Authors

Abstract

In this work the coupled nonlinear problem of optimal spacecraft rendezvous and docking (RVD) is addressed. In most of the previous studies on the subject of optimal RVD, decoupling is presumed to exist between the trajectory translational and the attitude motions and hence the optimal coupled analysis has not been yet addressed properly. However there are circumstances where these two motions are in fact coupled and interdependent and one such situation is investigated and analyzed in this article. By utilizing thrusters for the translational control and reaction wheels for the attitude control, one can uncouple the translational and rotational control to a high degree of approximation. However it can be shown that due to even very small thrust misalignments, the uncoupled problem changes to a highly coupled one. In this article, the nonlinear rendezvous and docking problem is assumed to be coupled and its optimal fuel-trajectory closed loop solution is obtained using two approaches of local linearization and Gauss Pseudospectral methods. Therefore the designed controllers are able to handle the highly nonlinear coupled rendezvous and docking optimally in the presence of system uncertainties as well as environmental disturbances. The results of the two solution approaches and their pertinent control strategies are compared and the merits and weaknesses of each are fully analyzed. Finally, a sensitivity analysis is also performed that shows the effects of thrust misalignments levels on the final state diversions.

Keywords

  1. Mengali, G. and Quarta, A. A., “Fuel Optimal Power Limited Rendezvous With Variable Thruster Efficiency,” Journal of Guidance, Control and Dynamics, Vol. 28, No. 6, 2005, pages, 1194–1199.
  2. Bevilacqua, R., Romano, M. and Yakimenko, O., “Online Generation of Quasi-Optimal Spacecraft Rendezvous Trajectories”, Science Direct, Acta Astronautica, 64, No. 2-3, 2008, pages 345-358.
  3. Carter, T. E., “Optimal Power-Limited Rendezvous of a Spacecraft with Bounded Thrust and General Linear Equations of Motion”, Springer, Journal of Optimization Theory and Applications, 87, No. 3/December, 1995, pages 487-515.
  4. Frieland, B. and Cohen, V., “Quasi-Optimum Control for Minimum-Time Rendezvous”, IEEE Transactions on Automatic Control, 11, Issue3, 1966, ISSN: 0018-9286, pages 525-528.
  5. Bevilaqua, R. and Romano, M., “Fuel Optimal Spacecraft Rendezvous With Hybrid on-off Continuous and Impulsive Thrust”, AIAA Journal of Guidance, Control and Dynamics, Vol. 30, No. 4, 2007, pages 1175-1178.
  6. Miele, A., Weeks, M.W. and Ciarcia, M. “Optimal Trajectories for Spacecraft Rendezvous”, Springer, Journal of Optimization Theory and Applications, 132, No. 3, 2007, pages 353-376(24).
  7. Alfriend, K. T. and Kashiwang, Y. “Minimum Time Orbital Rendezvous Between Neighboring Elliptic Orbits”, Springer, Journal of Optimization Theory and Applications, 4, No. 4, 1969, pages 260-276.
  8. Taur, D. R., Coverstone-Carroll and Prussing, E., “Optimal Impulsive Time Fixed Orbital Rendezvous and Interception With Path Constraints” Journal of Guidance, Control and Dynamics, 18, No. 1, 1995, page 54.
  9. Park, C. Guibout, V. and J. Scheeres, D. “Solving Optimal Continuous Thrust Rendezvous Problems with Generating Functions” Journal of guidance, control and dynamics, 29, No. 2, 2006, pages 321-331.
  10. Luo,Y. Z., Tang, G. J. and Li, H.Y., “Optimization of Multiple-Impulse Minimum Time Rendezvous Using Hybrid Genetic Algorithm”, Science Direct, Acta Astronautica,, 10, No. 6, 2006, pages 534-540
  11. kim, Y. H. and Spencer, D. B., “Optimal Spacecraft Rendezvous Using Genetic Algorithm,” Journal of Guidance, Control and Dynamics, Vol. 39, No. 6, 2002, pages 859-865.
