Spacecraft Trajectory Optimization

312 Pages·2010·3.468 MB·English

by  Conway B. (ed.)

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SPACECRAFT TRAJECTORY
OPTIMIZATION
This is a long-overdue volume dedicated to space trajectory
optimization. Interest in the subject has grown, as space missions of
increasing levels of sophistication, complexity, and scientific return –
hardly imaginable in the 1960s – have been designed and flown.
Although the basic tools of optimization theory remain an accepted
canon, there has been a revolution in the manner in which they are
applied and in the development of numerical optimization. This vol-
ume purposely includes a variety of both analytical and numerical
approachestotrajectoryoptimization.Thechoiceofauthorshasbeen
guidedbytheeditor’sintentiontoassemblethemostexpertandactive
researchersinthevariousspecialtiespresented.
Bruce A. Conway is a Professor of Aeronautical and Astronauti-
calEngineeringattheUniversityofIllinois, Urbana-Champaign. He
earned his Ph.D. in aeronautics and astronautics at Stanford Uni-
versity in 1981. Professor Conway’s research interests include orbital
mechanics,optimalcontrol,andimprovedmethodsforthenumerical
solution of problems in optimization. He is the author of numerous
refereedjournalarticlesand(withJohnPrussing)thetextbookOrbital
Mechanics.

CambridgeAerospaceSeries
Editors:WeiShyyandMichaelJ.Rycroft
1. J.M.RolfeandK.J.Staples(eds.):FlightSimulation
2. P.Berlin:TheGeostationaryApplicationsSatellite
3. M.J.T.Smith:AircraftNoise
4. N.X.Vinh:FlightMechanicsofHigh-PerformanceAircraft
5. W.A.MairandD.L.Birdsall:AircraftPerformance
6. M.J.AbzugandE.E.Larrabee:AirplaneStabilityandControl
7. M.J.Sidi:SpacecraftDynamicsandControl
8. J.D.Anderson:AHistoryofAerodynamics
9. A.M.Cruise,J.A.Bowles,C.V.Goodall,andT.J.Patrick:PrinciplesofSpace
InstrumentDesign
10. G.A.KhouryandJ.D.Gillett(eds.):AirshipTechnology
11. J.Fielding:IntroductiontoAircraftDesign
12. J.G.Leishman:PrinciplesofHelicopterAerodynamics,2ndEdition
13. J.KatzandA.Plotkin:LowSpeedAerodynamics,2ndEdition
14. M.J.AbzugandE.E.Larrabee:AirplaneStabilityandControl:AHistoryofthe
TechnologiesthatmadeAviationPossible,2ndEdition
15. D.H.HodgesandG.A.Pierce:IntroductiontoStructuralDynamicsandAeroelasticity
16. W.Fehse:AutomaticRendezvousandDockingofSpacecraft
17. R.D.Flack:FundamentalsofJetPropulsionwithApplications
18. E.A.Baskharone:PrinciplesofTurbomachineryinAir-BreathingEngines
19. D.D.Knight:NumericalMethodsforHigh-SpeedFlows
20. C.Wagner,T.Hüttl,P.Sagaut(eds.):Large-EddySimulationforAcoustics
21. D.Joseph,T.Funada,andJ.Wang:PotentialFlowsofViscousandViscoelasticFluids
22. W.Shyy,Y.Lian,H.Liu,J.Tang,D.Viieru:AerodynamicsofLowReynoldsNumber
Flyers
23. J.H.Saleh:AnalysesforDurabilityandSystemDesignLifetime
24. B.K.Donaldson:AnalysisofAircraftStructures,2/e
25. C.Segal:TheScramjetEngine:ProcessesandCharacteristics
26. J.Doyle:GuidedExplorationsoftheMechanicsofSolidsandStructures
27. A.Kundu:AircraftDesign
28. M.Friswell,J.Penny,S.Garvey,A.Lees:FundamentalsofRotorDynamics
29. B.A.Conway(ed.):SpacecraftTrajectoryOptimization
30. R.J.AdrianandJ.Westerweel:ParticleImageVelocimetry
31. S.Ching,Y.Eun,C.Gokcek,P.T.Kabamba,andS.M.Meerkov:QuasilinearControl
Theory:PerformanceAnalysisandDesignofFeedbackSystemswithNonlinear
ActuatorsandSensors

