel optimal performance. For the primary model considered, singular solutions occur only if the optimal solution is "pure translation". "Time optimal" singular solutions can be found which consist of intervals of "coast" and "full thrust". The shape of the optimal fuel consumption curve as a function of flight time was found to depend on whether or not the initial state is in the region admitting singular solutions. Comparisons of fuel optimal maneuvers in deep space with those relative to a point in circular orbit indicate that qualitative differences in the solutions can occur. Computation of fuel consumption for certain "pure translation" cases indicates that considerable savings in fuel can result from the fuel optimal maneuvers.

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.

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.

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.

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.

The Lunar IceCube Mission Challenge: Attaining Science Orbit Parameters from a Constrained Approach Trajectory

NASA Technical Reports Server (NTRS)

Folta, David C.; Bosanac, Natasha; Cox, Andrew; Howell, Kathleen C.

2017-01-01

The challenges of targeting specific lunar science orbit parameters from a concomitant Sun-EarthMoon system trajectory are examined. While the concept of ballistic lunar capture is well-studied, achieving and controlling the time evolution of the orbital elements to satisfy mission constraints is especially problematic when the spacecraft is equipped with a low-thrust propulsion system. Satisfying these requirements on the lunar approach and capture segments is critical to the success of the Lunar IceCube mission, a 6U CubeSat that will prospect for water in solid (ice), liquid, and vapor forms and other lunar volatiles from a low-periapsis, highly inclined elliptical lunar orbit.

The Lunar IceCube Mission Challenge: Attaining Science Orbit Parameters from a Constrained Approach Trajectory

NASA Technical Reports Server (NTRS)

Folta, David C.; Bosanac, Natasha; Cox, Andrew; Howell, Kathleen C.

2017-01-01

The challenges of targeting specific lunar science orbit parameters from a concomitant Sun-Earth/Moon system trajectory are examined. While the concept of ballistic lunar capture is well-studied, achieving and controlling the time evolution of the orbital elements to satisfy mission constraints is especially problematic when the spacecraft is equipped with a low-thrust propulsion system. Satisfying these requirements on the lunar approach and capture segments is critical to the success of the Lunar IceCube mission, a 6U CubeSat that will prospect for water in solid (ice), liquid, and vapor forms and other lunar volatiles from a low-periapsis, highly inclined elliptical lunar orbit.

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.

NASA Tech Briefs, April 2010

NASA Technical Reports Server (NTRS)

2010-01-01

Topics covered include: Active and Passive Hybrid Sensor; Quick-Response Thermal Actuator for Use as a Heat Switch; System for Hydrogen Sensing; Method for Detecting Perlite Compaction in Large Cryogenic Tanks; Using Thin-Film Thermometers as Heaters in Thermal Control Applications; Directional Spherical Cherenkov Detector; AlGaN Ultraviolet Detectors for Dual-Band UV Detection; K-Band Traveling-Wave Tube Amplifier; Simplified Load-Following Control for a Fuel Cell System; Modified Phase-meter for a Heterodyne Laser Interferometer; Loosely Coupled GPS-Aided Inertial Navigation System for Range Safety; Sideband-Separating, Millimeter-Wave Heterodyne Receiver; Coaxial Propellant Injectors With Faceplate Annulus Control; Adaptable Diffraction Gratings With Wavefront Transformation; Optimizing a Laser Process for Making Carbon Nanotubes; Thermogravimetric Analysis of Single-Wall Carbon Nanotubes; Robotic Arm Comprising Two Bending Segments; Magnetostrictive Brake; Low-Friction, Low-Profile, High-Moment Two-Axis Joint; Foil Gas Thrust Bearings for High-Speed Turbomachinery; Miniature Multi-Axis Mechanism for Hand Controllers; Digitally Enhanced Heterodyne Interferometry; Focusing Light Beams To Improve Atomic-Vapor Optical Buffers; Landmark Detection in Orbital Images Using Salience Histograms; Efficient Bit-to-Symbol Likelihood Mappings; Capacity Maximizing Constellations; Natural-Language Parser for PBEM; Policy Process Editor for P(sup 3)BM Software; A Quality System Database; Trajectory Optimization: OTIS 4; and Computer Software Configuration Item-Specific Flight Software Image Transfer Script Generator.

NASA Tech Briefs, July 2007

NASA Technical Reports Server (NTRS)

2007-01-01

Topics covered include: Miniature Intelligent Sensor Module; "Smart" Sensor Module; Portable Apparatus for Electrochemical Sensing of Ethylene; Increasing Linear Dynamic Range of a CMOS Image Sensor; Flight Qualified Micro Sun Sensor; Norbornene-Based Polymer Electrolytes for Lithium Cells; Making Single-Source Precursors of Ternary Semiconductors; Water-Free Proton-Conducting Membranes for Fuel Cells; Mo/Ti Diffusion Bonding for Making Thermoelectric Devices; Photodetectors on Coronagraph Mask for Pointing Control; High-Energy-Density, Low-Temperature Li/CFx Primary Cells; G4-FETs as Universal and Programmable Logic Gates; Fabrication of Buried Nanochannels From Nanowire Patterns; Diamond Smoothing Tools; Infrared Imaging System for Studying Brain Function; Rarefying Spectra of Whispering-Gallery-Mode Resonators; Large-Area Permanent-Magnet ECR Plasma Source; Slot-Antenna/Permanent-Magnet Device for Generating Plasma; Fiber-Optic Strain Gauge With High Resolution And Update Rate; Broadband Achromatic Telecentric Lens; Temperature-Corrected Model of Turbulence in Hot Jet Flows; Enhanced Elliptic Grid Generation; Automated Knowledge Discovery From Simulators; Electro-Optical Modulator Bias Control Using Bipolar Pulses; Generative Representations for Automated Design of Robots; Mars-Approach Navigation Using In Situ Orbiters; Efficient Optimization of Low-Thrust Spacecraft Trajectories; Cylindrical Asymmetrical Capacitors for Use in Outer Space; Protecting Against Faults in JPL Spacecraft; Algorithm Optimally Allocates Actuation of a Spacecraft; and Radar Interferometer for Topographic Mapping of Glaciers and Ice Sheets.

