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Spacecraft Formation Flying

Book Description

Space agencies are now realizing that much of what has previously been achieved using hugely complex and costly single platform projects—large unmanned and manned satellites (including the present International Space Station)—can be replaced by a number of smaller satellites networked together. The key challenge of this approach, namely ensuring the proper formation flying of multiple craft, is the topic of this second volume in Elsevier’s Astrodynamics Series, Spacecraft Formation Flying: Dynamics, control and navigation.

In this unique text, authors Alfriend et al. provide a coherent discussion of spacecraft relative motion, both in the unperturbed and perturbed settings, explain the main control approaches for regulating relative satellite dynamics, using both impulsive and continuous maneuvers, and present the main constituents required for relative navigation. The early chapters provide a foundation upon which later discussions are built, making this a complete, standalone offering.

Intended for graduate students, professors and academic researchers in the fields of aerospace and mechanical engineering, mathematics, astronomy and astrophysics, Spacecraft Formation Flying is a technical yet accessible, forward-thinking guide to this critical area of astrodynamics.



  • The first book dedicated to spacecraft formation flying, written by leading researchers and professors in the field
  • Develops the theory from an astrodynamical viewpoint, emphasizing modeling, control and navigation of formation flying satellites on Earth orbits
  • Examples used to illustrate the main developments, with a sample simulation of a formation flying mission included to illustrate high fidelity modeling, control and relative navigation