  12. Luo, Y. Z., Tang, G. J., “Spacecraft Optimal Rendezvous Controller Using Simulated Annealing”, Aerospace Science and Technology, 9, Issue 8, 2005, pages 732-737
  13. Lous, Y. Z., Lei, Y. J. and Tang, G. J., “Optimal Multi-Objective Impulsive Linear Rendezvous,” Journal of Guidance, Control and Dynamics, Vol. 30, No. 2, 2007, page 383.
  14. Lous, Y. Z., Lei, Y. J. and Tang., G. J., “Optimal Multi-Objective Impulsive Nonlinear Rendezvous,” Journal of Guidance, Control and Dynamics, Vol. 30, No. 4, 2007, page 994.
  15. Tang, G. J. Luo, Y. Z. and Li, H. Y. “Optimal Robust Linearized Impulsive Rendezvous”, Science Direct, Acta Astronautica, 11, No. 7-8, 2007, pages 563-569.
  16. Moradi, R., Nobahari, H. and Pourtakdoust, S. H., “Optimal Control of Spacecraft Rendezvous Using Multi Objective and Colony Optimization”, AIAA southern California Aerospace systems and technology conference,
  17. Park, J. U., Choi, K. H. and Lee, S., “Orbital Rendezvous Using Two-Step Sliding Mode Control”, Aerospace Science and Technology, 3, No. 4, 1999, pages 239-245.
  18. Matsumoto, Sh., Jacobsen, S., Dubowsky, S. and Ohkami, “Approach Planning and Guidance for Uncontrolled Rotating Satellite Capture Considering Collision Avoidance”, Proceeding of the 7th International Symposium on Artificial Intelligence, Robotics and Automation in Space, I-SAIRAS 2003, NARA, Japan, May 19-23, 2003.
  19. Jacobsen, S., Lee, Ch., Zhu, C., and Dubowsky, S., “Planning of Safe Kinematic Trajectories for The Free Flying Robots Approaching an Uncontrolled Spinning Satellite”, Proceedings of 02ASME 2002 Design Engineering Technical Conferences and Computers and Information in Engineering Conference Montreal, Canada, 2002.
  20. Louis S. Breger, Jonathan P How., “Safe Trajectories for Autonomous Rendezvous of Spacecraft” Journal of guidance, control and dynamics, Vol. 31, No. 5, 2008, pages 1478-1489.
  21. Zeng Y. and Singh, S. N., “Dynamic Feedback Linearizing Attitude Control of Spacecraft with Uncertain Dynamics”, AIAA Guidance, Navigation and Control, Conference and Exhibit, 1998- 4229.
  22. Wei, B., and Barba, P. M. “Quaternion Feedback for Spacecraft Large Angle Maneuvers” Journal of guidance, Control, and Dynamics, 8, 1985, 360-365.
  23. Wei, B., Weiss, H., and Arapostathis “Quaternion Feedback Regulator for Spacecraft Eigenaxis Rotation” Journal of Guidance, Control, and Dynamics, 128, 1989, 375-380.
  24. Tsiotras, P. “New Control Laws for the Attitude Stabilization of Rigid Bodies” Proceedings, IFAC Symposium on Automatic Control in Aerospace, Palo Alto, CA, Sept.1994, 316-321.
  25. Tsiotras, P, “A Passivity Approach to Attitude Stabilization Using Non redundant Kinematic Parameterizations”, Proceedings of the 34th Conference on Decision and Control, New Orleans, LA, Dec.1995, 515-520.
  26. Wei, B., and Lu, J, “Feedback Control Logic for Spacecraft Eigenaxis Rotations Under Slow Rate and Control Constraints”, Journal of Guidance, Control and Dynamics, 18, No.6, Nov.-Dec.1995, 1372-1379.
  27. Dwyer, T. A. W, “Exact Nonlinear Control of Large Angle Rotational Maneuvers”, IEEE Transactions on Automatic Control, AC-29, Sept.1984, 769-774.
  28. Singh, S. N., and De Araujo, A. D, “Asymptotic Reproducibility in Nonlinear Systems and Attitude Control of Gyrostat”, IEEE Transactions on Aerospace and Electronic Systems, 20, No.2 March 1984, 94-103.