Lubrication of optimized-design tapered-roller bearings to 2.4 million DN

NASA Technical Reports Server (NTRS)

Parker, R. J.; Pinel, S. I.; Signer, Hans R.

1980-01-01

The performance of 120.65 mm (4.75 in.) bore high speed design, tapered roller bearings was investigated at shaft speeds to 20,000 rpm (2.4 million DN) under combined thrust and radial load. The test bearing design was computer optimized for high speed operation. Temperature distribution bearing heat generation were determined as a function of shaft speed, radial and thrust loads, lubricant flow rates, and lubricant inlet temperature. The high speed design, tapered roller bearing operated successfully at shaft speeds up to 20,000 rpm under heavy thrust and radial loads. Bearing temperatures and heat generation with the high speed design bearing were significantly less than those of a modified standard bearing tested previously. Cup cooling was effective in decreasing the high cup temperatures to levels equal to the cone temperature.

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.

Computing and Visualizing Reachable Volumes for Maneuvering Satellites

NASA Astrophysics Data System (ADS)

Jiang, M.; de Vries, W.; Pertica, A.; Olivier, S.

2011-09-01

Detecting and predicting maneuvering satellites is an important problem for Space Situational Awareness. The spatial envelope of all possible locations within reach of such a maneuvering satellite is known as the Reachable Volume (RV). As soon as custody of a satellite is lost, calculating the RV and its subsequent time evolution is a critical component in the rapid recovery of the satellite. In this paper, we present a Monte Carlo approach to computing the RV for a given object. Essentially, our approach samples all possible trajectories by randomizing thrust-vectors, thrust magnitudes and time of burn. At any given instance, the distribution of the "point-cloud" of the virtual particles defines the RV. For short orbital time-scales, the temporal evolution of the point-cloud can result in complex, multi-reentrant manifolds. Visualization plays an important role in gaining insight and understanding into this complex and evolving manifold. In the second part of this paper, we focus on how to effectively visualize the large number of virtual trajectories and the computed RV. We present a real-time out-of-core rendering technique for visualizing the large number of virtual trajectories. We also examine different techniques for visualizing the computed volume of probability density distribution, including volume slicing, convex hull and isosurfacing. We compare and contrast these techniques in terms of computational cost and visualization effectiveness, and describe the main implementation issues encountered during our development process. Finally, we will present some of the results from our end-to-end system for computing and visualizing RVs using examples of maneuvering satellites.

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.

Top-of-Climb Matching Method for Reducing Aircraft Trajectory Prediction Errors.

PubMed

Thipphavong, David P

2016-09-01

The inaccuracies of the aircraft performance models utilized by trajectory predictors with regard to takeoff weight, thrust, climb profile, and other parameters result in altitude errors during the climb phase that often exceed the vertical separation standard of 1000 feet. This study investigates the potential reduction in altitude trajectory prediction errors that could be achieved for climbing flights if just one additional parameter is made available: top-of-climb (TOC) time. The TOC-matching method developed and evaluated in this paper is straightforward: a set of candidate trajectory predictions is generated using different aircraft weight parameters, and the one that most closely matches TOC in terms of time is selected. This algorithm was tested using more than 1000 climbing flights in Fort Worth Center. Compared to the baseline trajectory predictions of a real-time research prototype (Center/TRACON Automation System), the TOC-matching method reduced the altitude root mean square error (RMSE) for a 5-minute prediction time by 38%. It also decreased the percentage of flights with absolute altitude error greater than the vertical separation standard of 1000 ft for the same look-ahead time from 55% to 30%.

Top-of-Climb Matching Method for Reducing Aircraft Trajectory Prediction Errors

PubMed Central

Thipphavong, David P.

2017-01-01

The inaccuracies of the aircraft performance models utilized by trajectory predictors with regard to takeoff weight, thrust, climb profile, and other parameters result in altitude errors during the climb phase that often exceed the vertical separation standard of 1000 feet. This study investigates the potential reduction in altitude trajectory prediction errors that could be achieved for climbing flights if just one additional parameter is made available: top-of-climb (TOC) time. The TOC-matching method developed and evaluated in this paper is straightforward: a set of candidate trajectory predictions is generated using different aircraft weight parameters, and the one that most closely matches TOC in terms of time is selected. This algorithm was tested using more than 1000 climbing flights in Fort Worth Center. Compared to the baseline trajectory predictions of a real-time research prototype (Center/TRACON Automation System), the TOC-matching method reduced the altitude root mean square error (RMSE) for a 5-minute prediction time by 38%. It also decreased the percentage of flights with absolute altitude error greater than the vertical separation standard of 1000 ft for the same look-ahead time from 55% to 30%. PMID:28684883

Top-of-Climb Matching Method for Reducing Aircraft Trajectory Prediction Errors

NASA Technical Reports Server (NTRS)

Thipphavong, David P.

