Spacecraft Formation Flying: Dynamics, control and navigation

✍ Scribed by Kyle Alfriend, Srinivas Rao Vadali, Pini Gurfil, Jonathan How, Louis Breger

• Publisher: Butterworth-Heinemann
• Year: 2009
• Tongue: English
• Leaves: 386
• Series: Elsevier Astrodynamics
• Edition: 1
• Category: Library

✦ Synopsis

Spacecraft formation flying (SFF) is of huge importance to the aerospace and space community. Not the stuff of science-fiction, SFF involves flying multiple small satellites together, to deliver benefits which far outweigh a single larger craft or space station. The first autonomous formation flying earth science mission was in 196 and NASA now has 35 SFF mission sets. By networking several smaller and cheaper craft, scientists can make simultaneous measurements that enable higher resolution astronomical imagery, provide robust and fault-tolerant spacecraft system architectures, and enable complex earth science and space science networks dispersed over clusters of satellites in space. This is the first book to introduce and explore SFF. It is a topic of enormous importance to aerospace engineers, astrodynamicists, satellite engineers, astronomers, physicists, and applied mathematicions. This book provides a complete introduction to the subject and is supported by graduate level student exercises plus Matlab and Maple code sets for running SFF simulations. * The first book dedicated to spacecraft formation flying which is the enabling element of distributed spacecraft systems * Written by the leading researchers and teachers in the field; perfect for research and graduate students * Accompanied by Matlab and Maple code sets and exercises for graduate level students of aerospace science, astrodynamics and orbital mechanics

