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.
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
Hodograph analysis in aircraft trajectory optimization
NASA Technical Reports Server (NTRS)
Cliff, Eugene M.; Seywald, Hans; Bless, Robert R.
1993-01-01
An account is given of key geometrical concepts involved in the use of a hodograph as an optimal control theory resource which furnishes a framework for geometrical interpretation of the minimum principle. Attention is given to the effects of different convexity properties on the hodograph, which bear on the existence of solutions and such types of controls as chattering controls, 'bang-bang' control, and/or singular control. Illustrative aircraft trajectory optimization problems are examined in view of this use of the hodograph.
Programs To Optimize Spacecraft And Aircraft Trajectories
NASA Technical Reports Server (NTRS)
Brauer, G. L.; Petersen, F. M.; Cornick, D.E.; Stevenson, R.; Olson, D. W.
1994-01-01
POST/6D POST is set of two computer programs providing ability to target and optimize trajectories of powered or unpowered spacecraft or aircraft operating at or near rotating planet. POST treats point-mass, three-degree-of-freedom case. 6D POST treats more-general rigid-body, six-degree-of-freedom (with point masses) case. Used to solve variety of performance, guidance, and flight-control problems for atmospheric and orbital vehicles. Applications include computation of performance or capability of vehicle in ascent, or orbit, and during entry into atmosphere, simulation and analysis of guidance and flight-control systems, dispersion-type analyses and analyses of loads, general-purpose six-degree-of-freedom simulation of controlled and uncontrolled vehicles, and validation of performance in six degrees of freedom. Written in FORTRAN 77 and C language. Two machine versions available: one for SUN-series computers running SunOS(TM) (LAR-14871) and one for Silicon Graphics IRIS computers running IRIX(TM) operating system (LAR-14869).
An aircraft noise pollution model for trajectory optimization
NASA Technical Reports Server (NTRS)
Barkana, A.; Cook, G.
1976-01-01
A mathematical model describing the generation of aircraft noise is developed with the ultimate purpose of reducing noise (noise-optimizing landing trajectories) in terminal areas. While the model is for a specific aircraft (Boeing 737), the methodology would be applicable to a wide variety of aircraft. The model is used to obtain a footprint on the ground inside of which the noise level is at or above 70 dB.
Application of trajectory optimization principles to minimize aircraft operating costs
NASA Technical Reports Server (NTRS)
Sorensen, J. A.; Morello, S. A.; Erzberger, H.
1979-01-01
This paper summarizes various applications of trajectory optimization principles that have been or are being devised by both government and industrial researchers to minimize aircraft direct operating costs (DOC). These costs (time and fuel) are computed for aircraft constrained to fly over a fixed range. Optimization theory is briefly outlined, and specific algorithms which have resulted from application of this theory are described. Typical results which demonstrate use of these algorithms and the potential savings which they can produce are given. Finally, need for further trajectory optimization research is presented.
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.
Cross-Polar Aircraft Trajectory Optimization and Potential Climate Impact
NASA Technical Reports Server (NTRS)
Sridhar, Banavar; Chen, Neil; Ng, Hok
2011-01-01
Cross-Polar routes offer new opportunities for air travel markets. Transpolar flights reduce travel times, fuel burns, and associated environmental emissions by flying direct paths between many North American and Asian cities. This study evaluates the potential benefits of flying wind-optimal polar routes and assessed their potential impact on climate change. An optimization algorithm is developed for transpolar flights to generate wind-optimal trajectories that minimize climate impact of aircraft, in terms of global warming potentials (relative to warming by one kg of CO2) of several types of emissions, while avoiding regions of airspace that facilitate persistent contrail formation. Estimations of global warming potential are incorporated into the objective function of the optimization algorithm to assess the climate impact of aircraft emissions discharged at a given location and altitude. The regions of airspace with very low ambient temperature and areas favorable to persistent contrail formation are modeled as undesirable regions that aircraft should avoid and are formulated as soft state constraints. The fuel burn and climate impact of cross-polar air traffic flying various types of trajectory including flightplan, great circle, wind-optimal, and contrail-avoidance are computed for 15 origin-destination pairs between major international airports in the U.S. and Asia. Wind-optimal routes reduce average fuel burn of flight plan routes by 4.4% on December 4, 2010 and 8.0% on August 7, 2010, respectively. The tradeoff between persistent contrail formation and additional global warming potential of aircraft emissions is investigated with and without altitude optimization. Without altitude optimization, the reduction in contrail travel times is gradual with increase in total fuel consumption. When altitude is optimized, a one percent increase in additional global warming potential, a climate impact equivalent to that of 4070kg and 4220kg CO2 emission, reduces 135
An Efficient Algorithm for Commercial Aircraft Trajectory Optimization in the Air Traffic System
NASA Astrophysics Data System (ADS)
Devulapalli, Raghuveer
A discrete search strategy is presented to determine optimal aircraft trajectories which can be unconstrained or regulated to follow current Air Traffic Control (ATC) procedures. The heuristic based Astar (A*) search algorithm has been selected for its efficiency and its inherent ability to handle numerous constraints as a discrete method. A point-mass aircraft model is assumed to accurately simulate commercial aircraft dynamics for the provided trajectories. The two dimensional space and the states of aircraft have been divided into discrete pieces. To show the effectiveness of the algorithm, two-dimensional vertical and horizontal profile are simulated. Simulation results compare optimal trajectories that range from unconstrained to those that completely adhere to strict ATC procedures. Those trajectories following ATC procedures follow a segmented flight pattern where each segment follows specified objectives, terminating when certain criteria has been met. Trajectories are optimized for a combination of time and fuel with an emphasis on reducing fuel consumption.
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.
The evaluation of several agility metrics for fighter aircraft using optimal trajectory analysis
NASA Technical Reports Server (NTRS)
Ryan, George W., III; Downing, David R.
1993-01-01
Several functional agility metrics, including the combat cycle time metric, dynamic speed turn plots, and relative energy state metric, are used to compare turning performance for generic F-18, X-29, and X-31-type aircraft models. These three-degree-of-freedom models have characteristics similar to the real aircraft. The performance comparisons are made using data from optimal test trajectories to reduce sensitivities to different pilot input techniques and to reduce the effects of control system limiters. The turn performance for all three aircraft is calculated for simulated minimum time 180 deg heading captures from simulation data. Comparisons of the three aircraft give more insight into turn performance than would be available from traditional measures of performance. Using the optimal test technique yields significant performance improvements as measured by the metrics. These performance improvements were found without significant increases in turn radius.
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.
Cross-Polar Aircraft Trajectory Optimization and the Potential Climate Impact
NASA Technical Reports Server (NTRS)
Ng, Hok K.; Sridhar, Banavar; Grabbe, Shon; Chen, Neil
2011-01-01
Cross-Polar routes offer new opportunities for air travel markets. Transpolar flights reduce travel times, fuel burns, and associated environmental emissions by flying direct paths between many North American and Asian cities. This study evaluates the potential benefits of flying wind-optimal polar routes and assessed their potential impact on climate change. An optimization algorithm is developed for transpolar flights to generate wind-optimal trajectories that minimize climate impact of aircraft, in terms of global warming potentials (relative to warming by one kg of CO2) of several types of emissions, while avoiding regions of airspace that facilitate persistent contrail formation. Estimations of global warming potential are incorporated into the objective function of the optimization algorithm to assess the climate impact of aircraft emissions discharged at a given location and altitude. The regions of airspace with very low ambient temperature and areas favorable to persistent contrail formation are modeled as undesirable regions that aircraft should avoid and are formulated as soft state constraints. The fuel burn and climate impact of cross-polar air traffic flying various types of trajectory including flight plan, great circle, wind-optimal, and contrail-avoidance are computed for 15 origin-destination pairs between major international airports in the U.S. and Asia. Wind-optimal routes reduce average fuel burn of flight plan routes by 4.4% on December 4, 2010 and 8.0% on August 7, 2010, respectively. The tradeoff between persistent contrail formation and additional global warming potential of aircraft emissions is investigated with and without altitude optimization. Without altitude optimization, the reduction in contrail travel times is gradual with increase in total fuel consumption. When altitude is optimized, a one percent increase in additional global warming potential, a climate impact equivalent to that of 4070kg and 4220kg CO2 emission, reduces 135
NASA Technical Reports Server (NTRS)
Rodionova, Olga; Sridhar, Banavar; Ng, Hok K.
2016-01-01
Air traffic in the North Atlantic oceanic airspace (NAT) experiences very strong winds caused by jet streams. Flying wind-optimal trajectories increases individual flight efficiency, which is advantageous when operating in the NAT. However, as the NAT is highly congested during peak hours, a large number of potential conflicts between flights are detected for the sets of wind-optimal trajectories. Conflict resolution performed at the strategic level of flight planning can significantly reduce the airspace congestion. However, being completed far in advance, strategic planning can only use predicted environmental conditions that may significantly differ from the real conditions experienced further by aircraft. The forecast uncertainties result in uncertainties in conflict prediction, and thus, conflict resolution becomes less efficient. This work considers wind uncertainties in order to improve the robustness of conflict resolution in the NAT. First, the influence of wind uncertainties on conflict prediction is investigated. Then, conflict resolution methods accounting for wind uncertainties are proposed.
Singular perturbation techniques for real time aircraft trajectory optimization and control
NASA Technical Reports Server (NTRS)
Calise, A. J.; Moerder, D. D.
1982-01-01
The usefulness of singular perturbation methods for developing real time computer algorithms to control and optimize aircraft flight trajectories is examined. A minimum time intercept problem using F-8 aerodynamic and propulsion data is used as a baseline. This provides a framework within which issues relating to problem formulation, solution methodology and real time implementation are examined. Theoretical questions relating to separability of dynamics are addressed. With respect to implementation, situations leading to numerical singularities are identified, and procedures for dealing with them are outlined. Also, particular attention is given to identifying quantities that can be precomputed and stored, thus greatly reducing the on-board computational load. Numerical results are given to illustrate the minimum time algorithm, and the resulting flight paths. An estimate is given for execution time and storage requirements.
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.
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.
NASA Technical Reports Server (NTRS)
Jacob, H. G.
1972-01-01
An optimization method has been developed that computes the optimal open loop inputs for a dynamical system by observing only its output. The method reduces to static optimization by expressing the inputs as series of functions with parameters to be optimized. Since the method is not concerned with the details of the dynamical system to be optimized, it works for both linear and nonlinear systems. The method and the application to optimizing longitudinal landing paths for a STOL aircraft with an augmented wing are discussed. Noise, fuel, time, and path deviation minimizations are considered with and without angle of attack, acceleration excursion, flight path, endpoint, and other constraints.
Aircraft flight test trajectory control
NASA Technical Reports Server (NTRS)
Menon, P. K. A.; Walker, R. A.
1988-01-01
Two design techniques for linear flight test trajectory controllers (FTTCs) are described: Eigenstructure assignment and the minimum error excitation technique. The two techniques are used to design FTTCs for an F-15 aircraft model for eight different maneuvers at thirty different flight conditions. An evaluation of the FTTCs is presented.
NASA Technical Reports Server (NTRS)
Hague, D. S.; Merz, A. W.
1976-01-01
Atmospheric sampling has been carried out by flights using an available high-performance supersonic aircraft. Altitude potential of an off-the-shelf F-15 aircraft is examined. It is shown that the standard F-15 has a maximum altitude capability in excess of 100,000 feet for routine flight operation by NASA personnel. This altitude is well in excess of the minimum altitudes which must be achieved for monitoring the possible growth of suspected aerosol contaminants.
Aircraft flight test trajectory control
NASA Technical Reports Server (NTRS)
Menon, P. K. A.; Walker, R. A.
1988-01-01
Two control law design techniques are compared and the performance of the resulting controllers evaluated. The design requirement is for a flight test trajectory controller (FTTC) capable of closed-loop, outer-loop control of an F-15 aircraft performing high-quality research flight test maneuvers. The maneuver modeling, linearization, and design methodologies utilized in this research, are detailed. The results of applying these FTTCs to a nonlinear F-15 simulation are presented.
Optimization Of Simulated Trajectories
NASA Technical Reports Server (NTRS)
Brauer, Garry L.; Olson, David W.; Stevenson, Robert
1989-01-01
Program To Optimize Simulated Trajectories (POST) provides ability to target and optimize trajectories of point-mass powered or unpowered vehicle operating at or near rotating planet. Used successfully to solve wide variety of problems in mechanics of atmospheric flight and transfer between orbits. Generality of program demonstrated by its capability to simulate up to 900 distinct trajectory phases, including generalized models of planets and vehicles. VAX version written in FORTRAN 77 and CDC version in FORTRAN V.
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.
Minimum noise impact aircraft trajectories
NASA Technical Reports Server (NTRS)
Jacobson, I. D.; Melton, R. G.
1981-01-01
Numerical optimization is used to compute the optimum flight paths, based upon a parametric form that implicitly includes some of the problem restrictions. The other constraints are formulated as penalties in the cost function. Various aircraft on multiple trajectores (landing and takeoff) can be considered. The modular design employed allows for the substitution of alternate models of the population distribution, aircraft noise, flight paths, and annoyance, or for the addition of other features (e.g., fuel consumption) in the cost function. A reduction in the required amount of searching over local minima was achieved through use of the presence of statistical lateral dispersion in the flight paths.
Perching aerodynamics and trajectory optimization
NASA Astrophysics Data System (ADS)
Wickenheiser, Adam; Garcia, Ephrahim
2007-04-01
Advances in smart materials, actuators, and control architecture have enabled new flight capabilities for aircraft. Perching is one such capability, described as a vertical landing maneuver using in-flight shape reconfiguration in lieu of high thrust generation. A morphing, perching aircraft design is presented that is capable of post stall flight and very slow landing on a vertical platform. A comprehensive model of the aircraft's aerodynamics, with special regard to nonlinear affects such as flow separation and dynamic stall, is discussed. Trajectory optimization using nonlinear programming techniques is employed to show the effects that morphing and nonlinear aerodynamics have on the maneuver. These effects are shown to decrease the initial height and distance required to initiate the maneuver, reduce the bounds on the trajectory, and decrease the required thrust for the maneuver. Perching trajectories comparing morphing versus fixed-configuration and stalled versus un-stalled aircraft are presented. It is demonstrated that a vertical landing is possible in the absence of high thrust if post-stall flight capabilities and vehicle reconfiguration are utilized.
Algorithm for fixed-range optimal trajectories
NASA Technical Reports Server (NTRS)
Lee, H. Q.; Erzberger, H.
1980-01-01
An algorithm for synthesizing optimal aircraft trajectories for specified range was developed and implemented in a computer program written in FORTRAN IV. The algorithm, its computer implementation, and a set of example optimum trajectories for the Boeing 727-100 aircraft are described. The algorithm optimizes trajectories with respect to a cost function that is the weighted sum of fuel cost and time cost. The optimum trajectory consists at most of a three segments: climb, cruise, and descent. The climb and descent profiles are generated by integrating a simplified set of kinematic and dynamic equations wherein the total energy of the aircraft is the independent or time like variable. At each energy level the optimum airspeeds and thrust settings are obtained as the values that minimize the variational Hamiltonian. Although the emphasis is on an off-line, open-loop computation, eventually the most important application will be in an on-board flight management system.
A performance measure for evaluating aircraft landing trajectories
NASA Technical Reports Server (NTRS)
Witt, R. M.; Cook, G.
1978-01-01
A general performance index is developed for evaluating aircraft landing trajectories. The primary term in the index is the effect of noise on people residing near the air terminal. Other terms included are passenger comfort, fuel consumed, and the time spent in the near-terminal area. Models are developed for aircraft engine noise, passenger comfort, the population distribution about a specific airport, and the aircraft flight behavior. While this performance index may be used in computing optimal trajectories, it is also useful for comparing nonoptimal trajectories which, for one reason or another, may be worthy of consideration. Some examples of such comparisons are included through simulations of landing. The aircraft considered is a Boeing 737.
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.
Helicopter trajectory planning using optimal control theory
NASA Technical Reports Server (NTRS)
Menon, P. K. A.; Cheng, V. H. L.; Kim, E.
1988-01-01
A methodology for optimal trajectory planning, useful in the nap-of-the-earth guidance of helicopters, is presented. This approach uses an adjoint-control transformation along with a one-dimensional search scheme for generating the optimal trajectories. In addition to being useful for helicopter nap-of-the-earth guidance, the trajectory planning solution is of interest in several other contexts, such as robotic vehicle guidance and terrain-following guidance for cruise missiles and aircraft. A distinguishing feature of the present research is that the terrain constraint and the threat envelopes are incorporated in the equations of motion. Second-order necessary conditions are examined.
Fractal aircraft trajectories and nonclassical turbulent exponents.
Lovejoy, S; Schertzer, D; Tuck, A F
2004-09-01
The dimension (D) of aircraft trajectories is fundamental in interpreting airborne data. To estimate D, we studied data from 18 trajectories of stratospheric aircraft flights 1600 km long taken during a "Mach cruise" (near constant Mach number) autopilot flight mode of the ER-2 research aircraft. Mach cruise implies correlated temperature and wind fluctuations so that DeltaZ approximately Deltax (H(z) ) where Z is the (fluctuating) vertical and x the horizontal coordinate of the aircraft. Over the range approximately 3-300 km , we found H(z) approximately 0.58+/-0.02 close to the theoretical 5/9=0.56 and implying D=1+ H(z) =14/9 , i.e., the trajectories are fractal. For distances <3 km aircraft inertia smooths the trajectories, for distances >300 km , D=1 again because of a rise of 1 m/km due to fuel consumption. In the fractal regime, the horizontal velocity and temperature exponents are close to the nonclassical value 1/2 (rather than 1/3 ). We discuss implications for aircraft measurements as well as for the structure of the atmosphere.
Trajectory Optimization: OTIS 4
NASA Technical Reports Server (NTRS)
Riehl, John P.; Sjauw, Waldy K.; Falck, Robert D.; Paris, Stephen W.
2010-01-01
The latest release of the Optimal Trajectories by Implicit Simulation (OTIS4) allows users to simulate and optimize aerospace vehicle trajectories. With OTIS4, one can seamlessly generate optimal trajectories and parametric vehicle designs simultaneously. New features also allow OTIS4 to solve non-aerospace continuous time optimal control problems. The inputs and outputs of OTIS4 have been updated extensively from previous versions. Inputs now make use of objectoriented constructs, including one called a metastring. Metastrings use a greatly improved calculator and common nomenclature to reduce the user s workload. They allow for more flexibility in specifying vehicle physical models, boundary conditions, and path constraints. The OTIS4 calculator supports common mathematical functions, Boolean operations, and conditional statements. This allows users to define their own variables for use as outputs, constraints, or objective functions. The user-defined outputs can directly interface with other programs, such as spreadsheets, plotting packages, and visualization programs. Internally, OTIS4 has more explicit and implicit integration procedures, including high-order collocation methods, the pseudo-spectral method, and several variations of multiple shooting. Users may switch easily between the various methods. Several unique numerical techniques such as automated variable scaling and implicit integration grid refinement, support the integration methods. OTIS4 is also significantly more user friendly than previous versions. The installation process is nearly identical on various platforms, including Microsoft Windows, Apple OS X, and Linux operating systems. Cross-platform scripts also help make the execution of OTIS and post-processing of data easier. OTIS4 is supplied free by NASA and is subject to ITAR (International Traffic in Arms Regulations) restrictions. Users must have a Fortran compiler, and a Python interpreter is highly recommended.
Advanced methods of structural and trajectory analysis for transport aircraft
NASA Technical Reports Server (NTRS)
Ardema, Mark D.
1995-01-01
This report summarizes the efforts in two areas: (1) development of advanced methods of structural weight estimation, and (2) development of advanced methods of trajectory optimization. The majority of the effort was spent in the structural weight area. A draft of 'Analytical Fuselage and Wing Weight Estimation of Transport Aircraft', resulting from this research, is included as an appendix.
Impact of Airspace Charges on Transatlantic Aircraft Trajectories
NASA Technical Reports Server (NTRS)
Sridhar, Banavar; Ng, Hok K.; Linke, Florian; Chen, Neil Y.
2015-01-01
Aircraft flying over the airspace of different countries are subject to over-flight charges. These charges vary from country to country. Airspace charges, while necessary to support the communication, navigation and surveillance services, may lead to aircraft flying routes longer than wind-optimal routes and produce additional carbon dioxide and other gaseous emissions. This paper develops an optimal route between city pairs by modifying the cost function to include an airspace cost whenever an aircraft flies through a controlled airspace without landing or departing from that airspace. It is assumed that the aircraft will fly the trajectory at a constant cruise altitude and constant speed. The computationally efficient optimal trajectory is derived by solving a non-linear optimal control problem. The operational strategies investigated in this study for minimizing aircraft fuel burn and emissions include flying fuel-optimal routes and flying cost-optimal routes that may completely or partially reduce airspace charges en route. The results in this paper use traffic data for transatlantic flights during July 2012. The mean daily savings in over-flight charges, fuel cost and total operation cost during the period are 17.6 percent, 1.6 percent, and 2.4 percent respectively, along the cost- optimal trajectories. The transatlantic flights can potentially save $600,000 in fuel cost plus $360,000 in over-flight charges daily by flying the cost-optimal trajectories. In addition, the aircraft emissions can be potentially reduced by 2,070 metric tons each day. The airport pairs and airspace regions that have the highest potential impacts due to airspace charges are identified for possible reduction of fuel burn and aircraft emissions for the transatlantic flights. The results in the paper show that the impact of the variation in fuel price on the optimal routes is to reduce the difference between wind-optimal and cost-optimal routes as the fuel price increases. The
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.
NASA Technical Reports Server (NTRS)
Hague, D. S.; Merz, A. W.
1975-01-01
Altitude potential of an off-the-shelf F4-C aircraft is examined. It is shown that the standard F4-C has a maximum altitude capability in the region from 85000 to 95000 ft, depending on the minimum dynamic pressures deemed acceptable for adequate flight control. By using engine overspeed capability and by making use of prevailing winds in the stratosphere, it is suggested that the maximum altitude achievable by an F4-C should be in the vicinity of 95000 ft for routine flight operation. This altitude is well in excess of the minimum altitudes which must be achieved for monitoring the possible growth of suspected aerosol contaminants.
Multiple Satellite Trajectory Optimization
2004-12-01
SOLVING OPTIMAL CONTROL PROBLEMS ........................................5...OPTIMIZATION A. SOLVING OPTIMAL CONTROL PROBLEMS The driving principle used to solve optimal control problems was first formalized by the Soviet...methods and processes of solving optimal control problems , this section will demonstrate how the formulations work as expected. Once coded, the
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.
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.
Trajectory optimization using regularized variables
NASA Technical Reports Server (NTRS)
Lewallen, J. M.; Szebehely, V.; Tapley, B. D.
1969-01-01
Regularized equations for a particular optimal trajectory are compared with unregularized equations with respect to computational characteristics, using perturbation type numerical optimization. In the case of the three dimensional, low thrust, Earth-Jupiter rendezvous, the regularized equations yield a significant reduction in computer time.
NASA Astrophysics Data System (ADS)
Shin, Sanghyun
workload while optimally utilizing limited resources, various aircraft rerouting strategies for Air Traffic Management (ATM) have been proposed. However, the number of rerouting tools available to address these issues for the center-level and the National Airspace System (NAS) are relatively less compared with the tools for the sector-level and terminal airspace. Additionally, previous works consider the airspace containing the weather as no-fly zones instead of reduced-traffic zones and do not explicitly consider controller workload when generating aircraft trajectories to avoid the weather-affected airspace, thereby reducing the overall performance of the airspace. In this thesis, a new rerouting algorithm for the center-level airspace is proposed to address these problems by introducing a feedback loop connecting a tactical rerouting algorithm with a strategic rerouting algorithm using dynamic programming and a modified A* algorithm respectively. This helps reduce the computational cost significantly while safely handling a large number of aircraft. In summary, this thesis suggests the ways in which the NAS's performance can be further improved, thereby supporting various concepts envisioned by the Next Generation Air Transportation System (NextGen) and providing vital information which can be used for suitable economic and environmental advantages.
Intelligent Aircraft Damage Assessment, Trajectory Planning, and Decision-Making under Uncertainty
NASA Astrophysics Data System (ADS)
Lopez, Israel; Sarigul-Klijn, Nesrin
Situational awareness and learning are necessary to identify and select the optimal set of mutually non-exclusive hypothesis in order to maximize mission performance and adapt system behavior accordingly. This paper presents a hierarchical and decentralized approach for integrated damage assessment and trajectory planning in aircraft with uncertain navigational decision-making. Aircraft navigation can be safely accomplished by properly addressing the following: decision-making, obstacle perception, aircraft state estimation, and aircraft control. When in-flight failures or damage occur, rapid and precise decision-making under imprecise information is required in order to regain and maintain control of the aircraft. To achieve planned aircraft trajectory and complete safe landing, the uncertainties in system dynamics of the damaged aircraft need to be learned and incorporated at the level of motion planning. The damaged aircraft is simulated via a simplified kinematic model. The different sources and perspectives of uncertainties in the damage assessment process and post-failure trajectory planning are presented and classified. The decision-making process for an emergency motion planning and landing is developed via the Dempster-Shafer evidence theory. The objective of the trajectory planning is to arrive at a target position while maximizing the safety of the aircraft given uncertain conditions. Simulations are presented for an emergency motion planning and landing that takes into account aircraft dynamics, path complexity, distance to landing site, runway characteristics, and subjective human decision.
Optimal Output Trajectory Redesign for Invertible Systems
NASA Technical Reports Server (NTRS)
Devasia, Santosh
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 multi-joint 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 be redesigned.
Probabilistic Modeling of Aircraft Trajectories for Dynamic Separation Volumes
NASA Technical Reports Server (NTRS)
Lewis, Timothy A.
2016-01-01
With a proliferation of new and unconventional vehicles and operations expected in the future, the ab initio airspace design will require new approaches to trajectory prediction for separation assurance and other air traffic management functions. This paper presents an approach to probabilistic modeling of the trajectory of an aircraft when its intent is unknown. The approach uses a set of feature functions to constrain a maximum entropy probability distribution based on a set of observed aircraft trajectories. This model can be used to sample new aircraft trajectories to form an ensemble reflecting the variability in an aircraft's intent. The model learning process ensures that the variability in this ensemble reflects the behavior observed in the original data set. Computational examples are presented.
An approximate method for calculating aircraft downwash on parachute trajectories
Strickland, J.H.
1989-01-01
An approximate method for calculating velocities induced by aircraft on parachute trajectories is presented herein. A simple system of quadrilateral vortex panels is used to model the aircraft wing and its wake. The purpose of this work is to provide a simple analytical tool which can be used to approximate the effect of aircraft-induced velocities on parachute performance. Performance issues such as turnover and wake recontact may be strongly influenced by velocities induced by the wake of the delivering aircraft, especially if the aircraft is maneuvering at the time of parachute deployment. 7 refs., 9 figs.
TAOS. Trajectory Analysis and Optimization System
Salguero, D.E.
1995-12-09
TAOS is a general-purpose software tool capable of analyzing nearly any type of three degree-of-freedom point-mass, high-speed trajectory. Input files contain aerodynamic coefficients, propulsion data, and a trajectory description. The trajectory description divides the trajectory into segments, and within each segment, guidance rules provided by the user describe how the trajectory is computed. Output files contain tabulated trajectory information such as position, velocity, and acceleration. Parametric optimization provides a powerful method for satisfying mission-planning constraints, and trajectories involving more than one vehicle can be computed within a single problem.
NBODY - a multipurpose trajectory optimization computer program
NASA Technical Reports Server (NTRS)
Strack, W. C.
1974-01-01
Documentation of the NBODY trajectory optimization program is presented in the form of a mathematical development plus a user's manual. Optimal multistage-launch ascent trajectories may be determined by variational thrust steering during the upper phase. Optimal low-thrust interplanetary spacecraft trajectories may also be calculated with solar power or constant power, all-propulsion or embedded coast arcs, fixed or optimal thrust angles, and a variety of terminal end conditions. A hybrid iteration scheme solves the boundary-value problem, while either transversality conditions or a univariate search scheme optimize vehicle or trajectory parameters.
Trajectory Control for Very Flexible Aircraft
2006-10-30
total airspeed and the classic aircraft longitudinal , lateral, and vertical velocity components are u positive out the nose, v positive out the right...wing flexibility is a secondary and minimal contribution to aircraft longitudinal motion. Using this assumption and the previous assumptions of
Three-dimensional trajectory optimization in constrained airspace
NASA Astrophysics Data System (ADS)
Dai, Ran
This dissertation deals with the generation of three-dimensional optimized trajectory in constrained airspace. It expands the previously used two-dimensional aircraft model to a three-dimensional model and includes the consideration of complex airspace constraints not included in previous trajectory optimization studies. Two major branches of optimization methods, indirect and direct methods, are introduced and compared. Both of the methods are applied to solve a two-dimensional minimum-time-to-climb (MTTC) problem. The solution procedure is described in detail. Two traditional problems, the Brachistochrone problem and Zermelo's problem, are solved using the direct collocation and nonlinear programming method. Because analytical solutions to these problems are known. These solutions provide verification of the numerical methods. Three discretization methods, trapezoidal, Hermite-Simpson and Chebyshev Pseudospectral (CP) are introduced and applied to solve the Brachistochrone problem. The solutions obtained using these discretization methods are compared with the analytical results. An 3-D aircraft model with six state variables and two control variables are presented. Two primary trajectory optimization problems are considered using this model in the dissertation. One is to assume that the aircraft climbs up from sea level to a desired altitude in a square cross section cylinder of arbitrary height. Another is to intercept a constant velocity, constant altitude target in minimum time starting from sea level. Results of the optimal trajectories are compared with the results from the proportional navigation guidance law. Field of View constraint is finally considered in this interception problem. The CP discretization and nonlinear programming method is shown to have advantages over indirect methods in solving three-dimensional (3-D) trajectory optimization problems with multiple controls and complex constraints. Conclusions from both problems are presented and
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.
Aircraft Trajectory Generation: A Literature Review
1989-06-01
optimum. Barman and Erzberger (1976) considered the case of a subsonic aircraft undergoing a short haul flight using energy state methods. The aim was to...energy states. This has implications in that it simplifies the calculus of variations approach to the problem. The paper by Barman and Erzberger...Electronics Conference (NAECON), Dayton Ohio 1988, pp 1128-1136. 4. Barman and Erzberger (1976). Barman , J.F. and Erzberger, H., ’Fixed-Range Optimum
Systematic Disturbance Of Optimal Rotational Trajectory
NASA Technical Reports Server (NTRS)
Grunwald, Arthur J.; Kaiser, Mary K.
1992-01-01
Algorithm introduces systematic disturbance into otherwise optimal rotation of body from prescribed initial to prescribed final orientation. Disturbance introduced as deviation of actual axis of rotation from optimal one, like wobble of top. Algorithm effects rotational transformations and solves differential equations necessary to compute disturbed trajectory. Devised for use with motion-control program and three-dimensional computer-graphical display to study ability of observers to distinguish between optimal and suboptimal rotational trajectories.
Multi-objective trajectory optimization for the space exploration vehicle
NASA Astrophysics Data System (ADS)
Qin, Xiaoli; Xiao, Zhen
2016-07-01
The research determines temperature-constrained optimal trajectory for the space exploration vehicle by developing an optimal control formulation and solving it using a variable order quadrature collocation method with a Non-linear Programming(NLP) solver. The vehicle is assumed to be the space reconnaissance aircraft that has specified takeoff/landing locations, specified no-fly zones, and specified targets for sensor data collections. A three degree of freedom aircraft model is adapted from previous work and includes flight dynamics, and thermal constraints.Vehicle control is accomplished by controlling angle of attack, roll angle, and propellant mass flow rate. This model is incorporated into an optimal control formulation that includes constraints on both the vehicle and mission parameters, such as avoidance of no-fly zones and exploration of space targets. In addition, the vehicle models include the environmental models(gravity and atmosphere). How these models are appropriately employed is key to gaining confidence in the results and conclusions of the research. Optimal trajectories are developed using several performance costs in the optimal control formation,minimum time,minimum time with control penalties,and maximum distance.The resulting analysis demonstrates that optimal trajectories that meet specified mission parameters and constraints can be quickly determined and used for large-scale space exloration.
Fixed-range optimum trajectories for short-haul aircraft
NASA Technical Reports Server (NTRS)
Erzberger, H.; Mclean, J. D.; Barman, J. F.
1975-01-01
An algorithm, based on the energy-state method, is derived for calculating optimum trajectories with a range constraint. The basis of the algorithm is the assumption that optimum trajectories consist of, at most, three segments: an increasing energy segment (climb); a constant energy segment (cruise); and a decreasing energy segment (descent). This assumption allows energy to be used as the independent variable in the increasing and decreasing energy segments, thereby eliminating the integration of a separate adjoint differential equation and simplifying the calculus of variations problem to one requiring only pointwise extremization of algebraic functions. The algorithm is used to compute minimum fuel, minimum time, and minimum direct-operating-cost trajectories, with range as a parameter, for an in-service CTOL aircraft and for an advanced STOL aircraft. For the CTOL aircraft and the minimum-fuel performance function, the optimum controls, consisting of air-speed and engine power setting, are continuous functions of the energy in both climb and descent as well as near the maximum or cruise energy. This is also true for the STOL aircraft except in the descent where at one energy level a nearly constant energy dive segment occurs, yielding a discontinuity in the airspeed at that energy. The reason for this segment appears to be the relatively high fuel flow at idle power of the engines used by this STOL aircraft. Use of a simplified trajectory which eliminates the dive increases the fuel consumption of the total descent trajectory by about 10 percent and the time to fly the descent by about 19 percent compared to the optimum.
Optimization in fractional aircraft ownership
NASA Astrophysics Data System (ADS)
Septiani, R. D.; Pasaribu, H. M.; Soewono, E.; Fayalita, R. A.
2012-05-01
Fractional Aircraft Ownership is a new concept in flight ownership management system where each individual or corporation may own a fraction of an aircraft. In this system, the owners have privilege to schedule their flight according to their needs. Fractional management companies (FMC) manages all aspects of aircraft operations, including utilization of FMC's aircraft in combination of outsourced aircrafts. This gives the owners the right to enjoy the benefits of private aviations. However, FMC may have complicated business requirements that neither commercial airlines nor charter airlines faces. Here, optimization models are constructed to minimize the number of aircrafts in order to maximize the profit and to minimize the daily operating cost. In this paper, three kinds of demand scenarios are made to represent different flight operations from different types of fractional owners. The problems are formulated as an optimization of profit and a daily operational cost to find the optimum flight assignments satisfying the weekly and daily demand respectively from the owners. Numerical results are obtained by Genetic Algorithm method.
Range optimization for a supersonic aircraft
NASA Technical Reports Server (NTRS)
Seywald, Hans; Cliff, Eugene M.; Well, Klaus H.
1991-01-01
Range optimal trajectories for an aircraft flying in the vertical plane are obtained from Pontryagin's Minimum Principle. Control variables are load factor n which appears nonlinearly in the equations of motion and throttle setting eta, which appears only linearly. Both controls are subject to fixed bounds, namely eta between values of 0 and 1 and absolute value of n not greater than n(max). Additionally, a dynamic pressure limit is imposed, which represents a first-order state-inequality constraint. For fixed flight time, fixed initial coordinates, and partially fixed final coordinates, the effect of the load factor limit absolute value of n not greater than n(max) is studied. Upon varying n(max), six different switching structures are obtained. All trajectories involve singular control along arcs with active dynamic pressure limit.
Aircraft configuration optimization including optimized flight profiles
NASA Technical Reports Server (NTRS)
Mccullers, L. A.
1984-01-01
The Flight Optimization System (FLOPS) is an aircraft configuration optimization program developed for use in conceptual design of new aircraft and in the assessment of the impact of advanced technology. The modular makeup of the program is illustrated. It contains modules for preliminary weights estimation, preliminary aerodynamics, detailed mission performance, takeoff and landing, and execution control. An optimization module is used to drive the overall design and in defining optimized profiles in the mission performance. Propulsion data, usually received from engine manufacturers, are used in both the mission performance and the takeoff and landing analyses. Although executed as a single in-core program, the modules are stored separately so that the user may select the appropriate modules (e.g., fighter weights versus transport weights) or leave out modules that are not needed.
System identification and trajectory optimization for guided store separation
NASA Astrophysics Data System (ADS)
Carter, Ryan E.
Combat aircraft utilize expendable stores such as missiles, bombs, flares, and external tanks to execute their missions. Safe and acceptable separation of these stores from the parent aircraft is essential for meeting the mission objectives. In many cases, the employed missile or bomb includes an onboard guidance and control system to enable precise engagement of the selected target. Due to potential interference, the guidance and control system is usually not activated until the store is sufficiently far away from the aircraft. This delay may result in large perturbations from the desired flight attitude caused by separation transients, significantly reducing the effectiveness of the store and jeopardizing mission objectives. The purpose of this research is to investigate the use of a transitional control system to guide the store during separation. The transitional control system, or "store separation autopilot", explicitly accounts for the nonuniform flow field through characterization of the spatially variant aerodynamics of the store during separation. This approach can be used to mitigate aircraft-store interference and leverage aerodynamic interaction to improve separation characteristics. This investigation proceeds in three phases. First, system identification is used to determine a parametric model for the spatially variant aerodynamics. Second, the store separation problem is recast into a trajectory optimization problem, and optimal control theory is used to establish a framework for designing a suitable reference trajectory with explicit dependence on the spatially variant aerodynamics. Third, neighboring optimal control is used to construct a linear-optimal feedback controller for correcting deviations from the nominal reference trajectory due varying initial conditions, modeling errors, and flowfield perturbations. An extended case study based on actual wind tunnel and flight test measurements is used throughout to illustrate the effectiveness of the
Optimizing Simulated Trajectories Of Rigid Bodies
NASA Technical Reports Server (NTRS)
Brauer, Garry L.; Olson, David W.; Stevenson, Robert
1989-01-01
6D POST is general-purpose, six-degree-of-freedom computer program for optimization of simulated trajectories of rigid bodies. Direct extension of three-degree-of-freedom POST program. 6D POST program models trajectory of powered or unpowered vehicle operating at or near rotating planet. Used to solve variety of performance, guidance, and flight-control problems for atmospheric and orbital vehicles. Written in FORTRAN 77 and FORTRAN V.
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
Optimal nonlinear estimation for aircraft flight control in wind shear
NASA Technical Reports Server (NTRS)
Mulgund, Sandeep S.
1994-01-01
The most recent results in an ongoing research effort at Princeton in the area of flight dynamics in wind shear are described. The first undertaking in this project was a trajectory optimization study. The flight path of a medium-haul twin-jet transport aircraft was optimized during microburst encounters on final approach. The assumed goal was to track a reference climb rate during an aborted landing, subject to a minimum airspeed constraint. The results demonstrated that the energy loss through the microburst significantly affected the qualitative nature of the optimal flight path. In microbursts of light to moderate strength, the aircraft was able to track the reference climb rate successfully. In severe microbursts, the minimum airspeed constraint in the optimization forced the aircraft to settle on a climb rate smaller than the target. A tradeoff was forced between the objectives of flight path tracking and stall prevention.
Real-time terminal area trajectory planning for runway independent aircraft
NASA Astrophysics Data System (ADS)
Xue, Min
The increasing demand for commercial air transportation results in delays due to traffic queues that form bottlenecks along final approach and departure corridors. In urban areas, it is often infeasible to build new runways, and regardless of automation upgrades traffic must remain separated to avoid the wakes of previous aircraft. Vertical or short takeoff and landing aircraft as Runway Independent Aircraft (RIA) can increase passenger throughput at major urban airports via the use of vertiports or stub runways. The concept of simultaneous non-interfering (SNI) operations has been proposed to reduce traffic delays by creating approach and departure corridors that do not intersect existing fixed-wing routes. However, SNI trajectories open new routes that may overfly noise-sensitive areas, and RIA may generate more noise than traditional jet aircraft, particularly on approach. In this dissertation, we develop efficient SNI noise abatement procedures applicable to RIA. First, we introduce a methodology based on modified approximated cell-decomposition and Dijkstra's search algorithm to optimize longitudinal plane (2-D) RIA trajectories over a cost function that minimizes noise, time, and fuel use. Then, we extend the trajectory optimization model to 3-D with a k-ary tree as the discrete search space. We incorporate geography information system (GIS) data, specifically population, into our objective function, and focus on a practical case study: the design of SNI RIA approach procedures to Baltimore-Washington International airport. Because solutions were represented as trim state sequences, we incorporated smooth transition between segments to enable more realistic cost estimates. Due to the significant computational complexity, we investigated alternative more efficient optimization techniques applicable to our nonlinear, non-convex, heavily constrained, and discontinuous objective function. Comparing genetic algorithm (GA) and adaptive simulated annealing (ASA
Constrained Trajectory Optimization Using Pseudospectral Methods (Preprint)
2008-08-05
at itu de , d eg POST SPOCS Figure 5. Trajectory Comparison of Integration Method Comparison IV.B. Basic Optimization Comparison The second set of...1500 2000 2500 3000 20 30 40 50 60 70 80 90 100 110 120 Altitude Time, sec A lti tu de , k m POST SPOCS Figure 7. Altitude Comparison of the First...Coordinates Z , k m POST SPOCS Figure 8. Range Comparison of the First Optimization Comparison 13 of 33 American Institute of Aeronautics and
Optimizing interplanetary trajectories with deep space maneuvers
NASA Astrophysics Data System (ADS)
Navagh, John
1993-09-01
Analysis of interplanetary trajectories is a crucial area for both manned and unmanned missions of the Space Exploration Initiative. A deep space maneuver (DSM) can improve a trajectory in much the same way as a planetary swingby. However, instead of using a gravitational field to alter the trajectory, the on-board propulsion system of the spacecraft is used when the vehicle is not near a planet. The purpose is to develop an algorithm to determine where and when to use deep space maneuvers to reduce the cost of a trajectory. The approach taken to solve this problem uses primer vector theory in combination with a non-linear optimizing program to minimize Delta(V). A set of necessary conditions on the primer vector is shown to indicate whether a deep space maneuver will be beneficial. Deep space maneuvers are applied to a round trip mission to Mars to determine their effect on the launch opportunities. Other studies which were performed include cycler trajectories and Mars mission abort scenarios. It was found that the software developed was able to locate quickly DSM's which lower the total Delta(V) on these trajectories.
Optimal trajectories for the aeroassisted flight experiment
NASA Technical Reports Server (NTRS)
Miele, A.; Wang, T.; Lee, W. Y.; Zhao, Z. G.
1989-01-01
The determination of optimal trajectories for the aeroassisted flight experiment (AFE) is discussed. The intent of this experiment is to simulate a GEO-to-LEO transfer, where GEO denotes a geosynchronous earth orbit and LEO denotes a low earth orbit. The trajectories of an AFE spacecraft are analyzed in a 3D-space, employing the full system of 6 ordinary differential equations (ODEs) describing the atmospheric pass. The atmospheric entry conditions are given, and the atmospheric exit conditions are adjusted. Two possible transfers are considered: (1) indirect ascent to a 178 NM perigee via a 197 NM apogee; and (2) direct ascent to a 178 NM apogee.
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.
Phugoid oscillations in optimal reentry trajectories
NASA Astrophysics Data System (ADS)
Vinh, N. X.; Chern, J. S.; Lin, C. F.
A major problem with operations of lifting reentry vehicle having an aft center-of-gravity location due to large engine mass at the rear is the required hypersonic trim to fight the desired trajectory. This condition is most severe for lifting maneuvers. As a first step toward analyzing this problem, this paper considers the lift requirement for some basic maneuvers in the plane of a great circle. Considerations are given to optimal lift control for achieving the maximization of either the final altitude, speed or range. For the maximum-range problem, phugoid oscillation along an optimal trajectory is less severe as compared to a glide with maximum lift-to-drag ratio. An explicit formula for the number of oscillations for an entry from orbital speed is proposed.
Trajectory optimization for kinematically redundant arms
NASA Technical Reports Server (NTRS)
Carignan, Craig R.
1991-01-01
A review of local optimization methods for resolving joint configurations in underconstrained manipulation tasks is conducted. A new approach is developed for observing joint limits and avoiding obstacles during the trajectory planning. The methodology is used in a four-link arm example to avoid a workspace singularity and is compared with results using the extended Moore-Penrose technique. An alternative measure of arm 'manipulability' based directly on the rank of the Jacobian is also introduced.
Design Methods and Optimization for Morphing Aircraft
NASA Technical Reports Server (NTRS)
Crossley, William A.
2005-01-01
This report provides a summary of accomplishments made during this research effort. The major accomplishments are in three areas. The first is the use of a multiobjective optimization strategy to help identify potential morphing features that uses an existing aircraft sizing code to predict the weight, size and performance of several fixed-geometry aircraft that are Pareto-optimal based upon on two competing aircraft performance objectives. The second area has been titled morphing as an independent variable and formulates the sizing of a morphing aircraft as an optimization problem in which the amount of geometric morphing for various aircraft parameters are included as design variables. This second effort consumed most of the overall effort on the project. The third area involved a more detailed sizing study of a commercial transport aircraft that would incorporate a morphing wing to possibly enable transatlantic point-to-point passenger service.
Trajectory optimization software for planetary mission design
NASA Technical Reports Server (NTRS)
D'Amario, Louis A.
1989-01-01
The development history and characteristics of the interactive trajectory-optimization programs MOSES (D'Amario et al., 1981) and PLATO (D'Amario et al., 1982) are briefly reviewed, with an emphasis on their application to the Galileo mission. The requirements imposed by a mission involving flybys of several planetary satellites or planets are discussed; the formulation of the parameter-optimization problem is outlined; and particular attention is given to the use of multiconic methods to model the gravitational attraction of Jupiter in MOSES. Diagrams and tables of numerical data are included.
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
Optimal trajectories for the aeroassisted flight experiment
NASA Astrophysics Data System (ADS)
Miele, A.; Wang, T.; Lee, W. Y.; Zhao, Z. G.
This paper deals with the determination of optimal trajectories for the aeroassisted flight experiment (AFE). The intent of this experiment is to simulate a GEO-to-LEO transfer, where GEO denotes a geosynchronous Earth orbit and LEO denotes a low Earth orbit. Specifically, the AFE spacecraft is released from the Space Shuttle and is accelerated by means of a solid rocket motor toward Earth, so as to achieve atmospheric entry conditions identical with those of a spacecraft returning from GEO. During the atmospheric pass, the angle of attack is kept constant, and the angle of bank is controlled in such a way that the following conditions are satisfied: (a) the atmospheric velocity depletion is such that, after exiting, the AFE spacecraft first ascends to a specified apogee and then descends to a specified perigee; and (b) the exit orbital plane is identical with the entry orbital plane. The final maneuver, not analyzed here, includes the rendezvous with and the capture by the Space Shuttle. In this paper, the trajectories of an AFE spacecraft are analyzed in a 3D space, employing the full system of 6 ODEs describing the atmospheric pass. The atmospheric entry conditions are given, and the atmospheric exit conditions are adjusted in such a way that requirements (a) and (b) are met, while simultaneously minimizing the total characteristic velocity, hence the propellant consumption required for orbital transfer. Two possible transfers are considered: indirect ascent (IA) to a 178 NM perigee via a 197 NM apogee; and direct ascent (DA) to a 178 NM apogee. For both transfers, two cases are investigated: (i) the bank angle is continuously variable; and (ii) the trajectory is divided into segments along which the bank angle is constant. For case (ii), the following subcases are studied; 2, 3, 4 and 5 segments; because the time duration of each segment is optimized, the above subcases involve 4, 6, 8 and 10 parameters, respectively. It is shown that the optimal trajectories
Development of Advanced Methods of Structural and Trajectory Analysis for Transport Aircraft
NASA Technical Reports Server (NTRS)
Ardema, Mark D.; Windhorst, Robert; Phillips, James
1998-01-01
This paper develops a near-optimal guidance law for generating minimum fuel, time, or cost fixed-range trajectories for supersonic transport aircraft. The approach uses a choice of new state variables along with singular perturbation techniques to time-scale decouple the dynamic equations into multiple equations of single order (second order for the fast dynamics). Application of the maximum principle to each of the decoupled equations, as opposed to application to the original coupled equations, avoids the two point boundary value problem and transforms the problem from one of a functional optimization to one of multiple function optimizations. It is shown that such an approach produces well known aircraft performance results such as minimizing the Brequet factor for minimum fuel consumption and the energy climb path. Furthermore, the new state variables produce a consistent calculation of flight path angle along the trajectory, eliminating one of the deficiencies in the traditional energy state approximation. In addition, jumps in the energy climb path are smoothed out by integration of the original dynamic equations at constant load factor. Numerical results performed for a supersonic transport design show that a pushover dive followed by a pullout at nominal load factors are sufficient maneuvers to smooth the jump.