2016-01-01

The inaccuracies of the aircraft performance models utilized by trajectory predictors with regard to takeoff weight, thrust, climb profile, and other parameters result in altitude errors during the climb phase that often exceed the vertical separation standard of 1000 feet. This study investigates the potential reduction in altitude trajectory prediction errors that could be achieved for climbing flights if just one additional parameter is made available: top-of-climb (TOC) time. The TOC-matching method developed and evaluated in this paper is straightforward: a set of candidate trajectory predictions is generated using different aircraft weight parameters, and the one that most closely matches TOC in terms of time is selected. This algorithm was tested using more than 1000 climbing flights in Fort Worth Center. Compared to the baseline trajectory predictions of a real-time research prototype (Center/TRACON Automation System), the TOC-matching method reduced the altitude root mean square error (RMSE) for a 5-minute prediction time by 38%. It also decreased the percentage of flights with absolute altitude error greater than the vertical separation standard of 1000 ft for the same look-ahead time from 55% to 30%.

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.

High-Speed Solution of Spacecraft Trajectory Problems Using Taylor Series Integration

NASA Technical Reports Server (NTRS)

Scott, James R.; Martini, Michael C.

2010-01-01

It has been known for some time that Taylor series (TS) integration is among the most efficient and accurate numerical methods in solving differential equations. However, the full benefit of the method has yet to be realized in calculating spacecraft trajectories, for two main reasons. First, most applications of Taylor series to trajectory propagation have focused on relatively simple problems of orbital motion or on specific problems and have not provided general applicability. Second, applications that have been more general have required use of a preprocessor, which inevitably imposes constraints on computational efficiency. The latter approach includes the work of Berryman et al., who solved the planetary n-body problem with relativistic effects. Their work specifically noted the computational inefficiencies arising from use of a preprocessor and pointed out the potential benefit of manually coding derivative routines. In this Engineering Note, we report on a systematic effort to directly implement Taylor series integration in an operational trajectory propagation code: the Spacecraft N-Body Analysis Program (SNAP). The present Taylor series implementation is unique in that it applies to spacecraft virtually anywhere in the solar system and can be used interchangeably with another integration method. SNAP is a high-fidelity trajectory propagator that includes force models for central body gravitation with N X N harmonics, other body gravitation with N X N harmonics, solar radiation pressure, atmospheric drag (for Earth orbits), and spacecraft thrusting (including shadowing). The governing equations are solved using an eighth-order Runge-Kutta Fehlberg (RKF) single-step method with variable step size control. In the present effort, TS is implemented by way of highly integrated subroutines that can be used interchangeably with RKF. This makes it possible to turn TS on or off during various phases of a mission. Current TS force models include central body gravitation with the J2 spherical harmonic, other body gravitation, thrust, constant atmospheric drag from Earth's atmosphere, and solar radiation pressure for a sphere under constant illumination. The purpose of this Engineering Note is to demonstrate the performance of TS integration in an operational trajectory analysis code and to compare it with a standard method, eighth-order RKF. Results show that TS is 16.6 times faster on average and is more accurate in 87.5% of the cases presented.

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.

Foil bearings for axial and radial support of high speed rotors: Design, development, and determination of operating characteristics

NASA Technical Reports Server (NTRS)

Licht, L.

1978-01-01

Flexible surface thrust and journal foil bearings were fabricated, and their performance was demonstrated, both individually and jointly as a unified rotor support system. Experimental results are documented with graphs and oscilloscopic data of trajectories, waveforms, and scans of amplitude response. At speeds of 40,000 to 45,000 rpm and a mean clearance of the order of 15 to 20 micrometers (600 to 800 micrometers, the resilient, air lubricated, spiral groove thrust bearings support a load of 127 N (29 lb; 13 kgf), equivalent to 3.0 N/sq cm (4.5 lb/sq in 0.31 kgf sq cm). Journal bearings with polygonal sections provided stable and highly damped supports at speeds up to 50,000 rpm.

A Study on Aircraft Engine Control Systems for Integrated Flight and Propulsion Control

NASA Astrophysics Data System (ADS)

Yamane, Hideaki; Matsunaga, Yasushi; Kusakawa, Takeshi; Yasui, Hisako

The Integrated Flight and Propulsion Control (IFPC) for a highly maneuverable aircraft and a fighter-class engine with pitch/yaw thrust vectoring is described. Of the two IFPC functions the aircraft maneuver control utilizes the thrust vectoring based on aerodynamic control surfaces/thrust vectoring control allocation specified by the Integrated Control Unit (ICU) of a FADEC (Full Authority Digital Electronic Control) system. On the other hand in the Performance Seeking Control (PSC) the ICU identifies engine's various characteristic changes, optimizes manipulated variables and finally adjusts engine control parameters in cooperation with the Engine Control Unit (ECU). It is shown by hardware-in-the-loop simulation that the thrust vectoring can enhance aircraft maneuverability/agility and that the PSC can improve engine performance parameters such as SFC (specific fuel consumption), thrust and gas temperature.

