×

Minimal energy maneuvering control of a rigid spacecraft with momentum transfer. (English) Zbl 1120.49036

Summary: The main goal of this study is to investigate a minimal energy rest-to-rest maneuvering control problem with open final time of a rigid spacecraft actuated by three orthogonal momentum wheels. Different from conventional shooting methods, this control problem is formulated and solved as a constrained nonlinear programming (NLP) one by utilizing an iterative procedure. In this novel method, the count of control steps is fixed initially and the sampling period is treated as a variable in the optimization process. An approach to find the initial feasible solutions of the NLP problem is also proposed. Since initial feasible solutions can be found easily, the optimization process of the NLP problem can be started from different points to find the minimal energy rest-to-rest maneuver of the rigid spacecraft between two attitudes. To show the feasibility of the proposed method, simulation results are included for illustration.

MSC:

49N90 Applications of optimal control and differential games
90C30 Nonlinear programming
Full Text: DOI

References:

[1] Vadali, S. R.; Junkins, J. L., Optimal open-loop and stable feedback control of rigid spacecraft attitude maneuvers, J. Astronaut. Sci., 32, 105-122 (1984)
[2] Dixon, M. V.; Edelbaum, T.; E Potter, J.; Vandervelde, W. E., Fuel optimal reorientation of axis symmetric spacecraft, J. Spacecr., 7, 1345-1351 (1970)
[3] Scrivener, S. L.; Thomson, R. C., Survey of time-optimal attitude maneuvers, J. Guidance Control Dyn., 17, 2, 225-233 (1994)
[4] Vadali, S. R.; Kraige, L. G.; Junkins, J. L., New results on the optimal spacecraft attitude maneuver problem, J. Guidance Control Dyn., 7, 3, 378-380 (1984)
[5] Junkins, J. L.; Turner, J. D., Optimal continuous torque attitude maneuvers, J. Guidance Control Dyn., 3, 3, 210-217 (1980)
[6] Li, F.; Bainum, P. M., Numerical approach for solving rigid spacecraft minimum time attitude maneuvers, J. Guidance Control Dyn., 13, 1, 38-45 (1994)
[7] Bourdache-Siguerdidjane, H., Further results on the optimal regulation of spacecraft angular momentum, Optim. Control Appl. Methods, 12, 273-278 (1991) · Zbl 0800.93440
[8] Kumar, K. S., Stabilization of a satellite via specific optimum control, IEEE Trans. Aerosp. Electron. Syst., 2, 446-449 (1966)
[9] Kumar, K. S., On the optimum stabilization of a satellite, IEEE Trans. Aerosp. Electron. Syst., 1, 82-83 (1965)
[10] Windeknecht, T. G., Optimal stabilization of rigid body attitude, J. Math. Anal. Appl., 6, 325 (1963) · Zbl 0116.08201
[11] Debs, A. S.; Athans, M., On the optimal angular velocity control of asymmetrical space vehicles, IEEE Trans. Autom. Control, 80-83 (1969)
[12] Dwyer, T. A.W., The control of angular momentum for asymmetric rigid bodies, IEEE Trans. Autom. Control, 3, 686-688 (1982) · Zbl 0488.93040
[13] Lin, Y. Y.; Kraige, L. G., Enhanced techniques for solving the two-point boundary-value problem associated with the optimal attitude control of spacecraft, J. Astronaut. Sci., 37, 1-15 (1989)
[14] Carrington, C. K.; Junkins, J. L., Optimal nonlinear feedback control for spacecraft attitude maneuvers, J. Guidance Control Dyn., 9, 1, 99-107 (1986) · Zbl 0596.93027
[16] Seywald, H.; Kumar, R. R.; Deshpande, S. S.; Heck, M. L., Minimum fuel spacecraft reorientation, J. Guidance Control Dyn., 17, 1, 21-29 (1994) · Zbl 0788.49033
[17] Goldstein, H., Classical Mechanics (1950), Addison-Wesley: Addison-Wesley Reading · Zbl 0041.32101
[18] Vadali, S. R.; Junkins, J. L., Spacecraft large angle rotational maneuvers with optimal momentum transfer, J. Astronaut. Sci., 31, 217-235 (1983)
[19] Pontryagin, L. S.; Boltyanskii, V. G.; Gamkrelidze, R. V.; Mishchenko, E. F., The Mathematical Theory of Optimal Processes (1986), Gordon and Beach: Gordon and Beach New York · Zbl 0882.01027
[20] Schaub, H.; Junkins, J. L., New penalty functions and optimal control formulation for spacecraft attitude control problems, J. Guidance Control Dyn., 20, 3, 428-434 (1997) · Zbl 0894.49021
[21] Dwyer, T. A.W., Exact nonlinear control of spacecraft slowing maneuvers with internal maneuver transfer, J. Guidance Control Dyn., 9, 2, 240-247 (1986) · Zbl 0596.93029
[22] Bryson, A. E., Dynamic Optimization (1999), Addison-Wesley: Addison-Wesley Reading
[23] Chung, T. S.; Wu, C. J., A computationally efficient numerical algorithm for the minimum-time control problem of continuous systems, Automatica, 28, 841-847 (1992) · Zbl 0765.93031
[24] Shuster, M. D., A survey of attitude representations, J. Astronaut. Sci., 41, 439-517 (1993)
[25] Luenberger, D. G., Linear and Nonlinear Programming (1973), Addison-Wesley: Addison-Wesley Reading · Zbl 0241.90052
[26] Jan, Y. W.; Chiou, J. C., Minimum-time spacecraft maneuver using sliding-mode control, Acta Astronaut., 54, 69-75 (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.