Spacecraft Formation Flying

by Alfriend; Vadali; Gurfil; How; Breger

• ISBN13: 9780750685337
• ISBN10: 0750685336
• Edition: 1st
• Format: Hardcover
• Copyright: 2009-12-03
• Publisher: Elsevier Science

Summary

The first book dedicated to spacecraft formation flying, written by leading researchers and professors in the field

Table of Contents

Foreword	p. xiii
Preface	p. xv
Introduction	p. 1
What is Spacecraft Formation Flying?	p. 1
Coordination Approaches	p. 2
Fuel-use Drivers	p. 3
Control of Spacecraft Formations	p. 4
Control Approaches	p. 5
Space Navigation and the Global Positioning System	p. 7
Formation Flying Missions	p. 8
Fundamental Astrodynamics	p. 13
Coordinate Systems	p. 14
The Keplerian Two-body Problem	p. 16
Solution of the Inertial Equations of Motion	p. 22
Nonsingular Orbital Elements	p. 25
Non-Keplerian Motion and Orbital Perturbations	p. 28
Averaging Theory	p. 36
The Basics of Analytical Mechanics, Optimization, Control and Estimation	p. 39
Lagrangian and Hamiltonian Mechanics	p. 39
The Delaunay Elements	p. 41
Canonical Transformations	p. 42
Brouwer Theory	p. 43
Constrained Static Optimization	p. 46
Control Lyapunov Functions	p. 47
Linear Quadratic Regulation	p. 48
Kalman Filtering	p. 49
The Unscented Kalman Filter	p. 52
Nonlinear Models of Relative Dynamics	p. 59
Equations of Relative Motion in the Unperturbed Case	p. 60
The Energy Matching Condition	p. 64
Impulsive Formation-keeping	p. 66
Another Outlook on Optimal Formation-keeping	p. 72
Circular Chief Orbit	p. 74
Lagrangian and Hamiltonian Derivations	p. 76
Equations of Relative Motion under the Influence of J2	p. 78
Linear Equations of Relative Motion	p. 83
The Clohessy-Wiltshire Equations	p. 84
Two-impulse Linear Rendezvous	p. 90
Lagrangian and Hamiltonian Derivations of the CW Equations	p. 94
Accommodating second-order nonlinearities	p. 97
Curvilinear vs. Cartesian Relative Coordinates	p. 99
Elliptic Reference Orbits	p. 103
Periodic Solutions to the TH Equations	p. 117
Modeling Relative Motion Using Orbital Elements	p. 123
General Solution to the Nonlinear Relative Motion Equations	p. 124
Bounds on Maximal and Minimal Distances	p. 128
Relative Motion Approximations with a Circular-Equatorial Reference Orbit	p. 129
Establishing the PCO Initial Conditions	p. 136
Hybrid Differential Equations with Non-linearity Compensation for Unperturbed Circular Orbits	p. 138
Modeling Perturbed Relative Motion Using Orbital Elements	p. 143
The Unit-Sphere Approach	p. 143
Relative Motion Description using Quaternions	p. 147
The Gim-Alfriend Geometric Method	p. 150
Averaged Relative Motion	p. 165
Linearized J2-Dirferential Equations for Circular Orbits	p. 169
Differential Equations from the Gim-Alfriend STM	p. 176
A Second-Order State Propagation Model	p. 180
Perturbation Mitigation	p. 185
Dynamic Constraints for J2 Mitigation	p. 185
A Nonlinear Theory based on Orbital Elements	p. 199
Dynamic Model Error Effect Comparison	p. 206
Perturbed Fundamental Frequencies for Formations in Near-circular Orbits	p. 212
Selection of the PCO Initial Conditions for Near-Circular Orbits	p. 214
Matching the In-plane and Cross-track Fundamental Frequencies	p. 216
PCO Formation Maintenance based on the Modified CW Equations	p. 219
Fuel Minimization and Balancing	p. 222
Rotation-Translation Coupling	p. 227
Relative Dynamics	p. 228
Kinematically-Coupled Relative Spacecraft Motion Model	p. 232
Formation Control	p. 241
Continuous Control	p. 241
Discrete-time LQR Control	p. 249
Impulsive Control based on Gauss' Variational Equations	p. 252
Two-impulse Formation Reconfiguration for Circular Orbits	p. 256
Two-impulse-per-orbit Formation Maintenance	p. 257
Implementation of ¿¿ Commands	p. 271
Plan Implementation	p. 272
Impact on Autonomous Rendezvous and Docking	p. 279
Relative Measurements and Navigation	p. 287
Dynamical Modeling	p. 288
Measurement Update: Carrier-Phase Differential GPS	p. 290
Comparison of EKF and UKF for Relative Navigation	p. 293
High-Fidelity Formation Flying Simulation	p. 305
Simulation Controller Configuration	p. 306
Simulation Results	p. 308
Summary and Future Prospects	p. 329
Risk Reduction	p. 329
Fuel Requirements	p. 330
Mission Operations	p. 330
Appendices	p. 331
The Transformation Matrix Σ(t)	p. 331
The Transformation Matrix Σ(t) -1	p. 332
The Matrix B(t)	p. 334
The State Transition Matrix for Relative Mean Elements	p. 335
Transformation from Mean to Osculating Elements	p. 338
Jacobian for Mean to Osculating Elements	p. 341
Small Eccentricity Theory	p. 351
Yan-Alfriend Nonlinear Theory Coefficients	p. 357
References	p. 363
Index	p. 379
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