Book contents
- Frontmatter
- Contents
- Preface
- 1 The Problem of Spacecraft Trajectory Optimization
- 2 Primer Vector Theory and Applications
- 3 Spacecraft Trajectory Optimization Using Direct Transcription and Nonlinear Programming
- 4 Elements of a Software System for Spacecraft Trajectory Optimization
- 5 Low-Thrust Trajectory Optimization Using Orbital Averaging and Control Parameterization
- 6 Analytic Representations of Optimal Low-Thrust Transfer in Circular Orbit
- 7 Global Optimization and Space Pruning for Spacecraft Trajectory Design
- 8 Incremental Techniques for Global Space Trajectory Design
- 9 Optimal Low-Thrust Trajectories Using Stable Manifolds
- 10 Swarming Theory Applied to Space Trajectory Optimization
- Index
- References
1 - The Problem of Spacecraft Trajectory Optimization
Published online by Cambridge University Press: 06 December 2010
Edited by
Book contents
- Frontmatter
- Contents
- Preface
- 1 The Problem of Spacecraft Trajectory Optimization
- 2 Primer Vector Theory and Applications
- 3 Spacecraft Trajectory Optimization Using Direct Transcription and Nonlinear Programming
- 4 Elements of a Software System for Spacecraft Trajectory Optimization
- 5 Low-Thrust Trajectory Optimization Using Orbital Averaging and Control Parameterization
- 6 Analytic Representations of Optimal Low-Thrust Transfer in Circular Orbit
- 7 Global Optimization and Space Pruning for Spacecraft Trajectory Design
- 8 Incremental Techniques for Global Space Trajectory Design
- 9 Optimal Low-Thrust Trajectories Using Stable Manifolds
- 10 Swarming Theory Applied to Space Trajectory Optimization
- Index
- References
Summary
Introduction
The subject of spacecraft trajectory optimization has a long and interesting history. The problem can be simply stated as the determination of a trajectory for a spacecraft that satisfies specified initial and terminal conditions, that is conducting a required mission, while minimizing some quantity of importance. The most common objective is to minimize the propellant required or equivalently to maximize the fraction of the spacecraft that is not devoted to propellant. Of course, as is common in the optimization of continuous dynamical systems, it is usually necessary to provide some practical upper bound for the final time or the optimizer will trade time for propellant. There are also spacecraft trajectory problems where minimizing flight time is the important thing, or problems, for example those using continuous thrust, where minimizing flight time and minimizing propellant use are synonymous.
Except in very special (integrable) cases, which reduce naturally to parameter optimization problems, the problem is a continuous optimization problem of an especially complicated kind.
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- Chapter
- Information
- Spacecraft Trajectory Optimization , pp. 1 - 15Publisher: Cambridge University PressPrint publication year: 2010
References
[1] et al. (1989) Galileo 1989 VEEGA Trajectory Design, Journal of the Astronautical Sciences, 37, 281–306.Google Scholar
[2] , and (1998) Optimal Formation-Reconfiguration for Multiple Spacecraft, AIAA-1998-4226, AIAA Guidance, Navigation, and Control Conference and Exhibit, Boston, MA, Collection of Technical Papers. Pt. 2 (A98-37001 10–63)Google Scholar
[3] , and (2008) Optimal Interception of Evasive Missile Warheads: Numerical Solution of the Differential Game, Journal of Guidance, Control and Dynamics, 31, 1111–1122.Google Scholar
[4] , and (2005) New Methods in Celestial Mechanics and Mission Design, Bulletin of the American Mathematical Society, 43, 43–73.CrossRefGoogle Scholar
[5] , , and (2007) Combined Optimal Low-Thrust and Stable-Manifold Trajectories to the Earth-Moon Halo Orbits, New Trends in Astrodynamics and Applications III, (ed.) 100–110.Google Scholar
[6] , and (2009) Optimal Strategies Found Using Genetic Algorithms for Deflecting Hazardous Near-Earth Objects, IEEE Congress on Evolutionary Computation, Trondheim, Norway.CrossRefGoogle Scholar
[7] (1997) Optimal Low-Thrust Interception of Earth-Crossing Asteroids, J. of Guidance, Control, and Dynamics, 20, 995–1002.CrossRefGoogle Scholar
[9] (1997) Reformulation of Edelbaum's Low-Thrust Transfer Problem Using Optimal Control Theory, J. of Guidance, Control and Dynamics, 20, 988–994.CrossRefGoogle Scholar
[10] (2000) Minimum-Time Constant Acceleration Orbit Transfer With First-Order Oblateness Effect, Journal of Guidance, Control, and Dynamics, 23, 595–603.CrossRefGoogle Scholar
[11] , and (1975) Applied Optimal Control, Revised Printing, Hemisphere Publ., Washington, DC.Google Scholar
[12] , and (1987) Direct Trajectory Optimization Using Nonlinear Programming and Collocation, Journal of Guidance, Control, and Dynamics, 10, 338–342.CrossRefGoogle Scholar
[13] , and (1996) Direct Optimization Using Collocation Based on High-Order Gauss-Lobatto Quadrature Rules, Journal of Guidance, Control, and Dynamics, 19, 592–599CrossRefGoogle Scholar
[14] , and (1992) Discrete Approximations to Optimal Trajectories Using Direct Transcription and Nonlinear Programming, Journal of Guidance, Control, and Dynamics, 15, 994–1002.CrossRefGoogle Scholar
[15] (1998) Survey of Numerical Methods for Trajectory Optimization, Journal of Guidance, Control and Dynamics, 21, 193–207.CrossRefGoogle Scholar
[16] (1989) Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley Publ., Reading, MA.Google Scholar
[17] , and (1968) The Primer Vector on Fixed-Time Impulsive trajectories, AIAA Journal, 6, 127–132.Google Scholar
[18] , and (2004) Shape-Based Algorithm for Automated Design of Low-Thrust, Gravity-Assist Trajectories, Journal of Spacecraft and Rockets, 41, 787–796.CrossRefGoogle Scholar
[19] , and (2009) Shape-Based Approach to Low-Thrust Trajectory Design, Journal of Guidance, Control and Dynamics, 32, 95–101.CrossRefGoogle Scholar
[21] (1991) Simple Proof of the Global Optimality of the Hohmann Transfer, Journal of Guidance, Control, and Dynamics, 15, 1037–1038.CrossRefGoogle Scholar
[22] , (1963) An Analytic Proof that the Hohmann-Type Transfer is the True Minimum Two-Impulse Transfer, Astronautica Acta, 9, 1–11.Google Scholar
[23] (1995) Improved Collocation Methods Used for Direct Trajectory Optimization, Ph.D. Thesis, University of Illinois at Urbana-Champaign.