Improved Propulsion Modeling for Low-Thrust Trajectory Optimization
NASA Technical Reports Server (NTRS)
Knittel, Jeremy M.; Englander, Jacob A.; Ozimek, Martin T.; Atchison, Justin A.; Gould, Julian J.
2017-01-01
Low-thrust trajectory design is tightly coupled with spacecraft systems design. In particular, the propulsion and power characteristics of a low-thrust spacecraft are major drivers in the design of the optimal trajectory. Accurate modeling of the power and propulsion behavior is essential for meaningful low-thrust trajectory optimization. In this work, we discuss new techniques to improve the accuracy of propulsion modeling in low-thrust trajectory optimization while maintaining the smooth derivatives that are necessary for a gradient-based optimizer. The resulting model is significantly more realistic than the industry standard and performs well inside an optimizer. A variety of deep-space trajectory examples are presented.
Matching trajectory optimization and nonlinear tracking control for HALE
NASA Astrophysics Data System (ADS)
Lee, Sangjong; Jang, Jieun; Ryu, Hyeok; Lee, Kyun Ho
2014-11-01
This paper concerns optimal trajectory generation and nonlinear tracking control for stratospheric airship platform of VIA-200. To compensate for the mismatch between the point-mass model of optimal trajectory and the 6-DOF model of the nonlinear tracking problem, a new matching trajectory optimization approach is proposed. The proposed idea reduces the dissimilarity of both problems and reduces the uncertainties in the nonlinear equations of motion for stratospheric airship. In addition, its refined optimal trajectories yield better results under jet stream conditions during flight. The resultant optimal trajectories of VIA-200 are full three-dimensional ascent flight trajectories reflecting the realistic constraints of flight conditions and airship performance with and without a jet stream. Finally, 6-DOF nonlinear equations of motion are derived, including a moving wind field, and the vectorial backstepping approach is applied. The desirable tracking performance is demonstrated that application of the proposed matching optimization method enables the smooth linkage of trajectory optimization to tracking control problems.
Optimal growth trajectories with finite carrying capacity.
Caravelli, F; Sindoni, L; Caccioli, F; Ududec, C
2016-08-01
We consider the problem of finding optimal strategies that maximize the average growth rate of multiplicative stochastic processes. For a geometric Brownian motion, the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a nonlinear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases we compute the optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.
Collocation points distributions for optimal spacecraft trajectories
NASA Astrophysics Data System (ADS)
Fumenti, Federico; Circi, Christian; Romagnoli, Daniele
2013-03-01
The method of direct collocation with nonlinear programming (DCNLP) is a powerful tool to solve optimal control problems (OCP). In this method the solution time history is approximated with piecewise polynomials, which are constructed using interpolation points deriving from the Jacobi polynomials. Among the Jacobi polynomials family, Legendre and Chebyshev polynomials are the most used, but there is no evidence that they offer the best performance with respect to other family members. By solving different OCPs with interpolation points not only taken within the Jacoby family, the behavior of the Jacobi polynomials in the optimization problems is discussed. This paper focuses on spacecraft trajectories optimization problems. In particular orbit transfers, interplanetary transfers and station keepings are considered.
Optimal growth trajectories with finite carrying capacity
NASA Astrophysics Data System (ADS)
Caravelli, F.; Sindoni, L.; Caccioli, F.; Ududec, C.
2016-08-01
We consider the problem of finding optimal strategies that maximize the average growth rate of multiplicative stochastic processes. For a geometric Brownian motion, the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a nonlinear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases we compute the optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.
Trajectory optimization in the presence of constraints
NASA Astrophysics Data System (ADS)
McQuade, Timothy E.
1989-06-01
In many aerospace problems, it is necessary to determine vehicle trajectories that satisfy constraints. Typically two types of constraints are of interest. First, it may be desirable to satisfy a set of boundary conditions. Second, it may be necessary to limit the motion of the vehicle so that physical limits and hardware limits are not exceeded. In addition to these requirements, it may be necessary to optimize some measure of vehicle performance. In this thesis, the square root sweep method is used to solve a discrete-time linear quadratic optimal control problem. The optimal control problem arises from a Mayer form continuous-time nonlinear optimization problem. A method for solving the optimal control problem is derived. Called the square root sweep algorithm, the solution consists of a set of backward recursions for a set of square root parameters. The square root sweep algorithm is shown to be capable of treating Mayer form optimization problems. Heuristics for obtaining solutions are discussed. The square root sweep algorithm is used to solve several example optimization problems.
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.
Air breathing engine/rocket trajectory optimization
NASA Technical Reports Server (NTRS)
Smith, V. K., III
1979-01-01
This research has focused on improving the mathematical models of the air-breathing propulsion systems, which can be mated with the rocket engine model and incorporated in trajectory optimization codes. Improved engine simulations provided accurate representation of the complex cycles proposed for advanced launch vehicles, thereby increasing the confidence in propellant use and payload calculations. The versatile QNEP (Quick Navy Engine Program) was modified to allow treatment of advanced turboaccelerator cycles using hydrogen or hydrocarbon fuels and operating in the vehicle flow field.
Capture Conditions for Merging Trajectory Segments to Model Realistic Aircraft Descents
NASA Technical Reports Server (NTRS)
Zhao, Yiyuan; Slattery, Rhonda A.
1996-01-01
A typical commercial aircraft trajectory consists of a series of flight segments. An aircraft switches from one segment to another when certain specified variables reach their desired values. Trajectory synthesis for air traffic control automation must be consistent with practical pilot procedures. We examine capture conditions for merging trajectory segments to model commercial aircraft descent in trajectory synthesis. These conditions translate into bounds on measurements of atmospheric wind, pressure, and temperature. They also define ranges of thrust and drag feasible for a descent trajectory. Capture conditions are derived for the Center-TRACON Automation System developed at NASA Ames Research Center for automated air traffic control. Various uses of capture conditions are discussed. A Boeing 727-200 aircraft is used to provide numerical examples of capture conditions.
Multi-objective optimisation of aircraft flight trajectories in the ATM and avionics context
NASA Astrophysics Data System (ADS)
Gardi, Alessandro; Sabatini, Roberto; Ramasamy, Subramanian
2016-05-01
The continuous increase of air transport demand worldwide and the push for a more economically viable and environmentally sustainable aviation are driving significant evolutions of aircraft, airspace and airport systems design and operations. Although extensive research has been performed on the optimisation of aircraft trajectories and very efficient algorithms were widely adopted for the optimisation of vertical flight profiles, it is only in the last few years that higher levels of automation were proposed for integrated flight planning and re-routing functionalities of innovative Communication Navigation and Surveillance/Air Traffic Management (CNS/ATM) and Avionics (CNS+A) systems. In this context, the implementation of additional environmental targets and of multiple operational constraints introduces the need to efficiently deal with multiple objectives as part of the trajectory optimisation algorithm. This article provides a comprehensive review of Multi-Objective Trajectory Optimisation (MOTO) techniques for transport aircraft flight operations, with a special focus on the recent advances introduced in the CNS+A research context. In the first section, a brief introduction is given, together with an overview of the main international research initiatives where this topic has been studied, and the problem statement is provided. The second section introduces the mathematical formulation and the third section reviews the numerical solution techniques, including discretisation and optimisation methods for the specific problem formulated. The fourth section summarises the strategies to articulate the preferences and to select optimal trajectories when multiple conflicting objectives are introduced. The fifth section introduces a number of models defining the optimality criteria and constraints typically adopted in MOTO studies, including fuel consumption, air pollutant and noise emissions, operational costs, condensation trails, airspace and airport operations
Optimization and guidance of trajectories for coplanar, aeroassisted orbital transfer
NASA Astrophysics Data System (ADS)
Miele, A.; Wang, T.; Lee, W. Y.
1990-09-01
Guidance trajectories for coplanar aeroassisted orbital transfer (AOT) from high earth orbit to LEO are presently optimized under the assumption of trajectory control during its endoatmospheric phase by alpha-dependent lift coefficient. Optimal trajectories are first computed by minimizing the total velocity impulse required for AOT; attention is then given to guidance trajectories capable of approximating such key properties of the optimal trajectories as minimum altitude, exit velocity, and exit path inclination, in real time. A switch is made from target-altitude guidance to target path inclination-guidance according to the velocity depletion required for optimum flight.
NASA Technical Reports Server (NTRS)
Cook, G.; Witt, R. M.
1976-01-01
The following areas related to landing trajectory optimization research were discussed: (1) programming and modifying the steepest descent optimization procedure, (2) successfully iterating toward the optimum for a four-mile trajectory, (3) beginning optimization runs for a twenty-mile trajectory, and (4) adapt wind tunnel data for computer usage. Other related areas were discussed in detail in the two previous annual reports.
Reentry trajectory optimization based on a multistage pseudospectral method.
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
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
Trajectory module of the NASA Ames Research Center aircraft synthesis program ACSYNT
NASA Technical Reports Server (NTRS)
Tauber, M. E.; Paterson, J. A.
1978-01-01
A program was developed to calculate trajectories for both military and commercial aircraft for use in the aircraft synthesis program, ACSYNT. The function of the trajectory module was to calculate the changes in the vehicle's flight conditions and weight, as fuel is consumed, during the flying of one or more missions. The trajectory calculations started with a takeoff, followed by up to 12 phases chosen from among the following: climb, cruise, acceleration, combat, loiter, descent, and paths. In addition, a balanced field length was computed. The emphasis was on relatively simple formulations and analytic expressions suitable for rapid computation since a prescribed trajectory had to be calculated many times in the process of converging an aircraft design, or finding an optimum configuration. The trajectory module consists of about 2500 cards and operational on a CDC 7600 computer.
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.
Chopper Gun Trajectory Optimization for Spray Forming in Automotive Manufacturing
NASA Astrophysics Data System (ADS)
Chen, Heping; Xi, Ning; Sheng, Weihua; Chen, Yifan; Dahl, Jeffrey
2004-06-01
Automatic chopper gun trajectory generation for spray forming is highly desirable for today's automotive manufacturing. Generating chopper gun trajectories for free-form surfaces to satisfy thickness requirements is still highly challenging due to the complex geometry of free-form surfaces. A CAD-guided chopper gun trajectory generation system for free-form surfaces has been developed in our previous work. A complex surface has to be divided into several patches to satisfy the given constraints. Optimization algorithms are developed to integrate the trajectories of patches to form a trajectory for the free-form surface. A thickness verification method is also provided to verify the generated trajectories. The results of experiments and simulations have shown that the trajectory generation system achieves satisfactory performance. This trajectory generation method can also be applied in many other CAD-guided robot trajectory planning applications.
NASA Technical Reports Server (NTRS)
Prevot, Thomas; Lee, Paul U.
2011-01-01
In this paper we introduce a new complexity metric to predict -in real-time- sector complexity for trajectory-based operations (TBO). TBO will be implemented in the Next Generation Air Transportation System (NextGen). Trajectory-Based Complexity (TBX) is a modified aircraft count that can easily be computed and communicated in a TBO environment based upon predictions of aircraft and weather trajectories. TBX is scaled to aircraft count and represents an alternate and additional means to manage air traffic demand and capacity with more consideration of dynamic factors such as weather, aircraft equipage or predicted separation violations, as well as static factors such as sector size. We have developed and evaluated TBX in the Airspace Operations Laboratory (AOL) at the NASA Ames Research Center during human-in-the-loop studies of trajectory-based concepts since 2009. In this paper we will describe the TBX computation in detail and present the underlying algorithm. Next, we will describe the specific TBX used in an experiment at NASA's AOL. We will evaluate the performance of this metric using data collected during a controller-inthe- loop study on trajectory-based operations at different equipage levels. In this study controllers were prompted at regular intervals to rate their current workload on a numeric scale. When comparing this real-time workload rating to the TBX values predicted for these time periods we demonstrate that TBX is a better predictor of workload than aircraft count. Furthermore we demonstrate that TBX is well suited to be used for complexity management in TBO and can easily be adjusted to future operational concepts.
Cruise flight optimization of a commercial aircraft with winds
NASA Astrophysics Data System (ADS)
Ansberry, Stephen
With high prices for fuel and airfare, companies are looking to minimize operational costs. Reducing aircraft fuel consumption is one strategy companies use to lower costs. During flights, commercial aircraft divide the cruise portion's range into cruise-steps, which are changes in altitude typically in increments of 2,000 ft. These cruise-steps allow the aircraft to ascend in a manner easily tracked by Air Traffic Control. This study focuses on the cruise portion of a commercial aircraft's flight. The number and size of the cruise-steps are free. The amount of cruise-steps corresponds to the number of segments comprising the cruise range. The free variables are the velocity and altitude profiles, and the throttle setting for the step-climbs. Optimized results are compared with the analytical range equations and an actual flight. An upper atmospheric wind model is incorporated into this scenario to determine the effects of jet streams. The main objective of this study is to show an optimized flight trajectory by minimizing fuel costs thereby reducing financial costs of flying.
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.
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.
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
Cascaded Optimization for a Persistent Data Ferrying Unmanned Aircraft
NASA Astrophysics Data System (ADS)
Carfang, Anthony
This dissertation develops and assesses a cascaded method for designing optimal periodic trajectories and link schedules for an unmanned aircraft to ferry data between stationary ground nodes. This results in a fast solution method without the need to artificially constrain system dynamics. Focusing on a fundamental ferrying problem that involves one source and one destination, but includes complex vehicle and Radio-Frequency (RF) dynamics, a cascaded structure to the system dynamics is uncovered. This structure is exploited by reformulating the nonlinear optimization problem into one that reduces the independent control to the vehicle's motion, while the link scheduling control is folded into the objective function and implemented as an optimal policy that depends on candidate motion control. This formulation is proven to maintain optimality while reducing computation time in comparison to traditional ferry optimization methods. The discrete link scheduling problem takes the form of a combinatorial optimization problem that is known to be NP-Hard. A derived necessary condition for optimality guides the development of several heuristic algorithms, specifically the Most-Data-First Algorithm and the Knapsack Adaptation. These heuristics are extended to larger ferrying scenarios, and assessed analytically and through Monte Carlo simulation, showing better throughput performance in the same order of magnitude of computation time in comparison to other common link scheduling policies. The cascaded optimization method is implemented with a novel embedded software system on a small, unmanned aircraft to validate the simulation results with field experiments. To address the sensitivity of results on trajectory tracking performance, a system that combines motion and link control with waypoint-based navigation is developed and assessed through field experiments. The data ferrying algorithms are further extended by incorporating a Gaussian process to opportunistically learn
Trajectory analysis and optimization system (TAOS) user`s manual
Salguero, D.E.
1995-12-01
The Trajectory Analysis and Optimization System (TAOS) is software that simulates point--mass trajectories for multiple vehicles. It expands upon the capabilities of the Trajectory Simulation and Analysis program (TAP) developed previously at Sandia National Laboratories. TAOS is designed to be a comprehensive analysis tool capable of analyzing nearly any type of three degree-of-freedom, point-mass trajectory. Trajectories are broken into segments, and within each segment, guidance rules provided by the user control how the trajectory is computed. Parametric optimization provides a powerful method for satisfying mission-planning constraints. Althrough TAOS is not interactive, its input and output files have been designed for ease of use. When compared to TAP, the capability to analyze trajectories for more than one vehicle is the primary enhancement, although numerous other small improvements have been made. This report documents the methods used in TAOS as well as the input and output file formats.
Optimal singular control with applications to trajectory optimization
NASA Technical Reports Server (NTRS)
Vinh, N. X.
1977-01-01
A comprehensive discussion of the problem of singular control is presented. Singular control enters an optimal trajectory when the so called switching function vanishes identically over a finite time interval. Using the concept of domain of maneuverability, the problem of optical switching is analyzed. Criteria for the optimal direction of switching are presented. The switching, or junction, between nonsingular and singular subarcs is examined in detail. Several theorems concerning the necessary, and also sufficient conditions for smooth junction are presented. The concepts of quasi-linear control and linearized control are introduced. They are designed for the purpose of obtaining approximate solution for the difficult Euler-Lagrange type of optimal control in the case where the control is nonlinear.
Trajectory optimization for a hypersonic vehicle with constraint
NASA Astrophysics Data System (ADS)
Morimoto, Hitoshi
A new approach was developed to solve fuel-optimal problems for a hypersonic vehicle over an entire flight trajectory. A realistic vehicle model was proposed. Although shooting methods are accurate if they converge, initial guesses for costate variables which make the calculation to converge are difficult to obtain. The proposed approach allowed to divide an entire flight trajectory into two segments by selecting a connecting point in the middle of the trajectory. From the connecting point, a maximum-glide problem was solved first. It was proved that when a certain boundary conditions are satisfied, the maximum-glide trajectory constitutes a fuel-optimal trajectory over an entire flight profile. Determination of the maximum-glide trajectory provides with some of the initial values of the costate variables which are needed to start integration backwards from the connecting point. Since shooting methods are very sensitive to the initial guesses of the costates, obtaining accurate initial values of some of the costates is a large advantage. By combining the maximum-glide trajectory and the trajectory obtained by backward integration from the connecting point, an entire flight trajectory was obtained. This trajectory, in general, does not satisfy all the boundary conditions imposed. However, by adjusting the connecting points, the resulting entire flight trajectory approached the final solution. Periodic optimal cruise control problems were also solved with inequality constraints.
Computer optimization of a linac injector trajectory
Sawyer, C.; Detch, J.L. Jr.
1984-01-01
One can determine a computer prediction of the beam radius as a function of axial distance for a linac beam by providing a set of inputs to the computer code, ZFIELD. The trajectory may be improved by varying the magnet current values in the code, but repeated trails may still not attain the best trajectory. Starting with a set of points containing the desired trajectory, one may work the problem backwards and obtain the necessary magnet currents required by the trajectory. In the examples given, a portion of the trajectory is chosen to be parabolic. The trajectory information is used with a differential equation involving beam radius and its derivatives to yield the magnetic field as a function of axial position. Matrix methods are used to obtain the magnet currents from the magnetic field. 4 references, 6 figures.
Aircraft Optimization for Minimum Environmental Impact
NASA Technical Reports Server (NTRS)
Antoine, Nicolas; Kroo, Ilan M.
2001-01-01
The objective of this research is to investigate the tradeoff between operating cost and environmental acceptability of commercial aircraft. This involves optimizing the aircraft design and mission to minimize operating cost while constraining exterior noise and emissions. Growth in air traffic and airport neighboring communities has resulted in increased pressure to severely penalize airlines that do not meet strict local noise and emissions requirements. As a result, environmental concerns have become potent driving forces in commercial aviation. Traditionally, aircraft have been first designed to meet performance and cost goals, and adjusted to satisfy the environmental requirements at given airports. The focus of the present study is to determine the feasibility of including noise and emissions constraints in the early design of the aircraft and mission. This paper introduces the design tool and results from a case study involving a 250-passenger airliner.
Hypersonic Vehicle Trajectory Optimization and Control
NASA Technical Reports Server (NTRS)
Balakrishnan, S. N.; Shen, J.; Grohs, J. R.
1997-01-01
Two classes of neural networks have been developed for the study of hypersonic vehicle trajectory optimization and control. The first one is called an 'adaptive critic'. The uniqueness and main features of this approach are that: (1) they need no external training; (2) they allow variability of initial conditions; and (3) they can serve as feedback control. This is used to solve a 'free final time' two-point boundary value problem that maximizes the mass at the rocket burn-out while satisfying the pre-specified burn-out conditions in velocity, flightpath angle, and altitude. The second neural network is a recurrent network. An interesting feature of this network formulation is that when its inputs are the coefficients of the dynamics and control matrices, the network outputs are the Kalman sequences (with a quadratic cost function); the same network is also used for identifying the coefficients of the dynamics and control matrices. Consequently, we can use it to control a system whose parameters are uncertain. Numerical results are presented which illustrate the potential of these methods.
Trajectory optimization and guidance for a hypersonic vehicle
NASA Technical Reports Server (NTRS)
Lu, Ping
1991-01-01
The optimal ascent problem for a hypersonic vehicle is formulated as an inverse dynamic problem. This formulation is essential in solving the trajectory optimization problem via the nonlinear programming approach. Both minimum-fuel and minimax type of performance indices are considered. The results reveal important features of the optimal trajectory and controls, and they are subsequently used to construct a nonlinear feedback midcourse control law. This control law not only greatly simplifies the difficult constrained optimization problem and yields improved solutions, but is also suitable for onboard implementation. Finally, off-nominal trajectory guidance is addressed using combination of feedback compensation and onboard generation of control through the inverse dynamics approach.
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.
Properties of the optimal trajectories for coplanar, aeroassisted orbital transfer
NASA Astrophysics Data System (ADS)
Miele, A.; Wang, T.; Deaton, A. W.
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.
Aircraft design optimization with multidisciplinary performance criteria
NASA Technical Reports Server (NTRS)
Morris, Stephen; Kroo, Ilan
1989-01-01
The method described here for aircraft design optimization with dynamic response considerations provides an inexpensive means of integrating dynamics into aircraft preliminary design. By defining a dynamic performance index that can be added to a conventional objective function, a designer can investigate the trade-off between performance and handling (as measured by the vehicle's unforced response). The procedure is formulated to permit the use of control system gains as design variables, but does not require full-state feedback. The examples discussed here show how such an approach can lead to significant improvements in the design as compared with the more common sequential design of system and control law.
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.
A Sliding Mode Control with Optimized Sliding Surface for Aircraft Pitch Axis Control System
NASA Astrophysics Data System (ADS)
Lee, Sangchul; Kim, Kwangjin; Kim, Youdan
A sliding mode controller with an optimized sliding surface is proposed for an aircraft control system. The quadratic type of performance index for minimizing the angle of attack and the angular rate of the aircraft in the longitudinal motion is used to design the sliding surface. For optimization of the sliding surface, a Hamilton-Jacobi-Bellman (HJB) equation is formulated and it is solved through a numerical algorithm using a Generalized HJB (GHJB) equation and the Galerkin spectral method. The solution of this equation denotes a nonlinear sliding surface, on which the trajectory of the system approximately satisfies the optimality condition. Numerical simulation is performed for a nonlinear aircraft model with an optimized sliding surface and a simple linear sliding surface. The simulation result demonstrates that the proposed controller can be effectively applied to the longitudinal maneuver of an aircraft.
Rapid Parameterization Schemes for Aircraft Shape Optimization
NASA Technical Reports Server (NTRS)
Li, Wu
2012-01-01
A rapid shape parameterization tool called PROTEUS is developed for aircraft shape optimization. This tool can be applied directly to any aircraft geometry that has been defined in PLOT3D format, with the restriction that each aircraft component must be defined by only one data block. PROTEUS has eight types of parameterization schemes: planform, wing surface, twist, body surface, body scaling, body camber line, shifting/scaling, and linear morphing. These parametric schemes can be applied to two types of components: wing-type surfaces (e.g., wing, canard, horizontal tail, vertical tail, and pylon) and body-type surfaces (e.g., fuselage, pod, and nacelle). These schemes permit the easy setup of commonly used shape modification methods, and each customized parametric scheme can be applied to the same type of component for any configuration. This paper explains the mathematics for these parametric schemes and uses two supersonic configurations to demonstrate the application of these schemes.
Optimal combat maneuvers of a next-generation jet fighter aircraft
NASA Astrophysics Data System (ADS)
Dabney, James Bruster
This thesis deals with the optimization of four classes of combat maneuvers for a next-generation jet fighter aircraft: climb maneuvers, fly-to-point maneuvers, pop-up attack maneuvers, and dive recovery maneuvers. For the first three classes of maneuvers, the optimization criterion is the minimization of the flight time, resulting in a Mayer-Bolza problem of optimal control; for the fourth class, the optimization criterion is the minimization of the maximum altitude loss during dive recovery, resulting in a Chebyshev problem of optimal control. Each class of problems is solved using the sequential gradient-restoration algorithm for optimal control. Among the four classes of combat maneuvers studied, only dive recovery benefits from the ability of a next-generation fighter aircraft to maneuver at extremely high angles of attack. For the other three classes, relatively low angles of attack are required. The optimal climb trajectories are characterized by three distinct segments: a central segment often flown with a load factor of nearly 1 and two terminal segments (dive or zoom) to and from the central segment. The central and final segments are nearly independent of the initial conditions, instead being dominated by the final conditions. The optimal fly-to-point trajectories consist of three segments: turning, characterized by relatively high load factor; level acceleration at maximum thrust; and finally, resumption of steady-state cruising. The effects of the heading change magnitude and the load factor limit are discussed. The optimal pop-up trajectories consist of three segments flown at maximum power: pitch-up, zoom, and pitch-down. The effects of using the afterburner, heading change magnitude, and dive angle magnitude are discussed. The optimal dive recovery trajectories consist of one to three segments, depending on initial speed and flight path angle. All the optimal trajectories conclude with a pitch-up at the maximum available load factor. For very low
Solar sail time-optimal interplanetary transfer trajectory design
NASA Astrophysics Data System (ADS)
Gong, Sheng-Pin; Gao, Yun-Feng; Li, Jun-Feng
2011-08-01
The fuel consumption associated with some interplanetary transfer trajectories using chemical propulsion is not affordable. A solar sail is a method of propulsion that does not consume fuel. Transfer time is one of the most pressing problems of solar sail transfer trajectory design. This paper investigates the time-optimal interplanetary transfer trajectories to a circular orbit of given inclination and radius. The optimal control law is derived from the principle of maximization. An indirect method is used to solve the optimal control problem by selecting values for the initial adjoint variables, which are normalized within a unit sphere. The conditions for the existence of the time-optimal transfer are dependent on the lightness number of the sail and the inclination and radius of the target orbit. A numerical method is used to obtain the boundary values for the time-optimal transfer trajectories. For the cases where no time-optimal transfer trajectories exist, first-order necessary conditions of the optimal control are proposed to obtain feasible solutions. The results show that the transfer time decreases as the minimum distance from the Sun decreases during the transfer duration. For a solar sail with a small lightness number, the transfer time may be evaluated analytically for a three-phase transfer trajectory. The analytical results are compared with previous results and the associated numerical results. The transfer time of the numerical result here is smaller than the transfer time from previous results and is larger than the analytical result.
Rapid Trajectory Optimization for the ARES I Launch Vehicle
NASA Technical Reports Server (NTRS)
Dukeman, Greg A.; Hill, Ashley D.
2008-01-01
A simplified ascent trajectory optimization procedure has been developed with application to NASA's proposed Ares I launch vehicle. In the interest of minimizing bending loads and ensuring safe separation of the first-stage solid rocket motor, the vehicle is con- strained to follow a gravity-turn trajectory. This reduces the design space to just two free parameters, the pitch rate after a short vertical rise phase to clear the launch pad, and initial launch azimuth. The pitch rate primarily controls the in-plane parameters (altitude, speed, flight path angle) of the trajectory whereas the launch azimuth primarily controls the out-of-plane portion (velocity heading.) Thus, the optimization can be mechanized as two one-dimensional searches that converge quickly and reliably. The method is compared with POST-optimized trajectories to verify its optimality.
Programs To Optimize Simulated Trajectories (POST\\6DPOST)
NASA Technical Reports Server (NTRS)
Brauer, Garry L.; Olson, David W.; Stevenson, Robert
1993-01-01
Designed for optimizing simulated trajectories, POST is point mass, three degrees-of-freedom program while extended 6DPOST permits rigid-body six degrees-of-freedom models. Handles sophisticated problems such as ascent, orbital maneuvers, and reentry.
Multidisciplinary optimization applied to a transport aircraft
NASA Technical Reports Server (NTRS)
Giles, G. L.; Wrenn, G. A.
1984-01-01
Decomposition of a large optimization problem into several smaller subproblems has been proposed as an approach to making large-scale optimization problems tractable. To date, the characteristics of this approach have been tested on problems of limited complexity. The objective of the effort is to demonstrate the application of this multilevel optimization method on a large-scale design study using analytical models comparable to those currently being used in the aircraft industry. The purpose of the design study which is underway to provide this demonstration is to generate a wing design for a transport aircraft which will perform a specified mission with minimum block fuel. A definition of the problem; a discussion of the multilevel composition which is used for an aircraft wing; descriptions of analysis and optimization procedures used at each level; and numerical results obtained to date are included. Computational times required to perform various steps in the process are also given. Finally, a summary of the current status and plans for continuation of this development effort are given.
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.
Aircraft family design using enhanced collaborative optimization
NASA Astrophysics Data System (ADS)
Roth, Brian Douglas
Significant progress has been made toward the development of multidisciplinary design optimization (MDO) methods that are well-suited to practical large-scale design problems. However, opportunities exist for further progress. This thesis describes the development of enhanced collaborative optimization (ECO), a new decomposition-based MDO method. To support the development effort, the thesis offers a detailed comparison of two existing MDO methods: collaborative optimization (CO) and analytical target cascading (ATC). This aids in clarifying their function and capabilities, and it provides inspiration for the development of ECO. The ECO method offers several significant contributions. First, it enhances communication between disciplinary design teams while retaining the low-order coupling between them. Second, it provides disciplinary design teams with more authority over the design process. Third, it resolves several troubling computational inefficiencies that are associated with CO. As a result, ECO provides significant computational savings (relative to CO) for the test cases and practical design problems described in this thesis. New aircraft development projects seldom focus on a single set of mission requirements. Rather, a family of aircraft is designed, with each family member tailored to a different set of requirements. This thesis illustrates the application of decomposition-based MDO methods to aircraft family design. This represents a new application area, since MDO methods have traditionally been applied to multidisciplinary problems. ECO offers aircraft family design the same benefits that it affords to multidisciplinary design problems. Namely, it simplifies analysis integration, it provides a means to manage problem complexity, and it enables concurrent design of all family members. In support of aircraft family design, this thesis introduces a new wing structural model with sufficient fidelity to capture the tradeoffs associated with component
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.
Efficient Optimization of Low-Thrust Spacecraft Trajectories
NASA Technical Reports Server (NTRS)
Lee, Seungwon; Fink, Wolfgang; Russell, Ryan; Terrile, Richard; Petropoulos, Anastassios; vonAllmen, Paul
2007-01-01
A paper describes a computationally efficient method of optimizing trajectories of spacecraft driven by propulsion systems that generate low thrusts and, hence, must be operated for long times. A common goal in trajectory-optimization problems is to find minimum-time, minimum-fuel, or Pareto-optimal trajectories (here, Pareto-optimality signifies that no other solutions are superior with respect to both flight time and fuel consumption). The present method utilizes genetic and simulated-annealing algorithms to search for globally Pareto-optimal solutions. These algorithms are implemented in parallel form to reduce computation time. These algorithms are coupled with either of two traditional trajectory- design approaches called "direct" and "indirect." In the direct approach, thrust control is discretized in either arc time or arc length, and the resulting discrete thrust vectors are optimized. The indirect approach involves the primer-vector theory (introduced in 1963), in which the thrust control problem is transformed into a co-state control problem and the initial values of the co-state vector are optimized. In application to two example orbit-transfer problems, this method was found to generate solutions comparable to those of other state-of-the-art trajectory-optimization methods while requiring much less computation time.
Nonlinear Optimal Trajectories Using Successive Linearization
1977-06-28
integral sign represents a penalty for the local vertical and passing through the vehicle deviations of the perturbed trajectory from the at time equals... integral sign represents the penalty for control variations about the nominal, and needs z s - sin y (14) to be weighted to ensure that the control does
Optimal trajectories for efficient atomic transport without final excitation
Chen Xi; Torrontegui, E.; Muga, J. G.; Stefanatos, Dionisis; Li, Jr-Shin
2011-10-15
We design optimal harmonic-trap trajectories to transport cold atoms without final excitation, combining an inverse engineering technique based on Lewis-Riesenfeld invariants with optimal control theory. Since actual traps are not really harmonic, we keep the relative displacement between the center of mass of the transport modes and the trap center bounded. Under this constraint, optimal protocols are found according to different physical criteria. The minimum time solution has a ''bang-bang'' form, and the minimum displacement solution is of ''bang-off-bang'' form. The optimal trajectories for minimizing the transient energy are also discussed.
Integrating the Base of Aircraft Data (BADA) in CTAS Trajectory Synthesizer
NASA Technical Reports Server (NTRS)
Abramson, Michael; Ali, Kareem
2012-01-01
The Center-Terminal Radar Approach Control (TRACON) Automation System (CTAS), developed at NASA Ames Research Center for assisting controllers in the management and control of air traffic in the extended terminal area, supports the modeling of more than four hundred aircraft types. However, 90% of them are supported indirectly by mapping them to one of a relatively few aircraft types for which CTAS has detailed drag and engine thrust models. On the other hand, the Base of Aircraft Data (BADA), developed and maintained by Eurocontrol, supports more than 300 aircraft types, about one third of which are directly supported, i.e. they have validated performance data. All these data were made available for CTAS by integrating BADA version 3.8 into CTAS Trajectory Synthesizer (TS). Several validation tools were developed and used to validate the integrated code and to evaluate the accuracy of trajectory predictions generated using CTAS "native" and BADA Aircraft Performance Models (APM) comparing them with radar track data. Results of these comparisons indicate that the two models have different strengths and weaknesses. The BADA APM can improve the accuracy of CTAS predictions at least for some aircraft types, especially small aircraft, and for some flight phases, especially climb.
NASA Astrophysics Data System (ADS)
Masternak, Tadeusz J.
This research determines temperature-constrained optimal trajectories for a scramjet-based hypersonic reconnaissance vehicle by developing an optimal control formulation and solving it using a variable order Gauss-Radau quadrature collocation method with a Non-Linear Programming (NLP) solver. The vehicle is assumed to be an air-breathing reconnaissance aircraft that has specified takeoff/landing locations, airborne refueling constraints, specified no-fly zones, and specified targets for sensor data collections. A three degree of freedom scramjet aircraft model is adapted from previous work and includes flight dynamics, aerodynamics, and thermal constraints. Vehicle control is accomplished by controlling angle of attack, roll angle, and propellant mass flow rate. This model is incorporated into an optimal control formulation that includes constraints on both the vehicle and mission parameters, such as avoidance of no-fly zones and coverage of high-value targets. To solve the optimal control formulation, a MATLAB-based package called General Pseudospectral Optimal Control Software (GPOPS-II) is used, which transcribes continuous time optimal control problems into an NLP problem. In addition, since a mission profile can have varying vehicle dynamics and en-route imposed constraints, the optimal control problem formulation can be broken up into several "phases" with differing dynamics and/or varying initial/final constraints. Optimal trajectories are developed using several different performance costs in the optimal control formulation: minimum time, minimum time with control penalties, and maximum range. The resulting analysis demonstrates that optimal trajectories that meet specified mission parameters and constraints can be quickly determined and used for larger-scale operational and campaign planning and execution.
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.
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.
Some impulsive rendezvous trajectories and their possible optimality.
NASA Technical Reports Server (NTRS)
Peltier, J. P.
1972-01-01
Two- and three-impulse trajectories are investigated for fixed-time, fixed-angle rendezvous between vacant circular coplanar orbits, for trip angles less than, or equal to 2 pi in magnitude. For two-impulse trajectories, general features of the characteristic velocity function are outlined. Parameters of the intermediate orbit are reviewed. Attention is given to limiting cases. Computation of the adjoint system helps to define the domain of possible optimality foajectories: it is a closed domain in the trip time, trip angle plane. Waiting periods on terminal orbits are considered. The domain of possible optimality is defined using Lawden's primer vrtory. This domain extends to infinity if the radius ratio of terminal orbits is less than 15.6. Three-impulse trajectories are tried in cases where two-impulse trajectories, with or without cost, have been found nonoptimal. Improvements on the characteristic velocity are thus obtained.
Optimal Aircraft Control Upset Recovery With and Without Component Failures
NASA Technical Reports Server (NTRS)
Sparks, Dean W.; Moerder, Daniel D.
2002-01-01
This paper treats the problem of recovering sustainable nondescending (safe) flight in a transport aircraft after one or more of its control effectors fail. Such recovery can be a challenging goal for many transport aircraft currently in the operational fleet for two reasons. First, they have very little redundancy in their means of generating control forces and moments. These aircraft have, as primary control surfaces, a single rudder and pairwise elevators and aileron/spoiler units that provide yaw, pitch, and roll moments with sufficient bandwidth to be used in stabilizing and maneuvering the airframe. Beyond this, throttling the engines can provide additional moments, but on a much slower time scale. Other aerodynamic surfaces, such as leading and trailing edge flaps, are only intended to be placed in a position and left, and are, hence, very slow-moving. Because of this, loss of a primary control surface strongly degrades the controllability of the vehicle, particularly when the failed effector becomes stuck in a non-neutral position where it exerts a disturbance moment that must be countered by the remaining operating effectors. The second challenge in recovering safe flight is that these vehicles are not agile, nor can they tolerate large accelerations. This is of special importance when, at the outset of the recovery maneuver, the aircraft is flying toward the ground, as is frequently the case when there are major control hardware failures. Recovery of safe flight is examined in this paper in the context of trajectory optimization. For a particular transport aircraft, and a failure scenario inspired by an historical air disaster, recovery scenarios are calculated with and without control surface failures, to bring the aircraft to safe flight from the adverse flight condition that it had assumed, apparently as a result of contact with a vortex from a larger aircraft's wake. An effort has been made to represent relevant airframe dynamics, acceleration limits
An optimal trajectory design for debris deorbiting
NASA Astrophysics Data System (ADS)
Ouyang, Gaoxiang; Dong, Xin; Li, Xin; Zhang, Yang
2016-01-01
The problem of deorbiting debris is studied in this paper. As a feasible measure, a disposable satellite would be launched, attach to debris, and deorbit the space debris using a technology named electrodynamic tether (EDT). In order to deorbit multiple debris as many as possible, a suboptimal but feasible and efficient trajectory set has been designed to allow a deorbiter satellite tour the LEO small bodies per one mission. Finally a simulation given by this paper showed that a 600 kg satellite is capable of deorbiting 6 debris objects in about 230 days.
Stratospheric balloons trajectories predictions and optimizations
NASA Astrophysics Data System (ADS)
Musso, I.; Cardillo, A.; Memmo, A.
Trajectory predictions are becoming an important part of the stratospheric balloons activities due to the increased safety and scientific requirements Often high-populated areas must be avoided while the balloon could be asked to reach regions interesting for scientific measurements The balloon trajectory s reconstruction is essentially a time propagation of local wind vectors along the expected altitudes As consequence the predictor is composed of two interconnected subsystems one for the definition of vertical position and one for the wind predictions and horizontal propagation at every time step Forecast data permits up to 6 days of wind vector predictions Below 10mb altitude mesoscale models reduce the wind prediction uncertainty Directly measured information comes from radiosoundings few hours before flight or during it GPS onboard the balloon telemetry is a second direct wind data source The software has to mesh these different flows of information giving to the measured values a weight inversely proportional to the time and space distance from wind measurements In this way sounding data if properly used are able to reduce the path s dispersion A thermodynamic model reconstructs the balloon vertical positions Heat exchanges between internal gas and external environment are very sensitive to air temperature infrared radiance and albedo Again forecast data have to be properly meshed with radiosoundings and satellite images to obtain the best values of these border conditions They will apply the thermodynamic balloon model We
NASA Astrophysics Data System (ADS)
Striepe, Scott Allen
The objectives of this research were to develop a reconstruction capability using the Program to Optimize Simulated Trajectories II (POST2), apply this capability to reconstruct the Huygens Titan probe entry, descent, and landing (EDL) trajectory, evaluate the newly developed POST2 reconstruction module, analyze the reconstructed trajectory, and assess the pre-flight simulation models used for Huygens EDL simulation. An extended Kalman filter (EKF) module was developed and integrated into POST2 to enable trajectory reconstruction (especially when using POST2-based mission specific simulations). Several validation cases, ranging from a single, constant parameter estimate to multivariable estimation cases similar to an actual mission flight, were executed to test the POST2 reconstruction module. Trajectory reconstruction of the Huygens entry probe at Titan was accomplished using accelerometer measurements taken during flight to adjust an estimated state (e.g., position, velocity, parachute drag, wind velocity, etc.) in a POST2-based simulation developed to support EDL analyses and design prior to entry. Although the main emphasis of the trajectory reconstruction was to evaluate models used in the NASA pre-entry trajectory simulation, the resulting reconstructed trajectory was also assessed to provide an independent evaluation of the ESA result. Major findings from this analysis include: Altitude profiles from this analysis agree well with other NASA and ESA results but not with Radar data, whereas a scale factor of about 0.93 would bring the radar measurements into compliance with these results; entry capsule aerodynamics predictions (axial component only) were well within 3-sigma bounds established pre-flight for most of the entry when compared to reconstructed values; Main parachute drag of 9% to 19% above ESA model was determined from the reconstructed trajectory; based on the tilt sensor and accelerometer data, the conclusion from this assessment was that the
Optimization and sensitivity studies of flight-path trajectories. [computer programs
NASA Technical Reports Server (NTRS)
Cook, G.; Witt, R. M.
1975-01-01
The optimization of landing trajectories of the Boeing 737 is presented. The primary factor considered was the noise delivered to the population residing near an air terminal but passenger comfort, fuel consumption and time elapsed during the maneuver were also considered. A digital simulation of the aircraft, a noise model and a passenger comfort model, was completed. The digital simulation was made more efficient time-wise. A population model for an urban area was developed and the noise model was integrated into the population model. A steepest descent optimization algorithm was programmed. Some constant glide slope trajectories into an urban Airport were simulated and evaluated with respect to the performance index, and their ground track plotted.
A system approach to aircraft optimization
NASA Technical Reports Server (NTRS)
Sobieszczanski-Sobieski, Jaroslaw
1991-01-01
Mutual couplings among the mathematical models of physical phenomena and parts of a system such as an aircraft complicate the design process because each contemplated design change may have a far reaching consequence throughout the system. Techniques are outlined for computing these influences as system design derivatives useful for both judgemental and formal optimization purposes. The techniques facilitate decomposition of the design process into smaller, more manageable tasks and they form a methodology that can easily fit into existing engineering organizations and incorporate their design tools.
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.
Trajectory Optimization for Spacecraft Collision Avoidance
2013-09-01
versus out-of plane maneuvering. This study made use of the Radau Pseudospectral Method to develop this minimum thrust profile. This method was run in... p Equinoctial element q Equinoctial element r Inertial position vector r Magnitude of the inertial position vector T Thrust magnitude t Time t0...imported into MATLAB® for optimization using General Pseudospectral Optimal Control Software (GPOPS-II). This software utilized the Radau Pseudospectral
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.
The vibro-acoustic mapping of low gravity trajectories on a Learjet aircraft
NASA Technical Reports Server (NTRS)
Grodsinsky, C. M.; Sutliff, T. J.
1990-01-01
Terrestrial low gravity research techniques have been employed to gain a more thorough understanding of basic science and technology concepts. One technique frequently used involves flying parabolic trajectories aboard the NASA Lewis Research Center Learjet aircraft. A measurement program was developed to support an isolation system conceptual design. This program primarily was intended to measure time correlated high frequency accelerations (up to 100 Hz) present at various locations throughout the Learjet during a series of trajectories and flights. As suspected, the measurements obtained revealed that the environment aboard such an aircraft can not simply be described in terms of the static level low gravity g vector obtained, but that it also must account for both rigid body and high frequency vibro-acoustic dynamics.
Optimal Trajectory Generation for Multiple Asteroid Rendezvous
2007-06-01
distinguishable ways. For this research, the lack of perturbations to the orbits permits the simple use of the equations generated by Johannes Kepler and Isaac...on careful observations. Kepler used the data collected throughout Tycho Brahe’s life to come up with his three laws; 1) the orbits of the planets...these problems, Isaac Newton invented calculus of variations.7 Johannes Bernoulli was also instrumental in the initial surge for optimization as he
Trajectory Control and Optimization for Responsive Spacecraft
2012-03-22
36 3.2.2 Controlling the Position of the Spacecraft Within the Orbit . . 37 vi Page 3.2.3 Thrust-coast Duty...focuses on methods for performing minimum time in-plane maneuvers. The optimal control problem for an orbiting spacecraft perturbed by a small, constant...focuses on feedback control methods for performing in-plane maneuvers. Lyapunov theory is applied to the nonlinear equations of motion for an orbiting space
Program to Optimize Simulated Trajectories (POST). Volume 3: Programmer's manual
NASA Technical Reports Server (NTRS)
Brauer, G. L.; Cornick, D. E.; Habeger, A. R.; Petersen, F. M.; Stevenson, R.
1975-01-01
Information pertinent to the programmer and relating to the program to optimize simulated trajectories (POST) is presented. Topics discussed include: program structure and logic, subroutine listings and flow charts, and internal FORTRAN symbols. The POST core requirements are summarized along with program macrologic.
Research in navigation and optimization for space trajectories
NASA Technical Reports Server (NTRS)
Pines, S.; Kelley, H. J.
1979-01-01
Topics covered include: (1) initial Cartesian coordinates for rapid precision orbit prediction; (2) accelerating convergence in optimization methods using search routines by applying curvilinear projection ideas; (3) perturbation-magnitude control for difference-quotient estimation of derivatives; and (4) determining the accelerometer bias for in-orbit shuttle trajectories.
Heliocentric interplanetary low thrust trajectory optimization program, supplement 1
NASA Technical Reports Server (NTRS)
Mann, F. I.; Horsewood, J. L.
1974-01-01
The modifications and improvements made to the HILTOP electric propulsion trajectory optimization computer program up through the end of 1974 is described. 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. The report contains the new analysis describing these features, a complete description of program input quantities, and sample cases of computer output illustrating the new program capabilities.
Calculation of an optimal two impulse Earth-Moon trajectory
NASA Astrophysics Data System (ADS)
McGreevy, John Joseph
In this paper, variational methods are applied to the the two-impulse Earth-Moon trajectory problem. Advantages of the circular-restricted three-body problem are utilized to solve the optimal control problem for this orbital transfer. The free terminal time problem is solved by performing calculations using a fixed terminal time approach, and determining the optimal terminal time from the results of the fixed-time calculations. The effect of changing initial orbit conditions is also studied.
Singular perturbation analysis of AOTV-related trajectory optimization problems
NASA Technical Reports Server (NTRS)
Calise, Anthony J.; Bae, Gyoung H.
1990-01-01
The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality
Flow rate and trajectory of water spray produced by an aircraft tire
NASA Technical Reports Server (NTRS)
Daugherty, Robert H.; Stubbs, Sandy M.
