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 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 specialties 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 relevant to contemporary problems.

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.

Preface	p. xi
The Problem of Spacecraft Trajectory Optimization	p. 1
Introduction	p. 1
Solution Methods	p. 3
The Situation Today with Regard to Solving Optimal Control Problems	p. 12
References	p. 13
Primer Vector Theory and Applications	p. 16
Introduction	p. 16
First-Order Necessary Conditions	p. 17
Solution to the Primer Vector Equation	p. 23
Application of Primer Vector Theory to an Optimal Impulsive Trajectory	p. 24
References	p. 36
Spacecraft Trajectory Optimization Using Direct Transcription and Nonlinear Programming	p. 37
Introduction	p. 37
Transcription Methods	p. 40
Selection of Coordinates	p. 52
Modeling Propulsion Systems	p. 60
Generating an Initial Guess	p. 62
Computational Considerations	p. 65
Verifying Optimally	p. 71
References	p. 76
Elements of a Software System for Spacecraft Trajectory Optimization	p. 79
Introduction	p. 79
Trajectory Model	p. 80
Equations of Motion	p. 85
Finite Burn Control Models	p. 85
Solution Methods	p. 90
Trajectory Design and Optimization Examples	p. 93
Concluding Remarks	p. 110
References	p. 110
Low-Thrust Trajectory Optimization Using Orbital Averaging and Control Parameterization	p. 112
Introduction and Background	p. 112
Low-Thrust Trajectory Optimization	p. 113
Numerical Results	p. 125
Conclusions	p. 136
Nomenclature	p. 136
References	p. 138
Analytic Representations of Optimal Low-Thrust Transfer in Circular Orbit	p. 139
lntroduction	p. 139
The Optimal Unconstrained Transfer	p. 141
The Optimal Transfer with Altitude Constraints	p. 145
The Split-Sequence Transfers	p. 157
References	p. 177
Global Optimization and Space Pruning for Spacecraft Trajectory Design	p. 178
Introduction	p. 178
Notation	p. 179
Problem Transcription	p. 179
The MGA Problem	p. 181
The MGA-1DSM Problem	p. 183
Benchmark Problems	p. 186
Global Optimization	p. 190
Space Pruning	p. 194
Concluding Remarks	p. 197
	p. 198
	p. 199
References	p. 200
Incremental Techniques for Global Space Trajectory Design	p. 202
Introduction	p. 202
Modeling MGA Trajectories	p. 203
The Incremental Approach	p. 209
Testing Procedure and Performance Indicators	p. 216
Case Studies	p. 221
Conclusions	p. 234
References	p. 235
Optimal Low-Thrust Trajectories Using Stable Manifolds	p. 238
Introduction	p. 238
System Dynamics	p. 240
Basics of Trajectory Optimization	p. 247
Generation of Periodic Orbit Constructed as an Optimization Problem	p. 250
Optimal Earth Orbit to Lunar Orbit Transfer: Part 1-GTO to Periodic Orbit	p. 253
Optimal Earth Orbit to Lunar Orbit Transfer: Part 2-Periodic Orbit to Low-Lunar Orbit	p. 256
Extension of the Work to Interplanetary Flight	p. 259
Conclusions	p. 260
References	p. 26l
Swarming Theory Applied to Space Trajectory Optimization	p. 263
Introduction	p. 263
Description of the Method	p. 266
Lyapunov Periodic Orbits	p. 269
Lunar Periodic Orbits	p. 274
Optimal Low-Impulse Orbital Rendezvous	p. 277
Optimal Low-Thrust Orbital Transfers	p. 284
Concluding Remarks	p. 290
References	p. 291
Index	p. 295
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Spacecraft Trajectory Optimization

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