[24] , and (1968) An Efficient Method for Calculating Optimal Free-Space N-Impulse Trajectories, AIAA Journal, 6, 2160–2165.CrossRefGoogle Scholar
[25] , and (2004) A Review of Some Exact Solutions to the Planar Equations of Motion of a Thrusting Spacecraft, DSpace at JPL, http://hdl.handle.net/2014/8673
[26] , and (1984) Optimal Low-Thrust Transfers to Synchronous Orbit, Journal of Guidance, Control, and Dynamics, 7, 148–155.CrossRefGoogle Scholar
[27] (1957) The Numerical Solution of Two-Point Boundary Problems, Oxford Press, New York.Google Scholar
[28] (1968) Numerical Methods for Two-Point Boundary Value Problems, Blaisdell, New York.Google Scholar
[29] (2006) Mystic: Implementation of the Static Dynamic Optimal Control Algorithm for High-Fidelity, Low-Thrust Trajectory Design, http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/40782/1/06-2356.pdf
[30] , and (2002) Application of the SDC Optimal Control Algorithm to Low-Thrust Escape and Capture Including Fourth Body Effects, Second International Symposium on Low Thrust Trajectories, Toulouse, France.Google Scholar
[31] , and (2006) Solving Two-Point Boundary Value Problems Using Generating Functions: Theory and Applications to Astrodynamics, in Modern Astrodynamics, (ed.), Elsevier, Amsterdam, 53–105.CrossRefGoogle Scholar
[32] , , and (2003) Solving Optimal Control Problems with Generating Functions, Paper AAS 03-575.
[33] , , and (1970) Theory of Optimal Control and Mathematical Programming, McGraw-Hill, New York.Google Scholar
[34] , and (1975) Approximate Solution of Optimal Control Problems Using Third-Order Hermite Polynomial Functions, Proceedings of the 6th Technical Conference on Optimization Techniques, IFIP-TC7, Springer–Verlag, New York.Google Scholar
[35] , , and (2005) SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization. SIAM Review, 47, 99–131.CrossRefGoogle Scholar
[36] et al. (1993) User's Guide for NZOPT 1.0: A Fortran Package For Nonlinear Programming, McDonnell Douglas Aerospace, Huntington Beach, CA.Google Scholar
[37] , , and (2006) Enhanced Procedures for Direct Trajectory Optimization Using Nonlinear Programming and Implicit Integration, Paper AIAA-2006-6309, AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Keystone, Colorado.CrossRefGoogle Scholar
[38] , and (1997) Sparse Optimal Control Software SOCS, Mathematics and Engineering Analysis Technical Document, MEA-LR-085, Boeing Information and Support Services, The Boeing Company, Seattle.Google Scholar
[39] , and (2003) Legendre Pseudospectral Approximations of Optimal Control Problems, Lecture Notes in Control and Information Sciences, 295, Springer–Verlag, New York, 327–342.Google Scholar
[40] (2004) User's Manual for DIDO: A MATLAB Application Package for Solving Optimal Control Problems, TOMLAB Optimization, Sweden.Google Scholar
[41] (1992) OTIS-Optimal Trajectories by Implicit Simulation, User's Manual, The Boeing Company.Google Scholar
[42] , , and (1997) ALTOS-A Trajectory Analysis and Optimization Software for Launch and Reentry Vehicles, International Astronautical Federation Paper IAF-97-V4.04.
[43] , , , , and (1999) ALTOSESA's Trajectory Optimization Tool Applied to Reentry Vehicle Trajectory Design, International Astronautical Federation Paper IAF-99-A.6.09
[44] , and (2005) Near-Optimal Low-Thrust Earth-Mars Trajectories Found Via a Genetic Algorithm,” Journal of Guidance, Control, and Dynamics, 28, 1027–1031.CrossRefGoogle Scholar
[45] (2007) Computational Intelligence, 2nd ed., John Wiley & Sons, West Sussex, England.CrossRefGoogle Scholar
[46] , and (1994) Optimization of Very-Low-Thrust, Many Revolution Spacecraft Trajectories, Journal of Guidance, Control, and Dynamics, 17, 1185–1192.CrossRefGoogle Scholar
[47] , and (1998) Optimal Low-Thrust, Earth-Moon Orbit Transfer, Journal of Guidance, Control, and Dynamics, 21, 141–147.CrossRefGoogle Scholar
[48] , and (2003) Optimal Low Thrust Trajectories to the Moon, SIAM Journal on Applied Dynamical Systems, 2, 144–170.CrossRefGoogle Scholar
[49] , and (1995) Optimization of Low-Thrust Interplanetary Trajectories Using Collocation and Nonlinear Programming, Journal of Guidance, Control, and Dynamics, 18, 599–604.CrossRefGoogle Scholar
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