Spacecraft Trajectory Optimization
Edited by
Bruce A. Conway
UniversityofIllinoisatUrbana-Champaign
CAMBRIDGE UNIVERSITY PRESS
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Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
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Information on this title: www.cambridge.org/9780521518505
© Cambridge University Press 2010
This publication is in copyright. Subject to statutory exception and to the
provision of relevant collective licensing agreements, no reproduction of any part
may take place without the written permission of Cambridge University Press.
First published in print format 2010
ISBN-13 978-0-511-90945-0 eBook (NetLibrary)
ISBN-13 978-0-521-51850-5 Hardback
Cambridge University Press has no responsibility for the persistence or accuracy
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and does not guarantee that any content on such websites is, or will remain,
accurate or appropriate.
Contents
Preface page xi
1 TheProblemofSpacecraftTrajectoryOptimization . . . . . 1
BruceA.Conway
1.1 Introduction 1
1.2 SolutionMethods 3
1.3 TheSituationTodaywithRegardtoSolvingOptimal
ControlProblems 12
References 13
2 PrimerVectorTheoryandApplications . . . . . . . . . . . 16
JohnE.Prussing
2.1 Introduction 16
2.2 First-OrderNecessaryConditions 17
2.3 SolutiontothePrimerVectorEquation 23
2.4 ApplicationofPrimerVectorTheorytoanOptimal
ImpulsiveTrajectory 24
References 36
3 SpacecraftTrajectoryOptimizationUsingDirectTranscription
andNonlinearProgramming . . . . . . . . . . . . . . . . 37
BruceA.ConwayandStephenW.Paris
3.1 Introduction 37
3.2 TranscriptionMethods 40
3.3 SelectionofCoordinates 52
3.4 ModelingPropulsionSystems 60
3.5 GeneratinganInitialGuess 62
3.6 ComputationalConsiderations 65
3.7 VerifyingOptimality 71
References 76
vii
viii Contents
4 ElementsofaSoftwareSystemforSpacecraftTrajectory
Optimization . . . . . . . . . . . . . . . . . . . . . . . . 79
CesarOcampo
4.1 Introduction 79
4.2 TrajectoryModel 80
4.3 EquationsofMotion 85
4.4 FiniteBurnControlModels 85
4.5 SolutionMethods 90
4.6 TrajectoryDesignandOptimizationExamples 93
4.7 ConcludingRemarks 110
References 110
5 Low-ThrustTrajectoryOptimizationUsingOrbitalAveraging
andControlParameterization . . . . . . . . . . . . . . . . 112
CraigA.Kluever
5.1 IntroductionandBackground 112
5.2 Low-ThrustTrajectoryOptimization 113
5.3 NumericalResults 125
5.4 Conclusions 136
Nomenclature 136
References 138
6 AnalyticRepresentationsofOptimalLow-ThrustTransfer
inCircularOrbit . . . . . . . . . . . . . . . . . . . . . . 139
JeanA.Kéchichian
6.1 Introduction 139
6.2 TheOptimalUnconstrainedTransfer 141
6.3 TheOptimalTransferwithAltitudeConstraints 145
6.4 TheSplit-SequenceTransfers 157
References 177
7 GlobalOptimizationandSpacePruningforSpacecraft
TrajectoryDesign . . . . . . . . . . . . . . . . . . . . . 178
DarioIzzo
7.1 Introduction 178
7.2 Notation 179
7.3 ProblemTranscription 179
7.4 TheMGAProblem 181
7.5 TheMGA-1DSMProblem 183
7.6 BenchmarkProblems 186
7.7 GlobalOptimization 190
7.8 SpacePruning 194
7.9 ConcludingRemarks 197