SeGRAm - A practical and versatile tool for spacecraft trajectory optimization

NASA Technical Reports Server (NTRS)

Rishikof, Brian H.; Mccormick, Bernell R.; Pritchard, Robert E.; Sponaugle, Steven J.

1991-01-01

An implementation of the Sequential Gradient/Restoration Algorithm, SeGRAm, is presented along with selected examples. This spacecraft trajectory optimization and simulation program uses variational calculus to solve problems of spacecraft flying under the influence of one or more gravitational bodies. It produces a series of feasible solutions to problems involving a wide range of vehicles, environments and optimization functions, until an optimal solution is found. The examples included highlight the various capabilities of the program and emphasize in particular its versatility over a wide spectrum of applications from ascent to interplanetary trajectories.

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.

Ballistic representation for kinematic access

NASA Astrophysics Data System (ADS)

Alfano, Salvatore

2011-01-01

This work uses simple two-body orbital dynamics to initially determine the kinematic access for a ballistic vehicle. Primarily this analysis was developed to assess when a rocket body might conjunct with an orbiting satellite platform. A family of access opportunities can be represented as a volume for a specific rocket relative to its launch platform. Alternately, the opportunities can be represented as a geographical footprint relative to aircraft or satellite position that encompasses all possible launcher locations for a specific rocket. A thrusting rocket is treated as a ballistic vehicle that receives all its energy at launch and follows a coasting trajectory. To do so, the rocket's burnout energy is used to find its equivalent initial velocity for a given launcher's altitude. Three kinematic access solutions are then found that account for spherical Earth rotation. One solution finds the maximum range for an ascent-only trajectory while another solution accommodates a descending trajectory. In addition, the ascent engagement for the descending trajectory is used to depict a rapid access scenario. These preliminary solutions are formulated to address ground-, sea-, or air-launched vehicles.

Entry Atmospheric Flight Control Authority Impacts on GN and C and Trajectory Performance for Orion Exploration Flight Test 1

NASA Technical Reports Server (NTRS)

McNamara, Luke W.

2012-01-01

One of the key design objectives of NASA's Orion Exploration Flight Test 1 (EFT-1) is to execute a guided entry trajectory demonstrating GN&C capability. The focus of this paper is the ight control authority of the vehicle throughout the atmospheric entry ight to the target landing site and its impacts on GN&C, parachute deployment, and integrated performance. The vehicle's attitude control authority is obtained from thrusting 12 Re- action Control System (RCS) engines, with four engines to control yaw, four engines to control pitch, and four engines to control roll. The static and dynamic stability derivatives of the vehicle are determined to assess the inherent aerodynamic stability. The aerodynamic moments at various locations in the entry trajectory are calculated and compared to the available torque provided by the RCS system. Interaction between the vehicle's RCS engine plumes and the aerodynamic conditions are considered to assess thruster effectiveness. This document presents an assessment of Orion's ight control authority and its effectiveness in controlling the vehicle during critical events in the atmospheric entry trajectory.

Variation of parameters using Battin's universal functions

NASA Astrophysics Data System (ADS)

Burton, James R., III; Melton, Robert G.

This paper presents a variation of parameters analysis, suitable for use in situations involving small perturbations to the two-body problem, using Battin's universal functions. Unlike the universal variable formulation, this approach avoids the need to switch among different functional representations if the orbit transitions from elliptical, through parabolic, to hyperbolic state, making it attractive for use in simulating low-thrust trajectories ascending to escape or capturing into orbit.

Regularization in Orbital Mechanics; Theory and Practice

NASA Astrophysics Data System (ADS)

Roa, Javier

2017-09-01

Regularized equations of motion can improve numerical integration for the propagation of orbits, and simplify the treatment of mission design problems. This monograph discusses standard techniques and recent research in the area. While each scheme is derived analytically, its accuracy is investigated numerically. Algebraic and topological aspects of the formulations are studied, as well as their application to practical scenarios such as spacecraft relative motion and new low-thrust trajectories.

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.

Numerical analysis and design optimization of supersonic after-burning with strut fuel injectors for scramjet engines

NASA Astrophysics Data System (ADS)

Candon, M. J.; Ogawa, H.

2018-06-01

Scramjets are a class of hypersonic airbreathing engine that offer promise for economical, reliable and high-speed access-to-space and atmospheric transport. The expanding flow in the scramjet nozzle comprises of unburned hydrogen. An after-burning scheme can be used to effectively utilize the remaining hydrogen by supplying additional oxygen into the nozzle, aiming to augment the thrust. This paper presents the results of a single-objective design optimization for a strut fuel injection scheme considering four design variables with the objective of maximizing thrust augmentation. Thrust is found to be augmented significantly owing to a combination of contributions from aerodynamic and combustion effects. Further understanding and physical insights have been gained by performing variance-based global sensitivity analysis, scrutinizing the nozzle flowfields, analyzing the distributions and contributions of the forces acting on the nozzle wall, and examining the combustion efficiency.

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.

Preliminary Design of a Ramjet for Integration with Ground-Based Launch Assist

NASA Technical Reports Server (NTRS)

Sayles, Emily L.

