Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-01-13T23:30:38.010Z Has data issue: false hasContentIssue false

1 - The Problem of Spacecraft Trajectory Optimization

Published online by Cambridge University Press:  06 December 2010

By
Bruce A. Conway
Edited by
Bruce A. Conway
Bruce A. Conway
Affiliation:
Dept. of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL
Bruce A. Conway
Affiliation:
University of Illinois, Urbana-Champaign
Get access

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.

Type
Chapter
Information
Spacecraft Trajectory Optimization , pp. 1 - 15
Publisher: Cambridge University Press
Print publication year: 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] D'Amario, L. et al. (1989) Galileo 1989 VEEGA Trajectory Design, Journal of the Astronautical Sciences, 37, 281–306.Google Scholar
[2] Wang, P. K. C., and Hadaegh, F. Y. (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] Pontani, M., and Conway, B. A. (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] Marsden, J. E., and Ross, S. D. (2005) New Methods in Celestial Mechanics and Mission Design, Bulletin of the American Mathematical Society, 43, 43–73.CrossRefGoogle Scholar
[5] Mingotti, G., Topputo, F., and Bernelli-Zazzera, F. (2007) Combined Optimal Low-Thrust and Stable-Manifold Trajectories to the Earth-Moon Halo Orbits, New Trends in Astrodynamics and Applications III, E., Belbruno (ed.) 100–110.Google Scholar
[6] Englander, J., and Conway, B. A. (2009) Optimal Strategies Found Using Genetic Algorithms for Deflecting Hazardous Near-Earth Objects, IEEE Congress on Evolutionary Computation, Trondheim, Norway.CrossRefGoogle Scholar
[7] Conway, B. A. (1997) Optimal Low-Thrust Interception of Earth-Crossing Asteroids, J. of Guidance, Control, and Dynamics, 20, 995–1002.CrossRefGoogle Scholar
[8] Lawden, D. F. (1963) Optimal Trajectories for Space Navigation, Butterworths, London.Google Scholar
[9] Kechichian, J. A. (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] Kechichian, J. A. (2000) Minimum-Time Constant Acceleration Orbit Transfer With First-Order Oblateness Effect, Journal of Guidance, Control, and Dynamics, 23, 595–603.CrossRefGoogle Scholar
[11] Bryson, A. E., and Ho, Y-C. (1975) Applied Optimal Control, Revised Printing, Hemisphere Publ., Washington, DC.Google Scholar
[12] Hargraves, C. R., and Paris, S. W. (1987) Direct Trajectory Optimization Using Nonlinear Programming and Collocation, Journal of Guidance, Control, and Dynamics, 10, 338–342.CrossRefGoogle Scholar
[13] Herman, A. L., and Conway, B. A. (1996) Direct Optimization Using Collocation Based on High-Order Gauss-Lobatto Quadrature Rules, Journal of Guidance, Control, and Dynamics, 19, 592–599CrossRefGoogle Scholar
[14] Enright, P. J., and Conway, B. A. (1992) Discrete Approximations to Optimal Trajectories Using Direct Transcription and Nonlinear Programming, Journal of Guidance, Control, and Dynamics, 15, 994–1002.CrossRefGoogle Scholar
[15] Betts, J. T. (1998) Survey of Numerical Methods for Trajectory Optimization, Journal of Guidance, Control and Dynamics, 21, 193–207.CrossRefGoogle Scholar
[16] Goldberg, D. (1989) Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley Publ., Reading, MA.Google Scholar
[17] Lion, P. M., and Handelsman, M. (1968) The Primer Vector on Fixed-Time Impulsive trajectories, AIAA Journal, 6, 127–132.Google Scholar
[18] Petropoulos, A. E., and Longuski, J. M. (2004) Shape-Based Algorithm for Automated Design of Low-Thrust, Gravity-Assist Trajectories, Journal of Spacecraft and Rockets, 41, 787–796.CrossRefGoogle Scholar
[19] Wall, B. J., and Conway, B. A. (2009) Shape-Based Approach to Low-Thrust Trajectory Design, Journal of Guidance, Control and Dynamics, 32, 95–101.CrossRefGoogle Scholar
[20] Hohmann, W. (1925). Die Erreichbarkeit der Himmelskörper. Verlag Oldenbourg, München.Google Scholar
[21] Prussing, J. E. (1991) Simple Proof of the Global Optimality of the Hohmann Transfer, Journal of Guidance, Control, and Dynamics, 15, 1037–1038.CrossRefGoogle Scholar
