Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-13T22:30:18.009Z Has data issue: false hasContentIssue false
  • English
  • Français

STOCHASTIC MODEL PREDICTIVE CONTROL FOR SPACECRAFT RENDEZVOUS AND DOCKING VIA A DISTRIBUTIONALLY ROBUST OPTIMIZATION APPROACH

Part of: Miscellaneous topics in calculus of variations and optimal control

Published online by Cambridge University Press:  19 April 2021

ZUOXUN LI Open the ORCID record for ZUOXUN LI [Opens in a new window]  and
KAI ZHANG Open the ORCID record for KAI ZHANG [Opens in a new window]
ZUOXUN LI
Affiliation:
The College of Electrical Engineering, Sichuan University, 610065Chengdu, China; [email protected]
KAI ZHANG*
Affiliation:
The College of Electrical Engineering, Southwest Jiaotong University, 610031Chengdu, China
*
[email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A stochastic model predictive control (SMPC) algorithm is developed to solve the problem of three-dimensional spacecraft rendezvous and docking with unbounded disturbance. In particular, we only assume that the mean and variance information of the disturbance is available. In other words, the probability density function of the disturbance distribution is not fully known. Obstacle avoidance is considered during the rendezvous phase. Line-of-sight cone, attitude control bandwidth, and thrust direction constraints are considered during the docking phase. A distributionally robust optimization based algorithm is then proposed by reformulating the SMPC problem into a convex optimization problem. Numerical examples show that the proposed method improves the existing model predictive control based strategy and the robust model predictive control based strategy in the presence of disturbance.

Keywords

stochastic model predictive controlrendezvous and dockingMonte Carlo

MSC classification

Secondary: 49N10: Linear-quadratic problems
Type
Research Article
Information
The ANZIAM Journal , Volume 63 , Issue 1 , January 2021 , pp. 39 - 57
Check for updates
Copyright
© Australian Mathematical Society 2021