2008-01-01

This viewgraph presentation reviews the preliminary design of a ramjet for integration with a ground based launch assist. The reasons for the use of ground-based launch assist and the proposed mechanism for a system are reviewed. The use of a Optimal Trajectory by Implicit Simulation (OTIS), to model the flight and comparison with an actual rocket trajectory is given. The OTIS system is reviewed, The benefits of a launch assist system are analyzed concluding that a launch assist can provide supersonic speeds thus allowing ignition of ramjet without an onboard compressor. This means a further reduction in total launch weight. The Ramjet study is reviewed next. This included a review of the ONX simulations, the verification of the ONX results with the use of Holloman Sled experiment data as derived from the Feasibility of Ramjet Engine Test Capability on The Holloman AFB Sled Track. The conclusion was that the ONX system was not sufficient to meet the needs for the modeling required. The GECAT (Graphical Engine Cycle Analysis Tool) is examined. The results of the GECAT simulations was verified with data from Stataltex and D21 flights. The Next steps are: to create a GECAT Model of a launch assist ramjet, to adjust the geometry to produce the desired thrust, and to survey the ramjet's performance over a range of Mach numbers. The assumptions and requirements of a launch assist ramjet are given, and the acceptable flight regimes are reviewed.

Tubular copper thrust chamber design study

NASA Technical Reports Server (NTRS)

Masters, A. I.; Galler, D. E.

1992-01-01

The use of copper tubular thrust chambers is particularly important in high performance expander cycle space engines. Tubular chambers have more surface area than flat wall chambers, and this extra surface area provides enhanced heat transfer for additional energy to power the cycle. This paper was divided into two sections: (1) a thermal analysis and sensitivity study; and (2) a preliminary design of a selected thrust chamber configuration. The thermal analysis consisted of a statistical optimization to determine the optimum tube geometry, tube booking, thrust chamber geometry, and cooling routing to achieve the maximum upper limit chamber pressure for a 25,000 pound thrust engine. The preliminary design effort produced a layout drawing of a tubular thrust chamber that is three inches shorter than the Advanced Expander Test Bed (AETB) milled channel chamber but is predicted to provide a five percent increase in heat transfer. Testing this chamber in the AETB would confirm the inherent advantages of tubular chamber construction and heat transfer.

Linear Test Bed. Volume 2: Test Bed No. 2. [linear aerospike test bed for thrust vector control

NASA Technical Reports Server (NTRS)

1974-01-01

Test bed No. 2 consists of 10 combustors welded in banks of 5 to 2 symmetrical tubular nozzle assemblies, an upper stationary thrust frame, a lower thrust frame which can be hinged, a power package, a triaxial combustion wave ignition system, a pneumatic control system, pneumatically actuated propellant valves, a purge and drain system, and an electrical control system. The power package consists of the Mark 29-F fuel turbopump, the Mark 29-0 oxidizer turbopump, a gas generator assembly, and propellant ducting. The system, designated as a linear aerospike system, was designed to demonstrate the feasibility of the concept and to explore technology related to thrust vector control, thrust vector optimization, improved sequencing and control, and advanced ignition systems. The propellants are liquid oxygen/liquid hydrogen. The system was designed to operate at 1200-psia chamber pressure at an engine mixture ratio of 5.5. With 10 combustors, the sea level thrust is 95,000 pounds.

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.

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.

Parallel Aircraft Trajectory Optimization with Analytic Derivatives

NASA Technical Reports Server (NTRS)

Falck, Robert D.; Gray, Justin S.; Naylor, Bret

2016-01-01

Trajectory optimization is an integral component for the design of aerospace vehicles, but emerging aircraft technologies have introduced new demands on trajectory analysis that current tools are not well suited to address. Designing aircraft with technologies such as hybrid electric propulsion and morphing wings requires consideration of the operational behavior as well as the physical design characteristics of the aircraft. The addition of operational variables can dramatically increase the number of design variables which motivates the use of gradient based optimization with analytic derivatives to solve the larger optimization problems. In this work we develop an aircraft trajectory analysis tool using a Legendre-Gauss-Lobatto based collocation scheme, providing analytic derivatives via the OpenMDAO multidisciplinary optimization framework. This collocation method uses an implicit time integration scheme that provides a high degree of sparsity and thus several potential options for parallelization. The performance of the new implementation was investigated via a series of single and multi-trajectory optimizations using a combination of parallel computing and constraint aggregation. The computational performance results show that in order to take full advantage of the sparsity in the problem it is vital to parallelize both the non-linear analysis evaluations and the derivative computations themselves. The constraint aggregation results showed a significant numerical challenge due to difficulty in achieving tight convergence tolerances. Overall, the results demonstrate the value of applying analytic derivatives to trajectory optimization problems and lay the foundation for future application of this collocation based method to the design of aircraft with where operational scheduling of technologies is key to achieving good performance.

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.

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.

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.

Automated Sensitivity Analysis of Interplanetary Trajectories for Optimal Mission Design

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.

Encke-Beta Predictor for Orion Burn Targeting and Guidance

NASA Technical Reports Server (NTRS)

Robinson, Shane; Scarritt, Sara; Goodman, John L.