✦ Table of Contents

Copyright page......Page 2
Dedication......Page 3
Foreword......Page 6
Preface......Page 8
What is Spacecraft Formation Flying?......Page 13
Swarming......Page 14
Atmospheric drag......Page 15
Control of Spacecraft Formations......Page 16
State transition matrix inversion......Page 17
Continuous linear control......Page 18
Space Navigation and the Global Positioning System......Page 19
Formation Flying Missions......Page 20
Fundamental Astrodynamics......Page 24
Coordinate Systems......Page 25
The Keplerian Two-body Problem......Page 27
Solution of the Inertial Equations of Motion......Page 33
Nonsingular Orbital Elements......Page 36
Variation of parameters......Page 39
Lagrange's planetary equations......Page 41
Zonal harmonics......Page 44
Gauss' variational equations......Page 45
Averaging Theory......Page 47
Lagrangian and Hamiltonian Mechanics......Page 50
The Delaunay Elements......Page 52
Canonical Transformations......Page 53
Brouwer Theory......Page 54
Constrained Static Optimization......Page 57
Control Lyapunov Functions......Page 58
Linear Quadratic Regulation......Page 59
Kalman Filtering......Page 60
The Unscented Kalman Filter......Page 63
The additive form of the UKF......Page 64
The square root form of the UKF......Page 66
Nonlinear Models of Relative Dynamics......Page 69
Equations of Relative Motion in the Unperturbed Case......Page 70
The Energy Matching Condition......Page 74
Impulsive Formation-keeping......Page 76
Another Outlook on Optimal Formation-keeping......Page 82
Circular Chief Orbit......Page 84
Lagrangian and Hamiltonian Derivations......Page 86
Equations of Relative Motion under the Influence of J2......Page 88
Relative motion states in the L frame......Page 90
Initial conditions......Page 91
Linear Equations of Relative Motion......Page 93
The Clohessy--Wiltshire Equations......Page 94
Two-impulse Linear Rendezvous......Page 100
Lagrangian and Hamiltonian Derivations of the CW Equations......Page 104
Accommodating second-order nonlinearities......Page 107
Curvilinear vs. Cartesian Relative Coordinates......Page 109
Time as the independent variable: Melton's STM......Page 113
Lawden and Tschauner--Hempel Equations......Page 115
Carter's STM......Page 116
Yamanaka and Ankersen's STM......Page 119
Broucke's STM......Page 120
STM of Lee, Cochran, and Jo......Page 121
STM of Nazarenko......Page 122
Initial conditions to prevent secular drift......Page 123
Periodic Solutions to the TH Equations......Page 127
Modeling Relative Motion Using Orbital Elements......Page 132
General Solution to the Nonlinear Relative Motion Equations......Page 133
The commensurable case......Page 137
Relative Motion Approximations with a Circular-Equatorial Reference Orbit......Page 138
High-order time-series approximations......Page 140
Second-order approximation......Page 142
First-order approximation: Hill's solutions......Page 144
Establishing the PCO Initial Conditions......Page 145
Hybrid Differential Equations with Non-linearity Compensation for Unperturbed Circular Orbits......Page 147
The Unit-Sphere Approach......Page 151
Relative Motion Description using Quaternions......Page 155
The Gim--Alfriend Geometric Method......Page 158
J2 effects revisited......Page 159
The geometric method......Page 161
Averaged Relative Motion......Page 173
Linearized J2 -Differential Equations for Circular Orbits......Page 177
Development of the model......Page 178
Short-periodic effects......Page 179
The linear model......Page 180
Differential Equations from the Gim--Alfriend STM......Page 184
A Second-Order State Propagation Model......Page 188
Dynamic Constraints for J2 Mitigation......Page 192
Three constraints......Page 195
Two constraints......Page 196
One constraint......Page 200
Energy considerations......Page 201
Numerical results......Page 202
A Nonlinear Theory based on Orbital Elements......Page 206
Dynamic Model Error Effect Comparison......Page 213
Perturbed Fundamental Frequencies for Formations in Near-circular Orbits......Page 219
In-plane and cross-track frequencies......Page 220
Selection of the PCO Initial Conditions for Near-Circular Orbits......Page 221
Matching the In-plane and Cross-track Fundamental Frequencies......Page 223
Amplitude considerations......Page 225
PCO Formation Maintenance based on the Modified CW Equations......Page 226
Formation maintenance without radial thrust......Page 228
Fuel Minimization and Balancing......Page 229
Rotation-Translation Coupling......Page 233
Relative Dynamics......Page 234
Kinematically-Coupled Relative Spacecraft Motion Model......Page 238
The CLF approach......Page 247
LQR control based on averaged orbital elements......Page 251
Discrete-time LQR Control......Page 255
Numerical results......Page 257
Impulsive Control based on Gauss' Variational Equations......Page 258
Formation establishment......Page 259
Two-impulse Formation Reconfiguration for Circular Orbits......Page 262
Two-impulse-per-orbit Formation Maintenance......Page 263
Analytical solution for circular orbits......Page 264
Determination of α for fuel balancing......Page 266
In-plane thrust requirements......Page 267
Implementation of Δ v Commands......Page 277
Plan Implementation......Page 278
Using accelerometers to improve Δ v implementation......Page 279
Discrete example......Page 283
Impact on Autonomous Rendezvous and Docking......Page 285
Impact on formation reconfiguration......Page 288
Relative Measurements and Navigation......Page 292
Dynamical Modeling......Page 293
Measurement Update: Carrier-Phase Differential GPS......Page 295
Comparison of EKF and UKF for Relative Navigation......Page 298
Comparison as baselines increase......Page 305
Comparison for FreeFlyerTM and GSFC simulations......Page 306
A final example......Page 307
High-Fidelity Formation Flying Simulation......Page 309
Simulation Controller Configuration......Page 310
Parameters examined......Page 311
Simulation Results......Page 312
Risk Reduction......Page 333
Mission Operations......Page 334
The Transformation Matrix Σ (t)......Page 335
The Transformation Matrix Σ (t) - 1......Page 336
The Matrix B (t)......Page 338
The State Transition Matrix for Relative Mean Elements......Page 339
Transformation from Mean to Osculating Elements......Page 342
Jacobian for Mean to Osculating Elements......Page 345
Small Eccentricity Theory......Page 355
Yan-Alfriend Nonlinear Theory Coefficients......Page 361
References......Page 367
Index......Page 383

✦ Subjects

Транспорт;Аэрокосмическая техника;