1986-01-01
One of the risks associated with wet runway aircraft operation is the ingestion of water spray produced by an aircraft's tires into its engines. This problem can be especially dangerous at or near rotation speed on the takeoff roll. An experimental investigation was conducted in the NASA Langley Research Center Hydrodynamics Research Facility to measure the flow rate and trajectory of water spray produced by an aircraft nose tire operating on a flooded runway. The effects of various parameters on the spray patterns including distance aft of nosewheel, speed, load, and water depth were evaluated. Variations in the spray pattern caused by the airflow about primary structure such as the fuselage and wing are discussed. A discussion of events in and near the tire footprint concerning spray generation is included.
A robust optimization methodology for preliminary aircraft design
NASA Astrophysics Data System (ADS)
Prigent, S.; Maréchal, P.; Rondepierre, A.; Druot, T.; Belleville, M.
2016-05-01
This article focuses on a robust optimization of an aircraft preliminary design under operational constraints. According to engineers' know-how, the aircraft preliminary design problem can be modelled as an uncertain optimization problem whose objective (the cost or the fuel consumption) is almost affine, and whose constraints are convex. It is shown that this uncertain optimization problem can be approximated in a conservative manner by an uncertain linear optimization program, which enables the use of the techniques of robust linear programming of Ben-Tal, El Ghaoui, and Nemirovski [Robust Optimization, Princeton University Press, 2009]. This methodology is then applied to two real cases of aircraft design and numerical results are presented.
Trajectory optimization based on differential inclusion
NASA Technical Reports Server (NTRS)
Seywald, Hans
1993-01-01
A method for generating finite-dimensional approximations to the solutions of optimal control problems is introduced. By employing a description of the dynamical system in terms of its attainable sets in favor of using differential equations, the controls are completely eliminated from the system model. Besides reducing the dimensionality of the discretized problem compared to state-of-the-art collocation methods, this approach also alleviates the search for initial guesses from where standard gradient search methods are able to converge. The mechanics of the new method are illustrated on a simple double integrator problem. The performance of the new algorithm is demonstrated on a 1-D rocket ascent problem ('Goddard Problem') in presence of a dynamic pressure constraint.
Calculation of free-fall trajectories using numerical optimization methods.
NASA Technical Reports Server (NTRS)
Hull, D. G.; Fowler, W. T.; Gottlieb, R. G.
1972-01-01
An important problem in space flight is the calculation of trajectories for nonthrusting vehicles between fixed points in a given time. A new procedure based on Hamilton's principle for solving such two-point boundary-value problems is presented. It employs numerical optimization methods to perform the extremization required by Hamilton's principle. This procedure is applied to the calculation of an Earth-Moon trajectory. The results show that the initial guesses required to obtain an iteration procedure which converges are not critical and that convergence can be obtained to any predetermined degree of accuracy.
Low thrust space vehicle trajectory optimization using regularized variables
NASA Technical Reports Server (NTRS)
Schwenzfeger, K. J.
1974-01-01
Optimizing the trajectory of a low thrust space vehicle usually means solving a nonlinear two point boundary value problem. In general, accuracy requirements necessitate extensive computation times. In celestial mechanics, regularizing transformations of the equations of motion are used to eliminate computational and analytical problems that occur during close approaches to gravitational force centers. It was shown in previous investigations that regularization in the formulation of the trajectory optimization problem may reduce the computation time. In this study, a set of regularized equations describing the optimal trajectory of a continuously thrusting space vehicle is derived. The computational characteristics of the set are investigated and compared to the classical Newtonian unregularized set of equations. The comparison is made for low thrust, minimum time, escape trajectories and numerical calculations of Keplerian orbits. The comparison indicates that in the cases investigated for bad initial guesses of the known boundary values a remarkable reduction in the computation time was achieved. Furthermore, the investigated set of regularized equations shows high numerical stability even for long duration flights and is less sensitive to errors in the guesses of the unknown boundary values.
Optimization Based Trajectory Planning of Human Upper Body
2004-01-01
such as the minimum torque change model. Considerable research has been done to obtain optimal robot path. Saramago et al. (1998; 2000; 2002) have...Robotics and Automation, Vol. 2, pp. 802-807. 25. Saramago , S.F.P. and Steffen Jr, V., 2000, “Optimal Trajectory Planning of Robot Manipulators in...the Presence of Moving Obstacles, ” Mechanism and Machine Theory 35(8), 1079–1094. 26. Saramago , S.F.P. and Steffen Jr, V., 1998, “Optimization of the
Optimal lunar soft landing trajectories using taboo evolutionary programming
NASA Astrophysics Data System (ADS)
Mutyalarao, M.; Raj, M. Xavier James
A safe lunar landing is a key factor to undertake an effective lunar exploration. Lunar lander consists of four phases such as launch phase, the earth-moon transfer phase, circumlunar phase and landing phase. The landing phase can be either hard landing or soft landing. Hard landing means the vehicle lands under the influence of gravity without any deceleration measures. However, soft landing reduces the vertical velocity of the vehicle before landing. Therefore, for the safety of the astronauts as well as the vehicle lunar soft landing with an acceptable velocity is very much essential. So it is important to design the optimal lunar soft landing trajectory with minimum fuel consumption. Optimization of Lunar Soft landing is a complex optimal control problem. In this paper, an analysis related to lunar soft landing from a parking orbit around Moon has been carried out. A two-dimensional trajectory optimization problem is attempted. The problem is complex due to the presence of system constraints. To solve the time-history of control parameters, the problem is converted into two point boundary value problem by using the maximum principle of Pontrygen. Taboo Evolutionary Programming (TEP) technique is a stochastic method developed in recent years and successfully implemented in several fields of research. It combines the features of taboo search and single-point mutation evolutionary programming. Identifying the best unknown parameters of the problem under consideration is the central idea for many space trajectory optimization problems. The TEP technique is used in the present methodology for the best estimation of initial unknown parameters by minimizing objective function interms of fuel requirements. The optimal estimation subsequently results into an optimal trajectory design of a module for soft landing on the Moon from a lunar parking orbit. Numerical simulations demonstrate that the proposed approach is highly efficient and it reduces the minimum fuel
Advances in low-thrust trajectory optimization and flight mechanics
NASA Astrophysics Data System (ADS)
Gao, Yang
The dissertation presents advances in trajectory optimization and flight mechanics of low-thrust spacecraft. With the aid of the extended multiple-shooting techniques with state and costate nodes, the hybrid method and the direct-shooting method are systematically described and used to solve a variety of optimal orbit transfer problems. The optimization methods are demonstrated by presenting solutions for optimal Earth-orbit and interplanetary trajectory examples, and complex interplanetary missions using solar electric propulsion (such as Eros sample return and Pluto-flyby missions). Alternative formulations of equations of motion are discussed, which include inertial frame transformation in terms of three Euler angles and a modified set of equinoctial elements using non-dimensional angular momentum. Finally, a low-thrust Earth-capture guidance scheme is developed and presented, which makes novel use of Perkins' low-thrust universal solution and doesn't require a stored reference trajectory. The simplicity and performance of this new guidance design makes it a viable candidate for onboard implementation.
Augmenting Parametric Optimal Ascent Trajectory Modeling with Graph Theory
NASA Technical Reports Server (NTRS)
Dees, Patrick D.; Zwack, Matthew R.; Edwards, Stephen; Steffens, Michael
2016-01-01
It has been well documented that decisions made in the early stages of Conceptual and Pre-Conceptual design commit up to 80% of total Life-Cycle Cost (LCC) while engineers know the least about the product they are designing [1]. Once within Preliminary and Detailed design however, making changes to the design becomes far more difficult to enact in both cost and schedule. Primarily this has been due to a lack of detailed data usually uncovered later during the Preliminary and Detailed design phases. In our current budget-constrained environment, making decisions within Conceptual and Pre-Conceptual design which minimize LCC while meeting requirements is paramount to a program's success. Within the arena of launch vehicle design, optimizing the ascent trajectory is critical for minimizing the costs present within such concerns as propellant, aerodynamic, aeroheating, and acceleration loads while meeting requirements such as payload delivered to a desired orbit. In order to optimize the vehicle design its constraints and requirements must be known, however as the design cycle proceeds it is all but inevitable that the conditions will change. Upon that change, the previously optimized trajectory may no longer be optimal, or meet design requirements. The current paradigm for adjusting to these updates is generating point solutions for every change in the design's requirements [2]. This can be a tedious, time-consuming task as changes in virtually any piece of a launch vehicle's design can have a disproportionately large effect on the ascent trajectory, as the solution space of the trajectory optimization problem is both non-linear and multimodal [3]. In addition, an industry standard tool, Program to Optimize Simulated Trajectories (POST), requires an expert analyst to produce simulated trajectories that are feasible and optimal [4]. In a previous publication the authors presented a method for combatting these challenges [5]. In order to bring more detailed information
NASA Technical Reports Server (NTRS)
Neuman, F.
1980-01-01
A method for determining fuel conservative terminal approaches that include changes in altitude, speed, and heading are described. Three different guidance system concepts for STOL aircraft were evaluated in flight: (1) a fixed trajectory system; (2) a system that included a fixed path and a real time synthesized capture flight path; and (3) a trajectory synthesizing system. Simulation results for the augmentor wing jet STOL research aircraft and for the Boeing 727 aircraft are discussed. The results indicate that for minimum fuel consumption, two guidance deceleration segments are required.
Coupled Low-thrust Trajectory and System Optimization via Multi-Objective Hybrid Optimal Control
NASA Technical Reports Server (NTRS)
Vavrina, Matthew A.; Englander, Jacob Aldo; Ghosh, Alexander R.
2015-01-01
The optimization of low-thrust trajectories is tightly coupled with the spacecraft hardware. Trading trajectory characteristics with system parameters ton identify viable solutions and determine mission sensitivities across discrete hardware configurations is labor intensive. Local independent optimization runs can sample the design space, but a global exploration that resolves the relationships between the system variables across multiple objectives enables a full mapping of the optimal solution space. A multi-objective, hybrid optimal control algorithm is formulated using a multi-objective genetic algorithm as an outer loop systems optimizer around a global trajectory optimizer. The coupled problem is solved simultaneously to generate Pareto-optimal solutions in a single execution. The automated approach is demonstrated on two boulder return missions.
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.
Combining Simulation Tools for End-to-End Trajectory Optimization
NASA Technical Reports Server (NTRS)
Whitley, Ryan; Gutkowski, Jeffrey; Craig, Scott; Dawn, Tim; Williams, Jacobs; Stein, William B.; Litton, Daniel; Lugo, Rafael; Qu, Min
2015-01-01
Trajectory simulations with advanced optimization algorithms are invaluable tools in the process of designing spacecraft. Due to the need for complex models, simulations are often highly tailored to the needs of the particular program or mission. NASA's Orion and SLS programs are no exception. While independent analyses are valuable to assess individual spacecraft capabilities, a complete end-to-end trajectory from launch to splashdown maximizes potential performance and ensures a continuous solution. In order to obtain end-to-end capability, Orion's in-space tool (Copernicus) was made to interface directly with the SLS's ascent tool (POST2) and a new tool to optimize the full problem by operating both simulations simultaneously was born.
Impulsive optimal control model for the trajectory of horizontal wells
NASA Astrophysics Data System (ADS)
Li, An; Feng, Enmin; Wang, Lei
2009-01-01
This paper presents an impulsive optimal control model for solving the optimal designing problem of the trajectory of horizontal wells. We take fully into account the effect of unknown disturbances in drilling. The optimal control problem can be converted into a nonlinear parametric optimization by integrating the state equation. We discuss here that the locally optimal solution depends in a continuous way on the parameters (disturbances) and utilize this property to propose a revised Hooke-Jeeves algorithm. The uniform design technique is incorporated into the revised Hooke-Jeeves algorithm to handle the multimodal objective function. The numerical simulation is in accordance with theoretical results. The numerical results illustrate the validity of the model and efficiency of the algorithm.
2009-09-01
INFORMATION-CENTRIC APPROACH TO AUTONOMOUS TRAJECTORY PLANNING UTILIZING OPTIMAL CONTROL TECHNIQUES by Michael A. Hurni September 2009...Dissertation 4. TITLE AND SUBTITLE: An Information-centric Approach to Autonomous Trajectory Planning Utilizing Optimal Control Techniques 6...then finding a time- optimal time scaling for the path subject to the actuator limits. The direct approach searches for the trajectory directly
Photogrammetric Trajectory Estimation of Foam Debris Ejected From an F-15 Aircraft
NASA Technical Reports Server (NTRS)
Smith, Mark S.
2006-01-01
Photogrammetric analysis of high-speed digital video data was performed to estimate trajectories of foam debris ejected from an F-15B aircraft. This work was part of a flight test effort to study the transport properties of insulating foam shed by the Space Shuttle external tank during ascent. The conical frustum-shaped pieces of debris, called "divots," were ejected from a flight test fixture mounted underneath the F-15B aircraft. Two onboard cameras gathered digital video data at two thousand frames per second. Time histories of divot positions were determined from the videos post flight using standard photogrammetry techniques. Divot velocities were estimated by differentiating these positions with respect to time. Time histories of divot rotations were estimated using four points on the divot face. Estimated divot position, rotation, and Mach number for selected cases are presented. Uncertainty in the results is discussed.
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.
Clustering Molecular Dynamics Trajectories for Optimizing Docking Experiments
De Paris, Renata; Quevedo, Christian V.; Ruiz, Duncan D.; Norberto de Souza, Osmar; Barros, Rodrigo C.
2015-01-01
Molecular dynamics simulations of protein receptors have become an attractive tool for rational drug discovery. However, the high computational cost of employing molecular dynamics trajectories in virtual screening of large repositories threats the feasibility of this task. Computational intelligence techniques have been applied in this context, with the ultimate goal of reducing the overall computational cost so the task can become feasible. Particularly, clustering algorithms have been widely used as a means to reduce the dimensionality of molecular dynamics trajectories. In this paper, we develop a novel methodology for clustering entire trajectories using structural features from the substrate-binding cavity of the receptor in order to optimize docking experiments on a cloud-based environment. The resulting partition was selected based on three clustering validity criteria, and it was further validated by analyzing the interactions between 20 ligands and a fully flexible receptor (FFR) model containing a 20 ns molecular dynamics simulation trajectory. Our proposed methodology shows that taking into account features of the substrate-binding cavity as input for the k-means algorithm is a promising technique for accurately selecting ensembles of representative structures tailored to a specific ligand. PMID:25873944
Clustering molecular dynamics trajectories for optimizing docking experiments.
De Paris, Renata; Quevedo, Christian V; Ruiz, Duncan D; Norberto de Souza, Osmar; Barros, Rodrigo C
2015-01-01
Molecular dynamics simulations of protein receptors have become an attractive tool for rational drug discovery. However, the high computational cost of employing molecular dynamics trajectories in virtual screening of large repositories threats the feasibility of this task. Computational intelligence techniques have been applied in this context, with the ultimate goal of reducing the overall computational cost so the task can become feasible. Particularly, clustering algorithms have been widely used as a means to reduce the dimensionality of molecular dynamics trajectories. In this paper, we develop a novel methodology for clustering entire trajectories using structural features from the substrate-binding cavity of the receptor in order to optimize docking experiments on a cloud-based environment. The resulting partition was selected based on three clustering validity criteria, and it was further validated by analyzing the interactions between 20 ligands and a fully flexible receptor (FFR) model containing a 20 ns molecular dynamics simulation trajectory. Our proposed methodology shows that taking into account features of the substrate-binding cavity as input for the k-means algorithm is a promising technique for accurately selecting ensembles of representative structures tailored to a specific ligand.
Definition and Demonstration of a Methodology for Validating Aircraft Trajectory Predictors
NASA Technical Reports Server (NTRS)
Vivona, Robert A.; Paglione, Mike M.; Cate, Karen T.; Enea, Gabriele
2010-01-01
This paper presents a new methodology for validating an aircraft trajectory predictor, inspired by the lessons learned from a number of field trials, flight tests and simulation experiments for the development of trajectory-predictor-based automation. The methodology introduces new techniques and a new multi-staged approach to reduce the effort in identifying and resolving validation failures, avoiding the potentially large costs associated with failures during a single-stage, pass/fail approach. As a case study, the validation effort performed by the Federal Aviation Administration for its En Route Automation Modernization (ERAM) system is analyzed to illustrate the real-world applicability of this methodology. During this validation effort, ERAM initially failed to achieve six of its eight requirements associated with trajectory prediction and conflict probe. The ERAM validation issues have since been addressed, but to illustrate how the methodology could have benefited the FAA effort, additional techniques are presented that could have been used to resolve some of these issues. Using data from the ERAM validation effort, it is demonstrated that these new techniques could have identified trajectory prediction error sources that contributed to several of the unmet ERAM requirements.
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.
Rapid near-optimal aerospace plane trajectory generation and guidance
NASA Technical Reports Server (NTRS)
Corban, J. E.; Calise, A. J.; Flandro, G. A.
1991-01-01
Problems associated with onboard trajectory optimization, propulsion system cycle selection, and the synthesis of guidance laws are addressed for ascent to low earth orbit of an airbreathing, single-stage-to-orbit vehicle. A multicycle propulsion system is assumed that incorporates turbojet, ramjet, scramjet, and rocket engines. An energy state approximation is applied to a singularly perturbed, four-state dynamic model for flight of a point mass over a spherical nonrotating earth. An algorithm is then derived for generating both the fuel-optimal climb profile and the guidance commands required to follow that profile. In particular, analytic switching conditions are derived that, under appropriate assumptions, efficiently govern optimal transition from one propulsion cycle to another. The algorithm proves to be computationally efficient and suitable for real-time implementation. The paper concludes with the presentation of representative numerical results that illustrate the nature of the fuel-optimal climb paths and the tracking performance of the guidance algorithm.
Rapid Generation of Optimal Asteroid Powered Descent Trajectories Via Convex Optimization
NASA Technical Reports Server (NTRS)
Pinson, Robin; Lu, Ping
2015-01-01
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.
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.
On a global aerodynamic optimization of a civil transport aircraft
NASA Technical Reports Server (NTRS)
Savu, G.; Trifu, O.
1991-01-01
An aerodynamic optimization procedure developed to minimize the drag to lift ratio of an aircraft configuration: wing - body - tail, in accordance with engineering restrictions, is described. An algorithm developed to search a hypersurface with 18 dimensions, which define an aircraft configuration, is discussed. The results, when considered from the aerodynamic point of view, indicate the optimal configuration is one that combines a lifting fuselage with a canard.
Ascent trajectory optimization for stratospheric airship with thermal effects
NASA Astrophysics Data System (ADS)
Guo, Xiao; Zhu, Ming
2013-09-01
Ascent trajectory optimization with thermal effects is addressed for a stratospheric airship. Basic thermal characteristics of the stratospheric airship are introduced. Besides, the airship’s equations of motion are constructed by including the factors about aerodynamic force, added mass and wind profiles which are developed based on horizontal-wind model. For both minimum-time and minimum-energy flights during ascent, the trajectory optimization problem is described with the path and terminal constraints in different scenarios and then, is converted into a parameter optimization problem by a direct collocation method. Sparse Nonlinear OPTimizer(SNOPT) is employed as a nonlinear programming solver and two scenarios are adopted. The solutions obtained illustrate that the trajectories are greatly affected by the thermal behaviors which prolong the daytime minimum-time flights of about 20.8% compared with that of nighttime in scenario 1 and of about 10.5% in scenario 2. And there is the same trend for minimum-energy flights. For the energy consumption of minimum-time flights, 6% decrease is abstained in scenario 1 and 5% decrease in scenario 2. However, a few energy consumption reduction is achieved for minimum-energy flights. Solar radiation is the principal component and the natural wind also affects the thermal behaviors of stratospheric airship during ascent. The relationship between take-off time and performance of airship during ascent is discussed. it is found that the take-off time at dusk is best choice for stratospheric airship. And in addition, for saving energy, airship prefers to fly downwind.
Optimization of interplanetary trajectories to Mars via electrical propulsion
NASA Astrophysics Data System (ADS)
Williams, Powtawche Neengay
Although chemical rocket propulsion is widely used in space transportation, large amounts of propellant mass limit designs for spacecraft missions to Mars. Electrical propulsion, which requires a smaller propellant load, is an alternative propulsion system that can be used for interplanetary flight. After the recent successes of the NASA Deep Space 1 spacecraft and the ESA SMART 1 spacecraft, which incorporate an electrical propulsion system, there is a strong need for trajectory tools to support these systems. This thesis describes the optimization of interplanetary trajectories from Earth to Mars for spacecraft utilizing low-thrust electrical propulsion systems. It is assumed that the controls are the thrust direction and the thrust setting. Specifically, the minimum time and minimum propellant problems are studied and solutions are computed with the sequential gradient-restoration algorithm (SGRA). The results indicate that, when the thrust direction and thrust setting are simultaneously optimized, the minimum time and minimum propellant solutions are not identical. For minimum time, it is found that the thrust setting must be at the maximum value; also, the thrust direction has a normal component with a switch at midcourse from upward to downward. This changes the curvature of the trajectory, has a beneficial effect on time, but a detrimental effect on propellant mass; indeed, the propellant mass ratio of the minimum time solution is about twice that of the Hohmann transfer solution. Thus, the minimum time solution yields a rather inefficient trajectory. For minimum propellant consumption, it is found that the best thrust setting is bang-zero-bang (maximum thrust, followed by coasting, followed by maximum thrust) and that the best thrust direction is tangent to the trajectory. This is a rather efficient trajectory; to three significant digits, the associated mass ratio is the same as that of the Hohmann transfer solution, even for thrust-to-weight ratios of
Aircraft design for mission performance using nonlinear multiobjective optimization methods
NASA Technical Reports Server (NTRS)
Dovi, Augustine R.; Wrenn, Gregory A.
1990-01-01
A new technique which converts a constrained optimization problem to an unconstrained one where conflicting figures of merit may be simultaneously considered was combined with a complex mission analysis system. The method is compared with existing single and multiobjective optimization methods. A primary benefit from this new method for multiobjective optimization is the elimination of separate optimizations for each objective, which is required by some optimization methods. A typical wide body transport aircraft is used for the comparative studies.
Terminal-Area Aircraft Intent Inference Approach Based on Online Trajectory Clustering
Yang, Yang; Zhang, Jun; Cai, Kai-quan
2015-01-01
Terminal-area aircraft intent inference (T-AII) is a prerequisite to detect and avoid potential aircraft conflict in the terminal airspace. T-AII challenges the state-of-the-art AII approaches due to the uncertainties of air traffic situation, in particular due to the undefined flight routes and frequent maneuvers. In this paper, a novel T-AII approach is introduced to address the limitations by solving the problem with two steps that are intent modeling and intent inference. In the modeling step, an online trajectory clustering procedure is designed for recognizing the real-time available routes in replacing of the missed plan routes. In the inference step, we then present a probabilistic T-AII approach based on the multiple flight attributes to improve the inference performance in maneuvering scenarios. The proposed approach is validated with real radar trajectory and flight attributes data of 34 days collected from Chengdu terminal area in China. Preliminary results show the efficacy of the presented approach. PMID:26171417
Trajectory optimization for intra-operative nuclear tomographic imaging.
Vogel, Jakob; Lasser, Tobias; Gardiazabal, José; Navab, Nassir
2013-10-01
Diagnostic nuclear imaging modalities like SPECT typically employ gantries to ensure a densely sampled geometry of detectors in order to keep the inverse problem of tomographic reconstruction as well-posed as possible. In an intra-operative setting with mobile freehand detectors the situation changes significantly, and having an optimal detector trajectory during acquisition becomes critical. In this paper we propose an incremental optimization method based on the numerical condition of the system matrix of the underlying iterative reconstruction method to calculate optimal detector positions during acquisition in real-time. The performance of this approach is evaluated using simulations. A first experiment on a phantom using a robot-controlled intra-operative SPECT-like setup demonstrates the feasibility of the approach.
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
Real-time trajectory optimization on parallel processors
NASA Technical Reports Server (NTRS)
Psiaki, Mark L.
1993-01-01
A parallel algorithm has been developed for rapidly solving trajectory optimization problems. The goal of the work has been to develop an algorithm that is suitable to do real-time, on-line optimal guidance through repeated solution of a trajectory optimization problem. The algorithm has been developed on an INTEL iPSC/860 message passing parallel processor. It uses a zero-order-hold discretization of a continuous-time problem and solves the resulting nonlinear programming problem using a custom-designed augmented Lagrangian nonlinear programming algorithm. The algorithm achieves parallelism of function, derivative, and search direction calculations through the principle of domain decomposition applied along the time axis. It has been encoded and tested on 3 example problems, the Goddard problem, the acceleration-limited, planar minimum-time to the origin problem, and a National Aerospace Plane minimum-fuel ascent guidance problem. Execution times as fast as 118 sec of wall clock time have been achieved for a 128-stage Goddard problem solved on 32 processors. A 32-stage minimum-time problem has been solved in 151 sec on 32 processors. A 32-stage National Aerospace Plane problem required 2 hours when solved on 32 processors. A speed-up factor of 7.2 has been achieved by using 32-nodes instead of 1-node to solve a 64-stage Goddard problem.
Closed form solutions of constrained trajectories - Application in optimal ascent of aerospace plane
NASA Technical Reports Server (NTRS)
Lu, Ping; Samsundar, John
1992-01-01
The present consideration of the flight trajectory of hypersonic aerospace vehicles subject to a class of path constraints notes the constrained dynamics to constitute a natural two-timescale system, so that problems of trajectory optimization and guidance can be dramatically simplified by means of the asymptotic analytical solutions thus obtained. An illustrative application in ascent trajectory optimization for an aerospace vehicle is presented.
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.
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.
Spin system trajectory analysis under optimal control pulses
NASA Astrophysics Data System (ADS)
Kuprov, Ilya
2013-08-01
Several methods are proposed for the analysis, visualization and interpretation of high-dimensional spin system trajectories produced by quantum mechanical simulations. It is noted that expectation values of specific observables in large spin systems often feature fast, complicated and hard-to-interpret time dynamics and suggested that populations of carefully selected subspaces of states are much easier to analyze and interpret. As an illustration of the utility of the proposed methods, it is demonstrated that the apparent "noisy" appearance of many optimal control pulses in NMR and EPR spectroscopy is an illusion - the underlying spin dynamics is shown to be smooth, orderly and very tightly controlled.
Recent Improvements to the Copernicus Trajectory Design and Optimization System
NASA Technical Reports Server (NTRS)
Williams, Jacob; Senent, Juan S.; Ocampo, Cesar; Lee, David E.
2012-01-01
Copernicus is a software tool for spacecraft trajectory design and optimization. The latest version (v3.0.1) was released in October 2011. It is available at no cost to NASA centers, government contractors, and organizations with a contractual affiliation with NASA. This paper is a brief overview of the recent development history of Copernicus. An overview of the evolution of the software and a discussion of significant new features and improvements is given, and how the tool is used to design spacecraft missions
Powered-descent trajectory optimization scheme for Mars landing
NASA Astrophysics Data System (ADS)
Liu, Rongjie; Li, Shihua; Chen, Xisong; Guo, Lei
2013-12-01
This paper presents a trajectory optimization scheme for powered-descent phase of Mars landing with considerations of disturbance. Firstly, θ-D method is applied to design a suboptimal control law with descent model in the absence of disturbance. Secondly, disturbance is estimated by disturbance observer, and the disturbance estimation is as feedforward compensation. Then, semi-global stability analysis of the composite controller consisting of the nonlinear suboptimal controller and the disturbance feedforward compensation is proposed. Finally, to verify the effectiveness of proposed control scheme, an application including relevant simulations on a Mars landing mission is demonstrated.
Measurements of Flow Rate and Trajectory of Aircraft Tire-Generated Water Spray
NASA Technical Reports Server (NTRS)
Daugherty, Robert H.; Stubbs, Sandy M.
1987-01-01
An experimental investigation was conducted at the NASA Langley Research Center to measure the flow rate and trajectory of water spray generated by an aircraft tire operating on a flooded runway. Tests were conducted in the Hydrodynamics Research Facility and made use of a partial airframe and a nose tire from a general aviation aircraft. Nose tires from a commercial transport aircraft were also used. The effects of forward speed, tire load, and water depth on water spray patterns were evaluated by measuring the amount and location of water captured by an array of tubes mounted behind the test tire. Water ejected from the side of the tire footprint had the most significant potential for ingestion into engine inlets. A lateral wake created on the water surface by the rolling tire can dominate the shape of the spray pattern as the distance aft of the tire is increased. Forward speed increased flow rates and moved the spray pattern inboard. Increased tire load caused the spray to become less dense. Near the tire, increased water depths caused flow rates to increase. Tests using a fuselage and partial wing along with the nose gear showed that for certain configurations, wing aerodynamics can cause a concentration of spray above the wing.
Methods for predicting unsteady takeoff and landing trajectories of the aircraft
NASA Astrophysics Data System (ADS)
Shevchenko, A.; Pavlov, B.; Nachinkina, G.
2017-01-01
Informational and situational awareness of the aircrew greatly affects the probability of accidents, during takeoff and landing in particular. For the purpose of assessing the current and predicting the future states of an aircraft the energy approach to the flight control is used. Key energy balance equation is generalized to the ground phases. The equation describes the process of accumulating of the total energy of the aircraft along the entire trajectory, including the segment ahead. This segment length is defined by the required terminal energy state. For the takeoff phase the predict algorithm calculates the aircraft position on a runway after which it is possible to accelerate up to the speed of steady level flight and to reach the altitude sufficient for overcoming the high-rise obstacles. For the landing phase the braking distance length is determined. For increasing the likelihood of predicting the correction of the algorithm is introduced. The results of modeling many takeoffs and landings of passenger liner with different weights with the ahead obstacle and the engine failure are given. Working availability of the algorithm correction is shown.
Earth-Moon low energy trajectory optimization in the real system
NASA Astrophysics Data System (ADS)
Lei, Hanlun; Xu, Bo; Sun, Yisui
2013-03-01
The problem of the Earth-Moon low energy trajectory optimization in the real system (the model defined by the JPL ephemeris DE405) is considered in this paper. First, this problem is investigated in the model of circular restricted three-body problem, since the fuel consumption is closely related to the Jacobi integral of the transfer trajectory, a method based on Jacobi integral is proposed and eight optimal trajectories are obtained. These optimal trajectories provide initial information (the flight time and the braking velocity impulse) to search the optimal low energy trajectories in the real system through optimization techniques. Considering the merit and drawback of particle swarm optimization and differential evolution algorithm in solving the space trajectory problem, an improved cooperative evolutionary algorithm is put forward. Result shows that the low energy trajectories in the real system are more fuel-efficient than the corresponding ones under the circular restricted three-body problem.
Decomposition technique and optimal trajectories for the aeroassisted flight experiment
NASA Technical Reports Server (NTRS)
Miele, A.; Wang, T.; Deaton, A. W.
1990-01-01
An actual geosynchronous Earth orbit-to-low Earth orbit (GEO-to-LEO) transfer is considered with reference to the aeroassisted flight experiment (AFE) spacecraft, and optimal trajectories are determined by minimizing the total characteristic velocity. The optimization is performed with respect to the time history of the controls (angle of attack and angle of bank), the entry path inclination and the flight time being free. Two transfer maneuvers are considered: direct ascent (DA) to LEO and indirect ascent (IA) to LEO via parking Earth orbit (PEO). By taking into account certain assumptions, the complete system can be decoupled into two subsystems: one describing the longitudinal motion and one describing the lateral motion. The angle of attack history, the entry path inclination, and the flight time are determined via the longitudinal motion subsystem. In this subsystem, the difference between the instantaneous bank angle and a constant bank angle is minimized in the least square sense subject to the specified orbital inclination requirement. Both the angles of attack and the angle of bank are shown to be constant. This result has considerable importance in the design of nominal trajectories to be used in the guidance of AFE and aeroassisted orbital transfer (AOT) vehicles.
Optimal Collision Avoidance Trajectories for Unmanned/Remotely Piloted Aircraft
2014-12-26
can be classified as indicator methods [92], including Big M [93, 94] and active set [95] methods, and mixed-norm methods [92, 96]; however, these...instance, Big M methods implement “either-or constraints” [94] using a binary indicator variable along with a suciently large constraint variable (M...indicator variable equivalent to those in Big M methods [95]. In addition, mixed-norm methods typically formulate a set of conditional constraints as a
Trajectory Optimization With Detection Avoidance for Visually Identifying an Aircraft
2005-06-01
Thesis Supervisor Certified by Brent Appleby Lecturer in Aeronautics and CSDL Technical Supervisor Thesis Advisor Accepted by Jaime Peraire Professor of...Leena Singh Title: Senior Member of the Technical Staff Thesis Advisor: Dr. Brent Appleby Title: Division Leader - Control, Information, and Decision...Systems 3 [This page intentionally left blank.] Acknowledgments I would like to thank my advisors Leena Singh and Brent Appleby for their help with this
Aircraft cabin noise prediction and optimization
NASA Technical Reports Server (NTRS)
Vaicaitis, R.
1985-01-01
Theoretical and experimental studies were conducted to determine the noise transmission into acoustic enclosures ranging from simple rectangular box models to full scale light aircraft in flight. The structural models include simple, stiffened, curved stiffened, and orthotropic panels and double wall windows. The theoretical solutions were obtained by model analysis. Transfer matrix and finite element procedures were utilized. Good agreement between theory and experiment has been achieved. An efficient acoustic add-on treatment was developed for interior noise control in a twin engine light aircraft.
Optimal Aircraft Maneuver against Two Proportional Navigation Guided Missiles
NASA Astrophysics Data System (ADS)
Kuroda, Takeshi; Imado, Fumiaki
Optimal aircraft maneuver against two missiles are studied. In this paper, the problem is formulated as a nonlinear optimal control problem and solved by the steepest ascent method. In order to maximize the miss distance against two missiles simultaneously, a special type of criterion function is employed by introducing a window function. Some examples obtained by our method show reasonable aircraft optimal controls, and verify the validity of our method. Our method will be applied to pursuit-evasion and collision avoidance problems with multi-vehicles.
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.
An interactive system for aircraft design and optimization
NASA Technical Reports Server (NTRS)
Kroo, Ilan M.
1992-01-01
A system for aircraft design utilizing a unique analysis architecture, graphical interface, and suite of numerical optimization methods is described in this paper. The non-procedural architecture provides extensibility and efficiency not possible with conventional programming techniques. The interface for analysis and optimization, developed for use with this method, is described and its application to example problems is discussed.
Development of Advanced Methods of Structural and Trajectory Analysis for Transport Aircraft
NASA Technical Reports Server (NTRS)
Ardema, Mark D.
1996-01-01
In this report the author describes: (1) development of advanced methods of structural weight estimation, and (2) development of advanced methods of flight path optimization. A method of estimating the load-bearing fuselage weight and wing weight of transport aircraft based on fundamental structural principles has been developed. This method of weight estimation represents a compromise between the rapid assessment of component weight using empirical methods based on actual weights of existing aircraft and detailed, but time-consuming, analysis using the finite element method. The method was applied to eight existing subsonic transports for validation and correlation. Integration of the resulting computer program, PDCYL, has been made into the weights-calculating module of the AirCraft SYNThesis (ACSYNT) computer program. ACSYNT bas traditionally used only empirical weight estimation methods; PDCYL adds to ACSYNT a rapid, accurate means of assessing the fuselage and wing weights of unconventional aircraft. PDCYL also allows flexibility in the choice of structural concept, as well as a direct means of determining the impact of advanced materials on structural weight.
Variational Trajectory Optimization Tool Set: Technical description and user's manual
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Queen, Eric M.; Cavanaugh, Michael D.; Wetzel, Todd A.; Moerder, Daniel D.
1993-01-01
The algorithms that comprise the Variational Trajectory Optimization Tool Set (VTOTS) package are briefly described. The VTOTS is a software package for solving nonlinear constrained optimal control problems from a wide range of engineering and scientific disciplines. The VTOTS package was specifically designed to minimize the amount of user programming; in fact, for problems that may be expressed in terms of analytical functions, the user needs only to define the problem in terms of symbolic variables. This version of the VTOTS does not support tabular data; thus, problems must be expressed in terms of analytical functions. The VTOTS package consists of two methods for solving nonlinear optimal control problems: a time-domain finite-element algorithm and a multiple shooting algorithm. These two algorithms, under the VTOTS package, may be run independently or jointly. The finite-element algorithm generates approximate solutions, whereas the shooting algorithm provides a more accurate solution to the optimization problem. A user's manual, some examples with results, and a brief description of the individual subroutines are included.
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
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.
Decision-Aiding and Optimization for Vertical Navigation of Long-Haul Aircraft
NASA Technical Reports Server (NTRS)
Patrick, Nicholas J. M.; Sheridan, Thomas B.
1996-01-01
Most decisions made in the cockpit are related to safety, and have therefore been proceduralized in order to reduce risk. There are very few which are made on the basis of a value metric such as economic cost. One which can be shown to be value based, however, is the selection of a flight profile. Fuel consumption and flight time both have a substantial effect on aircraft operating cost, but they cannot be minimized simultaneously. In addition, winds, turbulence, and performance vary widely with altitude and time. These factors make it important and difficult for pilots to (a) evaluate the outcomes associated with a particular trajectory before it is flown and (b) decide among possible trajectories. The two elements of this problem considered here are: (1) determining what constitutes optimality, and (2) finding optimal trajectories. Pilots and dispatchers from major u.s. airlines were surveyed to determine which attributes of the outcome of a flight they considered the most important. Avoiding turbulence-for passenger comfort-topped the list of items which were not safety related. Pilots' decision making about the selection of flight profile on the basis of flight time, fuel burn, and exposure to turbulence was then observed. Of the several behavioral and prescriptive decision models invoked to explain the pilots' choices, utility maximization is shown to best reproduce the pilots' decisions. After considering more traditional methods for optimizing trajectories, a novel method is developed using a genetic algorithm (GA) operating on a discrete representation of the trajectory search space. The representation is a sequence of command altitudes, and was chosen to be compatible with the constraints imposed by Air Traffic Control, and with the training given to pilots. Since trajectory evaluation for the GA is performed holistically, a wide class of objective functions can be optimized easily. Also, using the GA it is possible to compare the costs associated with
Optimal and suboptimal control technique for aircraft spin recovery
NASA Technical Reports Server (NTRS)
Young, J. W.
1974-01-01
An analytic investigation has been made of procedures for effecting recovery from equilibrium spin conditions for three assumed aircraft configurations. Three approaches which utilize conventional aerodynamic controls are investigated. Included are a constant control recovery mode, optimal recoveries, and a suboptimal control logic patterned after optimal recovery results. The optimal and suboptimal techniques are shown to yield a significant improvement in recovery performance over that attained by using a constant control recovery procedure.
Aircraft Conflict Analysis and Real-Time Conflict Probing Using Probabilistic Trajectory Modeling
NASA Technical Reports Server (NTRS)
Yang, Lee C.; Kuchar, James K.
2000-01-01
Methods for maintaining separation between aircraft in the current airspace system have been built from a foundation of structured routes and evolved procedures. However, as the airspace becomes more congested and the chance of failures or operational error become more problematic, automated conflict alerting systems have been proposed to help provide decision support and to serve as traffic monitoring aids. The problem of conflict detection and resolution has been tackled from a number of different ways, but in this thesis, it is recast as a problem of prediction in the presence of uncertainties. Much of the focus is concentrated on the errors and uncertainties from the working trajectory model used to estimate future aircraft positions. The more accurate the prediction, the more likely an ideal (no false alarms, no missed detections) alerting system can be designed. Additional insights into the problem were brought forth by a review of current operational and developmental approaches found in the literature. An iterative, trial and error approach to threshold design was identified. When examined from a probabilistic perspective, the threshold parameters were found to be a surrogate to probabilistic performance measures. To overcome the limitations in the current iterative design method, a new direct approach is presented where the performance measures are directly computed and used to perform the alerting decisions. The methodology is shown to handle complex encounter situations (3-D, multi-aircraft, multi-intent, with uncertainties) with relative ease. Utilizing a Monte Carlo approach, a method was devised to perform the probabilistic computations in near realtime. Not only does this greatly increase the method's potential as an analytical tool, but it also opens up the possibility for use as a real-time conflict alerting probe. A prototype alerting logic was developed and has been utilized in several NASA Ames Research Center experimental studies.
Optimizing conceptual aircraft designs for minimum life cycle cost
NASA Technical Reports Server (NTRS)
Johnson, Vicki S.
1989-01-01
A life cycle cost (LCC) module has been added to the FLight Optimization System (FLOPS), allowing the additional optimization variables of life cycle cost, direct operating cost, and acquisition cost. Extensive use of the methodology on short-, medium-, and medium-to-long range aircraft has demonstrated that the system works well. Results from the study show that optimization parameter has a definite effect on the aircraft, and that optimizing an aircraft for minimum LCC results in a different airplane than when optimizing for minimum take-off gross weight (TOGW), fuel burned, direct operation cost (DOC), or acquisition cost. Additionally, the economic assumptions can have a strong impact on the configurations optimized for minimum LCC or DOC. Also, results show that advanced technology can be worthwhile, even if it results in higher manufacturing and operating costs. Examining the number of engines a configuration should have demonstrated a real payoff of including life cycle cost in the conceptual design process: the minimum TOGW of fuel aircraft did not always have the lowest life cycle cost when considering the number of engines.
Automating Initial Guess Generation for High Fidelity Trajectory Optimization Tools
NASA Technical Reports Server (NTRS)
Villa, Benjamin; Lantoine, Gregory; Sims, Jon; Whiffen, Gregory
2013-01-01
Many academic studies in spaceflight dynamics rely on simplified dynamical models, such as restricted three-body models or averaged forms of the equations of motion of an orbiter. In practice, the end result of these preliminary orbit studies needs to be transformed into more realistic models, in particular to generate good initial guesses for high-fidelity trajectory optimization tools like Mystic. This paper reviews and extends some of the approaches used in the literature to perform such a task, and explores the inherent trade-offs of such a transformation with a view toward automating it for the case of ballistic arcs. Sample test cases in the libration point regimes and small body orbiter transfers are presented.
An analysis and comparison of several trajectory optimization methods
NASA Technical Reports Server (NTRS)
Lewallen, J. M.
1971-01-01
The sensitivities of the convergence characteristics of the methods to initially assumed parameters and trial solution, convergence times, computer logic, and storage requirements are discussed. Numerical comparison of the convergence characteristics is made by considering a minimum time, low thrust, Earth-Mars transfer trajectory. A modified quasi-linearization method reduces convergence time by approximately 70% when compared with the generalized Newton-Raphson method and allows the terminal boundary to be specified by a general function of the problem variables. A uniquely specified and easily determined, time dependent weighting matrix for the gradient techniques accelerates the shaping of the optimal control program and improves the convergence characteristics during the terminal iterations. Convergence envelopes, indicating how sensitive the convergence characteristics are to initially assumed parameters, are plotted for the perturbation and quasi-linearization methods. Several iteration schemes are proposed which increase the size of the convergence envelopes and decrease the sensitivity of the method to initially assumed parameters.
Optimal estimation of diffusion coefficients from single-particle trajectories
NASA Astrophysics Data System (ADS)
Vestergaard, Christian L.; Blainey, Paul C.; Flyvbjerg, Henrik
2014-02-01
How does one optimally determine the diffusion coefficient of a diffusing particle from a single-time-lapse recorded trajectory of the particle? We answer this question with an explicit, unbiased, and practically optimal covariance-based estimator (CVE). This estimator is regression-free and is far superior to commonly used methods based on measured mean squared displacements. In experimentally relevant parameter ranges, it also outperforms the analytically intractable and computationally more demanding maximum likelihood estimator (MLE). For the case of diffusion on a flexible and fluctuating substrate, the CVE is biased by substrate motion. However, given some long time series and a substrate under some tension, an extended MLE can separate particle diffusion on the substrate from substrate motion in the laboratory frame. This provides benchmarks that allow removal of bias caused by substrate fluctuations in CVE. The resulting unbiased CVE is optimal also for short time series on a fluctuating substrate. We have applied our estimators to human 8-oxoguanine DNA glycolase proteins diffusing on flow-stretched DNA, a fluctuating substrate, and found that diffusion coefficients are severely overestimated if substrate fluctuations are not accounted for.
Optimal estimation of diffusion coefficients from single-particle trajectories.
Vestergaard, Christian L; Blainey, Paul C; Flyvbjerg, Henrik
2014-02-01
How does one optimally determine the diffusion coefficient of a diffusing particle from a single-time-lapse recorded trajectory of the particle? We answer this question with an explicit, unbiased, and practically optimal covariance-based estimator (CVE). This estimator is regression-free and is far superior to commonly used methods based on measured mean squared displacements. In experimentally relevant parameter ranges, it also outperforms the analytically intractable and computationally more demanding maximum likelihood estimator (MLE). For the case of diffusion on a flexible and fluctuating substrate, the CVE is biased by substrate motion. However, given some long time series and a substrate under some tension, an extended MLE can separate particle diffusion on the substrate from substrate motion in the laboratory frame. This provides benchmarks that allow removal of bias caused by substrate fluctuations in CVE. The resulting unbiased CVE is optimal also for short time series on a fluctuating substrate. We have applied our estimators to human 8-oxoguanine DNA glycolase proteins diffusing on flow-stretched DNA, a fluctuating substrate, and found that diffusion coefficients are severely overestimated if substrate fluctuations are not accounted for.
Neighboring Optimal Aircraft Guidance in a General Wind Environment
NASA Technical Reports Server (NTRS)
Jardin, Matthew R. (Inventor)
2003-01-01
Method and system for determining an optimal route for an aircraft moving between first and second waypoints in a general wind environment. A selected first wind environment is analyzed for which a nominal solution can be determined. A second wind environment is then incorporated; and a neighboring optimal control (NOC) analysis is performed to estimate an optimal route for the second wind environment. In particular examples with flight distances of 2500 and 6000 nautical miles in the presence of constant or piecewise linearly varying winds, the difference in flight time between a nominal solution and an optimal solution is 3.4 to 5 percent. Constant or variable winds and aircraft speeds can be used. Updated second wind environment information can be provided and used to obtain an updated optimal route.
Decision-Aiding and Optimization for Vertical Navigation of Long-Haul Aircraft
NASA Technical Reports Server (NTRS)
Patrick, Nicholas J. M.; Sheridan, Thomas B.
1996-01-01
Most decisions made in the cockpit are related to safety, and have therefore been proceduralized in order to reduce risk. There are very few which are made on the basis of a value metric such as economic cost. One which can be shown to be value based, however, is the selection of a flight profile. Fuel consumption and flight time both have a substantial effect on aircraft operating cost, but they cannot be minimized simultaneously. In addition, winds, turbulence, and performance x,ary widely with altitude and time. These factors make it important and difficult for pilots to (a) evaluate the outcomes associated with a particular trajectory before it is flown and (b) decide among possible trajectories. The two elements of this problem considered here are (1) determining, what constitutes optimality, and (2) finding optimal trajectories. Pilots and dispatchers from major U.S. airlines were surveyed to determine which attributes of the outcome of a flight they considered the most important. Avoiding turbulence-for passenger comfort topped the list of items which were not safety related. Pilots' decision making about the selection of flight profile on the basis of flight time, fuel burn, and exposure to turbulence was then observed. Of the several behavioral and prescriptive decision models invoked to explain the pilots' choices, utility maximization is shown to best reproduce the pilots' decisions. After considering more traditional methods for optimizing trajectories, a novel method is developed using a genetic algorithm (GA) operating on a discrete representation of the trajectory search space. The representation is a sequence of command altitudes, and was chosen to be compatible with the constraints imposed by Air Traffic Control, and with the training given to pilots. Since trajectory evaluation for the GA is performed holistically, a wide class of objective functions can be optimized easily. Also, using the GA it is possible to compare the costs associated with
Energy management of three-dimensional minimum-time intercept. [for aircraft flight optimization
NASA Technical Reports Server (NTRS)
Kelley, H. J.; Cliff, E. M.; Visser, H. G.