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

Alfriend, K. T., Vadali, S. R., Gurfil, P., How, J. P. and Breger, L. S., Spacecraft formation flying, (Elsevier, Oxford, 2010); doi:10.1016/C2009-0-17485-8.Google Scholar
Batina, I., Stoorvogel, A. A. and Weiland, S., “Stochastic disturbance rejection in model predictive control by randomized algorithms”, Proc. 2001 Amer. Control Conf. (Cat. No. 01CH37148), Arlington, VA, 25–27 June 2001, (IEEE, Arlington, VA, 2001) 732–737; doi:10.1109/ACC.2001.945802.Google Scholar
Blackmore, L., Ono, M., Bektassov, A. and Williams, B. C., “A probabilistic particle-control approximation of chance-constrained stochastic predictive control”, IEEE Trans. Robot. 26 (2010) 502–517; doi:10.1109/TRO.2010.2044948.CrossRefGoogle Scholar
Cairano, S. D., Park, H. and Kolmanovsky, I., “Model predictive control approach for guidance of spacecraft rendezvous and proximity maneuvering”, Internat. J. Robust Nonlinear Control 22 (2012) 1398–1427; doi:10.1002/rnc.2827.CrossRefGoogle Scholar
Calafiore, G. C. and Fagiano, L., “Robust model predictive control via scenario optimization”, IEEE Trans. Automat. Contr. 58 (2012) 219–224; doi:10.1109/tac.2012.2203054.CrossRefGoogle Scholar
Calafiore, G. C. and Ghaoui, L. E., “On distributionally robust chance-constrained linear programs”, J. Optim. Theory Appl. 130 (2006) 1–22; doi:10.1007/s10957-006-9084-x.CrossRefGoogle Scholar
Camacho, E. F. and Bordons, C., Model predictive control, (Springer, London, 1999); doi:10.1007/978-1-4471-3398-8.CrossRefGoogle Scholar
Cannon, M., Kouvaritakis, B. and Wu, X. J., “Model predictive control for systems with stochastic multiplicative uncertainty and probabilistic constraints”, Automatica 45 (2009) 167–172; doi:10.1016/j.automatica.2008.06.017.CrossRefGoogle Scholar
Carter, E. T., “State transition matrices for terminal rendezvous studies: brief survey and new example”, J. Guid. Control Dynam. 21 (1998) 148–155; doi:10.2514/2.4211.CrossRefGoogle Scholar
Deaconu, G., Louembet, C. and Theron, A., “Minimizing the effects of navigation uncertainties on the spacecraft rendezvous precision”, J. Guid. Control Dynam. 37 (2014) 695–700; doi:10.2514/1.62219.CrossRefGoogle Scholar
Farina, M., Giulioni, L. and Scattolini, R., “Stochastic linear model predictive control with chance constraints – a review”, J. Process Control 44 (2016) 53–67; doi:10.1016/j.jprocont.2016.03.005.CrossRefGoogle Scholar
Fehse, W., Automated rendezvous and docking of spacecraft, (Cambridge University Press, Cambridge, 2003); doi:10.1017/CBO9780511543388.CrossRefGoogle Scholar
Gavilan, F., Vazquez, R. and Camacho, E. F., “Chance-constrained model predictive control for spacecraft rendezvous with disturbance estimation”, Control Eng. Pract. 20 (2012) 111–122; doi:10.1016/j.conengprac.2011.09.006.CrossRefGoogle Scholar
Grant, M. and Boyd, S., CVX: Matlab software for disciplined convex programming, version 2.1, 2014.Google Scholar
Hartley, E. N., Trodden, P. A., Richards, A. G. and Maciejowski, J. M., “Model predictive control system design and implementation for spacecraft rendezvous”, Control Eng. Pract. 20 (2012) 695–713; doi:10.1016/j.conengprac.2012.03.009.CrossRefGoogle Scholar
How, J. P. and Tillerson, M., “Analysis of the impact of sensor noise on formation flying control”, Proc. 2001 Amer. Control Conf. (Cat. No. 01CH37148), Arlington, VA, 25–27 June 2001, (IEEE, Arlington, VA, 2001) 3986–3991; doi:10.1109/ACC.2001.946298.CrossRefGoogle Scholar
Jiang, B. Y., Hu, Q. L. and Friswell, M. I., “Fixed-time rendezvous control of spacecraft with a tumbling target under loss of actuator effectiveness”, IEEE Trans. Aerosp. Electron. Syst. 52 (2016) 1576–1586; doi:10.1109/TAES.2016.140406.CrossRefGoogle Scholar
Li, P. and Zhu, Z. H., “Model predictive control for spacecraft rendezvous in elliptical orbit”, Acta Astronaut. 146 (2018) 339–348; doi:10.1016/j.actaastro.2018.03.025.CrossRefGoogle Scholar
Liu, R., Sun, Z. W. and Ye, D., “Adaptive sliding mode control for spacecraft autonomous rendezvous with elliptical orbits and thruster faults”, IEEE Access 5 (2017) 24853–24862; doi:10.1109/ACCESS.2017.2767179.CrossRefGoogle Scholar
Miele, A., Weeks, M. W. and Ciarcià, M., “Optimal trajectories for spacecraft rendezvous”, J. Optim. Theory Appl. 132 (2007) 353–376; doi:10.1007/s10957-007-9166-4.CrossRefGoogle Scholar
Nolet, S., Kong, E., and Miller, D. W., “Autonomous docking algorithm development and experimentation using the SPHERES testbed”, Proc. SPIE, Vol. 5419, Spacecraft Platforms and Infrastructure, Orlando, FL, 30 August 2004, (Society of Photographic Instrumentation Engineers – SPIE, Orlando, FL, 2004) 1–15; doi:10.1117/12.547430.Google Scholar
Wang, P. K. C. and Hadaegh, F. Y., “Formation flying of multiple spacecraft with autonomous rendezvous and docking capability”, IET Control Theory Appl. 1 (2007) 494–504; doi:10.1049/iet-cta:20050411.CrossRefGoogle Scholar
Weiss, A., Baldwin, M., Erwin, R. S. and Kolmanovsky, I., “Model predictive control for spacecraft rendezvous and docking: strategies for handling constraints and case studies”, IEEE Trans. Control Syst. Technol. 23 (2015) 1638–1647; doi:10.1109/TCST.2014.2379639.CrossRefGoogle Scholar
Wie, B., Space vehicle dynamics and control, (American Institute of Aeronautics and Astronautics, Reston, VA, 1998); doi:10.2514/4.103803.Google Scholar
Woffinden, D. C. and Geller, D. K., “Navigating the road to autonomous orbital rendezvous”, J. Spacecr. Rockets 44 (2007) 898–909; doi:10.2514/1.30734.CrossRefGoogle Scholar
Zhu, S. Y., Sun, R., Wang, J. L., Wang, J. H. and Shao, X. W., “Robust model predictive control for multi-step short range spacecraft rendezvous”, Adv. Space Res. 62 (2018) 111–126; doi:10.1016/j.asr.2018.03.037.CrossRefGoogle Scholar