  29. Chen, Y. P., and Lo, S. C, “Sliding Mode Controller Design for Spacecraft Attitude Tracking Maneuvers”, IEEE Transactions on Aerospace and Electronic Systems, 29, No.4, Oct. 1993, 1328-1333.
  30. Singh, S. N, “Nonlinear Adaptive attitude control of spacecraft”, IEEE Transactions on Aerospace and Electronic Systems, 23, No.3, 1987, 371-379
  31. Slotine, J. J. E., and Di Benedetto, M. D, Hamiltoman, “Adaptive Control of Spacecraft”, IEEE Transactions on Automatic Control, 35, No.7, 1990, 848-852.
  32. Cristi, R., Burl, J., and Russo, N, “Adaptive Quaternion Feedback Regulation of Eigen axis Rotations”, Journal of Guidance, Control and Dynamics, 17, No.6 Nov.-Dec.1994,
  33. Antony Satyadas and K. Krishnakumar, “GA-optimized Fuzzy Controller for Spacecraft Attitude Control”, IEEE Transactions on Automatic Control, SN: 0-7803-1896-X/94.
  34. Kwan, C. M., H. Xu, Lewis, F. L., Haynes, L. and Pryor, J. D., "Robust Spacecraft Attitude Control Using Fuzzy CMAC", Proceedings of the 1996 IEEE International Symposium on Intelligent Control Dearborn, MI September 15-18,1996.
  35. Liang, , “Time-Optimal Magnetic Attitude Control for Small Spacecraft”, 43rd IEEE Conference on Decision and Control, December 14-17, 2004, Atlantis, Paradise Island, Bahamas.
  36. Kim, J. and Crassidis, J.,"Spacecraft Attitude Control Using Approximate Receding-Horizon Model-Error Control Synthesis", Journal of guidance, Control and dynamics, Vol. 29, No. 5, September-October 2006, pages 1023-1031.
  37. Luo, W., Chu, YC. and Ling, KV., “HInverse Optimal Attitude-Tracking Control of Rigid Spacecraft”, Journal of Guidance, Navigation and Dynamics, Vol. 28. No. 3, May-June 2005, page 481-494.
  38. Li, Z. and Wang, B. “Robust Attitude Tracking Control of Spacecraft in the Presence of Disturbances”, Journal of Guidance Control and Dynamics, 2007, page 1156.
  39. Singla, , Subbarao, K., Hughes, D. and L. Junkins, J., “Structured Model Reference Adaptive Control for Vision Based Spacecraft Rendezvous and Docking”, Advances in the Astronautical Sciences, AAS/AIAA Spaceflight Mechnics Meeting, Punce, Puetro Rico, Vol. 114, 2003, pages 55-75.
  40. Philipa, N. K. and Ananthasayanam, M. R., "Relative Position and Attitude Estimation and Control Schemes for the Final Phase of an Autonomous Docking Mission of Spacecraft", Acta Astronautica, Vol. 52, No.7, 2003, pages 511 – 522.
  41. Irvin, D. and Captain, Jr.,"A Study of Linear Vs. Nonlinear Control Techniques for the Reconfiguration of Satellite Formations", Wright-Patterson Air Force Base, Ohio, Advances in the Astronautical Sciences, 2002.
  42. Sidi, M. J., Spacecraft Dynamics and Control, Cambridge Aerospace Series 2000.
  43. Pourtakdoust, S.H. and Moradi, R., Optimal Control of Coupled Spacecraft Rendezvous and Docking, Master Thesis, Sharif University of Technology, Aerospace Engineering Department, 2010.
  44. Benson, D. A., A Gauss Pseudo spectral Transcription for Optimal Control, D. Dissertation, Department of Aeronautics and Astronautics, MIT, November 2004.
  45. Benson, D. A., Huntington, G. T., Thorvaldsen, T. P. and Rao, A. V., "Direct Trajectory Optimization and Costate Estimation via an Orthogonal Collocation Method", Journal of Guidance, Control, and Dynamics, Vol. 29, No. 6, November-December, 2006, Page 1435–1440.
  46. Davis, P., Interpolation and Approximation, Dover Publications, 1975.
  47. Kirk, D. E., Optimal Control Theory, Dover Publications, 1970.