1985-01-01
A real-time computer algorithm to control and optimize aircraft flight profiles is described and applied to a three-dimensional minimum-time intercept mission. The proposed scheme has roots in two well known techniques: singular perturbations and neighboring-optimal guidance. Use of singular-perturbation ideas is made in terms of the assumed trajectory-family structure. A heading/energy family of prestored point-mass-model state-Euler solutions is used as the baseline in this scheme. The next step is to generate a near-optimal guidance law that will transfer the aircraft to the vicinity of this reference family. The control commands fed to the autopilot (bank angle and load factor) consist of the reference controls plus correction terms which are linear combinations of the altitude and path-angle deviations from reference values, weighted by a set of precalculated gains. In this respect the proposed scheme resembles neighboring-optimal guidance. However, in contrast to the neighboring-optimal guidance scheme, the reference control and state variables as well as the feedback gains are stored as functions of energy and heading in the present approach. Some numerical results comparing open-loop optimal and approximate feedback solutions are presented.
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.
Multidisciplinary Optimization Methods for Aircraft Preliminary Design
NASA Technical Reports Server (NTRS)
Kroo, Ilan; Altus, Steve; Braun, Robert; Gage, Peter; Sobieski, Ian
1994-01-01
This paper describes a research program aimed at improved methods for multidisciplinary design and optimization of large-scale aeronautical systems. The research involves new approaches to system decomposition, interdisciplinary communication, and methods of exploiting coarse-grained parallelism for analysis and optimization. A new architecture, that involves a tight coupling between optimization and analysis, is intended to improve efficiency while simplifying the structure of multidisciplinary, computation-intensive design problems involving many analysis disciplines and perhaps hundreds of design variables. Work in two areas is described here: system decomposition using compatibility constraints to simplify the analysis structure and take advantage of coarse-grained parallelism; and collaborative optimization, a decomposition of the optimization process to permit parallel design and to simplify interdisciplinary communication requirements.
Information fusion based optimal control for large civil aircraft system.
Zhen, Ziyang; Jiang, Ju; Wang, Xinhua; Gao, Chen
2015-03-01
Wind disturbance has a great influence on landing security of Large Civil Aircraft. Through simulation research and engineering experience, it can be found that PID control is not good enough to solve the problem of restraining the wind disturbance. This paper focuses on anti-wind attitude control for Large Civil Aircraft in landing phase. In order to improve the riding comfort and the flight security, an information fusion based optimal control strategy is presented to restrain the wind in landing phase for maintaining attitudes and airspeed. Data of Boeing707 is used to establish a nonlinear mode with total variables of Large Civil Aircraft, and then two linear models are obtained which are divided into longitudinal and lateral equations. Based on engineering experience, the longitudinal channel adopts PID control and C inner control to keep longitudinal attitude constant, and applies autothrottle system for keeping airspeed constant, while an information fusion based optimal regulator in the lateral control channel is designed to achieve lateral attitude holding. According to information fusion estimation, by fusing hard constraint information of system dynamic equations and the soft constraint information of performance index function, optimal estimation of the control sequence is derived. Based on this, an information fusion state regulator is deduced for discrete time linear system with disturbance. The simulation results of nonlinear model of aircraft indicate that the information fusion optimal control is better than traditional PID control, LQR control and LQR control with integral action, in anti-wind disturbance performance in the landing phase.
Control optimization, stabilization and computer algorithms for aircraft applications
NASA Technical Reports Server (NTRS)
1975-01-01
Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.
Optimization of the observations and control of aircraft
NASA Astrophysics Data System (ADS)
Malyshev, Veniamin V.; Krasil'Shchikov, Mikhail N.; Karlov, Valerii I.
Problems related to the optimization of the measured parameters, navigational equipment operation, aircraft control, and combined operation of control and navigation equipment are analyzed. The problems considered rely on probabilistic optimality criteria, with varying availability of data on the uncontrolled factors, such as measurement errors and perturbations. A new generalized approach is proposed which makes it possible to reduce the initially nonlinear control problems to equivalent linear (with respect to phase variables) problems by using the analytical properties of the Riccati problem.
Multidisciplinary optimization in aircraft design using analytic technology models
NASA Technical Reports Server (NTRS)
Malone, Brett; Mason, W. H.
1991-01-01
An approach to multidisciplinary optimization is presented which combines the Global Sensitivity Equation method, parametric optimization, and analytic technology models. The result is a powerful yet simple procedure for identifying key design issues. It can be used both to investigate technology integration issues very early in the design cycle, and to establish the information flow framework between disciplines for use in multidisciplinary optimization projects using much more computational intense representations of each technology. To illustrate the approach, an examination of the optimization of a short takeoff heavy transport aircraft is presented for numerous combinations of performance and technology constraints.
TRACON Aircraft Arrival Planning and Optimization Through Spatial Constraint Satisfaction
NASA Technical Reports Server (NTRS)
Bergh, Christopher P.; Krzeczowski, Kenneth J.; Davis, Thomas J.; Denery, Dallas G. (Technical Monitor)
1995-01-01
A new aircraft arrival planning and optimization algorithm has been incorporated into the Final Approach Spacing Tool (FAST) in the Center-TRACON Automation System (CTAS) developed at NASA-Ames Research Center. FAST simulations have been conducted over three years involving full-proficiency, level five air traffic controllers from around the United States. From these simulations an algorithm, called Spatial Constraint Satisfaction, has been designed, coded, undergone testing, and soon will begin field evaluation at the Dallas-Fort Worth and Denver International airport facilities. The purpose of this new design is an attempt to show that the generation of efficient and conflict free aircraft arrival plans at the runway does not guarantee an operationally acceptable arrival plan upstream from the runway -information encompassing the entire arrival airspace must be used in order to create an acceptable aircraft arrival plan. This new design includes functions available previously but additionally includes necessary representations of controller preferences and workload, operationally required amounts of extra separation, and integrates aircraft conflict resolution. As a result, the Spatial Constraint Satisfaction algorithm produces an optimized aircraft arrival plan that is more acceptable in terms of arrival procedures and air traffic controller workload. This paper discusses the current Air Traffic Control arrival planning procedures, previous work in this field, the design of the Spatial Constraint Satisfaction algorithm, and the results of recent evaluations of the algorithm.
Design of the VISITOR Tool: A Versatile ImpulSive Interplanetary Trajectory OptimizeR
NASA Technical Reports Server (NTRS)
Corpaccioli, Luca; Linskens, Harry; Komar, David R.
2014-01-01
The design of trajectories for interplanetary missions represents one of the most complex and important problems to solve during conceptual space mission design. To facilitate conceptual mission sizing activities, it is essential to obtain sufficiently accurate trajectories in a fast and repeatable manner. To this end, the VISITOR tool was developed. This tool modularly augments a patched conic MGA-1DSM model with a mass model, launch window analysis, and the ability to simulate more realistic arrival and departure operations. This was implemented in MATLAB, exploiting the built-in optimization tools and vector analysis routines. The chosen optimization strategy uses a grid search and pattern search, an iterative variable grid method. A genetic algorithm can be selectively used to improve search space pruning, at the cost of losing the repeatability of the results and increased computation time. The tool was validated against seven flown missions: the average total mission (Delta)V offset from the nominal trajectory was 9.1%, which was reduced to 7.3% when using the genetic algorithm at the cost of an increase in computation time by a factor 5.7. It was found that VISITOR was well-suited for the conceptual design of interplanetary trajectories, while also facilitating future improvements due to its modular structure.
Adaptive Optimization of Aircraft Engine Performance Using Neural Networks
NASA Technical Reports Server (NTRS)
Simon, Donald L.; Long, Theresa W.
1995-01-01
Preliminary results are presented on the development of an adaptive neural network based control algorithm to enhance aircraft engine performance. This work builds upon a previous National Aeronautics and Space Administration (NASA) effort known as Performance Seeking Control (PSC). PSC is an adaptive control algorithm which contains a model of the aircraft's propulsion system which is updated on-line to match the operation of the aircraft's actual propulsion system. Information from the on-line model is used to adapt the control system during flight to allow optimal operation of the aircraft's propulsion system (inlet, engine, and nozzle) to improve aircraft engine performance without compromising reliability or operability. Performance Seeking Control has been shown to yield reductions in fuel flow, increases in thrust, and reductions in engine fan turbine inlet temperature. The neural network based adaptive control, like PSC, will contain a model of the propulsion system which will be used to calculate optimal control commands on-line. Hopes are that it will be able to provide some additional benefits above and beyond those of PSC. The PSC algorithm is computationally intensive, it is valid only at near steady-state flight conditions, and it has no way to adapt or learn on-line. These issues are being addressed in the development of the optimal neural controller. Specialized neural network processing hardware is being developed to run the software, the algorithm will be valid at steady-state and transient conditions, and will take advantage of the on-line learning capability of neural networks. Future plans include testing the neural network software and hardware prototype against an aircraft engine simulation. In this paper, the proposed neural network software and hardware is described and preliminary neural network training results are presented.
Application of an advanced trajectory optimization method to ramjet propelled missiles
NASA Technical Reports Server (NTRS)
Paris, S. W.; Fink, L. E.; Joosten, B. K.
1980-01-01
The mission performance characteristics of ramjet-propelled missiles are highly dependent upon the trajectory flown. Integration of the trajectory profile with the ramjet propulsion system performance characteristics to achieve optimal missile performance is very complex. Past trajectory optimization methods have been extremely problem dependent and require a high degree of familiarity to achieve success. A general computer code (CTOP) has been applied to ramjet-powered missiles to compute open-loop optimal trajectories. CTOP employs Chebyshev polynomial representations of the states and controls. This allows a transformation of the continuous optimal control problem to one of parameter optimization. With this method, the trajectory boundary conditions are always satisfied. State dynamics and path constraints are enforced via penalty functions. The presented results include solutions to minimum fuel-to-climb, minimum time-to-climb, and minimum time-to-target intercept problems.
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.
Optimizing aircraft performance with adaptive, integrated flight/propulsion control
NASA Technical Reports Server (NTRS)
Smith, R. H.; Chisholm, J. D.; Stewart, J. F.
1991-01-01
The Performance-Seeking Control (PSC) integrated flight/propulsion adaptive control algorithm presented was developed in order to optimize total aircraft performance during steady-state engine operation. The PSC multimode algorithm minimizes fuel consumption at cruise conditions, while maximizing excess thrust during aircraft accelerations, climbs, and dashes, and simultaneously extending engine service life through reduction of fan-driving turbine inlet temperature upon engagement of the extended-life mode. The engine models incorporated by the PSC are continually upgraded, using a Kalman filter to detect anomalous operations. The PSC algorithm will be flight-demonstrated by an F-15 at NASA-Dryden.
Control optimization, stabilization and computer algorithms for aircraft applications
NASA Technical Reports Server (NTRS)
Athans, M. (Editor); Willsky, A. S. (Editor)
1982-01-01
The analysis and design of complex multivariable reliable control systems are considered. High performance and fault tolerant aircraft systems are the objectives. A preliminary feasibility study of the design of a lateral control system for a VTOL aircraft that is to land on a DD963 class destroyer under high sea state conditions is provided. Progress in the following areas is summarized: (1) VTOL control system design studies; (2) robust multivariable control system synthesis; (3) adaptive control systems; (4) failure detection algorithms; and (5) fault tolerant optimal control theory.
Aircraft Range Optimization Using Singular Perturbations
NASA Technical Reports Server (NTRS)
Oconnor, Joseph Taffe
1973-01-01
An approximate analytic solution is developed for the problem of maximizing the range of an aircraft for a fixed end state. The problem is formulated as a singular perturbation and solved by matched inner and outer asymptotic expansions and the minimum principle of Pontryagin. Cruise in the stratosphere, and on transition to and from cruise at constant Mach number are discussed. The state vector includes altitude, flight path angle, and mass. Specific fuel consumption becomes a linear function of power approximating that of the cruise values. Cruise represents the outer solution; altitude and flight path angle are constants, and only mass changes. Transitions between cruise and the specified initial and final conditions correspond to the inner solutions. The mass is constant and altitude and velocity vary. A solution is developed which is valid for cruise but which is not for the initial and final conditions. Transforming of the independent variable near the initial and final conditions result in solutions which are valid for the two inner solutions but not for cruise. The inner solutions can not be obtained without simplifying the state equations. The singular perturbation approach overcomes this difficulty. A quadratic approximation of the state equations is made. The resulting problem is solved analytically, and the two inner solutions are matched to the outer solution.
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.
NASA Astrophysics Data System (ADS)
Kharitonov, A. M.
2013-09-01
An approach to optimize trajectories of interplanetary transfers combining low and high trust is proposed. The approach employs the modified method of transporting trajectory to optimize the heliocentric section of the trajectory. An Earth-Mars transfer in 180 astronomical days is used as an example to compare the optimal trajectories and parameters of spacecraft predicted by the classical and modified methods of transporting trajectory
Optimization of Conformational Dynamics in an Epistatic Evolutionary Trajectory.
González, Mariano M; Abriata, Luciano A; Tomatis, Pablo E; Vila, Alejandro J
2016-07-01
The understanding of protein evolution depends on the ability to relate the impact of mutations on molecular traits to organismal fitness. Biological activity and robustness have been regarded as important features in shaping protein evolutionary landscapes. Conformational dynamics, which is essential for protein function, has received little attention in the context of evolutionary analyses. Here we employ NMR spectroscopy, the chief experimental tool to describe protein dynamics at atomic level in solution at room temperature, to study the intrinsic dynamic features of a metallo- Β: -lactamase enzyme and three variants identified during a directed evolution experiment that led to an expanded substrate profile. We show that conformational dynamics in the catalytically relevant microsecond to millisecond timescale is optimized along the favored evolutionary trajectory. In addition, we observe that the effects of mutations on dynamics are epistatic. Mutation Gly262Ser introduces slow dynamics on several residues that surround the active site when introduced in the wild-type enzyme. Mutation Asn70Ser removes the slow dynamics observed for few residues of the wild-type enzyme, but increases the number of residues that undergo slow dynamics when introduced in the Gly262Ser mutant. These effects on dynamics correlate with the epistatic interaction between these two mutations on the bacterial phenotype. These findings indicate that conformational dynamics is an evolvable trait, and that proteins endowed with more dynamic active sites also display a larger potential for promoting evolution.
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.
TROJID: A portable software package for upper-stage trajectory optimization
NASA Technical Reports Server (NTRS)
Hammes, Steven M.
1990-01-01
Performance optimization for upper-stage exoatmospheric vehicles often is performed within the framework of a full capability trajectory simulation package requiring either a large mainframe computer or powerful work-station. Since these software packages tend to include capabilities providing for high-fidelity boost and reentry simulations, the programs usually are quite large and not very portable. The program TROJID is an attempt to provide an environment for the optimization of upper-stage trajectories within a small package capable of being run on a standard desktop microcomputer. Utilizing a state-of-the-art nonlinear programming algorithm and a trajectory simulator implementing impulsive burns and an analytic coast phase propagator, TROJID is capable of producing trajectories for optimal multi-burn upper-stage orbit transfers. The package has been designed to allow full generality in definition of both the trajectory simulator and the parameter optimization problem.
Experiences performing conceptual design optimization of transport aircraft
NASA Technical Reports Server (NTRS)
Arbuckle, P. D.; Sliwa, S. M.
1984-01-01
Optimum Preliminary Design of Transports (OPDOT) is a computer program developed at NASA Langley Research Center for evaluating the impact of new technologies upon transport aircraft. For example, it provides the capability to look at configurations which have been resized to take advantage of active controls and provide and indication of economic sensitivity to its use. Although this tool returns a conceptual design configuration as its output, it does not have the accuracy, in absolute terms, to yield satisfactory point designs for immediate use by aircraft manufacturers. However, the relative accuracy of comparing OPDOT-generated configurations while varying technological assumptions has been demonstrated to be highly reliable. Hence, OPDOT is a useful tool for ascertaining the synergistic benefits of active controls, composite structures, improved engine efficiencies and other advanced technological developments. The approach used by OPDOT is a direct numerical optimization of an economic performance index. A set of independent design variables is iterated, given a set of design constants and data. The design variables include wing geometry, tail geometry, fuselage size, and engine size. This iteration continues until the optimum performance index is found which satisfies all the constraint functions. The analyst interacts with OPDOT by varying the input parameters to either the constraint functions or the design constants. Note that the optimization of aircraft geometry parameters is equivalent to finding the ideal aircraft size, but with more degrees of freedom than classical design procedures will allow.
Design optimization of high-speed proprotor aircraft
NASA Technical Reports Server (NTRS)
Schleicher, David R.; Phillips, James D.; Carbajal, Kevin B.
1993-01-01
NASA's high-speed rotorcraft (HSRC) studies have the objective of investigating technology for vehicles that have both low downwash velocities and forward flight speed capability of up to 450 knots. This paper investigates a tilt rotor, a tilt wing, and a folding tilt rotor designed for a civil transport mission. Baseline aircraft models using current technology are developed for each configuration using a vertical/short takeoff and landing (V/STOL) aircraft design synthesis computer program to generate converged vehicle designs. Sensitivity studies and numerical optimization are used to illustrate each configuration's key design tradeoffs and constraints. Minimization of the gross takeoff weight is used as the optimization objective function. Several advanced technologies are chosen, and their relative impact on future configurational development is discussed. Finally, the impact of maximum cruise speed on vehicle figures of merit (gross weight, productivity, and direct operating cost) is analyzed. The three most important conclusions from the study are payload ratios for these aircraft will be commensurate with current fixed-wing commuter aircraft; future tilt rotors and tilt wings will be significantly lighter, more productive, and cheaper than competing folding tilt rotors; and the most promising technologies are an advanced-technology proprotor for both tilt rotor and tilt wing and advanced structural materials for the folding tilt rotor.
NASA Technical Reports Server (NTRS)
Mehra, R. K.; Washburn, R. B.; Sajan, S.; Carroll, J. V.
1979-01-01
A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions.
Shan, S.; Bevis, M.; Kendrick, E.; Mader, G.L.; Raleigh, D.; Hudnut, K.; Sartori, M.; Phillips, D.
2007-01-01
When kinematic GPS processing software is used to estimate the trajectory of an aircraft, unless the delays imposed on the GPS signals by the atmosphere are either estimated or calibrated via external observations, then vertical height errors of decimeters can occur. This problem is clearly manifested when the aircraft is positioned against multiple base stations in areas of pronounced topography because the aircraft height solutions obtained using different base stations will tend to be mutually offset, or biased, in proportion to the elevation differences between the base stations. When performing kinematic surveys in areas with significant topography it should be standard procedure to use multiple base stations, and to separate them vertically to the maximum extent possible, since it will then be much easier to detect mis-modeling of the atmosphere. Copyright 2007 by the American Geophysical Union.
Optimal path planning for single and multiple aircraft using a reduced order formulation
NASA Astrophysics Data System (ADS)
Twigg, Shannon S.
High-flying unmanned reconnaissance and surveillance systems are now being used extensively in the United States military. Current development programs are producing demonstrations of next-generation unmanned flight systems that are designed to perform combat missions. Their use in first-strike combat operations will dictate operations in densely cluttered environments that include unknown obstacles and threats, and will require the use of terrain for masking. The demand for autonomy of operations in such environments dictates the need for advanced trajectory optimization capabilities. In addition, the ability to coordinate the movements of more than one aircraft in the same area is an emerging challenge. This thesis examines using an analytical reduced order formulation for trajectory generation for minimum time and terrain masking cases. First, pseudo-3D constant velocity equations of motion are used for path planning for a single vehicle. In addition, the inclusion of winds, moving targets and moving threats is considered. Then, this formulation is increased to using 3D equations of motion, both with a constant velocity and with a simplified varying velocity model. Next, the constant velocity equations of motion are expanded to include the simultaneous path planning of an unspecified number of vehicles, for both aircraft avoidance situations and formation flight cases.
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
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
Aircraft optimization by a system approach: Achievements and trends
NASA Technical Reports Server (NTRS)
Sobieszczanski-Sobieski, Jaroslaw
1992-01-01
Recently emerging methodology for optimal design of aircraft treated as a system of interacting physical phenomena and parts is examined. The methodology is found to coalesce into methods for hierarchic, non-hierarchic, and hybrid systems all dependent on sensitivity analysis. A separate category of methods has also evolved independent of sensitivity analysis, hence suitable for discrete problems. References and numerical applications are cited. Massively parallel computer processing is seen as enabling technology for practical implementation of the methodology.
Optimal Discrete Event Supervisory Control of Aircraft Gas Turbine Engines
NASA Technical Reports Server (NTRS)
Litt, Jonathan (Technical Monitor); Ray, Asok
2004-01-01
This report presents an application of the recently developed theory of optimal Discrete Event Supervisory (DES) control that is based on a signed real measure of regular languages. The DES control techniques are validated on an aircraft gas turbine engine simulation test bed. The test bed is implemented on a networked computer system in which two computers operate in the client-server mode. Several DES controllers have been tested for engine performance and reliability.
Optimization of aircraft seat cushion fire blocking layers
NASA Technical Reports Server (NTRS)
Kourtides, D. A.; Parker, J. A.; Ling, A. C.; Hovatter, W. R.
1983-01-01
This report describes work completed by the National Aeronautics and Space Administration - for the Federal Aviation Administration Technical Center. The purpose of this work was to examine the potential of fire blocking mechanisms for aircraft seat cushions in order to provide an optimized seat configuration with adequate fire protection and minimum weight. Aluminized thermally stable fabrics were found to provide adequate fire protection when used in conjunction with urethane foams, while maintaining minimum weight and cost penalty.
Optimal input design for aircraft instrumentation systematic error estimation
NASA Technical Reports Server (NTRS)
Morelli, Eugene A.
1991-01-01
A new technique for designing optimal flight test inputs for accurate estimation of instrumentation systematic errors was developed and demonstrated. A simulation model of the F-18 High Angle of Attack Research Vehicle (HARV) aircraft was used to evaluate the effectiveness of the optimal input compared to input recorded during flight test. Instrumentation systematic error parameter estimates and their standard errors were compared. It was found that the optimal input design improved error parameter estimates and their accuracies for a fixed time input design. Pilot acceptability of the optimal input design was demonstrated using a six degree-of-freedom fixed base piloted simulation of the F-18 HARV. The technique described in this work provides a practical, optimal procedure for designing inputs for data compatibility experiments.
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.
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.
Flow simulation and shape optimization for aircraft design
NASA Astrophysics Data System (ADS)
Kroll, Norbert; Gauger, Nicolas R.; Brezillon, Joel; Dwight, Richard; Fazzolari, Antonio; Vollmer, Daniel; Becker, Klaus; Barnewitz, Holger; Schulz, Volker; Hazra, Subhendu
2007-06-01
Within the framework of the German aerospace research program, the CFD project MEGADESIGN was initiated. The main goal of the project is the development of efficient numerical methods for shape design and optimization. In order to meet the requirements of industrial implementations a co-operative effort has been set up which involves the German aircraft industry, the DLR, several universities and some small enterprises specialized in numerical optimization. This paper outlines the planned activities within MEGADESIGN, the status at the beginning of the project and it presents some early results achieved in the project.
Time optimal trajectories for mobile robots with two independently driven wheels
Reister, D.B.; Pin, F.G.
1992-03-01
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 acceleration 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.
Time optimal trajectories for mobile robots with two independently driven wheels
Reister, D.B.; Pin, F.G.
1992-03-01
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 acceleration 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.
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.
NASA Technical Reports Server (NTRS)
Striepe, Scott A.; Blanchard, Robert C.; Kirsch, Michael F.; Fowler, Wallace T.
2007-01-01
On January 14, 2005, ESA's Huygens probe separated from NASA's Cassini spacecraft, entered the Titan atmosphere and landed on its surface. As part of NASA Engineering Safety Center Independent Technical Assessment of the Huygens entry, descent, and landing, and an agreement with ESA, NASA provided results of all EDL analyses and associated findings to the Huygens project team prior to probe entry. In return, NASA was provided the flight data from the probe so that trajectory reconstruction could be done and simulation models assessed. Trajectory reconstruction of the Huygens entry probe at Titan was accomplished using two independent approaches: a traditional method and a POST2-based method. Results from both approaches are discussed in this paper.
2002-01-01
Company, Washington, DC Boeing Commercial Aircraft Division, Seattle, WA and Long Beach, CA Boeing Military Aircraft and Missile Division, St. Louis, MO and... aircraft ; military fixed-wing aircraft ; rotorcraft (helicopters and tiltrotor aircraft ); and aircraft jet engines. Two companies dominate the commercial... aircraft business, Boeing and Airbus. Four companies dominate the military fixed-wing market, Boeing, Lockheed Martin, BAE Systems, and European
Advances in aircraft design: Multiobjective optimization and a markup language
NASA Astrophysics Data System (ADS)
Deshpande, Shubhangi
Today's modern aerospace systems exhibit strong interdisciplinary coupling and require a multidisciplinary, collaborative approach. Analysis methods that were once considered feasible only for advanced and detailed design are now available and even practical at the conceptual design stage. This changing philosophy for conducting conceptual design poses additional challenges beyond those encountered in a low fidelity design of aircraft. This thesis takes some steps towards bridging the gaps in existing technologies and advancing the state-of-the-art in aircraft design. The first part of the thesis proposes a new Pareto front approximation method for multiobjective optimization problems. The method employs a hybrid optimization approach using two derivative free direct search techniques, and is intended for solving blackbox simulation based multiobjective optimization problems with possibly nonsmooth functions where the analytical formof the objectives is not known and/or the evaluation of the objective function(s) is very expensive (very common in multidisciplinary design optimization). A new adaptive weighting scheme is proposed to convert a multiobjective optimization problem to a single objective optimization problem. Results show that the method achieves an arbitrarily close approximation to the Pareto front with a good collection of well-distributed nondominated points. The second part deals with the interdisciplinary data communication issues involved in a collaborative mutidisciplinary aircraft design environment. Efficient transfer, sharing, and manipulation of design and analysis data in a collaborative environment demands a formal structured representation of data. XML, a W3C recommendation, is one such standard concomitant with a number of powerful capabilities that alleviate interoperability issues. A compact, generic, and comprehensive XML schema for an aircraft design markup language (ADML) is proposed here to provide a common language for data
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.
Systematic low-thrust trajectory optimization for a multi-rendezvous mission using adjoint scaling
NASA Astrophysics Data System (ADS)
Jiang, Fanghua; Tang, Gao
2016-04-01
A deep-space exploration mission with low-thrust propulsion to rendezvous with multiple asteroids is investigated. Indirect methods, based on the optimal control theory, are implemented to optimize the fuel consumption. The application of indirect methods for optimizing low-thrust trajectories between two asteroids is briefly given. An effective method is proposed to provide initial guesses for transfers between close near-circular near-coplanar orbits. The conditions for optimality of a multi-asteroid rendezvous mission are determined. The intuitive method of splitting the trajectories into several legs that are solved sequentially is applied first. Then the results are patched together by a scaling method to provide a tentative guess for optimizing the whole trajectory. Numerical examples of optimizing three probe exploration sequences that contain a dozen asteroids each demonstrate the validity and efficiency of these methods.
A multi-objective approach to the design of low thrust space trajectories using optimal control
NASA Astrophysics Data System (ADS)
Dellnitz, Michael; Ober-Blöbaum, Sina; Post, Marcus; Schütze, Oliver; Thiere, Bianca
2009-11-01
In this article, we introduce a novel three-step approach for solving optimal control problems in space mission design. We demonstrate its potential by the example task of sending a group of spacecraft to a specific Earth L 2 halo orbit. In each of the three steps we make use of recently developed optimization methods and the result of one step serves as input data for the subsequent one. Firstly, we perform a global and multi-objective optimization on a restricted class of control functions. The solutions of this problem are (Pareto-)optimal with respect to Δ V and flight time. Based on the solution set, a compromise trajectory can be chosen suited to the mission goals. In the second step, this selected trajectory serves as initial guess for a direct local optimization. We construct a trajectory using a more flexible control law and, hence, the obtained solutions are improved with respect to control effort. Finally, we consider the improved result as a reference trajectory for a formation flight task and compute trajectories for several spacecraft such that these arrive at the halo orbit in a prescribed relative configuration. The strong points of our three-step approach are that the challenging design of good initial guesses is handled numerically by the global optimization tool and afterwards, the last two steps only have to be performed for one reference trajectory.
Implementation of a Low-Thrust Trajectory Optimization Algorithm for Preliminary Design
NASA Technical Reports Server (NTRS)
Sims, Jon A.; Finlayson, Paul A.; Rinderle, Edward A.; Vavrina, Matthew A.; Kowalkowski, Theresa D.
2006-01-01
A tool developed for the preliminary design of low-thrust trajectories is described. The trajectory is discretized into segments and a nonlinear programming method is used for optimization. The tool is easy to use, has robust convergence, and can handle many intermediate encounters. In addition, the tool has a wide variety of features, including several options for objective function and different low-thrust propulsion models (e.g., solar electric propulsion, nuclear electric propulsion, and solar sail). High-thrust, impulsive trajectories can also be optimized.
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.
NASA Astrophysics Data System (ADS)
Ross, Steven M.
A method is presented to couple and solve the optimal control and the optimal estimation problems simultaneously, allowing systems with bearing-only sensors to maneuver to obtain observability for relative navigation without unnecessarily detracting from a primary mission. A fundamentally new approach to trajectory optimization and the dual control problem is presented, constraining polynomial approximations of the Fisher Information Matrix to provide an information gradient and allow prescription of the level of future estimation certainty required for mission accomplishment. Disturbances, modeling deficiencies, and corrupted measurements are addressed recursively using Radau pseudospectral collocation methods and sequential quadratic programming for the optimal path and an Unscented Kalman Filter for the target position estimate. The underlying real-time optimal control (RTOC) algorithm is developed, specifically addressing limitations of current techniques that lose error integration. The resulting guidance method can be applied to any bearing-only system, such as submarines using passive sonar, anti-radiation missiles, or small UAVs seeking to land on power lines for energy harvesting. System integration, variable timing methods, and discontinuity management techniques are provided for actual hardware implementation. Validation is accomplished with both simulation and flight test, autonomously landing a quadrotor helicopter on a wire.
NASA Technical Reports Server (NTRS)
Aziz, Jonathan D.; Parker, Jeffrey S.; Scheeres, Daniel J.; Englander, Jacob A.
2017-01-01
Low-thrust trajectories about planetary bodies characteristically span a high count of orbital revolutions. Directing the thrust vector over many revolutions presents a challenging optimization problem for any conventional strategy. This paper demonstrates the tractability of low-thrust trajectory optimization about planetary bodies by applying a Sundman transformation to change the independent variable of the spacecraft equations of motion to the eccentric anomaly and performing the optimization with differential dynamic programming. Fuel-optimal geocentric transfers are shown in excess of 1000 revolutions while subject to Earths J2 perturbation and lunar gravity.
Material Distribution Optimization for the Shell Aircraft Composite Structure
NASA Astrophysics Data System (ADS)
Shevtsov, S.; Zhilyaev, I.; Oganesyan, P.; Axenov, V.
2016-09-01
One of the main goal in aircraft structures designing isweight decreasing and stiffness increasing. Composite structures recently became popular in aircraft because of their mechanical properties and wide range of optimization possibilities.Weight distribution and lay-up are keys to creating lightweight stiff strictures. In this paperwe discuss optimization of specific structure that undergoes the non-uniform air pressure at the different flight conditions and reduce a level of noise caused by the airflowinduced vibrations at the constrained weight of the part. Initial model was created with CAD tool Siemens NX, finite element analysis and post processing were performed with COMSOL Multiphysicsr and MATLABr. Numerical solutions of the Reynolds averaged Navier-Stokes (RANS) equations supplemented by k-w turbulence model provide the spatial distributions of air pressure applied to the shell surface. At the formulation of optimization problem the global strain energy calculated within the optimized shell was assumed as the objective. Wall thickness has been changed using parametric approach by an initiation of auxiliary sphere with varied radius and coordinates of the center, which were the design variables. To avoid a local stress concentration, wall thickness increment was defined as smooth function on the shell surface dependent of auxiliary sphere position and size. Our study consists of multiple steps: CAD/CAE transformation of the model, determining wind pressure for different flow angles, optimizing wall thickness distribution for specific flow angles, designing a lay-up for optimal material distribution. The studied structure was improved in terms of maximum and average strain energy at the constrained expense ofweight growth. Developed methods and tools can be applied to wide range of shell-like structures made of multilayered quasi-isotropic laminates.
An investigation of the fuel-optimal periodic trajectories of a hypersonic vehicle
NASA Technical Reports Server (NTRS)
Dewell, Larry D.; Speyer, Jason L.
1993-01-01
Periodic trajectories were found to minimize the range-averaged fuel consumption. For a realistic hypersonic aircraft modeled as a point mass over a nonrotating, spherical Earth, the periodic orbit yielded a 15 percent improvement in fuel consumption over static cruise. Moreover, vehicle dynamic loading was contained within a realistic survivability envelope of 8 g's. The resulting periodic orbit is composed of very distinct flight regimes (Keplerian arc, atmospheric glide and powered climb), which may offer mission advantages over the static path.
Parameter optimization capability in the trajectory code PMAST (Point-Mass Simulation Tool)
Outka, D.E.
1987-01-28
Trajectory optimization capability has been added to PMAST through addition of the Recursive Quadratic Programming code VF02AD. The scope of trajectory optimization problems the resulting code can solve is very broad, as it takes advantage of the versatility of the original PMAST code. Most three-degree-of-freedom flight-vehicle problems can be simulated with PMAST, and up to 25 parameters specifying initial conditions, weights, control histories and other problem-deck inputs can be used to meet trajectory constraints in some optimal manner. This report outlines the mathematical formulation of the optimization technique, describes the input requirements and suggests guidelines for problem formulation. An example problem is presented to demonstrate the use and features of the optimization portions of the code.
Global Optimization of Low-Thrust Interplanetary Trajectories Subject to Operational Constraints
NASA Technical Reports Server (NTRS)
Englander, Jacob A.; Vavrina, Matthew A.; Hinckley, David
2016-01-01
Low-thrust interplanetary space missions are highly complex and there can be many locally optimal solutions. While several techniques exist to search for globally optimal solutions to low-thrust trajectory design problems, they are typically limited to unconstrained trajectories. The operational design community in turn has largely avoided using such techniques and has primarily focused on accurate constrained local optimization combined with grid searches and intuitive design processes at the expense of efficient exploration of the global design space. This work is an attempt to bridge the gap between the global optimization and operational design communities by presenting a mathematical framework for global optimization of low-thrust trajectories subject to complex constraints including the targeting of planetary landing sites, a solar range constraint to simplify the thermal design of the spacecraft, and a real-world multi-thruster electric propulsion system that must switch thrusters on and off as available power changes over the course of a mission.
A technique for integrating engine cycle and aircraft configuration optimization
NASA Technical Reports Server (NTRS)
Geiselhart, Karl A.
1994-01-01
A method for conceptual aircraft design that incorporates the optimization of major engine design variables for a variety of cycle types was developed. The methodology should improve the lengthy screening process currently involved in selecting an appropriate engine cycle for a given application or mission. The new capability will allow environmental concerns such as airport noise and emissions to be addressed early in the design process. The ability to rapidly perform optimization and parametric variations using both engine cycle and aircraft design variables, and to see the impact on the aircraft, should provide insight and guidance for more detailed studies. A brief description of the aircraft performance and mission analysis program and the engine cycle analysis program that were used is given. A new method of predicting propulsion system weight and dimensions using thermodynamic cycle data, preliminary design, and semi-empirical techniques is introduced. Propulsion system performance and weights data generated by the program are compared with industry data and data generated using well established codes. The ability of the optimization techniques to locate an optimum is demonstrated and some of the problems that had to be solved to accomplish this are illustrated. Results from the application of the program to the analysis of three supersonic transport concepts installed with mixed flow turbofans are presented. The results from the application to a Mach 2.4, 5000 n.mi. transport indicate that the optimum bypass ratio is near 0.45 with less than 1 percent variation in minimum gross weight for bypass ratios ranging from 0.3 to 0.6. In the final application of the program, a low sonic boom fix a takeoff gross weight concept that would fly at Mach 2.0 overwater and at Mach 1.6 overland is compared with a baseline concept of the same takeoff gross weight that would fly Mach 2.4 overwater and subsonically overland. The results indicate that for the design mission
Multi-level systems modeling and optimization for novel aircraft
NASA Astrophysics Data System (ADS)
Subramanian, Shreyas Vathul
This research combines the disciplines of system-of-systems (SoS) modeling, platform-based design, optimization and evolving design spaces to achieve a novel capability for designing solutions to key aeronautical mission challenges. A central innovation in this approach is the confluence of multi-level modeling (from sub-systems to the aircraft system to aeronautical system-of-systems) in a way that coordinates the appropriate problem formulations at each level and enables parametric search in design libraries for solutions that satisfy level-specific objectives. The work here addresses the topic of SoS optimization and discusses problem formulation, solution strategy, the need for new algorithms that address special features of this problem type, and also demonstrates these concepts using two example application problems - a surveillance UAV swarm problem, and the design of noise optimal aircraft and approach procedures. This topic is critical since most new capabilities in aeronautics will be provided not just by a single air vehicle, but by aeronautical Systems of Systems (SoS). At the same time, many new aircraft concepts are pressing the boundaries of cyber-physical complexity through the myriad of dynamic and adaptive sub-systems that are rising up the TRL (Technology Readiness Level) scale. This compositional approach is envisioned to be active at three levels: validated sub-systems are integrated to form conceptual aircraft, which are further connected with others to perform a challenging mission capability at the SoS level. While these multiple levels represent layers of physical abstraction, each discipline is associated with tools of varying fidelity forming strata of 'analysis abstraction'. Further, the design (composition) will be guided by a suitable hierarchical complexity metric formulated for the management of complexity in both the problem (as part of the generative procedure and selection of fidelity level) and the product (i.e., is the mission
Generalized Newton-Raphson trajectory optimization-generator 1
NASA Technical Reports Server (NTRS)
Cope, D. D.; Eskridge, C. D.; Hanafy, L. M.
1968-01-01
Computer program constructs a sequence of optimal solutions to dynamically-approximate linear equations. Specification of the number and type of subarcs in the optimal solution allows simultaneous satisfaction of all switching criteria.
Simulation of Airplane and Rocket Trajectories
NASA Technical Reports Server (NTRS)
Wahbah, Magdy M.; Berning, Michael J.; Choy, Tony S.
1987-01-01
Simulation and Optimization of Rocket Trajectories program (SORT) contains comprehensive mathematical models for simulating aircraft dynamics, freely falling objects, and many types of ballistic trajectories. Provides high-fidelity, three-degrees-of-freedom simulation for atmospheric and exoatmospheric flight. It numerically models vehicle subsystems and vehicle environment. Used for wide range of simulations. Written in machine-independent FORTRAN 77.
Trajectory Optimization for Helicopter Unmanned Aerial Vehicles (UAVs)
2010-06-01
INTRODUCTION For quite some time, mathematicians have struggled with a reliable method for solving optimal control problems with complicated nonlinear...problems have several fundamental differences from the computation of PDEs. Solving optimal control problems asks for the collective and...and differentiations. These are all critical pieces for solving optimal control problems . The derivative of ( )Nix t at the LGL node kt is
Optimization of Low Thrust Trajectories With Terminal Aerocapture
2003-06-01
38 F. NECESSARY CONDITIONS ......................................................................39 VI. OPTIMAL LOW THRUST RESULTS...does the solution satisfy the necessary conditions for optimality ? Recalling Eqn. (84), analytical expressions can be obtained by taking the partial...multiplier associated with path constraint relating the three controls [Eqn. (117)]. Applying the necessary condition for optimality by taking the
NASA Astrophysics Data System (ADS)
Tsuchiya, Takeshi; Takenaka, Youichi; Taguchi, Hideyuki; Sawai, Shujiro
Japan Aerospace Exploration Agency, JAXA announced a long-term vision recently. In the vision, JAXA aims to develop hypersonic aircrafts. A pre-cooled turbojet engine has great potential as one of newly developed hypersonic air-breathing engines. We also expect the engine to be installed in space transportation vehicles in future. For combustion test in real flight condition of the engines, JAXA has an experimental plan with a small test vehicle falling from a high-altitude balloon. This paper applies numerical analysis and optimization techniques to conceptual designs of the test vehicle in order to obtain the best configuration and trajectory that can achieve the flight test. The results show helpful knowledge when we design prototype vehicles.
NASA Astrophysics Data System (ADS)
Tsuchiya, Takeshi; Takenaka, Youichi; Taguchi, Hideyuki; Sawai, Shujiro
The Japan Aerospace Exploration Agency, JAXA, announced a long-term vision recently. In the vision, JAXA aims to develop hypersonic aircrafts. A pre-cooled turbojet engine has great potential as one of newly developed hypersonic airbreathing engines. We also expect the engine to be installed in space transportation vehicles in the future. For combustion test in the real flight conditions of the engines, JAXA has an experimental plan where a small test vehicle is released from a high-altitude balloon. This paper applies numerical analysis and optimization techniques to conceptual designs of the test vehicle in order to obtain the best configuration and trajectory for the flight test. The results show helpful knowledge for designing prototype vehicles.
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.
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.
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.
Xu, Y; Li, N
2014-09-01
Biological species have produced many simple but efficient rules in their complex and critical survival activities such as hunting and mating. A common feature observed in several biological motion strategies is that the predator only moves along paths in a carefully selected or iteratively refined subspace (or manifold), which might be able to explain why these motion strategies are effective. In this paper, a unified linear algebraic formulation representing such a predator-prey relationship is developed to simplify the construction and refinement process of the subspace (or manifold). Specifically, the following three motion strategies are studied and modified: motion camouflage, constant absolute target direction and local pursuit. The framework constructed based on this varying subspace concept could significantly reduce the computational cost in solving a class of nonlinear constrained optimal trajectory planning problems, particularly for the case with severe constraints. Two non-trivial examples, a ground robot and a hypersonic aircraft trajectory optimization problem, are used to show the capabilities of the algorithms in this new computational framework.
2007-09-01
used to converge to the optimal solution. This numerical approach is applied to the Common Aero Vehicle (CAV) as the test platform for the full three...6 EAGLE Evolved Acceleration Guidance Logic for Entry . . . . . . 10 POSTII Program To Optimize Simulated Trajectories II...11 LQR linear quadratic regulator . . . . . . . . . . . . . . . . . . 12 MILP Mixed- Integer Linear Programming
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.
Optimism and Pessimism as Predictors of Alcohol Use Trajectories in Adolescence
ERIC Educational Resources Information Center
Wray, Tyler B.; Dvorak, Rob D.; Hsia, Jennifer F.; Arens, Ashley M.; Schweinle, William E.
2013-01-01
A range of research has recognized the benefits of optimism in a variety of health-related outcomes. Pessimism has received less attention but may be a distinct concept that is uniquely related to certain health behaviors, including drug use. The present study examined relationships between optimism and pessimism and alcohol use trajectories of…
NASA Technical Reports Server (NTRS)
Merritt, S. R.; Cliff, E. M.; Kelley, H. J.
1985-01-01
F. Kaiser's germinal 1944 report on his 'resultant-height' concept, now known as energy modelling, is reviewed. The data base for the Me. 262 jet fighter is recreated via spline-lattice representation of specific excess power. Minimum-time and 'distance'-climb trajectories are generated in an attempt to check Kaiser's results. Agreement is good for the minimum-time calculations but only qualitative agreement is obtained for the mysterious 'distance climbs' whose documentation is fragmentary. The character of optimal climb-dash trajectories in energy approximation is examined and illustrated.
NASA Astrophysics Data System (ADS)
Wu, Q.; Xiong, F.; Wang, F.; Xiong, Y.
2016-10-01
In order to reduce the computational time, a fully parallel implementation of the particle swarm optimization (PSO) algorithm on a graphics processing unit (GPU) is presented. Instead of being executed on the central processing unit (CPU) sequentially, PSO is executed in parallel via the GPU on the compute unified device architecture (CUDA) platform. The processes of fitness evaluation, updating of velocity and position of all particles are all parallelized and introduced in detail. Comparative studies on the optimization of four benchmark functions and a trajectory optimization problem are conducted by running PSO on the GPU (GPU-PSO) and CPU (CPU-PSO). The impact of design dimension, number of particles and size of the thread-block in the GPU and their interactions on the computational time is investigated. The results show that the computational time of the developed GPU-PSO is much shorter than that of CPU-PSO, with comparable accuracy, which demonstrates the remarkable speed-up capability of GPU-PSO.
Fault Tolerant Optimal Trajectory Generation for Reusable Launch Vehicles (Preprint)
2006-12-01
solving optimal control problems , particularly state-constrained problems, are widely considered to be difficult,26,27 it...15 Conclusions By integrating recent advances in solving optimal control problems with inner-loop con- trol allocation, it has been shown that it is...Package for Solving Optimal Control Problems ,” Tech. Rep. 04-01.0, Naval Postgraduate School, Monterey, CA, December 2003. 19 of 36 List of Figures
Calculation of free fall trajectories based on numerical optimization techniques
NASA Technical Reports Server (NTRS)
1972-01-01
The development of a means of computing free-fall (nonthrusting) trajectories from one specified point in the solar system to another specified point in the solar system in a given amount of time was studied. The problem is that of solving a two-point boundary value problem for which the initial slope is unknown. Two standard methods of attack exist for solving two-point boundary value problems. The first method is known as the initial value or shooting method. The second method of attack for two-point boundary value problems is to approximate the nonlinear differential equations by an appropriate linearized set. Parts of both boundary value problem solution techniques described above are used. A complete velocity history is guessed such that the corresponding position history satisfies the given boundary conditions at the appropriate times. An iterative procedure is then followed until the last guessed velocity history and the velocity history obtained from integrating the acceleration history agree to some specified tolerance everywhere along the trajectory.
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
High-accuracy optimal finite-thrust trajectories for Moon escape
NASA Astrophysics Data System (ADS)
Shen, Hong-Xin; Casalino, Lorenzo
2017-02-01
The optimization problem of fuel-optimal trajectories from a low circular Moon orbit to a target hyperbolic excess velocity vector using finite-thrust propulsion is solved. The ability to obtain the most accurate satisfaction of necessary optimality conditions in a high-accuracy dynamic model is the main motivation of the current study. The solutions allow attaining anytime-return Earth-interface conditions from a low lunar orbit. Gravitational effects of the Sun, Earth, and Moon are included throughout the entire trajectory. Severe constraints on the fuel budget combined with high-accuracy demands on the endpoint conditions necessitate a high-fidelity solution to the trajectory optimization problem and JPL DE405 ephemeris model is used to determine the perturbing bodies' positions. The optimization problem is solved using an indirect method. The optimality of the solution is verified by an application of Pontryagin's maximum principle. More accurate and fuel-efficient trajectories are found for the same mission objectives and constraints published in other research, emphasizing the advantages of this technique. It is also shown that the thrust structure consists of three finite burns. In contrast to previous research, no singular arc is required in the optimal solutions, and all the controls appear bang-bang.
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
Simulation to Support Local Search in Trajectory Optimization Planning
NASA Technical Reports Server (NTRS)
Morris, Robert A.; Venable, K. Brent; Lindsey, James
2012-01-01
NASA and the international community are investing in the development of a commercial transportation infrastructure that includes the increased use of rotorcraft, specifically helicopters and civil tilt rotors. However, there is significant concern over the impact of noise on the communities surrounding the transportation facilities. One way to address the rotorcraft noise problem is by exploiting powerful search techniques coming from artificial intelligence coupled with simulation and field tests to design low-noise flight profiles which can be tested in simulation or through field tests. This paper investigates the use of simulation based on predictive physical models to facilitate the search for low-noise trajectories using a class of automated search algorithms called local search. A novel feature of this approach is the ability to incorporate constraints directly into the problem formulation that addresses passenger safety and comfort.
