Optimal reconfiguration of a tetrahedral formation via a gauss pseudospectral method

Advances in the Astronautical Sciences

Volumn 123 II, Issue , 2006, Pages 1337-1358

  Huntington, Geoffrey T ^a,b,c   Rao, Anil V ^d  

^a Draper Laboratory   (United States)

^b Guidance and Navigation Division

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^d CHARLES STARK DRAPER LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GAUSS PSEUDOSPECTRAL METHOD; OPTIMAL RECONFIGURATION; PROPULSIVE MANEUVERS; TETRAHEDRAL FORMATION;

COMPUTATIONAL METHODS; CONSTRAINT THEORY; NONLINEAR CONTROL SYSTEMS; OPTIMAL CONTROL SYSTEMS; ORBITS; PROBLEM SOLVING; SPACECRAFT PROPULSION;

SPACECRAFT;

EID: 33749322248     PISSN: 00653438     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (40)

1. Scharf, D. P., Hadaegh, F. Y., and Ploen, S. R., "A Survey of Spacecraft Formation Flying Guidance and Control (Part II): Control," Proceedings of the American Control Conference, Boston, MA, pp. 2976-2985, 2004.
2. Scharf, D. P., Hadaegh, F. Y., and Ploen, S. R., "A Survey of Spacecraft Formation Flying Guidance and Control (Part I): Guidance," Proceedings of the American Control Conference, Denver, CO, pp. 1733-1739, 2003.
3. Guzman, J., Schiff, C., "A Preliminary Study for a Tetrahedron Formation: Quality Factors and Visualization," AIAA Guid, Nav, & Contr, Conf., 2002
4. Hughes, S. "Formation Tetrahedron Design for Phase 1 of the Magnetospheric Multiscale Mission," Flight Dynamics Analysis Branch, NASA Goddard Space Flight Center, 2004.
5. Gim, D., Alfriend, K., "Criteria for Best Configuration and Sub-optimal Reconfiguration for MMS Mission," AAS Spaceflight Mechanics Meeting, Maul, HI, Feb., 2004.
6. Breger, L., et. al."Distributed Control of Formation Flying Spacecraft Build on OA," AIAA Guidance, Nav, & Control Conference, Austin, TX, Aug 2003.
7. Clemente, D., Atkins, E., "Optimization of a Tetrahedral Satellite Formation," AIAA Guidance, Nav, & Control Conference, Aug 2004.
8. Huntington, G. T., and Rao, A. V., "Optimal Configuration of Spacecraft Formations via a Gauss Pseudospectral Method," AAS Spaceflight Mechanics Meeting, AAS 05-103, Copper Mountain, CO, Jan 2005.
9. Mailhe, Laurie M., Guzman, Jose J., "Initialization and Resizing of Formation Flying using Global and Local Optimization Methods," Proceedings of the IEEE Aerospace Conference, Big Sky, Montana, paper #1425, 2004.
10. Guzman, Jose J. "Tetrahedron Formation Control," Journal of the Astronautical Sciences, Vol. 51, No. 4, pp. 419-431, 2003.
11. Tsuda, Y., "Global Optimization of Maneuver Schedule for Multiple Spacecrafts Flying in Formation," 55th International Astronautical Congress, Vancouver, Canada, IAC-04-A.2.01, 2004.
12. Betts, J. T., "Survey of Numerical Methods for Trajectory Optimization," Journal of Guidance, Control, and Dynamics, Vol. 21, No. 2, 1998, pp. 193-207.
13. Athans, M. and Falb, P. L., Optimal Control, McGraw-Hill, New York, 1966, pp. 284-351.
14. Betts, J. T., Practical Methods for Optimal Control Using Nonlinear Programming, Society for Industrial and Applied Mathematics Press, 2001.
15. Betts, J. T. and Frank, P. D., "A Sparse Nonlinear Optimization Algorithm," Journal of Optimization Theory and Applications, Vol. 82, pp. 519-541, 1994.
16. Gill, P. E., Murray, W., and Saunders, M. A., "SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization," SIAM Journal on Optimization, Vol. 12, No. 4, 2002, pp. 979-1006.
17. Hargraves, C. R. and Paris, S. W., "Direct Trajectory Optimization Using Nonlinear Programming and Collocation," Journal of Guidance, Control, and Dynamics, Vol. 10, No. 4, 1987, pp. 338-342.
18. Williams, P., "A Comparison of Differentiation and Integration Based Direct Transcription Methods", AAS/AIAA Space Flight Mechanics Conference, Copper Mountain, CO, Jan. 23-27, 2005. Paper AAS 05-128.