2016-01-01

The state vector prediction algorithm selected for Orion on-board targeting and guidance is known as the Encke-Beta method. Encke-Beta uses a universal anomaly (beta) as the independent variable, valid for circular, elliptical, parabolic, and hyperbolic orbits. The variable, related to the change in eccentric anomaly, results in integration steps that cover smaller arcs of the trajectory at or near perigee, when velocity is higher. Some burns in the EM-1 and EM-2 mission plans are much longer than burns executed with the Apollo and Space Shuttle vehicles. Burn length, as well as hyperbolic trajectories, has driven the use of the Encke-Beta numerical predictor by the predictor/corrector guidance algorithm in place of legacy analytic thrust and gravity integrals.

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.

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.

Flyby Geometry Optimization Tool

NASA Technical Reports Server (NTRS)

Karlgaard, Christopher D.

2007-01-01

The Flyby Geometry Optimization Tool is a computer program for computing trajectories and trajectory-altering impulsive maneuvers for spacecraft used in radio relay of scientific data to Earth from an exploratory airplane flying in the atmosphere of Mars.

Three Orbital Burns to Molniya Orbit Via Shuttle_Centaur G Upper Stage

NASA Technical Reports Server (NTRS)

Williams, Craig H.

2015-01-01

An unclassified analytical trajectory design, performance, and mission study was done for the 1982 to 1986 joint National Aeronautics and Space Administration (NASA)-United States Air Force (USAF) Shuttle/Centaur G upper stage development program to send performance-demanding payloads to high orbits such as Molniya using an unconventional orbit transfer. This optimized three orbital burn transfer to Molniya orbit was compared to the then-baselined two burn transfer. The results of the three dimensional trajectory optimization performed include powered phase steering data and coast phase orbital element data. Time derivatives of the orbital elements as functions of thrust components were evaluated and used to explain the optimization's solution. Vehicle performance as a function of parking orbit inclination was given. Performance and orbital element data was provided for launch windows as functions of launch time. Ground track data was given for all burns and coasts including variation within the launch window. It was found that a Centaur with fully loaded propellant tanks could be flown from a 37 deg inclination low Earth parking orbit and achieve Molniya orbit with comparable performance to the baselined transfer which started from a 57 deg inclined orbit: 9,545 versus 9,552 lb of separated spacecraft weight, respectively. There was a significant reduction in the need for propellant launch time reserve for a 1 hr window: only 78 lb for the three burn transfer versus 320 lb for the two burn transfer. Conversely, this also meant that longer launch windows over more orbital revolutions could be done for the same amount of propellant reserve. There was no practical difference in ground tracking station or airborne assets needed to secure telemetric data, even though the geometric locations of the burns varied considerably. There was a significant adverse increase in total mission elapsed time for the three versus two burn transfer (12 vs. 1-1/4 hr), but could be accommodated by modest modifications to Centaur systems. Future applications were discussed. The three burn transfer was found to be a viable, arguably preferable, alternative to the two burn transfer.

Three Orbital Burns to Molniya Orbit via Shuttle Centaur G Upper Stage

NASA Technical Reports Server (NTRS)

Williams, Craig H.

2014-01-01

An unclassified analytical trajectory design, performance, and mission study was done for the 1982-86 joint NASA-USAF Shuttle/Centaur G upper stage development program to send performance-demanding payloads to high orbits such as Molniya using an unconventional orbit transfer. This optimized three orbital burn transfer to Molniya orbit was compared to the then-baselined two burn transfer. The results of the three dimensional trajectory optimization performed include powered phase steering data and coast phase orbital element data. Time derivatives of the orbital elements as functions of thrust components were evaluated and used to explain the optimization's solution. Vehicle performance as a function of parking orbit inclination was given. Performance and orbital element data was provided for launch windows as functions of launch time. Ground track data was given for all burns and coasts including variation within the launch window. It was found that a Centaur with fully loaded propellant tanks could be flown from a 37deg inclination low Earth parking orbit and achieve Molniya orbit with comparable performance to the baselined transfer which started from a 57deg inclined orbit: 9,545 lb vs. 9,552 lb of separated spacecraft weight respectively. There was a significant reduction in the need for propellant launch time reserve for a one hour window: only 78 lb for the three burn transfer vs. 320 lb for the two burn transfer. Conversely, this also meant that longer launch windows over more orbital revolutions could be done for the same amount of propellant reserve. There was no practical difference in ground tracking station or airborne assets needed to secure telemetric data, even though the geometric locations of the burns varied considerably. There was a significant adverse increase in total mission elapsed time for the three vs. two burn transfer (12 vs. 11/4 hrs), but could be accommodated by modest modifications to Centaur systems. Future applications were discussed. The three burn transfer was found to be a viable, arguably preferable, alternative to the two burn transfer.

Preliminary tests of the electrostatic plasma accelerator

NASA Technical Reports Server (NTRS)

Aston, G.; Acker, T.

1990-01-01

This report describes the results of a program to verify an electrostatic plasma acceleration concept and to identify those parameters most important in optimizing an Electrostatic Plasma Accelerator (EPA) thruster based upon this thrust mechanism. Preliminary performance measurements of thrust, specific impulse and efficiency were obtained using a unique plasma exhaust momentum probe. Reliable EPA thruster operation was achieved using one power supply.

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.

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.

