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 J_{2} | 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 J_{2} 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 żż 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 &SIGMA;(t) | p. 331 |

The Transformation Matrix &SIGMA;(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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