Inclusion of known integrals in the optimal trajectory problem
NASA Technical Reports Server (NTRS)
Burns, R. E.
1974-01-01
The classical problem of determination of the rocket trajectory which minimizes mass expenditure during motion between two points in the field of a single gravitating body is analyzed. The known integrals of the system are incorporated into the adjoint equations resulting in a reduction from a seventh-order adjoint system to a third-order adjoint system. The first case which is treated in that of planar motion under specific end conditions. In this case a regularization of the recently derived equations is achieved. The general three-dimensional case is also reduced from a seventh-order adjoint system to a third-order adjoint system. In this case a regularization has not been found.
Optimal low-thrust trajectories for nuclear and solar electric propulsion
NASA Astrophysics Data System (ADS)
Genta, G.; Maffione, P. F.
2016-01-01
The optimization of the trajectory and of the thrust profile of a low-thrust interplanetary transfer is usually solved under the assumption that the specific mass of the power generator is constant. While this is reasonable in the case of nuclear electric propulsion, if solar electric propulsion is used the specific mass depends on the distance of the spacecraft from the Sun. In the present paper the optimization of the trajectory of the spacecraft and of the thrust profile is solved under the latter assumption, to obtain optimized interplanetary trajectories for solar electric spacecraft, also taking into account all phases of the journey, from low orbit about the starting planet to low orbit about the destination one. General plots linking together the travel time, the specific mass of the generator and the propellant consumption are obtained.
Research of trajectory optimization on feeding manipulator based on internal penalty function
NASA Astrophysics Data System (ADS)
Wei, Chunli
2016-10-01
This paper has discussed the problems of trajectory optimization of feeding manipulator based on penalty function. Has selected the types of feeding robot, which work on NC machining center of the flexible workshop, and created the mathematical model with penalty function, for the purpose not only to optimize its walking path to reduce the production cost, but also improve its safety and efficiency of production. It has been verified by theoretical analysis and practice, the path optimization method is feasible.
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.
Optimization and Sensitivity Analysis for a Launch Trajectory
2014-12-01
LIST OF ACRONYMS AND ABBREVIATIONS BVP boundary value problem DIDO MATLAB optimal control toolbox ECI Earth centered inertial GPS global...research, the algorithm that will be used is DIDO. DIDO is a MATLAB optimal control toolbox that was named after Dido, the founder and first queen of...the unknown initial values [13]. This is where the MATLAB tool DIDO can make life a lot easier. Once the cost function, dynamics equations
NASA Astrophysics Data System (ADS)
Miller, Michael; Strom, Ben; Breuer, Kenneth; Mandre, Shreyas
2014-11-01
We determine the feasibility of applying optimization algorithms to an oscillating hydrofoil's motion trajectory to determine maximum efficiency of energy capture. Optimization is performed using the Nelder-Meade downhill simplex method. The objective function is the energy captured measured experimentally in run-time with an oscillating hydrofoil capable of measuring mechanical energy capture in a laboratory flume. For sinusoidal trajectories, optimization is performed over pitch and heave amplitudes as well as frequency; this system is shown to be capable of optimization in run-time. The optimum efficiency of 30% is found for a pitch amplitude of 70°, a heave amplitude of 0.8* chord and a dimensionless frequency of 0.13. To treat non-sinusoidal trajectories, we expand them in a truncated Fourier series and consider the coefficients of this series as variables for optimization. The sinusoidal case is simply an extreme case of such a truncated Fourier series, with only one term in the series retained. We present a systematic method for optimization over general non-sinusoidal trajectories by including more and more terms in the Fourier series.
Application of the steepest ascent optimization method to a reentry trajectory problem
NASA Technical Reports Server (NTRS)
Junkin, B. G.
1971-01-01
The direct optimization method is presented in detail. Nominal values of the control variables are input parameters. Perturbations are introduced into the control variables and the resulting first order predictions of changes in the payoff, and constraint functions are then determined. Through a sequence of prescribed cycles, a trajectory is eventually obtained which is reasonably close to the optimum. The method is successfully applied to an Apollo three-dimensional reentry problem. The study of this Apollo application problem has resulted in the development of a highly flexible computer program that can be modified to consider other trajectory optimization problems.
Space safety trajectory optimization and debris analysis using ASTOS at ESA
NASA Astrophysics Data System (ADS)
Ortega, Guillermo; Blasco, Ana; Weikert, Sven
This paper describes the coupling of the space trajectory optimization software ASTOS with a tool for splashdown analysis of separated spacecraft stages and debris called DARS (Destructive Analysis for Re-entry Spacecraft), and a Risk Analysis Module called RAM. ASTOS is a main reference tool for space trajectory optimization at ESA. It is also used to compute demise and break up of rocket stages and re-entry vehicles and analyze the risk to populated areas. ASTOS software is a simulation and optimization environment to compute optimal trajectories for a variety of complex multi-phase optimal control problems. It consists of fast and powerful optimization programs, PROMIS, CAMTOS, SOCS and TROPIC, that handle large and highly discretized problems, a user interface with multiple plot capability, and GISMO, an integrated graphical iteration monitor to review the optimization process and plot the state and control histories at intermediate steps during the optimization. The optimization programs used by ASTOS use Non-Linear Programming (NLP) mathematical solvers like NPSOL, SLSQP, SLLSQP, and SNOPT. These solvers use Sequential Quadratic Programming (SQP) mathematical algorithms to find the solution of the non-linear programming problems in trajectory optimization. ASTOS comprises an extensive model library, which allows launcher and re-entry spacecraft trajectory optimization without programming work. DARS considers not only a stage break-up, but also ablation and melting of the fragments, taking diverse materials and shapes into account. The paper discusses hazard due to stage and debris impact, considering the ESA launchers and re-entry vehicles as examples. Previous approaches for the impact point calculation during trajectory optimization are presented. Subsequently the results of these approaches are compared to DARS results. This paper shows that ASTOS and the DARS and RAM extensions can calculate impact points with satisfactory accuracy and calculation time
An inverse dynamics approach to trajectory optimization and guidance for an aerospace plane
NASA Technical Reports Server (NTRS)
Lu, Ping
1992-01-01
The optimal ascent problem for an aerospace planes is formulated as an optimal inverse dynamic problem. Both minimum-fuel and minimax type of performance indices are considered. Some important features of the optimal trajectory and controls are used to construct a nonlinear feedback midcourse controller, which not only greatly simplifies the difficult constrained optimization problem and yields improved solutions, but is also suited for onboard implementation. Robust ascent guidance is obtained by using combination of feedback compensation and onboard generation of control through the inverse dynamics approach. Accurate orbital insertion can be achieved with near-optimal control of the rocket through inverse dynamics even in the presence of disturbances.
A fast ascent trajectory optimization method for hypersonic air-breathing vehicles
NASA Astrophysics Data System (ADS)
Murillo, Oscar J., Jr.
The objective of this dissertation is to investigate a fast and reliable method to generate three-dimensional optimal ascent trajectories for hypersonic air-breathing vehicles. The problem is notoriously difficult because of the strong nonlinear coupling amongst aerodynamics, propulsion, vehicle attitude and trajectory state. As such an algorithm matures, the ultimate goal is to realize optimal closed-loop ascent guidance for hypersonic air-breathing vehicles. The problem is formulated as a fuel-optimal control problem. The corresponding necessary conditions are given. It is shown how the original problem of search for the optimal control commands can be reduced to a univariate root-finding problem at each point along the trajectory. A finite difference scheme is used to numerically solve the associated two-point-boundary-value problem. Evaluation of the approach is done through open-loop solutions and closed-loop simulations. The results show promising potential of the proposed approach as a rapid trajectory optimization tool for the class of hypersonic air-breathing vehicles.
Optimal return-to-launchsite abort trajectories for an HL-20 Personnel Launch System vehicle
NASA Technical Reports Server (NTRS)
Dutton, Kevin E.
1993-01-01
The Personnel Launch System (PLS) being studied by NASA is a system to complement the Space Shuttle and provide alternative access to space. The PLS consists of a manned spacecraft launched by an expendable launch vehicle (ELV). A candidate for the manned spacecraft is the HL-20 lifting body. In the event of an ELV malfunction during the initial portion of the ascent trajectory, the HL-20 will separate from the rocket and perform an unpowered return-to-launchsite (RTLS) abort. This paper describes an investigation of the RTLS abort scenario using optimal control theory. The objective of the abort trajectory is to maximize final altitude at a point near the runway. The assumption is then made that there exists a control history to steer the vehicle to any final altitude lower than the final optimal altitude. With this selection of cost function, and with this assumption, the feasibility of an RTLS abort at different times along the ascent trajectory can be determined. The method of differential inclusions, which allows the determination of optimal states and eliminates the need for determining the optimal controls, is used to determine the optimal trajectories.
Optimal return-to-launchsite abort trajectories for an HL-20 Personnel Launch System vehicle
NASA Astrophysics Data System (ADS)
Dutton, Kevin E.
The Personnel Launch System (PLS) being studied by NASA is a system to complement the Space Shuttle and provide alternative access to space. The PLS consists of a manned spacecraft launched by an expendable launch vehicle (ELV). A candidate for the manned spacecraft is the HL-20 lifting body. In the event of an ELV malfunction during the initial portion of the ascent trajectory, the HL-20 will separate from the rocket and perform an unpowered return-to-launchsite (RTLS) abort. This paper describes an investigation of the RTLS abort scenario using optimal control theory. The objective of the abort trajectory is to maximize final altitude at a point near the runway. The assumption is then made that there exists a control history to steer the vehicle to any final altitude lower than the final optimal altitude. With this selection of cost function, and with this assumption, the feasibility of an RTLS abort at different times along the ascent trajectory can be determined. The method of differential inclusions, which allows the determination of optimal states and eliminates the need for determining the optimal controls, is used to determine the optimal trajectories.
Trajectory optimization using parallel shooting method on parallel computer
Wirthman, D.J.; Park, S.Y.; Vadali, S.R.
1995-03-01
The efficiency of a parallel shooting method on a parallel computer for solving a variety of optimal control guidance problems is studied. Several examples are considered to demonstrate that a speedup of nearly 7 to 1 is achieved with the use of 16 processors. It is suggested that further improvements in performance can be achieved by parallelizing in the state domain. 10 refs.
Global Optimal Trajectory in Chaos and NP-Hardness
NASA Astrophysics Data System (ADS)
Latorre, Vittorio; Gao, David Yang
This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. A newly developed canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by linear iterative methods are mainly due to the intrinsic numerical error accumulations. Otherwise, the global optimization problem could be NP-hard and the nonlinear system can be really chaotic. A conjecture is proposed, which reveals the connection between chaos in nonlinear dynamics and NP-hardness in computer science. The methodology and the conjecture are verified by applications to the well-known logistic equation, a forced memristive circuit and the Lorenz system. Computational results show that the canonical duality theory can be used to identify chaotic systems and to obtain realistic global optimal solutions in nonlinear dynamical systems. The method and results presented in this paper should bring some new insights into nonlinear dynamical systems and NP-hardness in computational complexity theory.
Aerostructural Shape and Topology Optimization of Aircraft Wings
NASA Astrophysics Data System (ADS)
James, Kai
A series of novel algorithms for performing aerostructural shape and topology optimization are introduced and applied to the design of aircraft wings. An isoparametric level set method is developed for performing topology optimization of wings and other non-rectangular structures that must be modeled using a non-uniform, body-fitted mesh. The shape sensitivities are mapped to computational space using the transformation defined by the Jacobian of the isoparametric finite elements. The mapped sensitivities are then passed to the Hamilton-Jacobi equation, which is solved on a uniform Cartesian grid. The method is derived for several objective functions including mass, compliance, and global von Mises stress. The results are compared with SIMP results for several two-dimensional benchmark problems. The method is also demonstrated on a three-dimensional wingbox structure subject to fixed loading. It is shown that the isoparametric level set method is competitive with the SIMP method in terms of the final objective value as well as computation time. In a separate problem, the SIMP formulation is used to optimize the structural topology of a wingbox as part of a larger MDO framework. Here, topology optimization is combined with aerodynamic shape optimization, using a monolithic MDO architecture that includes aerostructural coupling. The aerodynamic loads are modeled using a three-dimensional panel method, and the structural analysis makes use of linear, isoparametric, hexahedral elements. The aerodynamic shape is parameterized via a set of twist variables representing the jig twist angle at equally spaced locations along the span of the wing. The sensitivities are determined analytically using a coupled adjoint method. The wing is optimized for minimum drag subject to a compliance constraint taken from a 2 g maneuver condition. The results from the MDO algorithm are compared with those of a sequential optimization procedure in order to quantify the benefits of the MDO
Closed Loop Guidance with Multiple Constraints for Low Orbit Vehicle Trajectory Optimization
NASA Astrophysics Data System (ADS)
Zhang, Rufei; Zhao, Shifan
Low orbit has features of strong invisibility and penetration, but needs more shutdown energy comparable to high orbit under the same range, which strongly requires studying the problem of delivery capacity optimization for multi-stage launch vehicles. Based on remnant apparent velocity and constraints models, multi-constraint closed-loop guidance with constraints of trajectory maximum height and azimuth was proposed, which adopted elliptical orbit theory and Newton iteration algorithm to optimize trajectory and thrust direction, reached to take full advantage of multi-stage launch vehicle propellant, and guided low orbit vehicle to enter maximum range trajectory. Theory deduction and numerical example demonstrate that the proposed guidance method could extend range and achieve precise control for orbit maximum height and azimuth.
NASA Technical Reports Server (NTRS)
Williams, D. H.
1986-01-01
Advanced flight management systems are being developed which are capable of calculating optimal 3-D and 4-D flight trajectories for arbitrary fuel and time costs. These systems require mathematical models of airplane performance in order to compute the optimal profiles. Mismodeled idle engine characteristics can result in descent trajectories requiring excessive throttle and/or speedbrake activity in order to achieve the desired end conditions. This paper evaluates the cost and fuel penalties, trajectory variations, and flight control requirements associated with typical idle engine modeling errors for a twin-jet transport airplane. Variations in idle power setting, thrust, fuel flow, and surge bleed operation were evaluated for a cruise/descent flight segment. The results of this analysis provide insight into the penalties associated with uncertainties in idle engine performance and suggest methods of modeling which minimize these penalties.
SU-E-T-436: Fluence-Based Trajectory Optimization for Non-Coplanar VMAT
Smyth, G; Bamber, JC; Bedford, JL; Evans, PM; Saran, FH; Mandeville, HC
2015-06-15
Purpose: To investigate a fluence-based trajectory optimization technique for non-coplanar VMAT for brain cancer. Methods: Single-arc non-coplanar VMAT trajectories were determined using a heuristic technique for five patients. Organ at risk (OAR) volume intersected during raytracing was minimized for two cases: absolute volume and the sum of relative volumes weighted by OAR importance. These trajectories and coplanar VMAT formed starting points for the fluence-based optimization method. Iterative least squares optimization was performed on control points 24° apart in gantry rotation. Optimization minimized the root-mean-square (RMS) deviation of PTV dose from the prescription (relative importance 100), maximum dose to the brainstem (10), optic chiasm (5), globes (5) and optic nerves (5), plus mean dose to the lenses (5), hippocampi (3), temporal lobes (2), cochleae (1) and brain excluding other regions of interest (1). Control point couch rotations were varied in steps of up to 10° and accepted if the cost function improved. Final treatment plans were optimized with the same objectives in an in-house planning system and evaluated using a composite metric - the sum of optimization metrics weighted by importance. Results: The composite metric decreased with fluence-based optimization in 14 of the 15 plans. In the remaining case its overall value, and the PTV and OAR components, were unchanged but the balance of OAR sparing differed. PTV RMS deviation was improved in 13 cases and unchanged in two. The OAR component was reduced in 13 plans. In one case the OAR component increased but the composite metric decreased - a 4 Gy increase in OAR metrics was balanced by a reduction in PTV RMS deviation from 2.8% to 2.6%. Conclusion: Fluence-based trajectory optimization improved plan quality as defined by the composite metric. While dose differences were case specific, fluence-based optimization improved both PTV and OAR dosimetry in 80% of cases.
A concept for adaptive performance optimization on commercial transport aircraft
NASA Technical Reports Server (NTRS)
Jackson, Michael R.; Enns, Dale F.
1995-01-01
An adaptive control method is presented for the minimization of drag during flight for transport aircraft. The minimization of drag is achieved by taking advantage of the redundant control capability available in the pitch axis, with the horizontal tail used as the primary surface and symmetric deflection of the ailerons and cruise flaps used as additional controls. The additional control surfaces are excited with sinusoidal signals, while the altitude and velocity loops are closed with guidance and control laws. A model of the throttle response as a function of the additional control surfaces is formulated and the parameters in the model are estimated from the sensor measurements using a least squares estimation method. The estimated model is used to determine the minimum drag positions of the control surfaces. The method is presented for the optimization of one and two additional control surfaces. The adaptive control method is extended to optimize rate of climb with the throttle fixed. Simulations that include realistic disturbances are presented, as well as the results of a Monte Carlo simulation analysis that shows the effects of changing the disturbance environment and the excitation signal parameters.
Trajectory Optimization of a Bimodal Nuclear Powered Spacecraft to Mars
1990-05-29
high power bimodal system has been designed , it will be assumed in this initial optimization that a separate power source shall be carried...utilizing the rocket reactor in a low power output mode when the high thrusting rocket was not in use. The power created was designated for use by the...to .30. For a non-bimodal system, i.e. separate reactors for the high thrust and power generation systems, one may set 1 -0.0 or 1WL T IV-28 Power
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.
NASA Astrophysics Data System (ADS)
Kingston, Andrew M.; Myers, Glenn R.; Latham, Shane J.; Li, Heyang; Veldkamp, Jan P.; Sheppard, Adrian P.
2016-10-01
With the GPU computing becoming main-stream, iterative tomographic reconstruction (IR) is becoming a com- putationally viable alternative to traditional single-shot analytical methods such as filtered back-projection. IR liberates one from the continuous X-ray source trajectories required for analytical reconstruction. We present a family of novel X-ray source trajectories for large-angle CBCT. These discrete (sparsely sampled) trajectories optimally fill the space of possible source locations by maximising the degree of mutually independent information. They satisfy a discrete equivalent of Tuy's sufficiency condition and allow high cone-angle (high-flux) tomog- raphy. The highly isotropic nature of the trajectory has several advantages: (1) The average source distance is approximately constant throughout the reconstruction volume, thus avoiding the differential-magnification artefacts that plague high cone-angle helical computed tomography; (2) Reduced streaking artifacts due to e.g. X-ray beam-hardening; (3) Misalignment and component motion manifests as blur in the tomogram rather than double-edges, which is easier to automatically correct; (4) An approximately shift-invariant point-spread-function which enables filtering as a pre-conditioner to speed IR convergence. We describe these space-filling trajectories and demonstrate their above-mentioned properties compared with a traditional helical trajectories.
Optimizing interplanetary trajectories with deep space maneuvers. M.S. Thesis
NASA Technical Reports Server (NTRS)
Navagh, John
1993-01-01
Analysis of interplanetary trajectories is a crucial area for both manned and unmanned missions of the Space Exploration Initiative. A deep space maneuver (DSM) can improve a trajectory in much the same way as a planetary swingby. However, instead of using a gravitational field to alter the trajectory, the on-board propulsion system of the spacecraft is used when the vehicle is not near a planet. The purpose is to develop an algorithm to determine where and when to use deep space maneuvers to reduce the cost of a trajectory. The approach taken to solve this problem uses primer vector theory in combination with a non-linear optimizing program to minimize Delta(V). A set of necessary conditions on the primer vector is shown to indicate whether a deep space maneuver will be beneficial. Deep space maneuvers are applied to a round trip mission to Mars to determine their effect on the launch opportunities. Other studies which were performed include cycler trajectories and Mars mission abort scenarios. It was found that the software developed was able to locate quickly DSM's which lower the total Delta(V) on these trajectories.
Flight Trajectory Control Investigation
1981-03-01
control algorithms for four-dimensional guidance of a transport air- craft were investigated for feasibility. Cost function constraints on the ptimal...21 3.1.6 Solution Constraints .... ............. ... 25 3.1.7 Trajectory Generator Review .. ......... .. 25 3.2 OPTIMAl CONTROLLER ALGORITHM...value formulation to a six-degree-of-freedom point mass aircraft with all the structural, maneuver, and mission constraints accounted for by using pelalty
Object Specific Trajectory Optimization for Industrial X-ray Computed Tomography
NASA Astrophysics Data System (ADS)
Fischer, Andreas; Lasser, Tobias; Schrapp, Michael; Stephan, Jürgen; Noël, Peter B.
2016-01-01
In industrial settings, X-ray computed tomography scans are a common tool for inspection of objects. Often the object can not be imaged using standard circular or helical trajectories because of constraints in space or time. Compared to medical applications the variance in size and materials is much larger. Adapting the acquisition trajectory to the object is beneficial and sometimes inevitable. There are currently no sophisticated methods for this adoption. Typically the operator places the object according to his best knowledge. We propose a detectability index based optimization algorithm which determines the scan trajectory on the basis of a CAD-model of the object. The detectability index is computed solely from simulated projections for multiple user defined features. By adapting the features the algorithm is adapted to different imaging tasks. Performance of simulated and measured data was qualitatively and quantitatively assessed.The results illustrate that our algorithm not only allows more accurate detection of features, but also delivers images with high overall quality in comparison to standard trajectory reconstructions. This work enables to reduce the number of projections and in consequence scan time by introducing an optimization algorithm to compose an object specific trajectory.
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.
Optimal lift and bank modulations for three-dimensional reentry trajectories with heat constraint
NASA Astrophysics Data System (ADS)
Chern, Jeng-Shing; Yang, Ching-Yew; Sheen, Jyh-Jong
For hypersonic reentry flight, the heat problem is usually the most severe problem. Therefore, it is of necessity and interest to consider the heat constraint in solving optimal reentry trajectories. This paper, under the facilities of the continuation method and the multiple shooting method, investigates the optimal lift and bank modulations for three-dimensional reentry trajectories with heating rate constraint. The modified Newton method is used to induce and accelerate convergence. From the variational formulation, the optimal lift and bank control laws and the transversality conditions are derived. The non-constrained optimal trajectories leading to the boundary of the maximum reachable domain of a typical lifting reentry vehicle are solved at first. It is a three-parameter two-point boundary-value problem. Then the heating rate constraint is imposed and the constrained maximum reachable domain is constructed finally. Because the equilibrium glide condition is eliminated in this paper, the maximum reachable domain obtained is larger than the one obtained under the equilibrium glide assumption. Besides, both optimal lift and optimal bank control histories are presented and discussed.
Optimal low-thrust spiral trajectories using Lyapunov-based guidance
NASA Astrophysics Data System (ADS)
Yang, Da-lin; Xu, Bo; Zhang, Lei
2016-09-01
For an increasing number of electric propulsion systems used for real missions, it is very important to design optimal low-thrust spiral trajectories for these missions. However, it is particularly challenging to search for optimal low-thrust transfers. This paper describes an efficient optimal guidance scheme for the design of time-optimal and time-fixed fuel-optimal low-thrust spiral trajectories. The time-optimal solution is obtained with Lyapunov-based guidance, in which the artificial neural network (ANN) is adopted to implement control gains steering and the evolutionary algorithm is used as the learning algorithm for ANN. Moreover, the relative efficiency introduced in Q-law is analyzed and a periapis-and-apoapsis-centered burn structure is proposed for solving time-fixed fuel-optimal low-thrust orbit transfer problem. In this guidance scheme, the ANN is adopted to determine the burn structure within each orbital revolution and the optimal low-thrust orbit transfer problem is converted to the parameter optimization problem. This guidance scheme runs without an initial guess and provides closed form solutions. In addition, Earth J2 perturbation and Earth-shadow eclipse effects are considered in this paper. Finally, a comparison with solutions given by the literature demonstrates the effectiveness of the proposed method.
General solution for the optimal trajectory of an AFE-type spacecraft
NASA Astrophysics Data System (ADS)
Miele, A.; Wang, T.
1991-10-01
The Aeroassisted Flight Experiment (AFE) involves the Space Shuttle-based launch and subsequent recovery of an experimental spacecraft, simulating a transfer from GEO to LEO. One such AFE transfer is presently considered under assumed conditions of identical orbital planes, circular initial and final orbits, and given initial phase angle in conjunction with a free final phase angle. The aeroassisted trajectory involves preatmospheric, GEO-to-entry, postatmospheric, and exit-to-LEO phases; the optimal trajectory is obtained by minimizing the total characteristic velocity.
NASA Technical Reports Server (NTRS)
Rommel, Bruce A.
1989-01-01
An overview of the Aeroelastic Design Optimization Program (ADOP) at the Douglas Aircraft Company is given. A pilot test program involving the animation of mode shapes with solid rendering as well as wire frame displays, a complete aircraft model of a high-altitude hypersonic aircraft to test ADOP procedures, a flap model, and an aero-mesh modeler for doublet lattice aerodynamics are discussed.
Traffic Aware Planner for Cockpit-Based Trajectory Optimization
NASA Technical Reports Server (NTRS)
Woods, Sharon E.; Vivona, Robert A.; Henderson, Jeffrey; Wing, David J.; Burke, Kelly A.
2016-01-01
The Traffic Aware Planner (TAP) software application is a cockpit-based advisory tool designed to be hosted on an Electronic Flight Bag and to enable and test the NASA concept of Traffic Aware Strategic Aircrew Requests (TASAR). The TASAR concept provides pilots with optimized route changes (including altitude) that reduce fuel burn and/or flight time, avoid interactions with known traffic, weather and restricted airspace, and may be used by the pilots to request a route and/or altitude change from Air Traffic Control. Developed using an iterative process, TAP's latest improvements include human-machine interface design upgrades and added functionality based on the results of human-in-the-loop simulation experiments and flight trials. Architectural improvements have been implemented to prepare the system for operational-use trials with partner commercial airlines. Future iterations will enhance coordination with airline dispatch and add functionality to improve the acceptability of TAP-generated route-change requests to pilots, dispatchers, and air traffic controllers.
Parker, G.G.; Eisler, G.R.; Feddema, J.T.
1994-09-01
Procedures for trajectory planning and control of flexible link robots are becoming increasingly important to satisfy performance requirements of hazardous waste removal efforts. It has been shown that utilizing link flexibility in designing open loop joint commands can result in improved performance as opposed to damping vibration throughout a trajectory. The efficient use of link compliance is exploited in this work. Specifically, experimental verification of minimum time, straight line tracking using a two-link planar flexible robot is presented. A numerical optimization process, using an experimentally verified modal model, is used for obtaining minimum time joint torque and angle histories. The optimal joint states are used as commands to the proportional-derivative servo actuated joints. These commands are precompensated for the nonnegligible joint servo actuator dynamics. Using the precompensated joint commands, the optimal joint angles are tracked with such fidelity that the tip tracking error is less than 2.5 cm.
Leaf trajectory calculation for dynamic multileaf collimation to realize optimized fluence profiles
NASA Astrophysics Data System (ADS)
Dirkx, M. L. P.; Heijmen, B. J. M.; van Santvoort, J. P. C.
1998-05-01
An algorithm for the calculation of the required leaf trajectories to generate optimized intensity modulated beam profiles by means of dynamic multileaf collimation is presented. This algorithm iteratively accounts for leaf transmission and collimator scatter and fully avoids tongue-and-groove underdosage effects. Tests on a large number of intensity modulated fields show that only a limited number of iterations, generally less than 10, are necessary to minimize the differences between optimized and realized fluence profiles. To assess the accuracy of the algorithm in combination with the dose calculation algorithm of the Cadplan 3D treatment planning system, predicted absolute dose distributions for optimized fluence profiles were compared with dose distributions measured on the MM50 Racetrack Microtron and resulting from the calculated leaf trajectories. Both theoretical and clinical cases yield an agreement within 2%, or within 2 mm in regions with a high dose gradient, showing that the accuracy is adequate for clinical application.
Leaf trajectory calculation for dynamic multileaf collimation to realize optimized fluence profiles.
Dirkx, M L; Heijmen, B J; van Santvoort, J P
1998-05-01
An algorithm for the calculation of the required leaf trajectories to generate optimized intensity modulated beam profiles by means of dynamic multileaf collimation is presented. This algorithm iteratively accounts for leaf transmission and collimator scatter and fully avoids tongue-and-groove underdosage effects. Tests on a large number of intensity modulated fields show that only a limited number of iterations, generally less than 10, are necessary to minimize the differences between optimized and realized fluence profiles. To assess the accuracy of the algorithm in combination with the dose calculation algorithm of the Cadplan 3D treatment planning system, predicted absolute dose distributions for optimized fluence profiles were compared with dose distributions measured on the MM50 Racetrack Microtron and resulting from the calculated leaf trajectories. Both theoretical and clinical cases yield an agreement within 2%, or within 2 mm in regions with a high dose gradient, showing that the accuracy is adequate for clinical application.
NASA Astrophysics Data System (ADS)
Wang, Qi; Zhou, Yihao; Chen, Yan Qiu
2011-12-01
Three-dimensional (3-D) tracking and trajectory measurement of group translating and rotating particles may greatly help applications in collective behavior study, motion measurement, etc. Binocular stereo methods are commonly used to track and measure 3-D trajectories of drifting particles. Nevertheless, binocular methods usually suffer from severe stereo-matching ambiguity facing these situations even if motion constraint is adopted to disambiguate stereo matching. We try to help the disambiguating by optimizing viewpoint placement. We model the stereo-matching ambiguity and test different viewpoint placements upon our geometrical analysis to show the influence on the disambiguation that utilizes motion constraint. When the targets undergo group translation and rotation which are highly ambiguous, we find the optimal viewpoint placement such that stereo-matching ambiguity decreases as fast as possible over time. The optimal viewpoint placement can greatly improve the performance of existing methods.
Optimal finite-thrust spacecraft trajectories using direct transcription and nonlinear programming
NASA Astrophysics Data System (ADS)
Enright, Paul James
1991-08-01
A class of methods for the numerical solution of optimal control problems is analyzed and applied to the optimization of finite-thrust spacecraft trajectories. These methods use discrete approximations to the state and control histories, and a discretization of the equations of motion to derive a mathematical programming problem which approximates the optimal control problem, and which is solved numerically. This conversion is referred to as transcription. Recent advances in nonlinear programming, however, have made it feasible to solve the original heavily-constrained nonlinear programming problem, which is referred to as the direct transcription of the optimal control problem. This method is referred to as direct transcription and nonlinear programming. A recently developed method for solving optimal trajectory problems uses a piecewise-polynomial representation of the state and control variables and enforces the equations of motion via a collocation procedure, resulting in a nonlinear programming problem, which is solved numerically. This method is identified as being of the general class of direct transcription methods described above. Also, a new direct transcription method which discretizes the equations of motion using a parallel-shooting approach is developed. Both methods are applied to thrust-limited spacecraft trajectory problems, including finite-thrust transfer, rendezvous, and orbit insertion, a low-thrust escape, and a low-thrust Earth-moon transfer.
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.
Generation of an Optimal Gait Trajectory for Biped Robots Using a Genetic Algorithm
NASA Astrophysics Data System (ADS)
Park, Jong Hyeon; Choi, Moosung
This paper proposes a method that minimizes the energy consumption in the locomotion of a biped robot. A real-coded genetic algorithm is employed in order to search for the optimal locomotion pattern, and at the same time the optimal locations of the mass centers of the links that compose the biped robot. Since many of the essential characteristics of the human walking motion can be captured with a seven-link planar biped walking in the saggital plane, a 6-DOF biped robot that consists of seven links is used as the model used in the work. For trajectories of the robot in a single stride, fourth-order polynomials are used as their basis functions to approximate the locomotion gait. The coefficients of the polynomials are defined as design variables. For the optimal locations of the mass centers of the links, three variables are added to the design variables under the assumption that the left and right legs are identical. Simulations were performed to compare locomotion trajectories obtained with the genetic algorithm and the one obtained with the gravity-compensated inverted pendulum mode (GCIPM). They show that the proposed trajectory with the optimized mass centers significantly reduces the energy consumption, indicating that the proposed optimized method is a valuable tool in the design of biped robots.
2015-01-01
The optimized mean-trajectory (OMT) approximation is a semiclassical method for computing vibrational response functions from action-quantized classical trajectories connected by discrete transitions representing radiation–matter interactions. Here we apply this method to an anharmonic chromophore coupled to a harmonic bath. A forward–backward trajectory implementation of the OMT method is described that addresses the numerical challenges of applying the OMT to large systems with disparate frequency scales. The OMT is shown to well reproduce line shapes and waiting time dynamics in the pure dephasing limit of weak coupling to an off-resonant bath. The OMT is also shown to describe a case where energy transfer is the predominant source of line broadening. PMID:25275943
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.
2015-01-01
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 allow-ing 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 com-putational efficiency. The approach is applied to several complex, interplanetary problems, achieving notable performance without a user-supplied initial guess.
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.
Analysis of LPFG sensor systems for aircraft wing drag optimization
NASA Astrophysics Data System (ADS)
Kazemi, Alex A.; Ishihara, Abe
2014-09-01
In normal fiber, the refractive indices of the core and cladding do not change along the length of the fiber; however, by inducing a periodic modulation of refractive index along the length in the core of the optical fiber, the optical fiber grating is produced. This exhibits very interesting spectral properties and for this reason we propose to develop and integrate a distributed sensor network based on long period fiber gratings (LPFGs) technology which has grating periods on the order of 100 μm to 1 mm to be embedded in the wing section of aircraft to measure bending and torsion in real-time in order to measure wing deformation of commercial airplanes resulting in extensive benefits such as reduced structural weight, mitigation of induced drag and lower fuel consumption which is fifty percent of total cost of operation for airline industry. Fiber optic sensors measurement capabilities are as vital as they are for other sensing technologies, but optical measurements differ in important ways. In this paper we focus on the testing and aviation requirements for LPFG sensors. We discuss the bases of aviation standards for fiber optic sensor measurements, and the quantities that are measured. Our main objective is to optimize the design for material, mechanical, optical and environmental requirements. We discuss the analysis and evaluation of extensive testing of LPFG sensor systems such as attenuation, environmental, humidity, fluid immersion, temperature cycling, aging, smoke, flammability, impact resistance, flexure endurance, tensile, vitiation and shock.
Structural Optimization Methodology for Rotating Disks of Aircraft Engines
NASA Technical Reports Server (NTRS)
Armand, Sasan C.
1995-01-01
In support of the preliminary evaluation of various engine technologies, a methodology has been developed for structurally designing the rotating disks of an aircraft engine. The structural design methodology, along with a previously derived methodology for predicting low-cycle fatigue life, was implemented in a computer program. An interface computer program was also developed that gathers the required data from a flowpath analysis program (WATE) being used at NASA Lewis. The computer program developed for this study requires minimum interaction with the user, thus allowing engineers with varying backgrounds in aeropropulsion to successfully execute it. The stress analysis portion of the methodology and the computer program were verified by employing the finite element analysis method. The 10th- stage, high-pressure-compressor disk of the Energy Efficient Engine Program (E3) engine was used to verify the stress analysis; the differences between the stresses and displacements obtained from the computer program developed for this study and from the finite element analysis were all below 3 percent for the problem solved. The computer program developed for this study was employed to structurally optimize the rotating disks of the E3 high-pressure compressor. The rotating disks designed by the computer program in this study were approximately 26 percent lighter than calculated from the E3 drawings. The methodology is presented herein.
Time-optimal control of the spacecraft trajectories in the Earth-Moon system
NASA Astrophysics Data System (ADS)
Starinova, O. L.; Fain, M. K.; Materova, I. L.
2017-01-01
This paper outlines the multiparametric optimization of the L1-L2 and L2-L1 missions in the Earth-Moon system using electric propulsion. The optimal control laws are obtained using the Fedorenko successful linearization method to estimate the derivatives and the gradient method to optimize the control laws. The study of the transfers is based on the restricted circular three-body problem. The mathematical model of the missions is described within the barycentric system of coordinates. The optimization criterion is the total flight time. The perturbation from the Earth, the Moon and the Sun are taking into account. The impact of the shaded areas, induced by the Earth and the Moon, is also accounted. As the results of the optimization we obtained optimal control laws, corresponding trajectories and minimal total flight times.
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.
Chen, Yiran; Sun, Bo; Li, Songjie
2014-01-01
An optimization method for condition based maintenance (CBM) of aircraft fleet considering prognostics uncertainty is proposed. The CBM and dispatch process of aircraft fleet is analyzed first, and the alternative strategy sets for single aircraft are given. Then, the optimization problem of fleet CBM with lower maintenance cost and dispatch risk is translated to the combinatorial optimization problem of single aircraft strategy. Remain useful life (RUL) distribution of the key line replaceable Module (LRM) has been transformed into the failure probability of the aircraft and the fleet health status matrix is established. And the calculation method of the costs and risks for mission based on health status matrix and maintenance matrix is given. Further, an optimization method for fleet dispatch and CBM under acceptable risk is proposed based on an improved genetic algorithm. Finally, a fleet of 10 aircrafts is studied to verify the proposed method. The results shows that it could realize optimization and control of the aircraft fleet oriented to mission success. PMID:24892046
Improving aircraft composite inspections using optimized reference standards
Roach, D.; Dorrell, L.; Kollgaard, J.; Dreher, T.
1998-10-01
The rapidly increasing use of composites on commercial airplanes coupled with the potential for economic savings associated with their use in aircraft structures means that the demand for composite materials technology will continue to increase. Inspecting these composite structures is a critical element in assuring this continued airworthiness. The FAA`s Airworthiness Assurance NDI Validation Center, in conjunction with the Commercial Aircraft Composite Repair committee, is developing a set of composite reference standards to be used in NDT equipment calibration for accomplishment of damage assessment and post-repair inspection of all commercial aircraft composites. In this program, a series of NDI tests on a matrix of composite aircraft structures and prototype reference standards were completed in order to minimize the number of standards needed to carry out composite inspections on aircraft. Two tasks, related to composite laminates and non-metallic composite honeycomb configurations, were addressed.
Enhanced Fuel-Optimal Trajectory-Generation Algorithm for Planetary Pinpoint Landing
NASA Technical Reports Server (NTRS)
Acikmese, Behcet; Blackmore, James C.; Scharf, Daniel P.
2011-01-01
An enhanced algorithm is developed that builds on a previous innovation of fuel-optimal powered-descent guidance (PDG) for planetary pinpoint landing. The PDG problem is to compute constrained, fuel-optimal trajectories to land a craft at a prescribed target on a planetary surface, starting from a parachute cut-off point and using a throttleable descent engine. The previous innovation showed the minimal-fuel PDG problem can be posed as a convex optimization problem, in particular, as a Second-Order Cone Program, which can be solved to global optimality with deterministic convergence properties, and hence is a candidate for onboard implementation. To increase the speed and robustness of this convex PDG algorithm for possible onboard implementation, the following enhancements are incorporated: 1) Fast detection of infeasibility (i.e., control authority is not sufficient for soft-landing) for subsequent fault response. 2) The use of a piecewise-linear control parameterization, providing smooth solution trajectories and increasing computational efficiency. 3) An enhanced line-search algorithm for optimal time-of-flight, providing quicker convergence and bounding the number of path-planning iterations needed. 4) An additional constraint that analytically guarantees inter-sample satisfaction of glide-slope and non-sub-surface flight constraints, allowing larger discretizations and, hence, faster optimization. 5) Explicit incorporation of Mars rotation rate into the trajectory computation for improved targeting accuracy. These enhancements allow faster convergence to the fuel-optimal solution and, more importantly, remove the need for a "human-in-the-loop," as constraints will be satisfied over the entire path-planning interval independent of step-size (as opposed to just at the discrete time points) and infeasible initial conditions are immediately detected. Finally, while the PDG stage is typically only a few minutes, ignoring the rotation rate of Mars can introduce 10s
Discrete approximations to optimal trajectories using direct transcription and nonlinear programming
NASA Technical Reports Server (NTRS)
Enright, Paul J.; Conway, Bruce A.
1990-01-01
A recently developed method for solving optimal trajectory problems uses a piecewise-polynomial representation of the state and control variables, enforces the equations of motion via a collocation procedure, and thus approximates the original calculus-of-variations problem with a nonlinear-programming problem, which is solved numerically. This paper identifies this method as a direct transcription method and proceeds to investigate the relationship between the original optimal-control problem and the nonlinear-programming problem. The discretized adjoint equation of the collocation method is found to have deficient accuracy, and an alternate scheme which discretizes the equations of motion using an explicit Runge-Kutta parallel-shooting approach is developed. Both methods are applied to finite-thrust spacecraft trajectory problems, including a low-thrust escape spiral, a three-burn rendezvous, and a low-thrust transfer to the moon.
A New Architecture for Extending the Capabilities of the Copernicus Trajectory Optimization Program
NASA Technical Reports Server (NTRS)
Williams, Jacob
2015-01-01
This paper describes a new plugin architecture developed for the Copernicus spacecraft trajectory optimization program. Details of the software architecture design and development are described, as well as examples of how the capability can be used to extend the tool in order to expand the type of trajectory optimization problems that can be solved. The inclusion of plugins is a significant update to Copernicus, allowing user-created algorithms to be incorporated into the tool for the first time. The initial version of the new capability was released to the Copernicus user community with version 4.1 in March 2015, and additional refinements and improvements were included in the recent 4.2 release. It is proving quite useful, enabling Copernicus to solve problems that it was not able to solve before.
Discrete approximations to optimal trajectories using direct transcription and nonlinear programming
NASA Astrophysics Data System (ADS)
Enright, Paul J.; Conway, Bruce A.
A recently developed method for solving optimal trajectory problems uses a piecewise-polynomial representation of the state and control variables, enforces the equations of motion via a collocation procedure, and thus approximates the original calculus-of-variations problem with a nonlinear-programming problem, which is solved numerically. This paper identifies this method as a direct transcription method and proceeds to investigate the relationship between the original optimal-control problem and the nonlinear-programming problem. The discretized adjoint equation of the collocation method is found to have deficient accuracy, and an alternate scheme which discretizes the equations of motion using an explicit Runge-Kutta parallel-shooting approach is developed. Both methods are applied to finite-thrust spacecraft trajectory problems, including a low-thrust escape spiral, a three-burn rendezvous, and a low-thrust transfer to the moon.
Optimal RTLS abort trajectories for an HL-20 personnel launch vehicle
NASA Astrophysics Data System (ADS)
Dutton, Kevin
1993-12-01
The primary objective of this study was to determine whether Return To Launch Site (RTLS) abort at T seconds along the launch trajectory of the Personnel Launch System (PLS) is possible using optimal control theory. The secondary objective is to assess effects of bank angle constraint, lift coefficient constraint, free and fixed final boundary conditions, etc. of the vehicle. The PLS is a complementary system to the Space Shuttle.
Optimal RTLS abort trajectories for an HL-20 personnel launch vehicle
NASA Technical Reports Server (NTRS)
Dutton, Kevin
1993-01-01
The primary objective of this study was to determine whether Return To Launch Site (RTLS) abort at T seconds along the launch trajectory of the Personnel Launch System (PLS) is possible using optimal control theory. The secondary objective is to assess effects of bank angle constraint, lift coefficient constraint, free and fixed final boundary conditions, etc. of the vehicle. The PLS is a complementary system to the Space Shuttle.
Trajectory optimization for dynamic couch rotation during volumetric modulated arc radiotherapy
NASA Astrophysics Data System (ADS)
Smyth, Gregory; Bamber, Jeffrey C.; Evans, Philip M.; Bedford, James L.
2013-11-01
Non-coplanar radiation beams are often used in three-dimensional conformal and intensity modulated radiotherapy to reduce dose to organs at risk (OAR) by geometric avoidance. In volumetric modulated arc radiotherapy (VMAT) non-coplanar geometries are generally achieved by applying patient couch rotations to single or multiple full or partial arcs. This paper presents a trajectory optimization method for a non-coplanar technique, dynamic couch rotation during VMAT (DCR-VMAT), which combines ray tracing with a graph search algorithm. Four clinical test cases (partial breast, brain, prostate only, and prostate and pelvic nodes) were used to evaluate the potential OAR sparing for trajectory-optimized DCR-VMAT plans, compared with standard coplanar VMAT. In each case, ray tracing was performed and a cost map reflecting the number of OAR voxels intersected for each potential source position was generated. The least-cost path through the cost map, corresponding to an optimal DCR-VMAT trajectory, was determined using Dijkstra’s algorithm. Results show that trajectory optimization can reduce dose to specified OARs for plans otherwise comparable to conventional coplanar VMAT techniques. For the partial breast case, the mean heart dose was reduced by 53%. In the brain case, the maximum lens doses were reduced by 61% (left) and 77% (right) and the globes by 37% (left) and 40% (right). Bowel mean dose was reduced by 15% in the prostate only case. For the prostate and pelvic nodes case, the bowel V50 Gy and V60 Gy were reduced by 9% and 45% respectively. Future work will involve further development of the algorithm and assessment of its performance over a larger number of cases in site-specific cohorts.
Aircraft design for mission performance using non-linear multiobjective optimization methods
NASA Technical Reports Server (NTRS)
Dovi, Augustine R.; Wrenn, Gregory A.
1989-01-01
A new technique which converts a constrained optimization problem to an unconstrained one where conflicting figures of merit may be simultaneously considered has been combined with a complex mission analysis system. The method is compared with existing single and multiobjective optimization methods. A primary benefit from this new method for multiobjective optimization is the elimination of separate optimizations for each objective, which is required by some optimization methods. A typical wide body transport aircraft is used for the comparative studies.
NASA Astrophysics Data System (ADS)
Jorris, Timothy R.
2007-12-01
To support the Air Force's Global Reach concept, a Common Aero Vehicle is being designed to support the Global Strike mission. "Waypoints" are specified for reconnaissance or multiple payload deployments and "no-fly zones" are specified for geopolitical restrictions or threat avoidance. Due to time critical targets and multiple scenario analysis, an autonomous solution is preferred over a time-intensive, manually iterative one. Thus, a real-time or near real-time autonomous trajectory optimization technique is presented to minimize the flight time, satisfy terminal and intermediate constraints, and remain within the specified vehicle heating and control limitations. This research uses the Hypersonic Cruise Vehicle (HCV) as a simplified two-dimensional platform to compare multiple solution techniques. The solution techniques include a unique geometric approach developed herein, a derived analytical dynamic optimization technique, and a rapidly emerging collocation numerical approach. This up-and-coming numerical technique is a direct solution method involving discretization then dualization, with pseudospectral methods and nonlinear programming used to converge to the optimal solution. This numerical approach is applied to the Common Aero Vehicle (CAV) as the test platform for the full three-dimensional reentry trajectory optimization problem. The culmination of this research is the verification of the optimality of this proposed numerical technique, as shown for both the two-dimensional and three-dimensional models. Additionally, user implementation strategies are presented to improve accuracy and enhance solution convergence. Thus, the contributions of this research are the geometric approach, the user implementation strategies, and the determination and verification of a numerical solution technique for the optimal reentry trajectory problem that minimizes time to target while satisfying vehicle dynamics and control limitation, and heating, waypoint, and no
Statistical analysis of piloted simulation of real time trajectory optimization algorithms
NASA Technical Reports Server (NTRS)
Price, D. B.
1982-01-01
A simulation of time-optimal intercept algorithms for on-board computation of control commands is described. The effects of three different display modes and two different computation modes on the pilots' ability to intercept a moving target in minimum time were tested. Both computation modes employed singular perturbation theory to help simplify the two-point boundary value problem associated with trajectory optimization. Target intercept time was affected by both the display and computation modes chosen, but the display mode chosen was the only significant influence on the miss distance.