Combustion Efficiency, Flameout Operability Limits and General Design Optimization for Integrated Ramjet-Scramjet Hypersonic Vehicles

NASA Astrophysics Data System (ADS)

Mbagwu, Chukwuka Chijindu

High speed, air-breathing hypersonic vehicles encounter a varied range of engine and operating conditions traveling along cruise/ascent missions at high altitudes and dynamic pressures. Variations of ambient pressure, temperature, Mach number, and dynamic pressure can affect the combustion conditions in conflicting ways. Computations were performed to understand propulsion tradeoffs that occur when a hypersonic vehicle travels along an ascent trajectory. Proper Orthogonal Decomposition methods were applied for the reduction of flamelet chemistry data in an improved combustor model. Two operability limits are set by requirements that combustion efficiency exceed selected minima and flameout be avoided. A method for flameout prediction based on empirical Damkohler number measurements is presented. Operability limits are plotted that define allowable flight corridors on an altitude versus flight Mach number performance map; fixed-acceleration ascent trajectories were considered for this study. Several design rules are also presented for a hypersonic waverider with a dual-mode scramjet engine. Focus is placed on ''vehicle integration" design, differing from previous ''propulsion-oriented" design optimization. The well-designed waverider falls between that of an aircraft (high lift-to-drag ratio) and a rocket (high thrust-to-drag ratio). 84 variations of an X-43-like vehicle were run using the MASIV scramjet reduced order model to examine performance tradeoffs. Informed by the vehicle design study, variable-acceleration trajectory optimization was performed for three constant dynamic pressures ascents. Computed flameout operability limits were implemented as additional constraints to the optimization problem. The Michigan-AFRL Scramjet In-Vehicle (MASIV) waverider model includes finite-rate chemistry, applied scaling laws for 3-D turbulent mixing, ram-scram transition and an empirical value of the flameout Damkohler number. A reduced-order modeling approach is justified (in lieu of higher-fidelity computational simulations) because all vehicle forces are computed multiple thousands of times to generate multi-dimensional performance maps. The findings of this thesis work present a number of compelling conclusions. It is found that the ideal operating conditions of a scramjet engine are heavily dependent on the ambient and combustor pressure (and less strongly on temperature). Combustor pressures of approximately 1.0 bar or greater achieve the highest combustion efficiency, in line with industry standards of more than 0.5 bar. Ascent trajectory analysis of combustion efficiency and lean-limit flameout dictate best operation at higher dynamic pressures and lower altitudes, but these goals are traded off by current structural limitations whereby dynamic pressures must remain below 100 kPa. Hypersonic waverider designs varied between an "airplane" and a "rocket" are found to have better performance with the latter design, with controllability and minimum elevon/rudder surface area as a stability constraint for the vehicle trim. Ultimately, these findings are beneficial and contribute to the overall understanding of dynamically stable waverider vehicles at hypersonic speeds. These types of vehicles have a range of applications from technology demonstration, to earth-to-low orbit payload transit, to most compellingly another step in the development and realization of viable supersonic commercial transport.

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.

The balance and harmony of control power for a combat aircraft in tactical maneuvering

NASA Technical Reports Server (NTRS)

Bocvarov, Spiro; Cliff, Eugene M.; Lutze, Frederick H.

1992-01-01

An analysis is presented for a family of regular extremal attitude-maneuvers for the High Angle-of-Attack Research Vehicle that has thrust-vectoring capability. Different levels of dynamic coupling are identified in the combat aircraft attitude model, and the characteristic extremal-family motion is explained. It is shown why the extremal-family trajectories develop small sideslip-angles, a highly desirable feature from a practical viewpoint.

A practical six-degree of freedom solar sail dynamics model for optimizing solar sail trajectories with torque constraints

NASA Technical Reports Server (NTRS)

Lisano, Michael E.

2004-01-01

Controlled flight of a solar sail-propelled spacecraft ('sailcraft') is a six-degree-of-freedom dynamics problem. Current state-of-the-art tools that simulate and optimize the trajectories flown by sailcraft do not treat the full kinetic (i.e. force and torque-constrained) motion, instead treating a discrete history of commanded sail attitudes, and either neglecting the sail attitude motion over an integration timestep, or treating the attitude evolution kinematically with a spline or similar treatment. The present paper discusses an aspect of developing a next generation sailcraf trajectory designing optimization tool JPL, for NASA's Solar Sail Spaceflight Simulation Software (SS). The aspect discussed in an experimental approach to modeling full six-degree-of-freedom kinetic motion of a solar sail in a trajectory propagator. Early results from implementing this approach in a new trajectory propagation tool are given.

Assessment of community noise for a medium-range airplane with open-rotor engines

NASA Astrophysics Data System (ADS)

Kopiev, V. F.; Shur, M. L.; Travin, A. K.; Belyaev, I. V.; Zamtfort, B. S.; Medvedev, Yu. V.

2017-11-01

Community noise of a hypothetical medium-range airplane equipped with open-rotor engines is assessed by numerical modeling of the aeroacoustic characteristics of an isolated open rotor with the simplest blade geometry. Various open-rotor configurations are considered at constant thrust, and the lowest-noise configuration is selected. A two-engine medium-range airplane at known thrust of bypass turbofan engines at different segments of the takeoff-landing trajectory is considered, after the replacement of those engines by the open-rotor engines. It is established that a medium-range airplane with two open-rotor engines meets the requirements of Chapter 4 of the ICAO standard with a significant margin. It is shown that airframe noise makes a significant contribution to the total noise of an airplane with open-rotor engines at landing.

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.

