Spacecraft Formation Flying

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2009-12-03
  • Publisher: Elsevier Science
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The first book dedicated to spacecraft formation flying, written by leading researchers and professors in the field

Table of Contents

Forewordp. xiii
Prefacep. xv
Introductionp. 1
What is Spacecraft Formation Flying?p. 1
Coordination Approachesp. 2
Fuel-use Driversp. 3
Control of Spacecraft Formationsp. 4
Control Approachesp. 5
Space Navigation and the Global Positioning Systemp. 7
Formation Flying Missionsp. 8
Fundamental Astrodynamicsp. 13
Coordinate Systemsp. 14
The Keplerian Two-body Problemp. 16
Solution of the Inertial Equations of Motionp. 22
Nonsingular Orbital Elementsp. 25
Non-Keplerian Motion and Orbital Perturbationsp. 28
Averaging Theoryp. 36
The Basics of Analytical Mechanics, Optimization, Control and Estimationp. 39
Lagrangian and Hamiltonian Mechanicsp. 39
The Delaunay Elementsp. 41
Canonical Transformationsp. 42
Brouwer Theoryp. 43
Constrained Static Optimizationp. 46
Control Lyapunov Functionsp. 47
Linear Quadratic Regulationp. 48
Kalman Filteringp. 49
The Unscented Kalman Filterp. 52
Nonlinear Models of Relative Dynamicsp. 59
Equations of Relative Motion in the Unperturbed Casep. 60
The Energy Matching Conditionp. 64
Impulsive Formation-keepingp. 66
Another Outlook on Optimal Formation-keepingp. 72
Circular Chief Orbitp. 74
Lagrangian and Hamiltonian Derivationsp. 76
Equations of Relative Motion under the Influence of J2p. 78
Linear Equations of Relative Motionp. 83
The Clohessy-Wiltshire Equationsp. 84
Two-impulse Linear Rendezvousp. 90
Lagrangian and Hamiltonian Derivations of the CW Equationsp. 94
Accommodating second-order nonlinearitiesp. 97
Curvilinear vs. Cartesian Relative Coordinatesp. 99
Elliptic Reference Orbitsp. 103
Periodic Solutions to the TH Equationsp. 117
Modeling Relative Motion Using Orbital Elementsp. 123
General Solution to the Nonlinear Relative Motion Equationsp. 124
Bounds on Maximal and Minimal Distancesp. 128
Relative Motion Approximations with a Circular-Equatorial Reference Orbitp. 129
Establishing the PCO Initial Conditionsp. 136
Hybrid Differential Equations with Non-linearity Compensation for Unperturbed Circular Orbitsp. 138
Modeling Perturbed Relative Motion Using Orbital Elementsp. 143
The Unit-Sphere Approachp. 143
Relative Motion Description using Quaternionsp. 147
The Gim-Alfriend Geometric Methodp. 150
Averaged Relative Motionp. 165
Linearized J2-Dirferential Equations for Circular Orbitsp. 169
Differential Equations from the Gim-Alfriend STMp. 176
A Second-Order State Propagation Modelp. 180
Perturbation Mitigationp. 185
Dynamic Constraints for J2 Mitigationp. 185
A Nonlinear Theory based on Orbital Elementsp. 199
Dynamic Model Error Effect Comparisonp. 206
Perturbed Fundamental Frequencies for Formations in Near-circular Orbitsp. 212
Selection of the PCO Initial Conditions for Near-Circular Orbitsp. 214
Matching the In-plane and Cross-track Fundamental Frequenciesp. 216
PCO Formation Maintenance based on the Modified CW Equationsp. 219
Fuel Minimization and Balancingp. 222
Rotation-Translation Couplingp. 227
Relative Dynamicsp. 228
Kinematically-Coupled Relative Spacecraft Motion Modelp. 232
Formation Controlp. 241
Continuous Controlp. 241
Discrete-time LQR Controlp. 249
Impulsive Control based on Gauss' Variational Equationsp. 252
Two-impulse Formation Reconfiguration for Circular Orbitsp. 256
Two-impulse-per-orbit Formation Maintenancep. 257
Implementation of żż Commandsp. 271
Plan Implementationp. 272
Impact on Autonomous Rendezvous and Dockingp. 279
Relative Measurements and Navigationp. 287
Dynamical Modelingp. 288
Measurement Update: Carrier-Phase Differential GPSp. 290
Comparison of EKF and UKF for Relative Navigationp. 293
High-Fidelity Formation Flying Simulationp. 305
Simulation Controller Configurationp. 306
Simulation Resultsp. 308
Summary and Future Prospectsp. 329
Risk Reductionp. 329
Fuel Requirementsp. 330
Mission Operationsp. 330
Appendicesp. 331
The Transformation Matrix Σ(t)p. 331
The Transformation Matrix Σ(t) -1p. 332
The Matrix B(t)p. 334
The State Transition Matrix for Relative Mean Elementsp. 335
Transformation from Mean to Osculating Elementsp. 338
Jacobian for Mean to Osculating Elementsp. 341
Small Eccentricity Theoryp. 351
Yan-Alfriend Nonlinear Theory Coefficientsp. 357
Referencesp. 363
Indexp. 379
Table of Contents provided by Ingram. All Rights Reserved.

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