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Summary
Summary
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 volume purposely includes a variety of both analytical and numerical approaches to trajectory optimization. The choice of authors has been guided by the editor's intention to assemble the most expert and active researchers in the various specialities presented. The authors were given considerable freedom to choose their subjects, and although this may yield a somewhat eclectic volume, it also yields chapters written with palpable enthusiasm and relevance to contemporary problems.
Author Notes
Bruce A. Conway is a Professor of Aeronautical and Astronautical Engineering at the University of Illinois, Urbana-Champaign. He earned his Ph.D. in aeronautics and astronautics at Stanford University in 1981. Professor Conway's research interests include orbital mechanics, optimal control, and improved methods for the numerical solution of problems in optimization. He is the author of numerous refereed journal articles and (with John Prussing) the textbook Orbital Mechanics.
Table of Contents
| Preface | p. xi |
| 1 The Problem of Spacecraft Trajectory Optimization | p. 1 |
| 1.1 Introduction | p. 1 |
| 1.2 Solution Methods | p. 3 |
| 1.3 The Situation Today with Regard to Solving Optimal Control Problems | p. 12 |
| References | p. 13 |
| 2 Primer Vector Theory and Applications | p. 16 |
| 2.1 Introduction | p. 16 |
| 2.2 First-Order Necessary Conditions | p. 17 |
| 2.3 Solution to the Primer Vector Equation | p. 23 |
| 2.4 Application of Primer Vector Theory to an Optimal Impulsive Trajectory | p. 24 |
| References | p. 36 |
| 3 Spacecraft Trajectory Optimization Using Direct Transcription and Nonlinear Programming | p. 37 |
| 3.1 Introduction | p. 37 |
| 3.2 Transcription Methods | p. 40 |
| 3.3 Selection of Coordinates | p. 52 |
| 3.4 Modeling Propulsion Systems | p. 60 |
| 3.5 Generating an Initial Guess | p. 62 |
| 3.6 Computational Considerations | p. 65 |
| 3.7 Verifying Optimally | p. 71 |
| References | p. 76 |
| 4 Elements of a Software System for Spacecraft Trajectory Optimization | p. 79 |
| 4.1 Introduction | p. 79 |
| 4.2 Trajectory Model | p. 80 |
| 4.3 Equations of Motion | p. 85 |
| 4.4 Finite Burn Control Models | p. 85 |
| 4.5 Solution Methods | p. 90 |
| 4.6 Trajectory Design and Optimization Examples | p. 93 |
| 4.7 Concluding Remarks | p. 110 |
| References | p. 110 |
| 5 Low-Thrust Trajectory Optimization Using Orbital Averaging and Control Parameterization | p. 112 |
| 5.1 Introduction and Background | p. 112 |
| 5.2 Low-Thrust Trajectory Optimization | p. 113 |
| 5.3 Numerical Results | p. 125 |
| 5.4 Conclusions | p. 136 |
| Nomenclature | p. 136 |
| References | p. 138 |
| 6 Analytic Representations of Optimal Low-Thrust Transfer in Circular Orbit | p. 139 |
| 6.1 lntroduction | p. 139 |
| 6.2 The Optimal Unconstrained Transfer | p. 141 |
| 6.3 The Optimal Transfer with Altitude Constraints | p. 145 |
| 6.4 The Split-Sequence Transfers | p. 157 |
| References | p. 177 |
| 7 Global Optimization and Space Pruning for Spacecraft Trajectory Design | p. 178 |
| 7.1 Introduction | p. 178 |
| 7.2 Notation | p. 179 |
| 7.3 Problem Transcription | p. 179 |
| 7.4 The MGA Problem | p. 181 |
| 7.5 The MGA-1DSM Problem | p. 183 |
| 7.6 Benchmark Problems | p. 186 |
| 7.7 Global Optimization | p. 190 |
| 7.8 Space Pruning | p. 194 |
| 7.9 Concluding Remarks | p. 197 |
| Appendix 7A p. 198 | |
| Appendix 7B p. 199 | |
| References | p. 200 |
| 8 Incremental Techniques for Global Space Trajectory Design | p. 202 |
| 8.1 Introduction | p. 202 |
| 8.2 Modeling MGA Trajectories | p. 203 |
| 8.3 The Incremental Approach | p. 209 |
| 8.4 Testing Procedure and Performance Indicators | p. 216 |
| 8.5 Case Studies | p. 221 |
| 8.6 Conclusions | p. 234 |
| References | p. 235 |
| 9 Optimal Low-Thrust Trajectories Using Stable Manifolds | p. 238 |
| 9.1 Introduction | p. 238 |
| 9.2 System Dynamics | p. 240 |
| 9.3 Basics of Trajectory Optimization | p. 247 |
| 9.4 Generation of Periodic Orbit Constructed as an Optimization Problem | p. 250 |
| 9.5 Optimal Earth Orbit to Lunar Orbit Transfer: Part 1-GTO to Periodic Orbit | p. 253 |
| 9.6 Optimal Earth Orbit to Lunar Orbit Transfer: Part 2-Periodic Orbit to Low-Lunar Orbit | p. 256 |
| 9.7 Extension of the Work to Interplanetary Flight | p. 259 |
| 9.8 Conclusions | p. 260 |
| References | p. 26l |
| 10 Swarming Theory Applied to Space Trajectory Optimization | p. 263 |
| 10.1 Introduction | p. 263 |
| 10.2 Description of the Method | p. 266 |
| 10.3 Lyapunov Periodic Orbits | p. 269 |
| 10.4 Lunar Periodic Orbits | p. 274 |
| 10.5 Optimal Low-Impulse Orbital Rendezvous | p. 277 |
| 10.6 Optimal Low-Thrust Orbital Transfers | p. 284 |
| 10.7 Concluding Remarks | p. 290 |
| References | p. 291 |
| Index | p. 295 |