The Control System for the X-33 Linear Aerospike Engine

NASA Technical Reports Server (NTRS)

Jackson, Jerry E.; Espenschied, Erich; Klop, Jeffrey

1998-01-01

The linear aerospike engine is being developed for single-stage -to-orbit (SSTO) applications. The primary advantages of a linear aerospike engine over a conventional bell nozzle engine include altitude compensation, which provides enhanced performance, and lower vehicle weight resulting from the integration of the engine into the vehicle structure. A feature of this integration is the ability to provide thrust vector control (TVC) by differential throttling of the engine combustion elements, rather than the more conventional approach of gimballing the entire engine. An analysis of the X-33 flight trajectories has shown that it is necessary to provide +/- 15% roll, pitch and yaw TVC authority with an optional capability of +/- 30% pitch at select times during the mission. The TVC performance requirements for X-33 engine became a major driver in the design of the engine control system. The thrust level of the X-33 engine as well as the amount of TVC are managed by a control system which consists of electronic, instrumentation, propellant valves, electro-mechanical actuators, spark igniters, and harnesses. The engine control system is responsible for the thrust control, mixture ratio control, thrust vector control, engine health monitoring, and communication to the vehicle during all operational modes of the engine (checkout, pre-start, start, main-stage, shutdown and post shutdown). The methodology for thrust vector control, the health monitoring approach which includes failure detection, isolation, and response, and the basic control system design are the topic of this paper. As an additional point of interest a brief description of the X-33 engine system will be included in this paper.

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.

Beam efflux measurements

NASA Technical Reports Server (NTRS)

Komatsu, G. K.; Stellen, J. M., Jr.

1976-01-01

Measurements have been made of the high energy thrust ions, (Group I), high angle/high energy ions (Group II), and high angle/low energy ions (Group IV) of a mercury electron bombardment thruster in the angular divergence range from 0 deg to greater than 90 deg. The measurements have been made as a function of thrust ion current, propellant utilization efficiency, bombardment discharge voltage, screen and accelerator grid potential (accel-decel ratio) and neutralizer keeper potential. The shape of the Group IV (charge exchange) ion plume has remained essentially fixed within the range of variation of the engine operation parameters. The magnitude of the charge exchange ion flux scales with thrust ion current, for good propellant utilization conditions. For fixed thrust ion current, charge exchange ion flux increases for diminishing propellant utilization efficiency. Facility effects influence experimental accuracies within the range of propellant utilization efficiency used in the experiments. The flux of high angle/high energy Group II ions is significantly diminished by the use of minimum decel voltages on the accelerator grid. A computer model of charge exchange ion production and motion has been developed. The program allows computation of charge exchange ion volume production rate, total production rate, and charge exchange ion trajectories for "genuine" and "facilities effects" particles. In the computed flux deposition patterns, the Group I and Group IV ion plumes exhibit a counter motion.

Fuel Burn Estimation Using Real Track Data

NASA Technical Reports Server (NTRS)

Chatterji, Gano B.

2011-01-01

A procedure for estimating fuel burned based on actual flight track data, and drag and fuel-flow models is described. The procedure consists of estimating aircraft and wind states, lift, drag and thrust. Fuel-flow for jet aircraft is determined in terms of thrust, true airspeed and altitude as prescribed by the Base of Aircraft Data fuel-flow model. This paper provides a theoretical foundation for computing fuel-flow with most of the information derived from actual flight data. The procedure does not require an explicit model of thrust and calibrated airspeed/Mach profile which are typically needed for trajectory synthesis. To validate the fuel computation method, flight test data provided by the Federal Aviation Administration were processed. Results from this method show that fuel consumed can be estimated within 1% of the actual fuel consumed in the flight test. Next, fuel consumption was estimated with simplified lift and thrust models. Results show negligible difference with respect to the full model without simplifications. An iterative takeoff weight estimation procedure is described for estimating fuel consumption, when takeoff weight is unavailable, and for establishing fuel consumption uncertainty bounds. Finally, the suitability of using radar-based position information for fuel estimation is examined. It is shown that fuel usage could be estimated within 5.4% of the actual value using positions reported in the Airline Situation Display to Industry data with simplified models and iterative takeoff weight computation.

Analysis on the multi-dimensional spectrum of the thrust force for the linear motor feed drive system in machine tools

NASA Astrophysics Data System (ADS)

Yang, Xiaojun; Lu, Dun; Ma, Chengfang; Zhang, Jun; Zhao, Wanhua

2017-01-01

The motor thrust force has lots of harmonic components due to the nonlinearity of drive circuit and motor itself in the linear motor feed drive system. What is more, in the motion process, these thrust force harmonics may vary with the position, velocity, acceleration and load, which affects the displacement fluctuation of the feed drive system. Therefore, in this paper, on the basis of the thrust force spectrum obtained by the Maxwell equation and the electromagnetic energy method, the multi-dimensional variation of each thrust harmonic is analyzed under different motion parameters. Then the model of the servo system is established oriented to the dynamic precision. The influence of the variation of the thrust force spectrum on the displacement fluctuation is discussed. At last the experiments are carried out to verify the theoretical analysis above. It can be found that the thrust harmonics show multi-dimensional spectrum characteristics under different motion parameters and loads, which should be considered to choose the motion parameters and optimize the servo control parameters in the high-speed and high-precision machine tools equipped with the linear motor feed drive system.