19. Vlases, W. G., Paris, S. W., Lajoie, R. M., Martens, M. J., and Hargraves, C. R., "Optimal Trajectories by Implicit Simulation," Boeing Aerospace and Electronics, Technical Report WRDC-TR-90-3056, Wright-Patterson Air Force Base, 1990.
20. Betts, J. T. and Huffman, W. P., "Sparse Optimal Control Software - SOCS," Mathematics and Engineering Analysis Library Report, MEA-LR-085, Boeing Information and Support Services, P. O. Box 3797, Seattle, WA, 98124-2297, 15 July 1997.
21. Well, K., Graphical Environment for Simulation and Optimization, Department of Optimization, Guidance, and Control, Stuttgart, Germany, 2002.
22. Von Stryk, O., "User's Guide for DIRCOL 2.1: A Direct Collocation Method for the Numerical Solution of Optimal Control Problems," Technische Universitat Darmstadt, 1999.
23. Ross, I. M., "User's Manual for DIDO (Ver. PR.1β): A MATLAB Application Package for Solving Optimal Control Problems", Technical Report 04-01.0, February 2004.
24. Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A., Spectral Methods in Fluid Dynamics, Springer-Verlag, New York, 1988.
25. Elnagar, G., Kazemi, M., Razzaghi, M., "The Pseudospectral Legendre Method for Discretizing Optimal Control Problems," IEEE Transactions on Automatic Control, Vol. 40, No. 10, October 1995.
26. Fahroo, F. and Ross, I. M., "Co-state Estimation by a Legendre Pseudospectral Method," Journal of Guidance, Control, and Dynamics, Vol. 24, No. 2, March-April 2002, pp. 270-277.
27. Fahroo, F. and Ross, I. M., "Direct Trajectory Optimization by a Chebyshev Pseudospectral Method," Journal of Guidance, Control, and Dynamics, Vol. 25, No. 1, January-February 2002, pp. 160-166.
28. Williams, P., "Jacobi Pseudospectral Method for Solving Optimal Control Problems", Journal of Guidance, Vol. 27, No. 2,2003
29. Williams, P., "Hermite-Legendre-Gauss-Lobatto Direct Transcription Methods in Trajectory Optimization", AAS/AIAA Space Flight Mechanics Conference, Copper Mountain, CO, Jan 23-27, 2005. Paper AAS 05-131.
30. Rao, A. V. and Clarke, K. A., "Performance Optimization of a Maneuvering Re-entry Vehicle Using a Legendre Pseudospectral Method," 2002 AIAA Atmospheric Flight Mechanics Conference, AIAA Paper 2002-4885, Monterey, CA August 5-8, 2002.
31. Stanton, S. and Proulx, R., "Optimal Orbital Transfer Using a Legendre Pseudospectral Method," AAS/AIAA Astrodynamics Specialist Conference, AAS-03-574, Big Sky, Montana, August 3-7, 2003.
32. Ross, I., King, J., and Fahroo, F., "Designing Optimal Spacecraft Formations," 2002 AIAA/AAS Astrodynamics Specialist Conference, AIAA Paper 2002-4635, Monterey, CA, August 5-8, 2002.
33. Ross, I. M. and D'Souza.C., "Hybrid Optimal Control Framework for Mission Planning," Journal of Guidance, Control, and Dynamics, Vol. 28,No. 4 July-August 2005.
34. Benson, D., A Gauss Pseudospectral Transcription for Optimal Control, Ph.D. Dissertation, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, November 2004.
35. rd Edition, Microcosm Press, El Segundo, CA and Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999, p. 694.
36. Battin, R. H., An Introduction to the Mathematics and Methods of Astrodynamics, AIAA Press, New York, 1987, pp. 490-493 and p. 119.
37. Robert, P., et.al., "Tetrahedron Geometric Factors," Analysis Methods for Multi-Spacecraft Data (G. Paschmann and P. Daly, eds.), pp. 323-348, Nordwijk, The Netherlands: ISSI Report SR-001, ESA Publications Division, 1998.
38. Hull, D. G., Optimal Control Theory for Applications, Springer-Verlag, New York, 2003.
39. Kirk, D. E., Optimal Control Theory, Prentice-Hall, Englewood Cliffs, NJ, 1970.
40. Gill, P.E., Users Guide for SNOPT Version 7, A Fortran Package for Large-Scale Nonlinear Programming, University of California, San Diego, La Jolla, CA, Sept 04.