Optimal Trajectories for the Helicopter in One-Engine-Inoperative Terminal-Area Operations
NASA Technical Reports Server (NTRS)
Chen, Robert T. N.; Zhao, Yi-Yuan
1997-01-01
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 non-linear 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 trajector 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.
Optimal integration of gravity in trajectory planning of vertical pointing movements.
Crevecoeur, Frédéric; Thonnard, Jean-Louis; Lefèvre, Philippe
2009-08-01
The planning and control of motor actions requires knowledge of the dynamics of the controlled limb to generate the appropriate muscular commands and achieve the desired goal. Such planning and control imply that the CNS must be able to deal with forces and constraints acting on the limb, such as the omnipresent force of gravity. The present study investigates the effect of hypergravity induced by parabolic flights on the trajectory of vertical pointing movements to test the hypothesis that motor commands are optimized with respect to the effect of gravity on the limb. Subjects performed vertical pointing movements in normal gravity and hypergravity. We use a model based on optimal control to identify the role played by gravity in the optimal arm trajectory with minimal motor costs. First, the simulations in normal gravity reproduce the asymmetry in the velocity profiles (the velocity reaches its maximum before half of the movement duration), which typically characterizes the vertical pointing movements performed on Earth, whereas the horizontal movements present symmetrical velocity profiles. Second, according to the simulations, the optimal trajectory in hypergravity should present an increase in the peak acceleration and peak velocity despite the increase in the arm weight. In agreement with these predictions, the subjects performed faster movements in hypergravity with significant increases in the peak acceleration and peak velocity, which were accompanied by a significant decrease in the movement duration. This suggests that movement kinematics change in response to an increase in gravity, which is consistent with the hypothesis that motor commands are optimized and the action of gravity on the limb is taken into account. The results provide evidence for an internal representation of gravity in the central planning process and further suggest that an adaptation to altered dynamics can be understood as a reoptimization process.
High order optimal control of space trajectories with uncertain boundary conditions
NASA Astrophysics Data System (ADS)
Di Lizia, P.; Armellin, R.; Bernelli-Zazzera, F.; Berz, M.
2014-01-01
A high order optimal control strategy is proposed in this work, based on the use of differential algebraic techniques. In the frame of orbital mechanics, differential algebra allows to represent, by high order Taylor polynomials, the dependency of the spacecraft state on initial conditions and environmental parameters. The resulting polynomials can be manipulated to obtain the high order expansion of the solution of two-point boundary value problems. Since the optimal control problem can be reduced to a two-point boundary value problem, differential algebra is used to compute the high order expansion of the solution of the optimal control problem about a reference trajectory. Whenever perturbations in the nominal conditions occur, new optimal control laws for perturbed initial and final states are obtained by the mere evaluation of polynomials. The performances of the method are assessed on lunar landing, rendezvous maneuvers, and a low-thrust Earth-Mars transfer.
Three-dimensional trajectory design for horizontal well based on optimal switching algorithms.
Wu, Xiang; Zhang, Kanjian
2015-09-01
This paper considers a three-dimensional trajectory design problem for horizontal well. The problem is formulated as an optimal control problem of switched systems with continuous state inequality constraints. Since the complexity of such constraints and the switching instants is unknown, it is difficult to solve the problem by standard optimization techniques. To overcome the difficulty, by a time-scaling transformation, a smoothing technique and a penalty function method, an efficient computational method is proposed for solving this problem. Convergence results show that, for a sufficiently large penalty parameter, any local optimal solution of the approximate problem is also a local optimal solution of the original problem. Two numerical examples are presented to illustrate the efficiency of the approach proposed.
Optimal trajectories for an aerospace plane. Part 2: Data, tables, and graphs
NASA Technical Reports Server (NTRS)
Miele, Angelo; Lee, W. Y.; Wu, G. D.
1990-01-01
Data, tables, and graphs relative to the optimal trajectories for an aerospace plane are presented. A single-stage-to-orbit (SSTO) configuration is considered, and the transition from low supersonic speeds to orbital speeds is studied for a single aerodynamic model (GHAME) and three engine models. Four optimization problems are solved using the sequential gradient-restoration algorithm for optimal control problems: (1) minimization of the weight of fuel consumed; (2) minimization of the peak dynamic pressure; (3) minimization of the peak heating rate; and (4) minimization of the peak tangential acceleration. The above optimization studies are carried out for different combinations of constraints, specifically: initial path inclination that is either free or given; dynamic pressure that is either free or bounded; and tangential acceleration that is either free or bounded.
Cascade Optimization Strategy for Aircraft and Air-Breathing Propulsion System Concepts
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Lavelle, Thomas M.; Hopkins, Dale A.; Coroneos, Rula M.
1996-01-01
Design optimization for subsonic and supersonic aircraft and for air-breathing propulsion engine concepts has been accomplished by soft-coupling the Flight Optimization System (FLOPS) and the NASA Engine Performance Program analyzer (NEPP), to the NASA Lewis multidisciplinary optimization tool COMETBOARDS. Aircraft and engine design problems, with their associated constraints and design variables, were cast as nonlinear optimization problems with aircraft weight and engine thrust as the respective merit functions. Because of the diversity of constraint types and the overall distortion of the design space, the most reliable single optimization algorithm available in COMETBOARDS could not produce a satisfactory feasible optimum solution. Some of COMETBOARDS' unique features, which include a cascade strategy, variable and constraint formulations, and scaling devised especially for difficult multidisciplinary applications, successfully optimized the performance of both aircraft and engines. The cascade method has two principal steps: In the first, the solution initiates from a user-specified design and optimizer, in the second, the optimum design obtained in the first step with some random perturbation is used to begin the next specified optimizer. The second step is repeated for a specified sequence of optimizers or until a successful solution of the problem is achieved. A successful solution should satisfy the specified convergence criteria and have several active constraints but no violated constraints. The cascade strategy available in the combined COMETBOARDS, FLOPS, and NEPP design tool converges to the same global optimum solution even when it starts from different design points. This reliable and robust design tool eliminates manual intervention in the design of aircraft and of air-breathing propulsion engines where it eases the cycle analysis procedures. The combined code is also much easier to use, which is an added benefit. This paper describes COMETBOARDS
Optimal three-dimensional reentry trajectories subject to deceleration and heating constraints
NASA Astrophysics Data System (ADS)
Chern, J.-S.; Yang, C.-Y.; Vinh, N. X.; Hwang, G. R.
1982-09-01
The lateral maneuver of a lifting reentry vehicle, exemplified by the Shuttle entry, is severely restricted by deceleration and heating constraints. This paper investigates the decrease in the lateral reachable domain when different constraints are imposed on the optimal trajectories. A characteristic of hypersonic reentry trajectories is that the deceleration and heating rate pass through several maxima. The first peak is always higher than the following maxima so that it suffices to control the first maximum to the required level. Thermal constraint is encountered at higher altitude so that, in general, thermal control usually limits the deceleration to acceptable level. Using the equilibrium glide assumption, the optimal lift and bank control to maximize the lateral range is obtained in explicit form. Numerical results have been obtained for a typical value of maximum lift-to-drag ratio, and for several values of deceleration and thermal constraints imposed on the entry trajectories. It is found that the peak deceleration and the peak heating rate can be lowered significantly with only a slight penalty on the reachable domain.
Trajectory optimization and guidance law development for national aerospace plane applications
NASA Technical Reports Server (NTRS)
Calise, A. J.; Corban, J. E.; Flandro, G. A.
1988-01-01
The problem of onboard trajectory optimization for an airbreathing, single-stage-to-orbit vehicle is examined. A simple model representative of the aerospace plane concept, including a dual-mode propulsion system composed of scramjet and rocket engines, is presented. Consideration is restricted to hypersonic flight within the atmosphere. An energy state approximation is used in a four-state model for flight of a point mass in a vertical plane. Trajectory constraints, including those of dynamic pressure and aerodynamic heating, are initially ignored. Singular perturbation methods are applied in solving the optimal control problem of minimum fuel climb. The resulting reduced solution for the energy state dynamics provides an optimal altitude profile dependent on energy level and control for rocket thrust. A boundary-layer analysis produces an approximate lift control solution in feedback form and accounts for altitude and flight path angle dynamics. The reduced solution optimal climb path is presented for the unconstrained case and the case for which a maximum dynamic pressure constraint is enforced.
NASA Astrophysics Data System (ADS)
Liau, Leo Chau-Kuang; Chen, Chung-Chun
The optimal heating trajectories to minimize the time required for the organic additives removal in yttria-stabilized zirconia (YSZ) green tapes were determined using a dynamic optimization method. The removal process model was described by the mass transport of the volatile gas evolved from the thermal decomposition of the organic additives inside the tapes and the kinetics of the decomposition. The pressure buildup of the sample tapes formed by the volatile gas can be estimated by a numerical simulation method; meanwhile, the deformation (strain) of the tape caused by the pressure buildup was measured by a thermal mechanical analyzer (TMA) during the thermal processing. Results show that the formation of the maximum pressure buildup at the center of the cubic tape is influenced by the sample size and heating conditions. In addition, the dynamic strain at the center of the sample measured by TMA agrees with the formation of the pressure buildup estimated by the numerical calculation. Moreover, the optimal heating trajectories determined by the dynamic optimization scheme with the constraint of the formation of the maximum pressure buildup were verified from the tape deformation analysis by the TMA tests.
NASA Technical Reports Server (NTRS)
Miele, A.; Wang, T.; Lee, W. Y.; Zhao, Z. G.
1989-01-01
The determination of optimal trajectories for the aero-assisted flight experiment (AFE) is investigated. The intent of this experiment is to simulate a GEO-to-LEO transfer, where GEO denotes a geosynchronous Earth orbit and LEO denotes a low Earth orbit. The trajectories of an AFE spacecraft are analyzed in a 3D-space, employing the full system of 6 ODEs describing the atmospheric pass. The atmospheric entry conditions are given, and the atmospheric exit conditions are adjusted in such a way that the following conditions are satisfied: (1) the atmospheric velocity depletion is such that, after exiting, the AFE spacecraft first ascends to a specified apogee and then descends to a specified perigee; and (2) the exit orbital plane is identical with the entry orbital plane. The final maneuver, not analyzed here, includes the rendezvous with and the capture by the space shuttle.
NASA Astrophysics Data System (ADS)
Miele, A.; Wang, T.; Lee, W. Y.; Zhao, Z. G.
1989-10-01
The determination of optimal trajectories for the aero-assisted flight experiment (AFE) is investigated. The intent of this experiment is to simulate a GEO-to-LEO transfer, where GEO denotes a geosynchronous Earth orbit and LEO denotes a low Earth orbit. The trajectories of an AFE spacecraft are analyzed in a 3D-space, employing the full system of 6 ODEs describing the atmospheric pass. The atmospheric entry conditions are given, and the atmospheric exit conditions are adjusted in such a way that the following conditions are satisfied: (1) the atmospheric velocity depletion is such that, after exiting, the AFE spacecraft first ascends to a specified apogee and then descends to a specified perigee; and (2) the exit orbital plane is identical with the entry orbital plane. The final maneuver, not analyzed here, includes the rendezvous with and the capture by the space shuttle.
NASA Technical Reports Server (NTRS)
Lovell, T. Alan; Schmidt, D. K.
1994-01-01
The class of hypersonic vehicle configurations with single stage-to-orbit (SSTO) capability reflect highly integrated airframe and propulsion systems. These designs are also known to exhibit a large degree of interaction between the airframe and engine dynamics. Consequently, even simplified hypersonic models are characterized by tightly coupled nonlinear equations of motion. In addition, hypersonic SSTO vehicles present a major system design challenge; the vehicle's overall mission performance is a function of its subsystem efficiencies including structural, aerodynamic, propulsive, and operational. Further, all subsystem efficiencies are interrelated, hence, independent optimization of the subsystems is not likely to lead to an optimum design. Thus, it is desired to know the effect of various subsystem efficiencies on overall mission performance. For the purposes of this analysis, mission performance will be measured in terms of the payload weight inserted into orbit. In this report, a trajectory optimization problem is formulated for a generic hypersonic lifting body for a specified orbit-injection mission. A solution method is outlined, and results are detailed for the generic vehicle, referred to as the baseline model. After evaluating the performance of the baseline model, a sensitivity study is presented to determine the effect of various subsystem efficiencies on mission performance. This consists of performing a parametric analysis of the basic design parameters, generating a matrix of configurations, and determining the mission performance of each configuration. Also, the performance loss due to constraining the total head load experienced by the vehicle is evaluated. The key results from this analysis include the formulation of the sizing problem for this vehicle class using trajectory optimization, characteristics of the optimal trajectories, and the subsystem design sensitivities.
Papp, Dávid Unkelbach, Jan
2014-01-15
Purpose: The authors propose a novel optimization model for volumetric modulated arc therapy (VMAT) planning that directly optimizes deliverable leaf trajectories in the treatment plan optimization problem, and eliminates the need for a separate arc-sequencing step. Methods: In this model, a 360° arc is divided into a given number of arc segments in which the leaves move unidirectionally. This facilitates an algorithm that determines the optimal piecewise linear leaf trajectories for each arc segment, which are deliverable in a given treatment time. Multileaf collimator constraints, including maximum leaf speed and interdigitation, are accounted for explicitly. The algorithm is customized to allow for VMAT delivery using constant gantry speed and dose rate, however, the algorithm generalizes to variable gantry speed if beneficial. Results: The authors demonstrate the method for three different tumor sites: a head-and-neck case, a prostate case, and a paraspinal case. The authors first obtain a reference plan for intensity modulated radiotherapy (IMRT) using fluence map optimization and 20 intensity-modulated fields in equally spaced beam directions, which is beyond the standard of care. Modeling the typical clinical setup for the treatment sites considered, IMRT plans using seven or nine beams are also computed. Subsequently, VMAT plans are optimized by dividing the 360° arc into 20 corresponding arc segments. Assuming typical machine parameters (a dose rate of 600 MU/min, and a maximum leaf speed of 3 cm/s), it is demonstrated that the optimized VMAT plans with 2–3 min delivery time are of noticeably better quality than the 7–9 beam IMRT plans. The VMAT plan quality approaches the quality of the 20-beam IMRT benchmark plan for delivery times between 3 and 4 min. Conclusions: The results indicate that high quality treatments can be delivered in a single arc with 20 arc segments if sufficient time is allowed for modulation in each segment.
Hibbs, B.D.; Lissaman, P.B.S.; Morgan, W.R.; Radkey, R.L.
1998-09-22
This disclosure provides a solar rechargeable aircraft that is inexpensive to produce, is steerable, and can remain airborne almost indefinitely. The preferred aircraft is a span-loaded flying wing, having no fuselage or rudder. Travelling at relatively slow speeds, and having a two-hundred foot wingspan that mounts photovoltaic cells on most all of the wing`s top surface, the aircraft uses only differential thrust of its eight propellers to turn. Each of five sections of the wing has one or more engines and photovoltaic arrays, and produces its own lift independent of the other sections, to avoid loading them. Five two-sided photovoltaic arrays, in all, are mounted on the wing, and receive photovoltaic energy both incident on top of the wing, and which is incident also from below, through a bottom, transparent surface. The aircraft is capable of a top speed of about ninety miles per hour, which enables the aircraft to attain and can continuously maintain altitudes of up to sixty-five thousand feet. Regenerative fuel cells in the wing store excess electricity for use at night, such that the aircraft can sustain its elevation indefinitely. A main spar of the wing doubles as a pressure vessel that houses hydrogen and oxygen gases for use in the regenerative fuel cell. The aircraft has a wide variety of applications, which include weather monitoring and atmospheric testing, communications, surveillance, and other applications as well. 31 figs.
Hibbs, Bart D.; Lissaman, Peter B. S.; Morgan, Walter R.; Radkey, Robert L.
1998-01-01
This disclosure provides a solar rechargeable aircraft that is inexpensive to produce, is steerable, and can remain airborne almost indefinitely. The preferred aircraft is a span-loaded flying wing, having no fuselage or rudder. Travelling at relatively slow speeds, and having a two-hundred foot wingspan that mounts photovoltaic cells on most all of the wing's top surface, the aircraft uses only differential thrust of its eight propellers to turn. Each of five sections of the wing has one or more engines and photovoltaic arrays, and produces its own lift independent of the other sections, to avoid loading them. Five two-sided photovoltaic arrays, in all, are mounted on the wing, and receive photovoltaic energy both incident on top of the wing, and which is incident also from below, through a bottom, transparent surface. The aircraft is capable of a top speed of about ninety miles per hour, which enables the aircraft to attain and can continuously maintain altitudes of up to sixty-five thousand feet. Regenerative fuel cells in the wing store excess electricity for use at night, such that the aircraft can sustain its elevation indefinitely. A main spar of the wing doubles as a pressure vessel that houses hydrogen and oxygen gasses for use in the regenerative fuel cell. The aircraft has a wide variety of applications, which include weather monitoring and atmospheric testing, communications, surveillance, and other applications as well.
NASA Astrophysics Data System (ADS)
Chen, Chun; Tseng, Lin-Yu
2014-10-01
Multi-objective optimization is widely used in science, engineering and business. In this article, an improved version of the multiple trajectory search (MTS) called MTS2 is presented and successfully applied to real-value multi-objective optimization problems. In the first step, MTS2 generates M initial solutions distributed over the solution space. These solutions are called seeds. Some seeds with good objective values are selected as foreground seeds. Then, MTS2 chooses a suitable region search method for each foreground seed according to the landscape of the neighbourhood of the seed. During the search, MTS2 focuses its search on some promising areas specified by the foreground seeds. The performance of MTS2 was examined by applying it to solve the benchmark problems provided by the Competition of Performance Assessment of Constrained/Bound Constrained Multi-Objective Optimization Algorithms held at the 2009 IEEE Congress on Evolutionary Computation.
User's guide to four-body and three-body trajectory optimization programs
NASA Technical Reports Server (NTRS)
Pu, C. L.; Edelbaum, T. N.
1974-01-01
A collection of computer programs and subroutines written in FORTRAN to calculate 4-body (sun-earth-moon-space) and 3-body (earth-moon-space) optimal trajectories is presented. The programs incorporate a variable step integration technique and a quadrature formula to correct single step errors. The programs provide capability to solve initial value problem, two point boundary value problem of a transfer from a given initial position to a given final position in fixed time, optimal 2-impulse transfer from an earth parking orbit of given inclination to a given final position and velocity in fixed time and optimal 3-impulse transfer from a given position to a given final position and velocity in fixed time.
Applications of structural optimization methods to fixed-wing aircraft and spacecraft in the 1980s
NASA Technical Reports Server (NTRS)
Miura, Hirokazu; Neill, Douglas J.
1992-01-01
This report is the summary of a technical survey on the applications of structural optimization in the U.S. aerospace industry through the 1980s. Since applications to rotary wing aircraft will be covered by other literature, applications to fixed-wing aircraft and spacecraft were considered. It became clear that very significant progress has been made during this decade, indicating this technology is about to become one of the practical tools in computer aided structural design.
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.
The primer vector in linear, relative-motion equations. [spacecraft trajectory optimization
NASA Technical Reports Server (NTRS)
1980-01-01
Primer vector theory is used in analyzing a set of linear, relative-motion equations - the Clohessy-Wiltshire equations - to determine the criteria and necessary conditions for an optimal, N-impulse trajectory. Since the state vector for these equations is defined in terms of a linear system of ordinary differential equations, all fundamental relations defining the solution of the state and costate equations, and the necessary conditions for optimality, can be expressed in terms of elementary functions. The analysis develops the analytical criteria for improving a solution by (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of (1) fixed-end conditions, two-impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized rendezvous problem. A sequence of rendezvous problems is solved to illustrate the analysis and the computational procedure.
Multi-Objective Optimization of Spacecraft Trajectories for Small-Body Coverage Missions
NASA Technical Reports Server (NTRS)
Hinckley, David, Jr.; Englander, Jacob; Hitt, Darren
2017-01-01
Visual coverage of surface elements of a small-body object requires multiple images to be taken that meet many requirements on their viewing angles, illumination angles, times of day, and combinations thereof. Designing trajectories capable of maximizing total possible coverage may not be useful since the image target sequence and the feasibility of said sequence given the rotation-rate limitations of the spacecraft are not taken into account. This work presents a means of optimizing, in a multi-objective manner, surface target sequences that account for such limitations.
Global Optimization of Interplanetary Trajectories in the Presence of Realistic Mission Contraints
NASA Technical Reports Server (NTRS)
Hinckley, David, Jr.; Englander, Jacob; Hitt, Darren
2015-01-01
Interplanetary missions are often subject to difficult constraints, like solar phase angle upon arrival at the destination, velocity at arrival, and altitudes for flybys. Preliminary design of such missions is often conducted by solving the unconstrained problem and then filtering away solutions which do not naturally satisfy the constraints. However this can bias the search into non-advantageous regions of the solution space, so it can be better to conduct preliminary design with the full set of constraints imposed. In this work two stochastic global search methods are developed which are well suited to the constrained global interplanetary trajectory optimization problem.
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.
Developing Optimized Trajectories Derived from Mission and Thermo-Structural Constraints
NASA Technical Reports Server (NTRS)
Lear, Matthew H.; McGrath, Brian E.; Anderson, Michael P.; Green, Peter W.
2008-01-01
In conjunction with NASA and the Department of Defense, the Johns Hopkins University Applied Physics Laboratory (JHU/APL) has been investigating analytical techniques to address many of the fundamental issues associated with solar exploration spacecraft and high-speed atmospheric vehicle systems. These issues include: thermo-structural response including the effects of thermal management via the use of surface optical properties for high-temperature composite structures; aerodynamics with the effects of non-equilibrium chemistry and gas radiation; and aero-thermodynamics with the effects of material ablation for a wide range of thermal protection system (TPS) materials. The need exists to integrate these discrete tools into a common framework that enables the investigation of interdisciplinary interactions (including analysis tool, applied load, and environment uncertainties) to provide high fidelity solutions. In addition to developing robust tools for the coupling of aerodynamically induced thermal and mechanical loads, JHU/APL has been studying the optimal design of high-speed vehicles as a function of their trajectory. Under traditional design methodology the optimization of system level mission parameters such as range and time of flight is performed independently of the optimization for thermal and mechanical constraints such as stress and temperature. A truly optimal trajectory should optimize over the entire range of mission and thermo-mechanical constraints. Under this research, a framework for the robust analysis of high-speed spacecraft and atmospheric vehicle systems has been developed. It has been built around a generic, loosely coupled framework such that a variety of readily available analysis tools can be used. The methodology immediately addresses many of the current analysis inadequacies and allows for future extension in order to handle more complex problems.
Vortex generator design for aircraft inlet distortion as a numerical optimization problem
NASA Technical Reports Server (NTRS)
Anderson, Bernhard H.; Levy, Ralph
1991-01-01
Aerodynamic compatibility of aircraft/inlet/engine systems is a difficult design problem for aircraft that must operate in many different flight regimes. Takeoff, subsonic cruise, supersonic cruise, transonic maneuvering, and high altitude loiter each place different constraints on inlet design. Vortex generators, small wing like sections mounted on the inside surfaces of the inlet duct, are used to control flow separation and engine face distortion. The design of vortex generator installations in an inlet is defined as a problem addressable by numerical optimization techniques. A performance parameter is suggested to account for both inlet distortion and total pressure loss at a series of design flight conditions. The resulting optimization problem is difficult since some of the design parameters take on integer values. If numerical procedures could be used to reduce multimillion dollar development test programs to a small set of verification tests, numerical optimization could have a significant impact on both cost and elapsed time to design new aircraft.
A Subsonic Aircraft Design Optimization With Neural Network and Regression Approximators
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Coroneos, Rula M.; Guptill, James D.; Hopkins, Dale A.; Haller, William J.
2004-01-01
The Flight-Optimization-System (FLOPS) code encountered difficulty in analyzing a subsonic aircraft. The limitation made the design optimization problematic. The deficiencies have been alleviated through use of neural network and regression approximations. The insight gained from using the approximators is discussed in this paper. The FLOPS code is reviewed. Analysis models are developed and validated for each approximator. The regression method appears to hug the data points, while the neural network approximation follows a mean path. For an analysis cycle, the approximate model required milliseconds of central processing unit (CPU) time versus seconds by the FLOPS code. Performance of the approximators was satisfactory for aircraft analysis. A design optimization capability has been created by coupling the derived analyzers to the optimization test bed CometBoards. The approximators were efficient reanalysis tools in the aircraft design optimization. Instability encountered in the FLOPS analyzer was eliminated. The convergence characteristics were improved for the design optimization. The CPU time required to calculate the optimum solution, measured in hours with the FLOPS code was reduced to minutes with the neural network approximation and to seconds with the regression method. Generation of the approximators required the manipulation of a very large quantity of data. Design sensitivity with respect to the bounds of aircraft constraints is easily generated.
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.
Small Spacecraft System-Level Design and Optimization for Interplanetary Trajectories
NASA Technical Reports Server (NTRS)
Spangelo, Sara; Dalle, Derek; Longmier, Ben
2014-01-01
The feasibility of an interplanetary mission for a CubeSat, a type of miniaturized spacecraft, that uses an emerging technology, the CubeSat Ambipolar Thruster (CAT) is investigated. CAT is a large delta-V propulsion system that uses a high-density plasma source that has been miniaturized for small spacecraft applications. An initial feasibility assessment that demonstrated escaping Low Earth Orbit (LEO) and achieving Earth-escape trajectories with a 3U CubeSat and this thruster technology was demonstrated in previous work. We examine a mission architecture with a trajectory that begins in Earth orbits such as LEO and Geostationary Earth Orbit (GEO) which escapes Earth orbit and travels to Mars, Jupiter, or Saturn. The goal was to minimize travel time to reach the destinations and considering trade-offs between spacecraft dry mass, fuel mass, and solar power array size. Sensitivities to spacecraft dry mass and available power are considered. CubeSats are extremely size, mass, and power constrained, and their subsystems are tightly coupled, limiting their performance potential. System-level modeling, simulation, and optimization approaches are necessary to find feasible and optimal operational solutions to ensure system-level interactions are modeled. Thus, propulsion, power/energy, attitude, and orbit transfer models are integrated to enable systems-level analysis and trades. The CAT technology broadens the possible missions achievable with small satellites. In particular, this technology enables more sophisticated maneuvers by small spacecraft such as polar orbit insertion from an equatorial orbit, LEO to GEO transfers, Earth-escape trajectories, and transfers to other interplanetary bodies. This work lays the groundwork for upcoming CubeSat launch opportunities and supports future development of interplanetary and constellation CubeSat and small satellite mission concepts.
Galatzer-Levy, Isaac R; Bonanno, George A
2014-12-01
The course of depression in relation to myocardial infarction (MI), commonly known as heart attack, and the consequences for mortality are not well characterized. Further, optimism may predict both the effects of MI on depression as well as mortality secondary to MI. In the current study, we utilized a large population-based prospective sample of older adults (N=2,147) to identify heterogeneous trajectories of depression from 6 years prior to their first-reported MI to 4 years after. Findings indicated that individuals were at significantly increased risk for mortality when depression emerged after their first-reported MI, compared with resilient individuals who had no significant post-MI elevation in depression symptomatology. Individuals with chronic depression and those demonstrating pre-event depression followed by recovery after MI were not at increased risk. Further, optimism, measured before MI, prospectively differentiated all depressed individuals from participants who were resilient.
Flight orientation behaviors promote optimal migration trajectories in high-flying insects.
Chapman, Jason W; Nesbit, Rebecca L; Burgin, Laura E; Reynolds, Don R; Smith, Alan D; Middleton, Douglas R; Hill, Jane K
2010-02-05
Many insects undertake long-range seasonal migrations to exploit temporary breeding sites hundreds or thousands of kilometers apart, but the behavioral adaptations that facilitate these movements remain largely unknown. Using entomological radar, we showed that the ability to select seasonally favorable, high-altitude winds is widespread in large day- and night-flying migrants and that insects adopt optimal flight headings that partially correct for crosswind drift, thus maximizing distances traveled. Trajectory analyses show that these behaviors increase migration distances by 40% and decrease the degree of drift from seasonally optimal directions. These flight behaviors match the sophistication of those seen in migrant birds and help explain how high-flying insects migrate successfully between seasonal habitats.
NASA Technical Reports Server (NTRS)
Brauer, G. L.; Cornick, D. E.; Stevenson, R.
1977-01-01
The capabilities and applications of the three-degree-of-freedom (3DOF) version and the six-degree-of-freedom (6DOF) version of the Program to Optimize Simulated Trajectories (POST) are summarized. The document supplements the detailed program manuals by providing additional information that motivates and clarifies basic capabilities, input procedures, applications and computer requirements of these programs. The information will enable prospective users to evaluate the programs, and to determine if they are applicable to their problems. Enough information is given to enable managerial personnel to evaluate the capabilities of the programs and describes the POST structure, formulation, input and output procedures, sample cases, and computer requirements. The report also provides answers to basic questions concerning planet and vehicle modeling, simulation accuracy, optimization capabilities, and general input rules. Several sample cases are presented.
Optimization of very-low-thrust, many-revolution spacecraft trajectories
NASA Astrophysics Data System (ADS)
Scheel, Wayne A.; Conway, Bruce A.
1994-11-01
Optimal minimum flight time solutions are obtained for continuous, very-low-thrust orbit transfers using a direct-transcription approach to convert the continuous optimal control problem into a nonlinear programming problem. The thrust accelerations used are characteristic of solar electric and nuclear electric propulsion, resulting in trajectories that require many revolutions of Earth to achieve the desired final orbits. Among the problems examined are transfers from low Earth orbit to geosynchronous orbit (GEO) and orbit raising from GEO to a specified radius. All initial and terminal orbits are circular, with motion constrained to the equatorial plane. Motion of the spacecraft is described using the equinoctial orbit elements. The variation of spacecraft mass and acceleration due to fuel consumption is modeled. The orbit transfers include the effect of Earth's oblateness through first order as well as third-body perturbations from the moon.
Shuttle ascent trajectory optimization with function space quasi-Newton techniques
NASA Technical Reports Server (NTRS)
Edge, E. R.; Powers, W. F.
1974-01-01
A Space Shuttle ascent trajectory optimization problem from lift-off to orbital insertion is solved with a function space version of a quasi-Newton parameter optimization method developed by Broyden. The problem includes five parameter and one bounded-function controls, two state-variable constraints, and four terminal conditions. The bounded controls are treated directly, while the remaining constraints are adjoined to the performance index (maximum payload) with penalty functions. The problem is formulated as a four-phase variational problem (liftoff, pitch-over, gravity-turn, linear tangent steering), and the appropriate gradients are developed by first variation theory. A projection operator is introduced to aid in the interpretation of the algorithm with mixed parameter and function controls.
Optimal Input Design for Aircraft Parameter Estimation using Dynamic Programming Principles
NASA Technical Reports Server (NTRS)
Morelli, Eugene A.; Klein, Vladislav
1990-01-01
A new technique was developed for designing optimal flight test inputs for aircraft parameter estimation experiments. The principles of dynamic programming were used for the design in the time domain. This approach made it possible to include realistic practical constraints on the input and output variables. A description of the new approach is presented, followed by an example for a multiple input linear model describing the lateral dynamics of a fighter aircraft. The optimal input designs produced by the new technique demonstrated improved quality and expanded capability relative to the conventional multiple input design method.
Optimal input design for aircraft parameter estimation using dynamic programming principles
NASA Technical Reports Server (NTRS)
Klein, Vladislav; Morelli, Eugene A.
1990-01-01
A new technique was developed for designing optimal flight test inputs for aircraft parameter estimation experiments. The principles of dynamic programming were used for the design in the time domain. This approach made it possible to include realistic practical constraints on the input and output variables. A description of the new approach is presented, followed by an example for a multiple input linear model describing the lateral dynamics of a fighter aircraft. The optimal input designs produced by the new technique demonstrated improved quality and expanded capability relative to the conventional multiple input design method.
NASA Technical Reports Server (NTRS)
Miele, A.; Wang, T.; Basapur, V. K.
1986-01-01
One of the most effective first-order algorithms for solving trajectory optimization problems is the sequential gradient-restoration algorithm (SGRA). Originally developed in the primal formulation, this algorithm is extended to incorporate a dual formulation. Both the primal formulation and the dual formulation involve a sequence of two-phase cycles, each cycle including a gradient phase and a restoration phase. In turn, each iteration of the gradient phase and the restoration phase requires the solution of an auxiliary minimization problem (AMP). In the primal formulation, the AMP is solved with respect to the variations of the state, the control, and the parameter. In the dual formulation, the AMP is solved with respect to the Lagrange multipliers. A characteristic of the dual formulation is that the AMPs associated with the gradient phase and the restoration phase of SGRA can be reduced to mathematical programming problems involving a finite number of parameters as unknowns. A comparison of the primal formulation and the dual formulation is presented. The comparison is done in terms of several trajectory optimization problems having current aerospace interest.
Flight test trajectory control analysis
NASA Technical Reports Server (NTRS)
Walker, R.; Gupta, N.
1983-01-01
Recent extensions to optimal control theory applied to meaningful linear models with sufficiently flexible software tools provide powerful techniques for designing flight test trajectory controllers (FTTCs). This report describes the principal steps for systematic development of flight trajectory controllers, which can be summarized as planning, modeling, designing, and validating a trajectory controller. The techniques have been kept as general as possible and should apply to a wide range of problems where quantities must be computed and displayed to a pilot to improve pilot effectiveness and to reduce workload and fatigue. To illustrate the approach, a detailed trajectory guidance law is developed and demonstrated for the F-15 aircraft flying the zoom-and-pushover maneuver.
Optimal guidance and control for investigating aircraft noise-impact reduction
NASA Technical Reports Server (NTRS)
Stewart, E. C.; Carson, T. M.
1978-01-01
A methodology for investigating the reduction of community noise impact is reported. This report is concerned with the development of two models to provide data: a guidance generator and an aircraft control generator suitable for various current and advanced types of aircraft. The guidance generator produces the commanded path information from inputs chosen by an operator from a graphic scope display of a land-use map of the terminal area. The guidance generator also produces smoothing at the junctions of straight-line paths.The aircraft control generator determines the optimal set of the available controls such that the aircraft will follow the commanded path. The solutions for the control functions are given and shown to be dependent on the class of aircraft to be considered, that is, whether the thrust vector is rotatable and whether the thrust vector affects the aerodynamic forces. For the class of aircraft possessing a rotatable thrust vector, the solution is redundant; this redundancy is removed by the additional condition that the noise inpact be minimized. Information from both the guidance generator and the aircraft control generator is used by the footprint program to construct the noise footprint.
NASA Technical Reports Server (NTRS)
Sandlin, Doral R.; Bauer, Brent Alan
1993-01-01
This paper discusses the development of a FORTRAN computer code to perform agility analysis on aircraft configurations. This code is to be part of the NASA-Ames ACSYNT (AirCraft SYNThesis) design code. This paper begins with a discussion of contemporary agility research in the aircraft industry and a survey of a few agility metrics. The methodology, techniques and models developed for the code are then presented. Finally, example trade studies using the agility module along with ACSYNT are illustrated. These trade studies were conducted using a Northrop F-20 Tigershark aircraft model. The studies show that the agility module is effective in analyzing the influence of common parameters such as thrust-to-weight ratio and wing loading on agility criteria. The module can compare the agility potential between different configurations. In addition one study illustrates the module's ability to optimize a configuration's agility performance.
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.
Optimization via CFD of aircraft hot-air anti-icing systems
NASA Astrophysics Data System (ADS)
Pellissier, Mathieu Paul Constantin
In-flight icing is a major concern in aircraft safety and a non-negligible source of incidents and accidents, and is still a serious hazard today. It remains consequently a design and certification challenge for aircraft manufacturers. The aerodynamic performance of an aircraft can indeed degrade rapidly when flying in icing conditions, leading to incidents or accidents. In-flight icing occurs when an aircraft passes through clouds containing supercooled water droplets at or below freezing temperature. Droplets impinge on its exposed surfaces and freeze, causing roughness and shape changes that increase drag, decrease lift and reduce the stall angle of attack, eventually inducing flow separation and stall. This hazardous ice accretion is prevented by the use of dedicated anti-icing systems, among which hot-air-types are the most common for turbofan aircraft. This work presents a methodology for the optimization of such aircraft hot-air-type anti-icing systems, known as Piccolo tubes. Having identified through 3D Computational Fluid Dynamics (CFD) the most critical in-flight icing conditions, as well as determined thermal power constraints, the objective is to optimize the heat distribution in such a way to minimize power requirements, while meeting or exceeding all safety regulation requirements. To accomplish this, an optimization method combining 3D CFD, Reduced-Order Models (ROM) and Genetic Algorithms (GA) is constructed to determine the optimal configuration of the Piccolo tube (angles of jets, spacing between holes, and position from leading edge). The methodology successfully results in increasingly optimal configurations from three up to five design variables.
NASA Technical Reports Server (NTRS)
Raiszadeh, Ben; Queen, Eric M.
2002-01-01
A capability to simulate trajectories Of Multiple interacting rigid bodies has been developed. This capability uses the Program to Optimize Simulated Trajectories II (POST II). Previously, POST II had the ability to simulate multiple bodies without interacting forces. The current implementation is used for the Simulation of parachute trajectories, in which the parachute and suspended bodies can be treated as rigid bodies. An arbitrary set of connecting lines can be included in the model and are treated as massless spring-dampers. This paper discusses details of the connection line modeling and results of several test cases used to validate the capability.
NASA Technical Reports Server (NTRS)
Patniak, Surya N.; Guptill, James D.; Hopkins, Dale A.; Lavelle, Thomas M.
1998-01-01
Nonlinear mathematical-programming-based design optimization can be an elegant method. However, the calculations required to generate the merit function, constraints, and their gradients, which are frequently required, can make the process computational intensive. The computational burden can be greatly reduced by using approximating analyzers derived from an original analyzer utilizing neural networks and linear regression methods. The experience gained from using both of these approximation methods in the design optimization of a high speed civil transport aircraft is the subject of this paper. The Langley Research Center's Flight Optimization System was selected for the aircraft analysis. This software was exercised to generate a set of training data with which a neural network and a regression method were trained, thereby producing the two approximating analyzers. The derived analyzers were coupled to the Lewis Research Center's CometBoards test bed to provide the optimization capability. With the combined software, both approximation methods were examined for use in aircraft design optimization, and both performed satisfactorily. The CPU time for solution of the problem, which had been measured in hours, was reduced to minutes with the neural network approximation and to seconds with the regression method. Instability encountered in the aircraft analysis software at certain design points was also eliminated. On the other hand, there were costs and difficulties associated with training the approximating analyzers. The CPU time required to generate the input-output pairs and to train the approximating analyzers was seven times that required for solution of the problem.
2003-01-01
national power. But with the recent events such as the war with Iraq, the Severe Acute Respiratory Syndrome (SARS) outbreak, some major carriers... TITLE AND SUBTITLE 2003 Industry Studies: Aircraft 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER
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
Optimal trajectories for an aerospace plane. Part 1: Formulation, results, and analysis
NASA Technical Reports Server (NTRS)
Miele, Angelo; Lee, W. Y.; Wu, G. D.
1990-01-01
The optimization of the trajectories of an aerospace plane is discussed. This is a hypervelocity vehicle capable of achieving orbital speed, while taking off horizontally. The vehicle is propelled by four types of engines: turbojet engines for flight at subsonic speeds/low supersonic speeds; ramjet engines for flight at moderate supersonic speeds/low hypersonic speeds; scramjet engines for flight at hypersonic speeds; and rocket engines for flight at near-orbital speeds. A single-stage-to-orbit (SSTO) configuration is considered, and the transition from low supersonic speeds to orbital speeds is studied under the following assumptions: the turbojet portion of the trajectory has been completed; the aerospace plane is controlled via the angle of attack and the power setting; the aerodynamic model is the generic hypersonic aerodynamics model example (GHAME). Concerning the engine model, three options are considered: (EM1), a ramjet/scramjet combination in which the scramjet specific impulse tends to a nearly-constant value at large Mach numbers; (EM2), a ramjet/scramjet combination in which the scramjet specific impulse decreases monotonically at large Mach numbers; and (EM3), a ramjet/scramjet/rocket combination in which, owing to stagnation temperature limitations, the scramjet operates only at M approx. less than 15; at higher Mach numbers, the scramjet is shut off and the aerospace plane is driven only by the rocket engines. Under the above assumptions, four optimization problems are solved using the sequential gradient-restoration algorithm for optimal control problems: (P1) minimization of the weight of fuel consumed; (P2) minimization of the peak dynamic pressure; (P3) minimization of the peak heating rate; and (P4) minimization of the peak tangential acceleration.
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
NASA Technical Reports Server (NTRS)
Gern, Frank; Vicroy, Dan D.; Mulani, Sameer B.; Chhabra, Rupanshi; Kapania, Rakesh K.; Schetz, Joseph A.; Brown, Derrell; Princen, Norman H.
2014-01-01
Traditional methods of control allocation optimization have shown difficulties in exploiting the full potential of controlling large arrays of control devices on innovative air vehicles. Artificial neutral networks are inspired by biological nervous systems and neurocomputing has successfully been applied to a variety of complex optimization problems. This project investigates the potential of applying neurocomputing to the control allocation optimization problem of Hybrid Wing Body (HWB) aircraft concepts to minimize control power, hinge moments, and actuator forces, while keeping system weights within acceptable limits. The main objective of this project is to develop a proof-of-concept process suitable to demonstrate the potential of using neurocomputing for optimizing actuation power for aircraft featuring multiple independently actuated control surfaces. A Nastran aeroservoelastic finite element model is used to generate a learning database of hinge moment and actuation power characteristics for an array of flight conditions and control surface deflections. An artificial neural network incorporating a genetic algorithm then uses this training data to perform control allocation optimization for the investigated aircraft configuration. The phase I project showed that optimization results for the sum of required hinge moments are improved by more than 12% over the best Nastran solution by using the neural network optimization process.
NASA Technical Reports Server (NTRS)
Whiffen, Gregory J.
2006-01-01
Mystic software is designed to compute, analyze, and visualize optimal high-fidelity, low-thrust trajectories, The software can be used to analyze inter-planetary, planetocentric, and combination trajectories, Mystic also provides utilities to assist in the operation and navigation of low-thrust spacecraft. Mystic will be used to design and navigate the NASA's Dawn Discovery mission to orbit the two largest asteroids, The underlying optimization algorithm used in the Mystic software is called Static/Dynamic Optimal Control (SDC). SDC is a nonlinear optimal control method designed to optimize both 'static variables' (parameters) and dynamic variables (functions of time) simultaneously. SDC is a general nonlinear optimal control algorithm based on Bellman's principal.
Aircraft nonlinear optimal control using fuzzy gain scheduling
NASA Astrophysics Data System (ADS)
Nusyirwan, I. F.; Kung, Z. Y.
2016-10-01
Fuzzy gain scheduling is a common solution for nonlinear flight control. The highly nonlinear region of flight dynamics is determined throughout the examination of eigenvalues and the irregular pattern of root locus plots that show the nonlinear characteristic. By using the optimal control for command tracking, the pitch rate stability augmented system is constructed and the longitudinal flight control system is established. The outputs of optimal control for 21 linear systems are fed into the fuzzy gain scheduler. This research explores the capability in using both optimal control and fuzzy gain scheduling to improve the efficiency in finding the optimal control gains and to achieve Level 1 flying qualities. The numerical simulation work is carried out to determine the effectiveness and performance of the entire flight control system. The simulation results show that the fuzzy gain scheduling technique is able to perform in real time to find near optimal control law in various flying conditions.
Survey - Applications of structural optimization methods to fixed wing aircraft and spacecraft
NASA Technical Reports Server (NTRS)
Miura, Hirokazu; Neill, Douglas J.
1992-01-01
Results of a technical survey of the practical applications of structural optimization methods in the U.S. aerospace industry through 1980s are summarized. One of the most important developments in the 80s is the more widespread acceptance of structural optimization as one of the design tools that support practical structural design. Another significant advance is the development of large software tools for production applications. Attention is also given to the tailoring of the computerized design process to the specific environment of each company. The two most important aspects of this tailoring are seamless and easy-to-use incorporation of structural optimization in the overall aerospace design/production process and multidisciplinary integration aimed at ultimate performance optimization of the final product. Some specific applications discussed include the X-29 forward swept wing demonstrator aircraft, composite wing and vertical tail program, fighter wing redesign evaluations, high speed aircraft design, and space structures.
Wu, Hao; Mey, Antonia S J S; Rosta, Edina; Noé, Frank
2014-12-07
We propose a discrete transition-based reweighting analysis method (dTRAM) for analyzing configuration-space-discretized simulation trajectories produced at different thermodynamic states (temperatures, Hamiltonians, etc.) dTRAM provides maximum-likelihood estimates of stationary quantities (probabilities, free energies, expectation values) at any thermodynamic state. In contrast to the weighted histogram analysis method (WHAM), dTRAM does not require data to be sampled from global equilibrium, and can thus produce superior estimates for enhanced sampling data such as parallel/simulated tempering, replica exchange, umbrella sampling, or metadynamics. In addition, dTRAM provides optimal estimates of Markov state models (MSMs) from the discretized state-space trajectories at all thermodynamic states. Under suitable conditions, these MSMs can be used to calculate kinetic quantities (e.g., rates, timescales). In the limit of a single thermodynamic state, dTRAM estimates a maximum likelihood reversible MSM, while in the limit of uncorrelated sampling data, dTRAM is identical to WHAM. dTRAM is thus a generalization to both estimators.
Optimization applications in aircraft engine design and test
NASA Technical Reports Server (NTRS)
Pratt, T. K.
1984-01-01
Starting with the NASA-sponsored STAEBL program, optimization methods based primarily upon the versatile program COPES/CONMIN were introduced over the past few years to a broad spectrum of engineering problems in structural optimization, engine design, engine test, and more recently, manufacturing processes. By automating design and testing processes, many repetitive and costly trade-off studies have been replaced by optimization procedures. Rather than taking engineers and designers out of the loop, optimization has, in fact, put them more in control by providing sophisticated search techniques. The ultimate decision whether to accept or reject an optimal feasible design still rests with the analyst. Feedback obtained from this decision process has been invaluable since it can be incorporated into the optimization procedure to make it more intelligent. On several occasions, optimization procedures have produced novel designs, such as the nonsymmetric placement of rotor case stiffener rings, not anticipated by engineering designers. In another case, a particularly difficult resonance contraint could not be satisfied using hand iterations for a compressor blade, when the STAEBL program was applied to the problem, a feasible solution was obtained in just two iterations.
Flight control systems research. [optimization of F-8 aircraft control system
NASA Technical Reports Server (NTRS)
Whitaker, H. P.; Baram, Y.; Cheng, Y.
1973-01-01
Theoretical development is reported for the parameter optimization design technique needed for digital flight control system design. The results of an example case study applying the optimization technique for continuous systems to an F-8 aircraft feedback control system are presented. The concept of evolving the simplest system configuration that is capable of meeting a specified set of performance requirements is illustrated in this work.