[22] Barrar, R. B., (1963) An Analytic Proof that the Hohmann-Type Transfer is the True Minimum Two-Impulse Transfer, Astronautica Acta, 9, 1–11.Google Scholar
[23] Herman, A. L. (1995) Improved Collocation Methods Used for Direct Trajectory Optimization, Ph.D. Thesis, University of Illinois at Urbana-Champaign.
[24] Jezewski, D. J., and Rozendaal, H. L. (1968) An Efficient Method for Calculating Optimal Free-Space N-Impulse Trajectories, AIAA Journal, 6, 2160–2165.CrossRefGoogle Scholar
[25] Petropoulos, A. E., and Sims, J. A. (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] Breakwell, J. V., and Redding, D. C. (1984) Optimal Low-Thrust Transfers to Synchronous Orbit, Journal of Guidance, Control, and Dynamics, 7, 148–155.CrossRefGoogle Scholar
[27] Fox, L. (1957) The Numerical Solution of Two-Point Boundary Problems, Oxford Press, New York.Google Scholar
[28] Keller, H.B. (1968) Numerical Methods for Two-Point Boundary Value Problems, Blaisdell, New York.Google Scholar
[29] Whiffen, G. (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] Whiffen, G. J., and Sims, J. A. (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] Guibout, V. M., and Scheeres, D. J. (2006) Solving Two-Point Boundary Value Problems Using Generating Functions: Theory and Applications to Astrodynamics, in Modern Astrodynamics, Gurfil, P. (ed.), Elsevier, Amsterdam, 53–105.CrossRefGoogle Scholar
[32] Scheeres, D. J., Park, C., and Guibout, V. (2003) Solving Optimal Control Problems with Generating Functions, Paper AAS 03-575.
[33] Canon, M. D., Cullum, C. D., and Polak, E. (1970) Theory of Optimal Control and Mathematical Programming, McGraw-Hill, New York.Google Scholar
[34] Dickmanns, E. D., and Well, K. H. (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] Gill, P., Murray, W., and Saunders, M. A. (2005) SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization. SIAM Review, 47, 99–131.CrossRefGoogle Scholar
[36] Gill, P. E. 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] Paris, S. W., Riehl, J. P., and Sjauw, W. K. (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] Betts, J. T., and Huffman, W. P. (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] Ross, I. M., and Fahroo, F. (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] Ross, I. M. (2004) User's Manual for DIDO: A MATLAB Application Package for Solving Optimal Control Problems, TOMLAB Optimization, Sweden.Google Scholar
[41] Paris, S. (1992) OTIS-Optimal Trajectories by Implicit Simulation, User's Manual, The Boeing Company.Google Scholar
[42] Well, K. H., Markl, A., and Mehlem, K. (1997) ALTOS-A Trajectory Analysis and Optimization Software for Launch and Reentry Vehicles, International Astronautical Federation Paper IAF-97-V4.04.
[43] Wiegand, A., Well, K. H., Mehlem, K., Steinkopf, M., and Ortega, G. (1999) ALTOSESA's Trajectory Optimization Tool Applied to Reentry Vehicle Trajectory Design, International Astronautical Federation Paper IAF-99-A.6.09
[44] Wall, B. J., and Conway, B. A. (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] Engelbrecht, A. P. (2007) Computational Intelligence, 2nd ed., John Wiley & Sons, West Sussex, England.CrossRefGoogle Scholar
[46] Scheel, W. A., and Conway, B. A. (1994) Optimization of Very-Low-Thrust, Many Revolution Spacecraft Trajectories, Journal of Guidance, Control, and Dynamics, 17, 1185–1192.CrossRefGoogle Scholar
[47] Herman, A. L., and Conway, B. A. (1998) Optimal Low-Thrust, Earth-Moon Orbit Transfer, Journal of Guidance, Control, and Dynamics, 21, 141–147.CrossRefGoogle Scholar
[48] Betts, J. T., and Erb, S. O. (2003) Optimal Low Thrust Trajectories to the Moon, SIAM Journal on Applied Dynamical Systems, 2, 144–170.CrossRefGoogle Scholar
[49] Tang, S., and Conway, B. A. (1995) Optimization of Low-Thrust Interplanetary Trajectories Using Collocation and Nonlinear Programming, Journal of Guidance, Control, and Dynamics, 18, 599–604.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×