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright page
  5. Dedication
    1. About the authors
  6. Foreword
  7. Preface
    1. Notation
    2. Book Organization
    3. Acknowledgments
  8. Chapter 1: Introduction
    1. Publisher Summary
    2. 1.1 What is Spacecraft Formation Flying?
    3. 1.2 Coordination Approaches
    4. 1.3 Fuel-use Drivers
    5. 1.4 Control of Spacecraft Formations
    6. 1.5 Control Approaches
    7. 1.6 Space Navigation and the Global Positioning System
    8. 1.7 Formation Flying Missions
  9. Chapter 2: Fundamental Astrodynamics
    1. Publisher Summary
    2. 2.1 Coordinate Systems
    3. 2.2 The Keplerian Two-body Problem
    4. 2.3 Solution of the Inertial Equations of Motion
    5. 2.4 Nonsingular Orbital Elements
    6. 2.5 Non-Keplerian Motion and Orbital Perturbations
    7. 2.6 Averaging Theory
    8. SUMMARY
  10. Chapter 3: The Basics of Analytical Mechanics, Optimization, Control and Estimation
    1. Publisher Summary
    2. 3.1 Lagrangian and Hamiltonian Mechanics
    3. 3.2 The Delaunay Elements
    4. 3.3 Canonical Transformations
    5. 3.4 Brouwer Theory
    6. 3.5 Constrained Static Optimization
    7. 3.6 Control Lyapunov Functions
    8. 3.7 Linear Quadratic Regulation
    9. 3.8 Kalman Filtering
    10. 3.9 The Unscented Kalman Filter
    11. SUMMARY
  11. Chapter 4: Nonlinear Models of Relative Dynamics
    1. Publisher Summary
    2. 4.1 Equations of Relative Motion in the Unperturbed Case
    3. 4.2 The Energy Matching Condition
    4. 4.3 Impulsive Formation-keeping
    5. 4.4 Another Outlook on Optimal Formation-keeping
    6. 4.5 Circular Chief Orbit
    7. 4.6 Lagrangian and Hamiltonian Derivations
    8. 4.7 Equations of Relative Motion under the Influence of <img xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" src="images/B9780750685337002098/si1049_e.gif" alt="si1049_e"></img>
    9. SUMMARY
  12. Chapter 5: Linear Equations of Relative Motion
    1. Publisher Summary
    2. 5.1 The Clohessy–Wiltshire Equations
    3. 5.2 Two-impulse Linear Rendezvous
    4. 5.3 Lagrangian and Hamiltonian Derivations of the CW Equations
    5. 5.4 Accommodating second-order nonlinearities
    6. 5.5 Curvilinear vs. Cartesian Relative Coordinates
    7. 5.6 Elliptic Reference Orbits
    8. 5.7 Periodic Solutions to the TH Equations
    9. SUMMARY
  13. Chapter 6: Modeling Relative Motion Using Orbital Elements
    1. Publisher Summary
    2. 6.1 General Solution to the Nonlinear Relative Motion Equations
    3. 6.2 Bounds on Maximal and Minimal Distances
    4. 6.3 Relative Motion Approximations with a Circular-Equatorial Reference Orbit
    5. 6.4 Establishing the PCO Initial Conditions
    6. 6.5 Hybrid Differential Equations with Nonlinearity Compensation for Unperturbed Circular Orbits
    7. SUMMARY
  14. Chapter 7: Modeling Perturbed Relative Motion Using Orbital Elements
    1. Publisher Summary
    2. 7.1 The Unit-Sphere Approach
    3. 7.2 Relative Motion Description using Quaternions
    4. 7.3 The Gim–Alfriend Geometric Method
    5. 7.4 Averaged Relative Motion
    6. 7.5 Linearized <img xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" src="images/B9780750685337002128/si2272_e.gif" alt="si2272_e"></img>-Differential Equations for Circular Orbits-Differential Equations for Circular Orbits
    7. 7.6 Differential Equations from the Gim–Alfriend STM
    8. 7.7 A Second-Order State Propagation Model
    9. SUMMARY
  15. Chapter 8: Perturbation Mitigation
    1. Publisher Summary
    2. 8.1 Dynamic Constraints for <img xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" src="images/B978075068533700213X/si2459_e.gif" alt="si2459_e"></img> Mitigation Mitigation
    3. 8.2 A Nonlinear Theory based on Orbital Elements
    4. 8.3 Dynamic Model Error Effect Comparison
    5. 8.4 Perturbed Fundamental Frequencies for Formations in Near-circular Orbits
    6. 8.5 Selection of the PCO Initial Conditions for Near-Circular Orbits
    7. 8.6 Matching the In-plane and Cross-track Fundamental Frequencies
    8. 8.7 PCO Formation Maintenance based on the Modified CW Equations
    9. 8.8 Fuel Minimization and Balancing
    10. SUMMARY
  16. Chapter 9: Rotation-Translation Coupling
    1. Publisher Summary
    2. 9.1 Relative Dynamics
    3. 9.2 Kinematically-Coupled Relative Spacecraft Motion Model
    4. SUMMARY
  17. Chapter 10: Formation Control
    1. Publisher Summary
    2. 10.1 Continuous Control
    3. 10.2 Discrete-time LQR Control
    4. 10.3 Impulsive Control based on Gauss’ Variational Equations
    5. 10.4 Two-impulse Formation Reconfiguration for Circular Orbits
    6. 10.5 Two-impulse-per-orbit Formation Maintenance
    7. SUMMARY
  18. Chapter 11: Implementation of Δυ Commands
    1. Publisher Summary
    2. 11.1 Plan Implementation
    3. 11.2 Impact on Autonomous Rendezvous and Docking
    4. SUMMARY
  19. Chapter 12: Relative Measurements and Navigation
    1. Publisher Summary
    2. 12.1 Dynamical Modeling
    3. 12.2 Measurement Update: Carrier-Phase Differential GPS
    4. 12.3 Comparison of EKF and UKF for Relative Navigation
    5. SUMMARY
  20. Chapter 13: High-Fidelity Formation Flying Simulation
    1. Publisher Summary
    2. 13.1 Simulation Controller Configuration
    3. 13.2 Simulation Results
    4. SUMMARY
  21. Chapter 14: Summary and Future Prospects
    1. Publisher Summary
    2. 14.1 Risk Reduction
    3. 14.2 Fuel Requirements
    4. 14.3 Mission Operations
  22. Appendices
    1. A The Transformation Matrix <img xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" src="images/B9780750685337002207/si3774_e.gif" alt="si3774_e"></img>
    2. B The Transformation Matrix <img xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" src="images/B9780750685337002207/si3814_e.gif" alt="si3814_e"></img>
    3. C The Matrix <img xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" src="images/B9780750685337002207/si3849_e.gif" alt="si3849_e"></img>
    4. D The State Transition Matrix for Relative Mean Elements
    5. E Transformation from Mean to Osculating Elements
    6. F Jacobian for Mean to Osculating Elements
    7. G Small Eccentricity Theory
    8. H Yan-Alfriend Nonlinear Theory Coefficients
  23. References
  24. Subject Index