Shanechi, Maryam M; Williams, Ziv M; Wornell, Gregory W; Hu, Rollin C; Powers, Marissa; Brown, Emery N
2013-01-01
Real-time brain-machine interfaces (BMI) have focused on either estimating the continuous movement trajectory or target intent. However, natural movement often incorporates both. Additionally, BMIs can be modeled as a feedback control system in which the subject modulates the neural activity to move the prosthetic device towards a desired target while receiving real-time sensory feedback of the state of the movement. We develop a novel real-time BMI using an optimal feedback control design that jointly estimates the movement target and trajectory of monkeys in two stages. First, the target is decoded from neural spiking activity before movement initiation. Second, the trajectory is decoded by combining the decoded target with the peri-movement spiking activity using an optimal feedback control design. This design exploits a recursive Bayesian decoder that uses an optimal feedback control model of the sensorimotor system to take into account the intended target location and the sensory feedback in its trajectory estimation from spiking activity. The real-time BMI processes the spiking activity directly using point process modeling. We implement the BMI in experiments consisting of an instructed-delay center-out task in which monkeys are presented with a target location on the screen during a delay period and then have to move a cursor to it without touching the incorrect targets. We show that the two-stage BMI performs more accurately than either stage alone. Correct target prediction can compensate for inaccurate trajectory estimation and vice versa. The optimal feedback control design also results in trajectories that are smoother and have lower estimation error. The two-stage decoder also performs better than linear regression approaches in offline cross-validation analyses. Our results demonstrate the advantage of a BMI design that jointly estimates the target and trajectory of movement and more closely mimics the sensorimotor control system.
Aircraft Route Optimization using the A-Star Algorithm
2014-03-27
16 Obstacle Avoidance... 16 Figure 9. Route Optimization Distance Matrix...29 Figure 15. Route between Key West and Brownsville using the TMA-Star model ........ 30 Figure 16 . Obstacle Avoidance model using
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.
NASA Technical Reports Server (NTRS)
Fishbach, L. H.
1980-01-01
The computational techniques are described which are utilized at Lewis Research Center to determine the optimum propulsion systems for future aircraft applications and to identify system tradeoffs and technology requirements. Cycle performance, and engine weight can be calculated along with costs and installation effects as opposed to fuel consumption alone. Almost any conceivable turbine engine cycle can be studied. These computer codes are: NNEP, WATE, LIFCYC, INSTAL, and POD DRG. Examples are given to illustrate how these computer techniques can be applied to analyze and optimize propulsion system fuel consumption, weight and cost for representative types of aircraft and missions.
NASA Astrophysics Data System (ADS)
Sayanjali, M.; Pourtakdoust, Seid H.
2015-05-01
This paper investigates the problem of optimal transfer trajectory design towards the L2 centered Halo orbit of the Sun-Earth three body system, where the initial launch is to start from a low Earth parking orbit (LEO). The proposed optimal transfer trajectory consists of an active part with low-thrust propulsion and a passive coasting part with no thrust or fuel consumption. In this respect a pseudo-stable manifold (SM) is initially determined through backward time integration of the bicircular four body (BCFB) equations of motion, whose initial states are obtained via stable manifolds of the restricted three body problem (R3BP). The optimal transfer trajectories are extracted via a hybrid direct-indirect optimization formulation applied on both R3BP as well as the BCFB models for comparative purposes. The optimal transfer trajectories are designed and analyzed for different Halo injection points (HOI), different Moon's final anomaly (FMA) and also for different locations of the burn-out conditions.
The optimal control frequency response problem in manual control. [of manned aircraft systems
NASA Technical Reports Server (NTRS)
Harrington, W. W.
1977-01-01
An optimal control frequency response problem is defined within the context of the optimal pilot model. The problem is designed to specify pilot model control frequencies reflective of important aircraft system properties, such as control feel system dynamics, airframe dynamics, and gust environment, as well as man machine properties, such as task and attention allocation. This is accomplished by determining a bounded set of control frequencies which minimize the total control cost. The bounds are given by zero and the neuromuscular control frequency response for each control actuator. This approach is fully adaptive, i.e., does not depend upon user entered estimates. An algorithm is developed to solve this optimal control frequency response problem. The algorithm is then applied to an attitude hold task for a bare airframe fighter aircraft case with interesting dynamic properties.
NASA Technical Reports Server (NTRS)
Malone, Brett; Mason, W. H.
1992-01-01
An extension of our parametric multidisciplinary optimization method to include design results connecting multiple objective functions is presented. New insight into the effect of the figure of merit (objective function) on aircraft configuration size and shape is demonstrated using this technique. An aircraft concept, subject to performance and aerodynamic constraints, is optimized using the global sensitivity equation method for a wide range of objective functions. These figures of merit are described parametrically such that a series of multiobjective optimal solutions can be obtained. Computational speed is facilitated by use of algebraic representations of the system technologies. Using this method, the evolution of an optimum design from one objective function to another is demonstrated. Specifically, combinations of minimum takeoff gross weight, fuel weight, and maximum cruise performance and productivity parameters are used as objective functions.
Aircraft Course Optimization Tool Using GPOPS MATLAB Code
2012-03-01
preceding paragraph and in reality relies heavily on the pseduospectral portion of GPOPS’ name. More specifically GPOPS uses the Radau Pseudospectral...Software for Solving Multiple-Phase Optimal Control Problems Using hp-Adaptive Pseu- dospectral Methods,” 2011. 9. Gill, P . E., Murray, W., and Saunders, M
Use of optimization to predict the effect of selected parameters on commuter aircraft performance
NASA Technical Reports Server (NTRS)
Wells, V. L.; Shevell, R. S.
1982-01-01
The relationships between field length and cruise speed and aircraft direct operating cost were determined. A gradient optimizing computer program was developed to minimize direct operating cost (DOC) as a function of airplane geometry. In this way, the best airplane operating under one set of constraints can be compared with the best operating under another. A constant 30-passenger fuselage and rubberized engines based on the General Electric CT-7 were used as a baseline. All aircraft had to have a 600 nautical mile maximum range and were designed to FAR part 25 structural integrity and climb gradient regulations. Direct operating cost was minimized for a typical design mission of 150 nautical miles. For purposes of C sub L sub max calculation, all aircraft had double-slotted flaps but with no Fowler action.
Aeroelastic Optimization of Generalized Tube and Wing Aircraft Concepts Using HCDstruct Version 2.0
NASA Technical Reports Server (NTRS)
Quinlan, Jesse R.; Gern, Frank H.
2017-01-01
Major enhancements were made to the Higher-fidelity Conceptual Design and structural optimization (HCDstruct) tool developed at NASA Langley Research Center (LaRC). Whereas previous versions were limited to hybrid wing body (HWB) configurations, the current version of HCDstruct now supports the analysis of generalized tube and wing (TW) aircraft concepts. Along with significantly enhanced user input options for all air- craft configurations, these enhancements represent HCDstruct version 2.0. Validation was performed using a Boeing 737-200 aircraft model, for which primary structure weight estimates agreed well with available data. Additionally, preliminary analysis of the NASA D8 (ND8) aircraft concept was performed, highlighting several new features of the tool.
Improved collocation methods with application to six-degree-of-freedom trajectory optimization
NASA Astrophysics Data System (ADS)
Desai, Prasun N.
2005-11-01
An improved collocation method is developed for a class of problems that is intractable, or nearly so, by conventional collocation. These are problems in which there are two distinct timescales of the system states, that is, where a subset of the states have high-frequency variations while the remaining states vary comparatively slowly. In conventional collocation, the timescale for the discretization would be set by the need to capture the high-frequency dynamics. The problem then becomes very large and the solution of the corresponding nonlinear programming problem becomes geometrically more time consuming and difficult. A new two-timescale discretization method is developed for the solution of such problems using collocation. This improved collocation method allows the use of a larger time discretization for the low-frequency dynamics of the motion, and a second finer time discretization scheme for the higher-frequency dynamics of the motion. The accuracy of the new method is demonstrated first on an example problem, an optimal lunar ascent. The method is then applied to the type of challenging problem for which it is designed, the optimization of the approach to landing trajectory for a winged vehicle returning from space, the HL-20 lifting body vehicle. The converged solution shows a realistic landing profile and fully captures the higher-frequency rotational dynamics. A source code using the sparse optimizer SNOPT is developed for the use of this method which generates constraint equations, gradients, and the system Jacobian for problems of arbitrary size. This code constitutes a much-improved tool for aerospace vehicle design but has application to all two-timescale optimization problems.
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.
1993-03-01
proposed for this purpose. Methods [31-33] based on variational calculus do not require such large computer memory resources, but require the numerical...methods [34-36] allow a more flexible problem setup than variational calculus based methods. Their reliance on numerical optimisation routines, usually
Near-optimal energy transitions for energy-state trajectories of hypersonic aircraft
NASA Technical Reports Server (NTRS)
Ardema, M. D.; Bowles, J. V.; Terjesen, E. J.; Whittaker, T.
1992-01-01
A problem of the instantaneous energy transition that occurs in energy-state approximation is considered. The transitions are modeled as a sequence of two load-factor bounded paths (either climb-dive or dive-climb). The boundary-layer equations associated with the energy-state dynamic model are analyzed to determine the precise location of the transition.
NASA Astrophysics Data System (ADS)
Dixon, Cory
This dissertation presents a decentralized gradient-based mobility control algorithm for the formation and maintenance of an optimal end-to-end communication chain using a team of unmanned aircraft acting as communication relays. With the use of unmanned aircraft (UA) as communication relays, a common mode of operation is to form a communication relay chain between a lead exploring node (which may be ground based or another UA) and a control station. In this type of operation the lead node is typically deployed to explore (sense) a remote region of interest that is beyond direct radio frequency (RF) communication range, or out of line-of-sight, to the control station. To provide non-line-of-sight service, and extend the communication range of the lead node, unmanned aircraft acting as communication relays are deployed in a convoy fashion behind the lead vehicle to form a cascaded relay chain. The focus of this work is the use of the mobility of a fixed number of relay aircraft to maximize the capacity of a directed communication chain from a source node to a destination node. Local objective functions are presented that use the signal-to-noise-and-interference ratio (SNIR) of neighbor communication links as inputs to maximize the end-to-end capacity of packet-based and repeater-type network chains. An adaptive gradient-based SNIR controller using the local objective function can show significant improvement in the capacity of the communication chain that is not possible with range-based controllers, or static deployment strategies, in RF environments containing unknown localized noise sources and terrain effects. Since the SNIR field is unknown, an online estimate of the SNIR field gradient is formed using methods of Stochastic Approximation from the orbital motion of the aircraft tracking a control point. Flight demonstrations using the Networked Unmanned Aircraft System Command, Control and Communications testbed were conducted to validate the controller
Neural Network and Regression Methods Demonstrated in the Design Optimization of a Subsonic Aircraft
NASA Technical Reports Server (NTRS)
Hopkins, Dale A.; Lavelle, Thomas M.; Patnaik, Surya
2003-01-01
The neural network and regression methods of NASA Glenn Research Center s COMETBOARDS design optimization testbed were used to generate approximate analysis and design models for a subsonic aircraft operating at Mach 0.85 cruise speed. The analytical model is defined by nine design variables: wing aspect ratio, engine thrust, wing area, sweep angle, chord-thickness ratio, turbine temperature, pressure ratio, bypass ratio, fan pressure; and eight response parameters: weight, landing velocity, takeoff and landing field lengths, approach thrust, overall efficiency, and compressor pressure and temperature. The variables were adjusted to optimally balance the engines to the airframe. The solution strategy included a sensitivity model and the soft analysis model. Researchers generated the sensitivity model by training the approximators to predict an optimum design. The trained neural network predicted all response variables, within 5-percent error. This was reduced to 1 percent by the regression method. The soft analysis model was developed to replace aircraft analysis as the reanalyzer in design optimization. Soft models have been generated for a neural network method, a regression method, and a hybrid method obtained by combining the approximators. The performance of the models is graphed for aircraft weight versus thrust as well as for wing area and turbine temperature. The regression method followed the analytical solution with little error. The neural network exhibited 5-percent maximum error over all parameters. Performance of the hybrid method was intermediate in comparison to the individual approximators. Error in the response variable is smaller than that shown in the figure because of a distortion scale factor. The overall performance of the approximators was considered to be satisfactory because aircraft analysis with NASA Langley Research Center s FLOPS (Flight Optimization System) code is a synthesis of diverse disciplines: weight estimation, aerodynamic
NASA Technical Reports Server (NTRS)
Sobieszczanski-Sobieski, Jaroslaw
1988-01-01
Optimization by decomposition, complex system sensitivity analysis, and a rapid growth of disciplinary sensitivity analysis are some of the recent developments that hold promise of a quantum jump in the support engineers receive from computers in the quantitative aspects of design. Review of the salient points of these techniques is given and illustrated by examples from aircraft design as a process that combines the best of human intellect and computer power to manipulate data.
Time-optimal aircraft pursuit-evasion with a weapon envelope constraint
NASA Technical Reports Server (NTRS)
Menon, P. K. A.; Duke, E. L.
1990-01-01
The optimal pursuit-evasion problem between two aircraft, including nonlinear point-mass vehicle models and a realistic weapon envelope, is analyzed. Using a linear combination of flight time and the square of the vehicle acceleration as the performance index, a closed-form solution is obtained in nonlinear feedback form. Due to its modest computational requirements, this guidance law can be used for onboard real-time implementation.
NASA Technical Reports Server (NTRS)
Sobieszczanski-Sobieski, Jaroslaw
1988-01-01
Optimization by decomposition, complex system sensitivity analysis, and a rapid growth of disciplinary sensitivity analysis are some of the recent developments that hold promise of a quantum jump in the support engineers receive from computers in the quantitative aspects of design. Review of the salient points of these techniques is given and illustrated by examples from aircraft design as a process that combines the best of human intellect and computer power to manipulate data.
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.
NASA Technical Reports Server (NTRS)
Quinlan, Jesse R.; Gern, Frank H.
2016-01-01
Simultaneously achieving the fuel consumption and noise reduction goals set forth by NASA's Environmentally Responsible Aviation (ERA) project requires innovative and unconventional aircraft concepts. In response, advanced hybrid wing body (HWB) aircraft concepts have been proposed and analyzed as a means of meeting these objectives. For the current study, several HWB concepts were analyzed using the Hybrid wing body Conceptual Design and structural optimization (HCDstruct) analysis code. HCDstruct is a medium-fidelity finite element based conceptual design and structural optimization tool developed to fill the critical analysis gap existing between lower order structural sizing approaches and detailed, often finite element based sizing methods for HWB aircraft concepts. Whereas prior versions of the tool used a half-model approach in building the representative finite element model, a full wing-tip-to-wing-tip modeling capability was recently added to HCDstruct, which alleviated the symmetry constraints at the model centerline in place of a free-flying model and allowed for more realistic center body, aft body, and wing loading and trim response. The latest version of HCDstruct was applied to two ERA reference cases, including the Boeing Open Rotor Engine Integration On an HWB (OREIO) concept and the Boeing ERA-0009H1 concept, and results agreed favorably with detailed Boeing design data and related Flight Optimization System (FLOPS) analyses. Following these benchmark cases, HCDstruct was used to size NASA's ERA HWB concepts and to perform a related scaling study.
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.
The multidisciplinary design optimization of a distributed propulsion blended-wing-body aircraft
NASA Astrophysics Data System (ADS)
Ko, Yan-Yee Andy
The purpose of this study is to examine the multidisciplinary design optimization (MDO) of a distributed propulsion blended-wing-body (BWB) aircraft. The BWB is a hybrid shape resembling a flying wing, placing the payload in the inboard sections of the wing. The distributed propulsion concept involves replacing a small number of large engines with many smaller engines. The distributed propulsion concept considered here ducts part of the engine exhaust to exit out along the trailing edge of the wing. The distributed propulsion concept affects almost every aspect of the BWB design. Methods to model these effects and integrate them into an MDO framework were developed. The most important effect modeled is the impact on the propulsive efficiency. There has been conjecture that there will be an increase in propulsive efficiency when there is blowing out of the trailing edge of a wing. A mathematical formulation was derived to explain this. The formulation showed that the jet 'fills in' the wake behind the body, improving the overall aerodynamic/propulsion system, resulting in an increased propulsive efficiency. The distributed propulsion concept also replaces the conventional elevons with a vectored thrust system for longitudinal control. An extension of Spence's Jet Flap theory was developed to estimate the effects of this vectored thrust system on the aircraft longitudinal control. It was found to provide a reasonable estimate of the control capability of the aircraft. An MDO framework was developed, integrating all the distributed propulsion effects modeled. Using a gradient based optimization algorithm, the distributed propulsion BWB aircraft was optimized and compared with a similarly optimized conventional BWB design. Both designs are for an 800 passenger, 0.85 cruise Mach number and 7000 nmi mission. The MDO results found that the distributed propulsion BWB aircraft has a 4% takeoff gross weight and a 2% fuel weight. Both designs have similar planform shapes
NASA Technical Reports Server (NTRS)
Miele, A.; Zhao, Z. G.; Lee, W. Y.
1989-01-01
The determination of optimal trajectories for the aeroassisted flight experiment (AFE) is discussed. The AFE refers to the study of the free flight of an autonomous spacecraft, shuttle-launched and shuttle-recovered. Its purpose is to gather atmospheric entry environmental data for use in designing aeroassisted orbital transfer vehicles (AOTV). It is assumed that: (1) the spacecraft is a particle of constant mass; (2) the Earth is rotating with constant angular velocity; (3) the Earth is an oblate planet, and the gravitational potential depends on both the radial distance and the latitude (harmonics of order higher than four are ignored); and (4) the atmosphere is at rest with respect to the Earth. Under these assumptions, the equations of motion for hypervelocity atmospheric flight (which can be used not only for AFE problems, but also for AOT problems and space shuttle problems) are derived in an inertial system. Transformation relations are supplied which allow one to pass from quantities computed in an inertial system to quantities computed in an Earth-fixed system and vice versa.
A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem
NASA Technical Reports Server (NTRS)
Hughes, Steven P.; Mailhe, Laurie M.; Guzman, Jose J.
2003-01-01
In this paper we present, a comparison of trajectory optimization approaches for the minimum fuel rendezvous problem. Both indirect and direct methods are compared for a variety of test cases. The indirect approach is based on primer vector theory. The direct approaches are implemented numerically and include Sequential Quadratic Programming (SQP). Quasi- Newton and Nelder-Meade Simplex. Several cost function parameterizations are considered for the direct approach. We choose one direct approach that appears to be the most flexible. Both the direct and indirect methods are applied to a variety of test cases which are chosen to demonstrate the performance of each method in different flight regimes. The first test case is a simple circular-to-circular coplanar rendezvous. The second test case is an elliptic-to-elliptic line of apsides rotation. The final test case is an orbit phasing maneuver sequence in a highly elliptic orbit. For each test case we present a comparison of the performance of all methods we consider in this paper.
Optimal cooperative control synthesis applied to a control-configured aircraft
NASA Technical Reports Server (NTRS)
Schmidt, D. K.; Innocenti, M.
1984-01-01
A multivariable control augmentation synthesis method is presented that is intended to enable the designer to directly optimize pilot opinion rating of the augmented system. The approach involves the simultaneous solution for the augmentation and predicted pilot's compensation via optimal control techniques. The methodology is applied to the control law synthesis for a vehicle similar to the AFTI F16 control-configured aircraft. The resulting dynamics, expressed in terms of eigenstructure and time/frequency responses, are presented with analytical predictions of closed loop tracking performance, pilot compensation, and other predictors of pilot acceptance.
Optimal lunar trajectories for a combined chemical-electric propulsion spacecraft
NASA Technical Reports Server (NTRS)
Kluever, Craig A.
1995-01-01
Spacecraft which utilize electric propulsion (EP) systems are capable of delivering a greater payload fraction compared to spacecraft using conventional chemical propulsion systems. Several researchers have investigated numerous applications of low-thrust EP including a manned Mars mission, scientific missions to the outer planets, and lunar missions. In contrast, the study of optimal combined high and low-thrust spacecraft trajectories has been limited. In response to the release of NASA's 1994 Announcement of Opportunity (AO) for Discovery class interplanetary exploration missions, a preliminary investigation of a lunar comet rendezvous mission using a solar electric propulsion (SEP) spacecraft was performed. The Discovery mission (eventually named Diana) was envisioned to be a two-phase scientific exploration mission: the first phase involved exploration of the moon and second phase 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 (LLO). After scientific data was collected 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 short period comet. An initial study that demonstrated the feasibility of using EP for the lunar and comet orbit transfer was performed under the grant NAG3-1581. This final report is a continuation of the initial research efforts in support of the Discovery mission proposal that was submitted to NASA Headquarters in October 1994. Section 2 discusses the lunar orbit transfer phase of the Diana mission which involves both chemical and electric propulsion stages. Section 3 discusses the chemical lunar orbit insertion (LOI) burn optimization. Finally, section 4 presents the
Automatic carrier landing system for V/STOL aircraft using L1 adaptive and optimal control
NASA Astrophysics Data System (ADS)
Hariharapura Ramesh, Shashank
This thesis presents a framework for developing automatic carrier landing systems for aircraft with vertical or short take-off and landing capability using two different control strategies---gain-scheduled linear optimal control, and L1 adaptive control. The carrier landing sequence of V/STOL aircraft involves large variations in dynamic pressure and aerodynamic coefficients arising because of the transition from aerodynamic-supported to jet-borne flight, descent to the touchdown altitude, and turns performed to align with the runway. Consequently, the dynamics of the aircraft exhibit a highly non-linear dynamical behavior with variations in flight conditions prior to touchdown. Therefore, the implication is the need for non-linear control techniques to achieve automatic landing. Gain-scheduling has been one of the most widely employed techniques for control of aircraft, which involves designing linear controllers for numerous trimmed flight conditions, and interpolating them to achieve a global non-linear control. Adaptive control technique, on the other hand, eliminates the need to schedule the controller parameters as they adapt to changing flight conditions.
NASA Technical Reports Server (NTRS)
Welstead, Jason; Crouse, Gilbert L., Jr.
2014-01-01
Empirical sizing guidelines such as tail volume coefficients have long been used in the early aircraft design phases for sizing stabilizers, resulting in conservatively stable aircraft. While successful, this results in increased empty weight, reduced performance, and greater procurement and operational cost relative to an aircraft with optimally sized surfaces. Including flight dynamics in the conceptual design process allows the design to move away from empirical methods while implementing modern control techniques. A challenge of flight dynamics and control is the numerous design variables, which are changing fluidly throughout the conceptual design process, required to evaluate the system response to some disturbance. This research focuses on addressing that challenge not by implementing higher order tools, such as computational fluid dynamics, but instead by linking the lower order tools typically used within the conceptual design process so each discipline feeds into the other. In thisresearch, flight dynamics and control was incorporated into the conceptual design process along with the traditional disciplines of vehicle sizing, weight estimation, aerodynamics, and performance. For the controller, a linear quadratic regulator structure with constant gains has been specified to reduce the user input. Coupling all the disciplines in the conceptual design phase allows the aircraft designer to explore larger design spaces where stabilizers are sized according to dynamic response constraints rather than historical static margin and volume coefficient guidelines.
Flight Test of an Adaptive Configuration Optimization System for Transport Aircraft
NASA Technical Reports Server (NTRS)
Gilyard, Glenn B.; Georgie, Jennifer; Barnicki, Joseph S.
1999-01-01
A NASA Dryden Flight Research Center program explores the practical application of real-time adaptive configuration optimization for enhanced transport performance on an L-1011 aircraft. This approach is based on calculation of incremental drag from forced-response, symmetric, outboard aileron maneuvers. In real-time operation, the symmetric outboard aileron deflection is directly optimized, and the horizontal stabilator and angle of attack are indirectly optimized. A flight experiment has been conducted from an onboard research engineering test station, and flight research results are presented herein. The optimization system has demonstrated the capability of determining the minimum drag configuration of the aircraft in real time. The drag-minimization algorithm is capable of identifying drag to approximately a one-drag-count level. Optimizing the symmetric outboard aileron position realizes a drag reduction of 2-3 drag counts (approximately 1 percent). Algorithm analysis of maneuvers indicate that two-sided raised-cosine maneuvers improve definition of the symmetric outboard aileron drag effect, thereby improving analysis results and consistency. Ramp maneuvers provide a more even distribution of data collection as a function of excitation deflection than raised-cosine maneuvers provide. A commercial operational system would require airdata calculations and normal output of current inertial navigation systems; engine pressure ratio measurements would be optional.
Global Optimization of Low-Thrust Interplanetary Trajectories Subject to Operational Constraints
NASA Technical Reports Server (NTRS)
Englander, Jacob Aldo; Vavrina, Matthew; Hinckley, David
2016-01-01
Low-thrust electric propulsion provides many advantages for mission to difficult targets-Comets and asteroids-Mercury-Outer planets (with sufficient power supply)Low-thrust electric propulsion is characterized by high power requirements but also very high specific impulse (Isp), leading to very good mass fractions. Low-thrust trajectory design is a very different process from chemical trajectory.
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.
Optimizing an Actuator Array for the Control of Multi-Frequency Noise in Aircraft Interiors
NASA Technical Reports Server (NTRS)
Palumbo, D. L.; Padula, S. L.
1997-01-01
Techniques developed for selecting an optimized actuator array for interior noise reduction at a single frequency are extended to the multi-frequency case. Transfer functions for 64 actuators were obtained at 5 frequencies from ground testing the rear section of a fully trimmed DC-9 fuselage. A single loudspeaker facing the left side of the aircraft was the primary source. A combinatorial search procedure (tabu search) was employed to find optimum actuator subsets of from 2 to 16 actuators. Noise reduction predictions derived from the transfer functions were used as a basis for evaluating actuator subsets during optimization. Results indicate that it is necessary to constrain actuator forces during optimization. Unconstrained optimizations selected actuators which require unrealistically large forces. Two methods of constraint are evaluated. It is shown that a fast, but approximate, method yields results equivalent to an accurate, but computationally expensive, method.
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.
NASA Technical Reports Server (NTRS)
Skillen, Michael D.; Crossley, William A.
2008-01-01
This report presents an approach for sizing of a morphing aircraft based upon a multi-level design optimization approach. For this effort, a morphing wing is one whose planform can make significant shape changes in flight - increasing wing area by 50% or more from the lowest possible area, changing sweep 30 or more, and/or increasing aspect ratio by as much as 200% from the lowest possible value. The top-level optimization problem seeks to minimize the gross weight of the aircraft by determining a set of "baseline" variables - these are common aircraft sizing variables, along with a set of "morphing limit" variables - these describe the maximum shape change for a particular morphing strategy. The sub-level optimization problems represent each segment in the morphing aircraft's design mission; here, each sub-level optimizer minimizes fuel consumed during each mission segment by changing the wing planform within the bounds set by the baseline and morphing limit variables from the top-level problem.
NASA Technical Reports Server (NTRS)
McNamara, Luke W.; Braun, Robert D.
2014-01-01
One of the key design objectives of NASA's Orion Exploration Mission 1 (EM- 1) is to execute a guided entry trajectory demonstrating GN&C capability. The focus of this paper is defining the flyable entry corridor for EM-1 taking into account multiple subsystem constraints such as complex aerothermal heating constraints, aerothermal heating objectives, landing accuracy constraints, structural load limits, Human-System-Integration-Requirements, Service Module debris disposal limits and other flight test objectives. During the EM-1 Design Analysis Cycle 1 design challenges came up that made defining the flyable entry corridor for the EM-1 mission critical to mission success. This document details the optimization techniques that were explored to use with the 6-DOF ANTARES simulation to assist in defining the design entry interface state and entry corridor with respect to key flight test constraints and objectives.
A Global Approach to the Optimal Trajectory Based on an Improved Ant Colony Algorithm for Cold Spray
NASA Astrophysics Data System (ADS)
Cai, Zhenhua; Chen, Tingyang; Zeng, Chunnian; Guo, Xueping; Lian, Huijuan; Zheng, You; Wei, Xiaoxu
2016-12-01
This paper is concerned with finding a global approach to obtain the shortest complete coverage trajectory on complex surfaces for cold spray applications. A slicing algorithm is employed to decompose the free-form complex surface into several small pieces of simple topological type. The problem of finding the optimal arrangement of the pieces is translated into a generalized traveling salesman problem (GTSP). Owing to its high searching capability and convergence performance, an improved ant colony algorithm is then used to solve the GTSP. Through off-line simulation, a robot trajectory is generated based on the optimized result. The approach is applied to coat real components with a complex surface by using the cold spray system with copper as the spraying material.
NASA Technical Reports Server (NTRS)
Jezewski, D.
1980-01-01
Prime vector theory is used in analyzing a set of linear relative-motion equations - the Clohessy-Wiltshire (C/W) equations - to determine the criteria and necessary conditions for an optimal N-impulse trajectory. The analysis develops the analytical criteria for improving a solution by: (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of: (1) fixed-end conditions, two impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized renezvous problem.
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.
Engine Yaw Augmentation for Hybrid-Wing-Body Aircraft via Optimal Control Allocation Techniques
NASA Technical Reports Server (NTRS)
Taylor, Brian R.; Yoo, Seung-Yeun
2011-01-01
Asymmetric engine thrust was implemented in a hybrid-wing-body non-linear simulation to reduce the amount of aerodynamic surface deflection required for yaw stability and control. Hybrid-wing-body aircraft are especially susceptible to yaw surface deflection due to their decreased bare airframe yaw stability resulting from the lack of a large vertical tail aft of the center of gravity. Reduced surface deflection, especially for trim during cruise flight, could reduce the fuel consumption of future aircraft. Designed as an add-on, optimal control allocation techniques were used to create a control law that tracks total thrust and yaw moment commands with an emphasis on not degrading the baseline system. Implementation of engine yaw augmentation is shown and feasibility is demonstrated in simulation with a potential drag reduction of 2 to 4 percent. Future flight tests are planned to demonstrate feasibility in a flight environment.
NASA Astrophysics Data System (ADS)
Davendralingam, Navindran
Conceptual design of aircraft and the airline network (routes) on which aircraft fly on are inextricably linked to passenger driven demand. Many factors influence passenger demand for various Origin-Destination (O-D) city pairs including demographics, geographic location, seasonality, socio-economic factors and naturally, the operations of directly competing airlines. The expansion of airline operations involves the identificaion of appropriate aircraft to meet projected future demand. The decisions made in incorporating and subsequently allocating these new aircraft to serve air travel demand affects the inherent risk and profit potential as predicted through the airline revenue management systems. Competition between airlines then translates to latent passenger observations of the routes served between OD pairs and ticket pricing---this in effect reflexively drives future states of demand. This thesis addresses the integrated nature of aircraft design, airline operations and passenger demand, in order to maximize future expected profits as new aircraft are brought into service. The goal of this research is to develop an approach that utilizes aircraft design, airline network design and passenger demand as a unified framework to provide better integrated design solutions in order to maximize expexted profits of an airline. This is investigated through two approaches. The first is a static model that poses the concurrent engineering paradigm above as an investment portfolio problem. Modern financial portfolio optimization techniques are used to leverage risk of serving future projected demand using a 'yet to be introduced' aircraft against potentially generated future profits. Robust optimization methodologies are incorporated to mitigate model sensitivity and address estimation risks associated with such optimization techniques. The second extends the portfolio approach to include dynamic effects of an airline's operations. A dynamic programming approach is
Optimum Three Impulse Trajectory Generator with Patched Conic Trajectory Model
NASA Technical Reports Server (NTRS)
Payne, M. H.; Pines, S.; Horsewood, J. L.
1972-01-01
Optimal multi-impulse trajectories were investigated as a nominal about which asymptotic expansion was used to obtain approximations of optimal low thrust trajectories. The work consisted of the analysis and description of an optimal 3-impulse trajectory program. A patched-conic trajectory model was specifically designed for compatibility with the subsequent addition of the low thrust expansion approximation.
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.
NASA Technical Reports Server (NTRS)
Jules, Kenol; Lin, Paul P.
2002-01-01
This paper reviews some of the recent applications of artificial neural networks taken from various works performed by the authors over the last four years at the NASA Glenn Research Center. This paper focuses mainly on two areas. First, artificial neural networks application in design and optimization of aircraft/engine propulsion systems to shorten the overall design cycle. Out of that specific application, a generic design tool was developed, which can be used for most design optimization process. Second, artificial neural networks application in monitoring the microgravity quality onboard the International Space Station, using on-board accelerometers for data acquisition. These two different applications are reviewed in this paper to show the broad applicability of artificial intelligence in various disciplines. The intent of this paper is not to give in-depth details of these two applications, but to show the need to combine different artificial intelligence techniques or algorithms in order to design an optimized or versatile system.
A Robust and Reliability-Based Optimization Framework for Conceptual Aircraft Wing Design
NASA Astrophysics Data System (ADS)
Paiva, Ricardo Miguel
A robustness and reliability based multidisciplinary analysis and optimization framework for aircraft design is presented. Robust design optimization and Reliability Based Design Optimization are merged into a unified formulation which streamlines the setup of optimization problems and aims at preventing foreseeable implementation issues in uncertainty based design. Surrogate models are evaluated to circumvent the intensive computations resulting from using direct evaluation in nondeterministic optimization. Three types of models are implemented in the framework: quadratic interpolation, regression Kriging and artificial neural networks. Regression Kriging presents the best compromise between performance and accuracy in deterministic wing design problems. The performance of the simultaneous implementation of robustness and reliability is evaluated using simple analytic problems and more complex wing design problems, revealing that performance benefits can still be achieved while satisfying probabilistic constraints rather than the simpler (and not as computationally intensive) robust constraints. The latter are proven to to be unable to follow a reliability constraint as uncertainty in the input variables increases. The computational effort of the reliability analysis is further reduced through the implementation of a coordinate change in the respective optimization sub-problem. The computational tool developed is a stand-alone application and it presents a user-friendly graphical user interface. The multidisciplinary analysis and design optimization tool includes modules for aerodynamics, structural, aeroelastic and cost analysis, that can be used either individually or coupled.
Automation of reverse engineering process in aircraft modeling and related optimization problems
NASA Technical Reports Server (NTRS)
Li, W.; Swetits, J.
1994-01-01
During the year of 1994, the engineering problems in aircraft modeling were studied. The initial concern was to obtain a surface model with desirable geometric characteristics. Much of the effort during the first half of the year was to find an efficient way of solving a computationally difficult optimization model. Since the smoothing technique in the proposal 'Surface Modeling and Optimization Studies of Aerodynamic Configurations' requires solutions of a sequence of large-scale quadratic programming problems, it is important to design algorithms that can solve each quadratic program in a few interactions. This research led to three papers by Dr. W. Li, which were submitted to SIAM Journal on Optimization and Mathematical Programming. Two of these papers have been accepted for publication. Even though significant progress has been made during this phase of research and computation times was reduced from 30 min. to 2 min. for a sample problem, it was not good enough for on-line processing of digitized data points. After discussion with Dr. Robert E. Smith Jr., it was decided not to enforce shape constraints in order in order to simplify the model. As a consequence, P. Dierckx's nonparametric spline fitting approach was adopted, where one has only one control parameter for the fitting process - the error tolerance. At the same time the surface modeling software developed by Imageware was tested. Research indicated a substantially improved fitting of digitalized data points can be achieved if a proper parameterization of the spline surface is chosen. A winning strategy is to incorporate Dierckx's surface fitting with a natural parameterization for aircraft parts. The report consists of 4 chapters. Chapter 1 provides an overview of reverse engineering related to aircraft modeling and some preliminary findings of the effort in the second half of the year. Chapters 2-4 are the research results by Dr. W. Li on penalty functions and conjugate gradient methods for
NASA Technical Reports Server (NTRS)
Reuther, James; Alonso, Juan Jose; Rimlinger, Mark J.; Jameson, Antony
1996-01-01
This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations. In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that this basic methodology could be ported to distributed memory parallel computing architectures. In this paper, our concern will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.
NASA Technical Reports Server (NTRS)
Reuther, James; Alonso, Juan Jose; Rimlinger, Mark J.; Jameson, Antony
1996-01-01
This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods (13, 12, 44, 38). The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method (19, 20, 21, 23, 39, 25, 40, 41, 42, 43, 9) was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations (39, 25). In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that the basic methodology could be ported to distributed memory parallel computing architectures [241. In this paper, our concem will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.
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.
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.
Taniai, Yoshiaki; Nishii, Jun
2015-08-01
When we move our body to perform a movement task, our central nervous system selects a movement trajectory from an infinite number of possible trajectories under constraints that have been acquired through evolution and learning. Minimization of the energy cost has been suggested as a potential candidate for a constraint determining locomotor parameters, such as stride frequency and stride length; however, other constraints have been proposed for a human upper-arm reaching task. In this study, we examined whether the minimum metabolic energy cost model can also explain the characteristics of the upper-arm reaching trajectories. Our results show that the optimal trajectory that minimizes the expected value of energy cost under the effect of signal-dependent noise on motor commands expresses not only the characteristics of reaching movements of typical speed but also those of slower movements. These results suggest that minimization of the energy cost would be a basic constraint not only in locomotion but also in upper-arm reaching.
Optimal Topology of Aircraft Rib and Spar Structures under Aeroelastic Loads
NASA Technical Reports Server (NTRS)
Stanford, Bret K.; Dunning, Peter D.
2014-01-01
Several topology optimization problems are conducted within the ribs and spars of a wing box. It is desired to locate the best position of lightening holes, truss/cross-bracing, etc. A variety of aeroelastic metrics are isolated for each of these problems: elastic wing compliance under trim loads and taxi loads, stress distribution, and crushing loads. Aileron effectiveness under a constant roll rate is considered, as are dynamic metrics: natural vibration frequency and flutter. This approach helps uncover the relationship between topology and aeroelasticity in subsonic transport wings, and can therefore aid in understanding the complex aircraft design process which must eventually consider all these metrics and load cases simultaneously.
NASA Technical Reports Server (NTRS)
Sensmeier, Mark D.; Samareh, Jamshid A.
2005-01-01
An approach is proposed for the application of rapid generation of moderate-fidelity structural finite element models of air vehicle structures to allow more accurate weight estimation earlier in the vehicle design process. This should help to rapidly assess many structural layouts before the start of the preliminary design phase and eliminate weight penalties imposed when actual structure weights exceed those estimated during conceptual design. By defining the structural topology in a fully parametric manner, the structure can be mapped to arbitrary vehicle configurations being considered during conceptual design optimization. A demonstration of this process is shown for two sample aircraft wing designs.
Use of optimization to predict the effect of selected parameters on commuter aircraft performance
NASA Technical Reports Server (NTRS)
Wells, V. L.; Shevell, R. S.
1982-01-01
An optimizing computer program determined the turboprop aircraft with lowest direct operating cost for various sets of cruise speed and field length constraints. External variables included wing area, wing aspect ratio and engine sea level static horsepower; tail sizes, climb speed and cruise altitude were varied within the function evaluation program. Direct operating cost was minimized for a 150 n.mi typical mission. Generally, DOC increased with increasing speed and decreasing field length but not by a large amount. Ride roughness, however, increased considerably as speed became higher and field length became shorter.
An overview of the Douglas Aircraft Company Aeroelastic Design Optimization Program (ADOP)
NASA Technical Reports Server (NTRS)
Dodd, Alan J.
1989-01-01
From a program manager's viewpoint, the history, scope and architecture of a major structural design program at Douglas Aircraft Company called Aeroelastic Design Optimization Program (ADOP) are described. ADOP was originally intended for the rapid, accurate, cost-effective evaluation of relatively small structural models at the advanced design level, resulting in improved proposal competitiveness and avoiding many costly changes later in the design cycle. Before release of the initial version in November 1987, however, the program was expanded to handle very large production-type analyses.
Terrien, N; Royer, D; Lepoutre, F; Déom, A
2007-06-01
To increase the sensitivity of Lamb waves to hidden corrosion in aircraft structures, a preliminary step is to understand the phenomena governing this interaction. A hybrid model combining a finite element approach and a modal decomposition method is used to investigate the interaction of Lamb modes with corrosion pits. The finite element mesh is used to describe the region surrounding the corrosion pits while the modal decomposition method permits to determine the waves reflected and transmitted by the damaged area. Simulations make easier the interpretation of some parts of the measured waveform corresponding to superposition of waves diffracted by the corroded area. Numerical results permit to extract significant information from the transmitted waveform and thus to optimize the signal processing for the detection of corrosion at an early stage. Now, we are able to detect corrosion pits down to 80-mum depth distributed randomly on a square centimeter of an aluminum plate. Moreover, thickness variations present on aircraft structures can be discriminated from a slightly corroded area. Finally, using this experimental setup, aircraft structures have been tested.
NASA Technical Reports Server (NTRS)
Welstead, Jason
2014-01-01
This research focused on incorporating stability and control into a multidisciplinary de- sign optimization on a Boeing 737-class advanced concept called the D8.2b. A new method of evaluating the aircraft handling performance using quantitative evaluation of the sys- tem to disturbances, including perturbations, continuous turbulence, and discrete gusts, is presented. A multidisciplinary design optimization was performed using the D8.2b transport air- craft concept. The con guration was optimized for minimum fuel burn using a design range of 3,000 nautical miles. Optimization cases were run using xed tail volume coecients, static trim constraints, and static trim and dynamic response constraints. A Cessna 182T model was used to test the various dynamic analysis components, ensuring the analysis was behaving as expected. Results of the optimizations show that including stability and con- trol in the design process drastically alters the optimal design, indicating that stability and control should be included in conceptual design to avoid system level penalties later in the design process.
A KBE-enabled design framework for cost/weight optimization study of aircraft composite structures
NASA Astrophysics Data System (ADS)
Wang, H.; La Rocca, G.; van Tooren, M. J. L.
2014-10-01
Traditionally, minimum weight is the objective when optimizing airframe structures. This optimization, however, does not consider the manufacturing cost which actually determines the profit of the airframe manufacturer. To this purpose, a design framework has been developed able to perform cost/weight multi-objective optimization of an aircraft component, including large topology variations of the structural configuration. The key element of the proposed framework is a dedicated knowledge based engineering (KBE) application, called multi-model generator, which enables modelling very different product configurations and variants and extract all data required to feed the weight and cost estimation modules, in a fully automated fashion. The weight estimation method developed in this research work uses Finite Element Analysis to calculate the internal stresses of the structural elements and an analytical composite plate sizing method to determine their minimum required thicknesses. The manufacturing cost estimation module was developed on the basis of a cost model available in literature. The capability of the framework was successfully demonstrated by designing and optimizing the composite structure of a business jet rudder. The study case indicates the design framework is able to find the Pareto optimal set for minimum structural weight and manufacturing costin a very quick way. Based on the Pareto set, the rudder manufacturer is in conditions to conduct both internal trade-off studies between minimum weight and minimum cost solutions, as well as to offer the OEM a full set of optimized options to choose, rather than one feasible design.
NASA Technical Reports Server (NTRS)
Chen, Robert T. N.; Zhao, Yi-Yuan; Aiken, Edwin W. (Technical Monitor)
1995-01-01
Engine failure represents a major safety concern to helicopter operations, especially in the critical flight phases of takeoff and landing from/to small, confined areas. As a result, the JAA and FAA both certificate a transport helicopter as either Category-A or Category-B according to the ability to continue its operations following engine failures. A Category-B helicopter must be able to land safely in the event of one or all engine failures. There is no requirement, however, for continued flight capability. In contrast, Category-A certification, which applies to multi-engine transport helicopters with independent engine systems, requires that they continue the flight with one engine inoperative (OEI). These stringent requirements, while permitting its operations from rooftops and oil rigs and flight to areas where no emergency landing sites are available, restrict the payload of a Category-A transport helicopter to a value safe for continued flight as well as for landing with one engine inoperative. The current certification process involves extensive flight tests, which are potentially dangerous, costly, and time consuming. These tests require the pilot to simulate engine failures at increasingly critical conditions, Flight manuals based on these tests tend to provide very conservative recommendations with regard to maximum takeoff weight or required runway length. There are very few theoretical studies on this subject to identify the fundamental parameters and tradeoff factors involved. Furthermore, a capability for real-time generation of OEI optimal trajectories is very desirable for providing timely cockpit display guidance to assist the pilot in reducing his workload and to increase safety in a consistent and reliable manner. A joint research program involving NASA Ames Research Center, the FAA, and the University of Minnesota is being conducted to determine OEI optimal control strategies and the associated optimal,trajectories for continued takeoff (CTO
Development of the quasi-procedural method for use in aircraft configuration optimization
NASA Technical Reports Server (NTRS)
Gage, P.; Kroo, I.
1992-01-01
The performance of the quasi-procedural analysis system in optimization tasks is investigated. In particular, the quasi-procedural method is applied to the complete mission optimization of a medium-sized transport aircraft using a vortex-lattice aerodynamic model and finite element structural analysis of the wing and the tail. Some modifications and improvements to the system, required in order to complete this task, are described. The performance of the system is compared with that of the standard procedural system, and it is shown that the quasi-procedural approach reduces the analysis required to reach the optimum. The overall cost is shown to be strongly dependent on the analysis architecture and data structure.
Reduced state feedback gain computation. [optimization and control theory for aircraft control
NASA Technical Reports Server (NTRS)
Kaufman, H.
1976-01-01
Because application of conventional optimal linear regulator theory to flight controller design requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. Therefore, a stochastic linear model that was developed is presented which accounts for aircraft parameter and initial uncertainty, measurement noise, turbulence, pilot command and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell. Results using a seventh order process show the proposed procedures to be very effective.
Three-dimensional canard-wing shape optimization in aircraft cruise and maneuver environments
NASA Technical Reports Server (NTRS)
De Silva, B. M. E.; Carmichael, R. L.
1978-01-01
This paper demonstrates a numerical technique for canard-wing shape optimization at two operating conditions. For purposes of simplicity, a mean surface wing paneling code is employed for the aerodynamic calculations. The optimization procedures are based on the method of feasible directions. The shape functions for describing the thickness, camber, and twist are based on polynomial representations. The primary design requirements imposed restrictions on the canard and wing volumes and on the lift coefficients at the operating conditions. Results indicate that significant improvements in minimum drag and lift-to-drag ratio are possible with reasonable aircraft geometries. Calculations were done for supersonic speeds with Mach numbers ranging from 1 to 6. Planforms were mainly of a delta shape with aspect ratio of 1.
Comparative study of flare control laws. [optimal control of b-737 aircraft approach and landing
NASA Technical Reports Server (NTRS)
Nadkarni, A. A.; Breedlove, W. J., Jr.
1979-01-01
A digital 3-D automatic control law was developed to achieve an optimal transition of a B-737 aircraft between various initial glid slope conditions and the desired final touchdown condition. A discrete, time-invariant, optimal, closed-loop control law presented for a linear regulator problem, was extended to include a system being acted upon by a constant disturbance. Two forms of control laws were derived to solve this problem. One method utilized the feedback of integral states defined appropriately and augmented with the original system equations. The second method formulated the problem as a control variable constraint, and the control variables were augmented with the original system. The control variable constraint control law yielded a better performance compared to feedback control law for the integral states chosen.
Planform, aero-structural, and flight control optimization for tailless morphing aircraft
NASA Astrophysics Data System (ADS)
Molinari, Giulio; Arrieta, Andres F.; Ermanni, Paolo
2015-04-01
Tailless airplanes with swept wings rely on variations of the spanwise lift distribution to provide controllability in roll, pitch and yaw. Conventionally, this is achieved utilizing multiple control surfaces, such as elevons, on the wing trailing edge. As every flight condition requires different control moments (e.g. to provide pitching moment equilibrium), these surfaces are practically permanently displaced. Due to their nature, causing discontinuities, corners and gaps, they bear aerodynamic penalties, mostly in terms of shape drag. Shape adaptation, by means of chordwise morphing, has the potential of varying the lift of a wing section by deforming its profile in a way that minimizes the resulting drag. Furthermore, as the shape can be varied differently along the wingspan, the lift distribution can be tailored to each specific flight condition. For this reason, tailless aircraft appear as a prime choice to apply morphing techniques, as the attainable benefits are potentially significant. In this work, we present a methodology to determine the optimal planform, profile shape, and morphing structure for a tailless aircraft. The employed morphing concept is based on a distributed compliance structure, actuated by Macro Fiber Composite (MFC) piezoelectric elements. The multidisciplinary optimization is performed considering the static and dynamic aeroelastic behavior of the resulting structure. The goal is the maximization of the aerodynamic efficiency while guaranteeing the controllability of the plane, by means of morphing, in a set of flight conditions.
Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation
NASA Technical Reports Server (NTRS)
Reuther, James; Jameson, Antony; Farmer, James; Martinelli, Luigi; Saunders, David
1996-01-01
This work describes the implementation of optimization techniques based on control theory for complex aircraft configurations. Here control theory is employed to derive the adjoint differential equations, the solution of which allows for a drastic reduction in computational costs over previous design methods (13, 12, 43, 38). In our earlier studies (19, 20, 22, 23, 39, 25, 40, 41, 42) it was shown that this method could be used to devise effective optimization procedures for airfoils, wings and wing-bodies subject to either analytic or arbitrary meshes. Design formulations for both potential flows and flows governed by the Euler equations have been demonstrated, showing that such methods can be devised for various governing equations (39, 25). In our most recent works (40, 42) the method was extended to treat wing-body configurations with a large number of mesh points, verifying that significant computational savings can be gained for practical design problems. In this paper the method is extended for the Euler equations to treat complete aircraft configurations via a new multiblock implementation. New elements include a multiblock-multigrid flow solver, a multiblock-multigrid adjoint solver, and a multiblock mesh perturbation scheme. Two design examples are presented in which the new method is used for the wing redesign of a transonic business jet.
NASA Technical Reports Server (NTRS)
Stepner, D. E.; Mehra, R. K.
1973-01-01
A new method of extracting aircraft stability and control derivatives from flight test data is developed based on the maximum likelihood cirterion. It is shown that this new method is capable of processing data from both linear and nonlinear models, both with and without process noise and includes output error and equation error methods as special cases. The first application of this method to flight test data is reported for lateral maneuvers of the HL-10 and M2/F3 lifting bodies, including the extraction of stability and control derivatives in the presence of wind gusts. All the problems encountered in this identification study are discussed. Several different methods (including a priori weighting, parameter fixing and constrained parameter values) for dealing with identifiability and uniqueness problems are introduced and the results given. The method for the design of optimal inputs for identifying the parameters of linear dynamic systems is also given. The criterion used for the optimization is the sensitivity of the system output to the unknown parameters. Several simple examples are first given and then the results of an extensive stability and control dervative identification simulation for a C-8 aircraft are detailed.
An Interpolation Approach to Optimal Trajectory Planning for Helicopter Unmanned Aerial Vehicles
2012-06-01
Armament Data Line DOF Degree of Freedom PS Pseudospectral LGL Legendre-Gauss- Lobatto quadrature nodes ODE Ordinary Differential Equation xiv...Gauss- Lobatto (LGL) quadrature nodes [14]. The trajectory solution, a function f(t) is approximated by Nth order Lagrange polynomials using the an
Fuel Optimal Low Thrust Trajectories for an Asteroid Sample Return Mission
2005-03-01
Transfer - State and Thrust Magnitude (U nsca led U nits) .......................................................................... . . 34 Figure 16...Earth Transfer - State and Thrust Angle (Scaled Units) ... 37 Figure 21. Asteroid to Earth Transfer - State and Thrust Magnitude (U nsca led U nits...Unconstrained Surface Time with no Phasing - Trajectory (U nsca led U nits) .......................................................................... . . 40
Optimal Tuner Selection for Kalman-Filter-Based Aircraft Engine Performance Estimation
NASA Technical Reports Server (NTRS)
Simon, Donald L.; Garg, Sanjay
2011-01-01
An emerging approach in the field of aircraft engine controls and system health management is the inclusion of real-time, onboard models for the inflight estimation of engine performance variations. This technology, typically based on Kalman-filter concepts, enables the estimation of unmeasured engine performance parameters that can be directly utilized by controls, prognostics, and health-management applications. A challenge that complicates this practice is the fact that an aircraft engine s performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters such as efficiencies and flow capacities related to each major engine module. Through Kalman-filter-based estimation techniques, the level of engine performance degradation can be estimated, given that there are at least as many sensors as health parameters to be estimated. However, in an aircraft engine, the number of sensors available is typically less than the number of health parameters, presenting an under-determined estimation problem. A common approach to address this shortcoming is to estimate a subset of the health parameters, referred to as model tuning parameters. The problem/objective is to optimally select the model tuning parameters to minimize Kalman-filterbased estimation error. A tuner selection technique has been developed that specifically addresses the under-determined estimation problem, where there are more unknown parameters than available sensor measurements. A systematic approach is applied to produce a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. Tuning parameter selection is performed using a multi-variable iterative search routine that seeks to minimize the theoretical mean-squared estimation error of the Kalman filter. This approach can significantly reduce the error in onboard aircraft engine parameter estimation
NASA Technical Reports Server (NTRS)
Jackson, Mark Charles
1994-01-01
Spacecraft proximity operations are complicated by the fact that exhaust plume impingement from the reaction control jets of space vehicles can cause structural damage, contamination of sensitive arrays and instruments, or attitude misalignment during docking. The occurrence and effect of jet plume impingement can be reduced by planning approach trajectories with plume effects considered. An A* node search is used to find plume-fuel optimal trajectories through a discretized six dimensional attitude-translation space. A plume cost function which approximates jet plume isopressure envelopes is presented. The function is then applied to find relative costs for predictable 'trajectory altering' firings and unpredictable 'deadbanding' firings. Trajectory altering firings are calculated by running the spacecraft jet selection algorithm and summing the cost contribution from each jet fired. A 'deadbanding effects' function is defined and integrated to determine the potential for deadbanding impingement along candidate trajectories. Plume costs are weighed against fuel costs in finding the optimal solution. A* convergence speed is improved by solving approach trajectory problems in reverse time. Results are obtained on a high fidelity space shuttle/space station simulation. Trajectory following is accomplished by a six degree of freedom autopilot. Trajectories planned with, and without, plume costs are compared in terms of force applied to the target structure.
NASA Technical Reports Server (NTRS)
Hopkins, Dale A.; Patnaik, Surya N.
2000-01-01
A preliminary aircraft engine design methodology is being developed that utilizes a cascade optimization strategy together with neural network and regression approximation methods. The cascade strategy employs different optimization algorithms in a specified sequence. The neural network and regression methods are used to approximate solutions obtained from the NASA Engine Performance Program (NEPP), which implements engine thermodynamic cycle and performance analysis models. The new methodology is proving to be more robust and computationally efficient than the conventional optimization approach of using a single optimization algorithm with direct reanalysis. The methodology has been demonstrated on a preliminary design problem for a novel subsonic turbofan engine concept that incorporates a wave rotor as a cycle-topping device. Computations of maximum thrust were obtained for a specific design point in the engine mission profile. The results (depicted in the figure) show a significant improvement in the maximum thrust obtained using the new methodology in comparison to benchmark solutions obtained using NEPP in a manual design mode.
Adaptive Flight Control Design with Optimal Control Modification on an F-18 Aircraft Model
NASA Technical Reports Server (NTRS)
Burken, John J.; Nguyen, Nhan T.; Griffin, Brian J.
2010-01-01
In the presence of large uncertainties, a control system needs to be able to adapt rapidly to regain performance. Fast adaptation is referred to as the implementation of adaptive control with a large adaptive gain to reduce the tracking error rapidly; however, a large adaptive gain can lead to high-frequency oscillations which can adversely affect the robustness of an adaptive control law. A new adaptive control modification is presented that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. The modification is based on the minimization of the Y2 norm of the tracking error, which is formulated as an optimal control problem. The optimality condition is used to derive the modification using the gradient method. The optimal control modification results in a stable adaptation and allows a large adaptive gain to be used for better tracking while providing sufficient robustness. A damping term (v) is added in the modification to increase damping as needed. Simulations were conducted on a damaged F-18 aircraft (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) with both the standard baseline dynamic inversion controller and the adaptive optimal control modification technique. The results demonstrate the effectiveness of the proposed modification in tracking a reference model.
NASA Astrophysics Data System (ADS)
Yang, Weizhu; Yue, Zhufeng; Li, Lei; Wang, Peiyan
2016-01-01
An optimization procedure combining an automated finite element modelling (AFEM) technique with a ground structure approach (GSA) is proposed for structural layout and sizing design of aircraft wings. The AFEM technique, based on CATIA VBA scripting and PCL programming, is used to generate models automatically considering the arrangement of inner systems. GSA is used for local structural topology optimization. The design procedure is applied to a high-aspect-ratio wing. The arrangement of the integral fuel tank, landing gear and control surfaces is considered. For the landing gear region, a non-conventional initial structural layout is adopted. The positions of components, the number of ribs and local topology in the wing box and landing gear region are optimized to obtain a minimum structural weight. Constraints include tank volume, strength, buckling and aeroelastic parameters. The results show that the combined approach leads to a greater weight saving, i.e. 26.5%, compared with three additional optimizations based on individual design approaches.
Application of parallel algorithmic differentiation to optimal CubeSat trajectory design
NASA Astrophysics Data System (ADS)
Ghosh, Alexander; Coverstone, Victoria
2017-01-01
CubeSats, the class of small standardized satellites, are becoming a viable scientific research platform. At present, a variety of high value Earth Science missions require multiple collecting instruments on separate platforms maintained in precise configurations. A new software tool was created to compute propellant-minimizing maneuvers for multiple CubeSats for use with mission preliminary design. This tool incorporates parallelization of the derivative calculations, and demonstrates speed improvements over previous parallel formulations of small satellite cooperative trajectory design problems.
Complexity Science Applications to Dynamic Trajectory Management: Research Strategies
NASA Technical Reports Server (NTRS)
Sawhill, Bruce; Herriot, James; Holmes, Bruce J.; Alexandrov, Natalia
2009-01-01
The promise of the Next Generation Air Transportation System (NextGen) is strongly tied to the concept of trajectory-based operations in the national airspace system. Existing efforts to develop trajectory management concepts are largely focused on individual trajectories, optimized independently, then de-conflicted among each other, and individually re-optimized, as possible. The benefits in capacity, fuel, and time are valuable, though perhaps could be greater through alternative strategies. The concept of agent-based trajectories offers a strategy for automation of simultaneous multiple trajectory management. The anticipated result of the strategy would be dynamic management of multiple trajectories with interacting and interdependent outcomes that satisfy multiple, conflicting constraints. These constraints would include the business case for operators, the capacity case for the Air Navigation Service Provider (ANSP), and the environmental case for noise and emissions. The benefits in capacity, fuel, and time might be improved over those possible under individual trajectory management approaches. The proposed approach relies on computational agent-based modeling (ABM), combinatorial mathematics, as well as application of "traffic physics" concepts to the challenge, and modeling and simulation capabilities. The proposed strategy could support transforming air traffic control from managing individual aircraft behaviors to managing systemic behavior of air traffic in the NAS. A system built on the approach could provide the ability to know when regions of airspace approach being "full," that is, having non-viable local solution space for optimizing trajectories in advance.
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
NASA Technical Reports Server (NTRS)
Fishbach, L. H.
1979-01-01
The computational techniques utilized to determine the optimum propulsion systems for future aircraft applications and to identify system tradeoffs and technology requirements are described. The characteristics and use of the following computer codes are discussed: (1) NNEP - a very general cycle analysis code that can assemble an arbitrary matrix fans, turbines, ducts, shafts, etc., into a complete gas turbine engine and compute on- and off-design thermodynamic performance; (2) WATE - a preliminary design procedure for calculating engine weight using the component characteristics determined by NNEP; (3) POD DRG - a table look-up program to calculate wave and friction drag of nacelles; (4) LIFCYC - a computer code developed to calculate life cycle costs of engines based on the output from WATE; and (5) INSTAL - a computer code developed to calculate installation effects, inlet performance and inlet weight. Examples are given to illustrate how these computer techniques can be applied to analyze and optimize propulsion system fuel consumption, weight, and cost for representative types of aircraft and missions.
a Graphical Optimization of Take-Off Noise Abatement Procedures for Subsonic Aircraft
NASA Astrophysics Data System (ADS)
Norgia, L.
1999-05-01
This paper describes a numerical approach to the simulation of noise contours generated during aircraft operations. Common features of many existing noise-contour programs make these procedures unsuitable for on-line piloted-simulator use. In fact, they usually require large computational tools and exhibit complex structure, so that they generally run quite slowly. The method proposed here is an attempt to overcome some of the above drawbacks. It works for arbitrarily complex take-off and landing paths, and reveals the influence of several quantitites on the shape and size of the contours. Besides, the calculations are simple enough to be implemented on a handheld programmable calculator. The method runs fast, and quickly provides contour shape, evaluates area and analyzes main characteristics of the end. The method has been used to optimize noise abatement procedures for subsonic aircraft; for every take-off procedure the model can generate an isofootprint on the ground which helps the operator to choose the best take-off solution.
NASA Technical Reports Server (NTRS)
Brauer, G. L.; Habeger, A. R.; Stevenson, R.
1974-01-01
The basic equations and models used in a computer program (6D POST) to optimize simulated trajectories with six degrees of freedom were documented. The 6D POST program was conceived as a direct extension of the program POST, which dealt with point masses, and considers the general motion of a rigid body with six degrees of freedom. It may be used to solve a wide variety of atmospheric flight mechanics and orbital transfer problems for powered or unpowered vehicles operating near a rotating oblate planet. Its principal features are: an easy to use NAMELIST type input procedure, an integrated set of Flight Control System (FCS) modules, and a general-purpose discrete parameter targeting and optimization capability. It was written in FORTRAN 4 for the CDC 6000 series computers.
NASA Technical Reports Server (NTRS)
Fishbach, L. H.
1979-01-01
The paper describes the computational techniques employed in determining the optimal propulsion systems for future aircraft applications and to identify system tradeoffs and technology requirements. The computer programs used to perform calculations for all the factors that enter into the selection process of determining the optimum combinations of airplanes and engines are examined. Attention is given to the description of the computer codes including NNEP, WATE, LIFCYC, INSTAL, and POD DRG. A process is illustrated by which turbine engines can be evaluated as to fuel consumption, engine weight, cost and installation effects. Examples are shown as to the benefits of variable geometry and of the tradeoff between fuel burned and engine weights. Future plans for further improvements in the analytical modeling of engine systems are also described.
NASA Technical Reports Server (NTRS)
Samareh, Jamshid A.; Sensmeier, mark D.; Stewart, Bret A.
2006-01-01
Algorithms for rapid generation of moderate-fidelity structural finite element models of air vehicle structures to allow more accurate weight estimation earlier in the vehicle design process have been developed. Application of these algorithms should help to rapidly assess many structural layouts before the start of the preliminary design phase and eliminate weight penalties imposed when actual structure weights exceed those estimated during conceptual design. By defining the structural topology in a fully parametric manner, the structure can be mapped to arbitrary vehicle configurations being considered during conceptual design optimization. Recent enhancements to this approach include the porting of the algorithms to a platform-independent software language Python, and modifications to specifically consider morphing aircraft-type configurations. Two sample cases which illustrate these recent developments are presented.
Time-optimal Aircraft Pursuit-evasion with a Weapon Envelope Constraint
NASA Technical Reports Server (NTRS)
Menon, P. K. A.
1990-01-01
The optimal pursuit-evasion problem between two aircraft including a realistic weapon envelope is analyzed using differential game theory. Six order nonlinear point mass vehicle models are employed and the inclusion of an arbitrary weapon envelope geometry is allowed. The performance index is a linear combination of flight time and the square of the vehicle acceleration. Closed form solution to this high-order differential game is then obtained using feedback linearization. The solution is in the form of a feedback guidance law together with a quartic polynomial for time-to-go. Due to its modest computational requirements, this nonlinear guidance law is useful for on-board real-time implementation.
Structural Analysis and Optimization of a Composite Fan Blade for Future Aircraft Engine
NASA Astrophysics Data System (ADS)
Coroneos, Rula M.; Gorla, Rama Subba Reddy
2012-09-01
This paper addresses the structural analysis and optimization of a composite sandwich ply lay-up of a NASA baseline solid metallic fan blade comparable to a future Boeing 737 MAX aircraft engine. Sandwich construction with a polymer matrix composite face sheet and honeycomb aluminum core replaces the original baseline solid metallic fan model made of Titanium. The focus of this work is to design the sandwich composite blade with the optimum number of plies for the face sheet that will withstand the combined pressure and centrifugal loads while the constraints are satisfied and the baseline aerodynamic and geometric parameters are maintained. To satisfy the requirements a sandwich construction for the blade is proposed with composite face sheets and a weak core made of honeycomb aluminum material. For aerodynamic considerations, the thickness of the core is optimized where as the overall blade thickness is held fixed in order not to alter the original airfoil geometry. Weight reduction is taken as the objective function by varying the core thickness of the blade within specified upper and lower bounds. Constraints are imposed on radial displacement limitations and ply failure strength. From the optimum design, the minimum number of plies, which will not fail, is back-calculated. The ply lay-up of the blade is adjusted from the calculated number of plies and final structural analysis is performed. Analyses were carried out by utilizing the OpenMDAO Framework, developed at NASA Glenn Research Center combining optimization with structural assessment.
Maity, Arnab; Hocht, Leonhard; Heise, Christian; Holzapfel, Florian
2016-11-28
A new efficient adaptive optimal control approach is presented in this paper based on the indirect model reference adaptive control (MRAC) architecture for improvement of adaptation and tracking performance of the uncertain system. The system accounts here for both matched and unmatched unknown uncertainties that can act as plant as well as input effectiveness failures or damages. For adaptation of the unknown parameters of these uncertainties, the frequency selective learning approach is used. Its idea is to compute a filtered expression of the system uncertainty using multiple filters based on online instantaneous information, which is used for augmentation of the update law. It is capable of adjusting a sudden change in system dynamics without depending on high adaptation gains and can satisfy exponential parameter error convergence under certain conditions in the presence of structured matched and unmatched uncertainties as well. Additionally, the controller of the MRAC system is designed using a new optimal control method. This method is a new linear quadratic regulator-based optimal control formulation for both output regulation and command tracking problems. It provides a closed-form control solution. The proposed overall approach is applied in a control of lateral dynamics of an unmanned aircraft problem to show its effectiveness.
Practical input optimization for aircraft parameter estimation experiments. Ph.D. Thesis, 1990
NASA Technical Reports Server (NTRS)
Morelli, Eugene A.
1993-01-01
The object of this research was to develop an algorithm for the design of practical, optimal flight test inputs for aircraft parameter estimation experiments. A general, single pass technique was developed which allows global optimization of the flight test input design for parameter estimation using the principles of dynamic programming with the input forms limited to square waves only. Provision was made for practical constraints on the input, including amplitude constraints, control system dynamics, and selected input frequency range exclusions. In addition, the input design was accomplished while imposing output amplitude constraints required by model validity and considerations of safety during the flight test. The algorithm has multiple input design capability, with optional inclusion of a constraint that only one control move at a time, so that a human pilot can implement the inputs. It is shown that the technique can be used to design experiments for estimation of open loop model parameters from closed loop flight test data. The report includes a new formulation of the optimal input design problem, a description of a new approach to the solution, and a summary of the characteristics of the algorithm, followed by three example applications of the new technique which demonstrate the quality and expanded capabilities of the input designs produced by the new technique. In all cases, the new input design approach showed significant improvement over previous input design methods in terms of achievable parameter accuracies.
Structural Analysis and Optimization of a Composite Fan Blade for Future Aircraft Engine
NASA Technical Reports Server (NTRS)
Coroneos, Rula M.
2012-01-01
This report addresses the structural analysis and optimization of a composite fan blade sized for a large aircraft engine. An existing baseline solid metallic fan blade was used as a starting point to develop a hybrid honeycomb sandwich construction with a polymer matrix composite face sheet and honeycomb aluminum core replacing the original baseline solid metallic fan model made of titanium. The focus of this work is to design the sandwich composite blade with the optimum number of plies for the face sheet that will withstand the combined pressure and centrifugal loads while the constraints are satisfied and the baseline aerodynamic and geometric parameters are maintained. To satisfy the requirements, a sandwich construction for the blade is proposed with composite face sheets and a weak core made of honeycomb aluminum material. For aerodynamic considerations, the thickness of the core is optimized whereas the overall blade thickness is held fixed so as to not alter the original airfoil geometry. Weight is taken as the objective function to be minimized by varying the core thickness of the blade within specified upper and lower bounds. Constraints are imposed on radial displacement limitations and ply failure strength. From the optimum design, the minimum number of plies, which will not fail, is back-calculated. The ply lay-up of the blade is adjusted from the calculated number of plies and final structural analysis is performed. Analyses were carried out by utilizing the OpenMDAO Framework, developed at NASA Glenn Research Center combining optimization with structural assessment.
NASA Technical Reports Server (NTRS)
Danilin, M. Y.; Ko, Malcolm K. W.; Bevilacqua, R. M.; Lyjak, L. V.; Froidevaux, L.; Santee, M. L.; Zawodny, J. M.; Hoppel, K. W.; Richard, E. C.; Spackman, J. R.; Jackman, Charles H. (Technical Monitor)
2001-01-01
We compared the version 5 Microwave Limb Sounder (MLS) aboard the Upper Atmosphere Research Satellite (UARS), version 3 Polar Ozone and Aerosol Measurement-III (POAM-111) aboard the French satellite SPOT-IV, version 6.0 Stratospheric Aerosol and Gas Experiment 11 (SAGE-II) aboard the Earth Radiation Budget Satellite, and NASA ER-2 aircraft measurements made in the northern hemisphere in January-February 2000 during the SAGE III Ozone Loss and Validation Experiment (SOLVE). This study addresses one of the key scientific objectives of the SOLVE campaign, namely, to validate multi-platform satellite measurements made in the polar stratosphere during winter. This intercomparison was performed using a traditional correlative analysis (TCA) and a trajectory hunting technique (THT). Launching backward and forward trajectories from the points of measurement, the THT identifies air parcels sampled at least twice within a prescribed match criterion during the course of 5 days. We found that the ozone measurements made by these four instruments agree most of the time within 110% in the stratosphere up to 1400 K (approximately 35 km). The water vapor measurements from POAM-III and the ER-2 Harvard Lyman-alpha hygrometer and JPL laser hygrometer agree to within 10.5 ppmv (or about +/-10%) in the lower stratosphere above 380 K. The MLS and ER-2 ClO measurements agree within their error bars for the TCA. The MLS and ER-2 nitric acid measurements near 17-20 km altitude agree within their uncertainties most of the time with a hint of a positive offset by MLS according to the TCA. We also applied the AER box model constrained by the ER-2 measurements for analysis of the ClO and HN03 measurements using the THT. We found that: (1) the model values of ClO are smaller by about 0.3-0.4 (0.2) ppbv below (above) 400 K than those by MLS and (2) the HN03 comparison shows a positive offset of MLS values by approximately 1 and 1-2 ppbv below 400 K and near 450 K, respectively. It is hard to
Multidisciplinary design and optimization (MDO) methodology for the aircraft conceptual design
NASA Astrophysics Data System (ADS)
Iqbal, Liaquat Ullah
An integrated design and optimization methodology has been developed for the conceptual design of an aircraft. The methodology brings higher fidelity Computer Aided Design, Engineering and Manufacturing (CAD, CAE and CAM) Tools such as CATIA, FLUENT, ANSYS and SURFCAM into the conceptual design by utilizing Excel as the integrator and controller. The approach is demonstrated to integrate with many of the existing low to medium fidelity codes such as the aerodynamic panel code called CMARC and sizing and constraint analysis codes, thus providing the multi-fidelity capabilities to the aircraft designer. The higher fidelity design information from the CAD and CAE tools for the geometry, aerodynamics, structural and environmental performance is provided for the application of the structured design methods such as the Quality Function Deployment (QFD) and the Pugh's Method. The higher fidelity tools bring the quantitative aspects of a design such as precise measurements of weight, volume, surface areas, center of gravity (CG) location, lift over drag ratio, and structural weight, as well as the qualitative aspects such as external geometry definition, internal layout, and coloring scheme early in the design process. The performance and safety risks involved with the new technologies can be reduced by modeling and assessing their impact more accurately on the performance of the aircraft. The methodology also enables the design and evaluation of the novel concepts such as the blended (BWB) and the hybrid wing body (HWB) concepts. Higher fidelity computational fluid dynamics (CFD) and finite element analysis (FEA) allow verification of the claims for the performance gains in aerodynamics and ascertain risks of structural failure due to different pressure distribution in the fuselage as compared with the tube and wing design. The higher fidelity aerodynamics and structural models can lead to better cost estimates that help reduce the financial risks as well. This helps in
High-Fidelity Real-Time Trajectory Optimization for Reusable Launch Vehicles
2006-12-01
indirect and direct methods, 3.) necessary optimality conditions and the minimum principle, 4.) the Karush-Kuhn-Tucker ( KKT ) Theorem, 5.) the NLP problem...instrumental in the automation of verifying the necessary conditions for optimality . It entails the application of the KKT theorem to the NLP problem such...39 3. Necessary Optimality Conditions and the Minimum Principle.....40 4. The Generalized Karush-Kuhn
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.
Efficient algorithms for future aircraft design: Contributions to aerodynamic shape optimization
NASA Astrophysics Data System (ADS)
Hicken, Jason Edward
Advances in numerical optimization have raised the possibility that efficient and novel aircraft configurations may be "discovered" by an algorithm. To begin exploring this possibility, a fast and robust set of tools for aerodynamic shape optimization is developed. Parameterization and mesh-movement are integrated to accommodate large changes in the geometry. This integrated approach uses a coarse B-spline control grid to represent the geometry and move the computational mesh; consequently, the mesh-movement algorithm is two to three orders faster than a node-based linear elasticity approach, without compromising mesh quality. Aerodynamic analysis is performed using a flow solver for the Euler equations. The governing equations are discretized using summation-by-parts finite-difference operators and simultaneous approximation terms, which permit C0 mesh continuity at block interfaces. The discretization results in a set of nonlinear algebraic equations, which are solved using an efficient parallel Newton-Krylov-Schur strategy. A gradient-based optimization algorithm is adopted. The gradient is evaluated using adjoint variables for the flow and mesh equations in a sequential approach. The flow adjoint equations are solved using a novel variant of the Krylov solver GCROT. This variant of GCROT is flexible to take advantage of non-stationary preconditioners and is shown to outperform restarted flexible GMRES. The aerodynamic optimizer is applied to several studies of induced-drag minimization. An elliptical lift distribution is recovered by varying spanwise twist, thereby validating the algorithm. Planform optimization based on the Euler equations produces a nonelliptical lift distribution, in contrast with the predictions of lifting-line theory. A study of spanwise vertical shape optimization confirms that a winglet-up configuration is more efficient than a winglet-down configuration. A split-tip geometry is used to explore nonlinear wake-wing interactions: the
NASA Astrophysics Data System (ADS)
Kenway, Gaetan K. W.
This thesis presents new tools and techniques developed to address the challenging problem of high-fidelity aerostructural optimization with respect to large numbers of design variables. A new mesh-movement scheme is developed that is both computationally efficient and sufficiently robust to accommodate large geometric design changes and aerostructural deformations. A fully coupled Newton-Krylov method is presented that accelerates the convergence of aerostructural systems and provides a 20% performance improvement over the traditional nonlinear block Gauss-Seidel approach and can handle more exible structures. A coupled adjoint method is used that efficiently computes derivatives for a gradient-based optimization algorithm. The implementation uses only machine accurate derivative techniques and is verified to yield fully consistent derivatives by comparing against the complex step method. The fully-coupled large-scale coupled adjoint solution method is shown to have 30% better performance than the segregated approach. The parallel scalability of the coupled adjoint technique is demonstrated on an Euler Computational Fluid Dynamics (CFD) model with more than 80 million state variables coupled to a detailed structural finite-element model of the wing with more than 1 million degrees of freedom. Multi-point high-fidelity aerostructural optimizations of a long-range wide-body, transonic transport aircraft configuration are performed using the developed techniques. The aerostructural analysis employs Euler CFD with a 2 million cell mesh and a structural finite element model with 300 000 DOF. Two design optimization problems are solved: one where takeoff gross weight is minimized, and another where fuel burn is minimized. Each optimization uses a multi-point formulation with 5 cruise conditions and 2 maneuver conditions. The optimization problems have 476 design variables are optimal results are obtained within 36 hours of wall time using 435 processors. The TOGW
Fuel-Optimal Trajectories in a Planet-Moon Environment Using Multiple Gravity Assists
NASA Technical Reports Server (NTRS)
Ross, Shane D.; Grover, Piyush
2007-01-01
For low energy spacecraft trajectories such as multi-moon orbiters for the Jupiter system, multiple gravity assists by moons could be used in conjunction with ballistic capture to drastically decrease fuel usage. In this paper, we outline a procedure to obtain a family of zero-fuel multi-moon orbiter trajectories, using a family of Keplerian maps derived by the first author previously. The maps capture well the dynamics of the full equations of motion; the phase space contains a connected chaotic zone where intersections between unstable resonant orbit manifolds provide the template for lanes of fast migration between orbits of different semimajor axes. Patched three body approach is used and the four body problem is broken down into two three-body problems, and the search space is considerably reduced by the use of properties of the Keplerian maps. We also introduce the notion of Switching Region where the perturbations due to the two perturbing moons are of comparable strength, and which separates the domains of applicability of the corresponding two Keplerian maps.
An Evaluation of a Flight Deck Interval Management Algorithm Including Delayed Target Trajectories
NASA Technical Reports Server (NTRS)
Swieringa, Kurt A.; Underwood, Matthew C.; Barmore, Bryan; Leonard, Robert D.
2014-01-01
NASA's first Air Traffic Management (ATM) Technology Demonstration (ATD-1) was created to facilitate the transition of mature air traffic management technologies from the laboratory to operational use. The technologies selected for demonstration are the Traffic Management Advisor with Terminal Metering (TMA-TM), which provides precise timebased scheduling in the terminal airspace; Controller Managed Spacing (CMS), which provides controllers with decision support tools enabling precise schedule conformance; and Interval Management (IM), which consists of flight deck automation that enables aircraft to achieve or maintain precise in-trail spacing. During high demand operations, TMA-TM may produce a schedule and corresponding aircraft trajectories that include delay to ensure that a particular aircraft will be properly spaced from other aircraft at each schedule waypoint. These delayed trajectories are not communicated to the automation onboard the aircraft, forcing the IM aircraft to use the published speeds to estimate the target aircraft's estimated time of arrival. As a result, the aircraft performing IM operations may follow an aircraft whose TMA-TM generated trajectories have substantial speed deviations from the speeds expected by the spacing algorithm. Previous spacing algorithms were not designed to handle this magnitude of uncertainty. A simulation was conducted to examine a modified spacing algorithm with the ability to follow aircraft flying delayed trajectories. The simulation investigated the use of the new spacing algorithm with various delayed speed profiles and wind conditions, as well as several other variables designed to simulate real-life variability. The results and conclusions of this study indicate that the new spacing algorithm generally exhibits good performance; however, some types of target aircraft speed profiles can cause the spacing algorithm to command less than optimal speed control behavior.
NASA Astrophysics Data System (ADS)
Trehan, Sumeet; Durlofsky, Louis J.
2016-12-01
A new reduced-order model based on trajectory piecewise quadratic (TPWQ) approximations and proper orthogonal decomposition (POD) is introduced and applied for subsurface oil-water flow simulation. The method extends existing techniques based on trajectory piecewise linear (TPWL) approximations by incorporating second-derivative terms into the reduced-order treatment. Both the linear and quadratic reduced-order methods, referred to as POD-TPWL and POD-TPWQ, entail the representation of new solutions as expansions around previously simulated high-fidelity (full-order) training solutions, along with POD-based projection into a low-dimensional space. POD-TPWQ entails significantly more offline preprocessing than POD-TPWL as it requires generating and projecting several third-order (Hessian-type) terms. The POD-TPWQ method is implemented for two-dimensional systems. Extensive numerical results demonstrate that it provides consistently better accuracy than POD-TPWL, with speedups of about two orders of magnitude relative to high-fidelity simulations for the problems considered. We demonstrate that POD-TPWQ can be used as an error estimator for POD-TPWL, which motivates the development of a trust-region-based optimization framework. This procedure uses POD-TPWL for fast function evaluations and a POD-TPWQ error estimator to determine when retraining, which entails a high-fidelity simulation, is required. Optimization results for an oil-water problem demonstrate the substantial speedups that can be achieved relative to optimizations based on high-fidelity simulation.
Elastically Shaped Wing Optimization and Aircraft Concept for Improved Cruise Efficiency
NASA Technical Reports Server (NTRS)
Nguyen, Nhan; Trinh, Khanh; Reynolds, Kevin; Kless, James; Aftosmis, Michael; Urnes, James, Sr.; Ippolito, Corey
2013-01-01
This paper presents the findings of a study conducted tn 2010 by the NASA Innovation Fund Award project entitled "Elastically Shaped Future Air Vehicle Concept". The study presents three themes in support of meeting national and global aviation challenges of reducing fuel burn for present and future aviation systems. The first theme addresses the drag reduction goal through innovative vehicle configurations via non-planar wing optimization. Two wing candidate concepts have been identified from the wing optimization: a drooped wing shape and an inflected wing shape. The drooped wing shape is a truly biologically inspired wing concept that mimics a seagull wing and could achieve about 5% to 6% drag reduction, which is aerodynamically significant. From a practical perspective, this concept would require new radical changes to the current aircraft development capabilities for new vehicles with futuristic-looking wings such as this concept. The inflected wing concepts could achieve between 3% to 4% drag reduction. While the drag reduction benefit may be less, the inflected-wing concept could have a near-term impact since this concept could be developed within the current aircraft development capabilities. The second theme addresses the drag reduction goal through a new concept of elastic wing shaping control. By aeroelastically tailoring the wing shape with active control to maintain optimal aerodynamics, a significant drag reduction benefit could be realized. A significant reduction in fuel burn for long-range cruise from elastic wing shaping control could be realized. To realize the potential of the elastic wing shaping control concept, the third theme emerges that addresses the drag reduction goal through a new aerodynamic control effector called a variable camber continuous trailing edge flap. Conventional aerodynamic control surfaces are discrete independent surfaces that cause geometric discontinuities at the trailing edge region. These discontinuities promote
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
Lin, Ciyun; Gong, Bowen; Qu, Xin
2015-01-01
A traditional traffic signal control system is established based on vehicular delay, queue length, saturation and other indicators. However, due to the increasing severity of urban environmental pollution issues and the development of a resource-saving and environmentally friendly social philosophy, the development of low-carbon and energy-efficient urban transport is required. This paper first defines vehicular trajectories and the calculation of vehicular emissions based on VSP. Next, a regression analysis method is used to quantify the relationship between vehicular emissions and delay, and a traffic signal control model is established to reduce emissions and delay using the enumeration method combined with saturation constraints. Finally, one typical intersection of Changchun is selected to verify the model proposed in this paper; its performance efficiency is also compared using simulations in VISSIM. The results of this study show that the proposed model can significantly reduce vehicle delay and traffic emissions simultaneously.
2015-01-01
A traditional traffic signal control system is established based on vehicular delay, queue length, saturation and other indicators. However, due to the increasing severity of urban environmental pollution issues and the development of a resource-saving and environmentally friendly social philosophy, the development of low-carbon and energy-efficient urban transport is required. This paper first defines vehicular trajectories and the calculation of vehicular emissions based on VSP. Next, a regression analysis method is used to quantify the relationship between vehicular emissions and delay, and a traffic signal control model is established to reduce emissions and delay using the enumeration method combined with saturation constraints. Finally, one typical intersection of Changchun is selected to verify the model proposed in this paper; its performance efficiency is also compared using simulations in VISSIM. The results of this study show that the proposed model can significantly reduce vehicle delay and traffic emissions simultaneously. PMID:26720095
Simulation modeling and tracing optimal trajectory of robotic mining machine effector
NASA Astrophysics Data System (ADS)
Fryanov, VN; Pavlova, LD
2017-02-01
Within the framework of the robotic coal mine design for deep-level coal beds with the high gas content in the seismically active areas in the southern Kuzbass, the motion path parameters for an effector of a robotic mining machine are evaluated. The simulation model is meant for selection of minimum energy-based optimum trajectory for the robot effector, calculation of stresses and strains in a coal bed in a variable perimeter shortwall in the course of coal extraction, determination of coordinates of a coal bed edge area with the maximum disintegration of coal, and for choice of direction of the robot effector to get in contact with the mentioned area and to break coal at the minimum energy input. It is suggested to use the model in the engineering of the robot intelligence.
NASA Technical Reports Server (NTRS)
Gilyard, Glenn B. (Inventor)
1999-01-01
Practical application of real-time (or near real-time) Adaptive Performance Optimization (APO) is provided for a transport aircraft in steady climb, cruise, turn descent or other flight conditions based on measurements and calculations of incremental drag from a forced response maneuver of one or more redundant control effectors defined as those in excess of the minimum set of control effectors required to maintain the steady flight condition in progress. The method comprises the steps of applying excitation in a raised-cosine form over an interval of from 100 to 500 sec. at the rate of 1 to 10 sets/sec of excitation, and data for analysis is gathered in sets of measurements made during the excitation to calculate lift and drag coefficients C.sub.L and C.sub.D from two equations, one for each coefficient. A third equation is an expansion of C.sub.D as a function of parasitic drag, induced drag, Mach and altitude drag effects, and control effector drag, and assumes a quadratic variation of drag with positions .delta..sub.i of redundant control effectors i=1 to n. The third equation is then solved for .delta..sub.iopt the optimal position of redundant control effector i, which is then used to set the control effector i for optimum performance during the remainder of said steady flight or until monitored flight conditions change by some predetermined amount as determined automatically or a predetermined minimum flight time has elapsed.
Yuvaraj, R; Murugappan, M; Ibrahim, Norlinah Mohamed; Sundaraj, Kenneth; Omar, Mohd Iqbal; Mohamad, Khairiyah; Palaniappan, R
2014-12-01
In addition to classic motor signs and symptoms, individuals with Parkinson's disease (PD) are characterized by emotional deficits. Ongoing brain activity can be recorded by electroencephalograph (EEG) to discover the links between emotional states and brain activity. This study utilized machine-learning algorithms to categorize emotional states in PD patients compared with healthy controls (HC) using EEG. Twenty non-demented PD patients and 20 healthy age-, gender-, and education level-matched controls viewed happiness, sadness, fear, anger, surprise, and disgust emotional stimuli while fourteen-channel EEG was being recorded. Multimodal stimulus (combination of audio and visual) was used to evoke the emotions. To classify the EEG-based emotional states and visualize the changes of emotional states over time, this paper compares four kinds of EEG features for emotional state classification and proposes an approach to track the trajectory of emotion changes with manifold learning. From the experimental results using our EEG data set, we found that (a) bispectrum feature is superior to other three kinds of features, namely power spectrum, wavelet packet and nonlinear dynamical analysis; (b) higher frequency bands (alpha, beta and gamma) play a more important role in emotion activities than lower frequency bands (delta and theta) in both groups and; (c) the trajectory of emotion changes can be visualized by reducing subject-independent features with manifold learning. This provides a promising way of implementing visualization of patient's emotional state in real time and leads to a practical system for noninvasive assessment of the emotional impairments associated with neurological disorders.
NASA Technical Reports Server (NTRS)
Sinha, Sujit
1988-01-01
A study was conducted to evaluate the performance implications of a heads-up ascent flight design for the Space Transportation System, as compared to the current heads-down flight mode. The procedure involved the use of the Minimum Hamiltonian Ascent Shuttle Trajectory Evaluation Program, which is a three-degree-of-freedom moment balance simulation of shuttle ascent. A minimum-Hamiltonian optimization strategy was employed to maximize injection weight as a function of maximum dynamic pressure constraint and Solid Rocket Motor burnrate. Performance Reference Mission Four trajectory groundrules were used for consistency. The major conclusions are that for heads-up ascent and a mission nominal design maximum dynamic pressure value of 680 psf, the optimum solid motor burnrate is 0.394 ips, which produces a performance enhancement of 4293 lbm relative to the baseline heads-down ascent, with 0.368 ips burnrate solid motors and a 680 psf dynamic pressure constraint. However, no performance advantage exists for heads-up flight if the current Solid Rocket Motor target burnrate of 0.368 ips is used. The advantage of heads-up ascent flight employing the current burnrate is that Space Shuttle Main Engine throttling for dynamic pressure control is not necessary.
Nonlinear Feedback Control for Rapid, On-Line Trajectory Optimization of Reentry Vehicles (PREPRINT)
2005-12-01
feedback without using an inner-loop tracking controller. The original concept dates back to the early 1990’s, when Pesch discussed off- line and on- line...approach is not mature enough for general optimal control problems. Although this paper 3 does not provide the “mathematical justification” that Pesch ...Guidance, Navigation, and Control Conference, AIAA Paper No. 2001-4429, Aug 2001. 14. Pesch , H.J., “Off-Line and On-Line Computation of Optimal
NASA Technical Reports Server (NTRS)
Lin, N. J.; Quinn, R. D.
1991-01-01
A locally-optimal trajectory management (LOTM) approach is analyzed, and it is found that care should be taken in choosing the Ritz expansion and cost function. A modified cost function for the LOTM approach is proposed which includes the kinetic energy along with the base reactions in a weighted and scale sum. The effects of the modified functions are demonstrated with numerical examples for robots operating in two- and three-dimensional space. It is pointed out that this modified LOTM approach shows good performance, the reactions do not fluctuate greatly, joint velocities reach their objectives at the end of the manifestation, and the CPU time is slightly more than twice the manipulation time.
Design of optimal fast scanning trajectory for the mechanical scanner of measurement instruments.
Ju, Bing-Feng; Bai, Xiaolong; Chen, Jian; Ge, Yaozheng
2014-01-01
This paper focuses on the design of the optimal scanning mode for the family of scanning probe microscopes. Based on different values of the maximum acceleration (deceleration) rate and maximum speed of X- and Y- axes of the mechanical scanner encountered in practice due to different mechanical design and loads, the design procedure of the optimal fast scanning mode is presented, which is found to be sensitive to the specific parameters of the scanning motion. By utilizing the simultaneous motion of the two axes, the fast raster scanning mode proposed can improve the scanning efficiency by 29% when comparing with the conventional raster (CR) scanning mode, if the scanning speeds of both axes are identical. In addition, the optimal fast mode provided by us has no effects on the image accuracy such as image degradation, image distortion when the efficiency is evaluated. No further difficulties are introduced to the control of the mechanical scanner and the data acquisition process. This optimal scanning mode is useful when the response time of the probe is very fast (such as ultrasonic probe in scanning acoustic microscope (SAM)), and the main limitations are due to the mechanical scanner. By applying different loads for both axes, the experiments with different scanning areas and scanning modes are conducted in a self-developed SAM. Experimental results coincide with the theoretical analysis and confirm the validation of our proposed optimal fast scanning mode and its superiority over the CR scanning mode.
Uncertainty Optimization Applied to the Monte Carlo Analysis of Planetary Entry Trajectories
NASA Technical Reports Server (NTRS)
Olds, John; Way, David
2001-01-01
Recently, strong evidence of liquid water under the surface of Mars and a meteorite that might contain ancient microbes have renewed interest in Mars exploration. With this renewed interest, NASA plans to send spacecraft to Mars approx. every 26 months. These future spacecraft will return higher-resolution images, make precision landings, engage in longer-ranging surface maneuvers, and even return Martian soil and rock samples to Earth. Future robotic missions and any human missions to Mars will require precise entries to ensure safe landings near science objective and pre-employed assets. Potential sources of water and other interesting geographic features are often located near hazards, such as within craters or along canyon walls. In order for more accurate landings to be made, spacecraft entering the Martian atmosphere need to use lift to actively control the entry. This active guidance results in much smaller landing footprints. Planning for these missions will depend heavily on Monte Carlo analysis. Monte Carlo trajectory simulations have been used with a high degree of success in recent planetary exploration missions. These analyses ascertain the impact of off-nominal conditions during a flight and account for uncertainty. Uncertainties generally stem from limitations in manufacturing tolerances, measurement capabilities, analysis accuracies, and environmental unknowns. Thousands of off-nominal trajectories are simulated by randomly dispersing uncertainty variables and collecting statistics on forecast variables. The dependability of Monte Carlo forecasts, however, is limited by the accuracy and completeness of the assumed uncertainties. This is because Monte Carlo analysis is a forward driven problem; beginning with the input uncertainties and proceeding to the forecasts outputs. It lacks a mechanism to affect or alter the uncertainties based on the forecast results. If the results are unacceptable, the current practice is to use an iterative, trial
Evaluating and minimizing noise impact due to aircraft flyover
NASA Technical Reports Server (NTRS)
Jacobson, I. D.; Cook, G.
1979-01-01
Existing techniques were used to assess the noise impact on a community due to aircraft operation and to optimize the flight paths of an approaching aircraft with respect to the annoyance produced. Major achievements are: (1) the development of a population model suitable for determining the noise impact, (2) generation of a numerical computer code which uses this population model along with the steepest descent algorithm to optimize approach/landing trajectories, (3) implementation of this optimization code in several fictitious cases as well as for the community surrounding Patrick Henry International Airport, Virginia.
A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem
NASA Technical Reports Server (NTRS)
Hughes, Steven P.; Mailhe, Laurie M.; Guzman, Jose J.
2002-01-01
In this paper we present a comparison of optimization approaches to the minimum fuel rendezvous problem. Both indirect and direct methods are compared for a variety of test cases. The indirect approach is based on primer vector theory. The direct approaches are implemented numerically and include Sequential Quadratic Programming (SQP), Quasi-Newton, Simplex, Genetic Algorithms, and Simulated Annealing. Each method is applied to a variety of test cases including, circular to circular coplanar orbits, LEO to GEO, and orbit phasing in highly elliptic orbits. We also compare different constrained optimization routines on complex orbit rendezvous problems with complicated, highly nonlinear constraints.
Optimal Trajectory Reconfiguration and Retargeting for the X-33 Reusable Launch Vehicle
2004-09-01
6 Figure 4 X-33 Simulation Coordinate System...between the different components of the optimization routine. B. REDUCED-ORDER DYNAMICAL MODEL 1. Coordinate Systems The simulation uses a three...reentry simulation . where γ = flight path angle, the angle made by the velocity vector and the x-y plane. β = azimuth angle, the angle made by
Global Optimization of Interplanetary Trajectories in the Presence of Realistic Mission Constraints
NASA Technical Reports Server (NTRS)
Hinckley, David; Englander, Jacob; Hitt, Darren
2015-01-01
Single trial evaluations Trial creation by Phase-wise GA-style or DE-inspired recombination Bin repository structure requires an initialization period Non-exclusionary Kill Distance Population collapse mechanic Main loop Creation Probabilistic switch between GA and DE creation types Locally optimize Submit to repository Repeat.
Rintoul, Mark Daniel; Wilson, Andrew T.; Valicka, Christopher G.; Kegelmeyer, W. Philip; Shead, Timothy M.; Newton, Benjamin D.; Czuchlewski, Kristina Rodriguez
2015-09-01
We want to organize a body of trajectories in order to identify, search for, classify and predict behavior among objects such as aircraft and ships. Existing compari- son functions such as the Fr'echet distance are computationally expensive and yield counterintuitive results in some cases. We propose an approach using feature vectors whose components represent succinctly the salient information in trajectories. These features incorporate basic information such as total distance traveled and distance be- tween start/stop points as well as geometric features related to the properties of the convex hull, trajectory curvature and general distance geometry. Additionally, these features can generally be mapped easily to behaviors of interest to humans that are searching large databases. Most of these geometric features are invariant under rigid transformation. We demonstrate the use of different subsets of these features to iden- tify trajectories similar to an exemplar, cluster a database of several hundred thousand trajectories, predict destination and apply unsupervised machine learning algorithms.