Abstract
The problems of optimal control of kinetic moment of a rigid body (for example, a spacecraft) during the reorientation maneuver from an arbitrary initial to a given final angular position, taking into account the requirements for the energy of rotation, are investigated. An analytical solution for the problem of optimal control of solid body reorientation is obtained. Formalized equations are presented and calculation expressions for the construction of an optimal control program are given. The task of controlling the turn is solved taking into account the restrictions on control moments. An analytical relationship is found between the turning time and the maximum rotational energy. The moment of the start of deceleration is determined by the actual parameters of movement (the mismatch quaternion and the kinetic moment), based on the principles of terminal control (using information about the angular position and measuring the angular velocity). Control algorithms created make it possible to make turns in a given time with a minimum rotational energy. For a dynamically symmetric solid body, the control problem is solved to the end — dependencies are obtained, as explicit functions of time, for control variables and relations for calculating the key parameters of the kinetic moment control law. A numerical example and the results of mathematical modeling of the motion of a spacecraft with optimal control, which demonstrate the practical feasibility of the developed orientation control algorithms, are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. N. Branets and I.P. Shmyglevskii, Application of Quaternions to Rigid Body Attitude Problems (Nauka, Moscow, 1973) [in Russian].
B.V. Raushenbakh and E. N. Tokar’, Control of Spacecraft Attitude (Nauka, Moscow, 1974) [in Russian].
A.V. Molodenkov and Ya.G. Sapunkov, “Special Control Regime in Optimal Turn Problem of Spherically Symmetric Spacecraft,” Izv. Akad. Nauk. Teor. Sist. Upr. No. 6, 47–54 (2009) [J. Comp. Sys. Sci. Int. (Engl. Transl.) 48 (6), 891–898 (2009)].
M.V. Levskii, “About Method for Solving the Optimal Control Problems of Spacecraft Spatial Orientation,” Int. J. Probl. Nonlin. Anal. Enging Sys. 21 (2), 61–75 (2015).
N. E. Zubov, “Optimal Control of the Spacecraft Terminal Retargeting on the Basis of the Predictive Model Algorithm,” Kosm. Issl. 29 (3), 340–351 (1991).
A. I. Van’kov, “Spacecraft Angular Motion Adaptive Robust Control Based on the Use of Predictive Models,” Kosm. Issl. 32 (4–5), 13–21 (1994).
M. A. Velishchanskii, A.P. Krishchenko, and S. B. Tkachev, “Synthesis of Spacecraft Reorientation Algorithms Using the Concept of the Inverse Dynamic Problem,” Izv. Akad. Nauk. Teor. Sist. Upr. No. 5, 47–54 (2003) [J. Comp. Sys. Sci. Int. (Engl. Transl.) 42 (5), 811–818 (2003)].
S. Liu and T. Singh, “Fuel/Time Optimal Control of Spacecraft Maneuvers,” J. Guid. 20 (2), 394–397 (1996).
S. Scrivener and R. Thompson, “Survey of Time-Optimal Attitude Maneuver,” J. Guid. Cont. Dyn. 17 (2), 225–233 (1994).
Shen H., Tsiotras P. “Time-Optimal Control of Axi-Symmetric Rigid Spacecraft with Two Controls,” AIAA J. Guid. Cont. Dyn. 22 (5), 682–694 (1999).
A.V. Molodenkov and Ya.G. Sapunkov, “A Solution of the Optimal Turn Problem of an Axially Symmetric Spacecraft with Bounded and Pulse Control Under Arbitrary Boundary Conditions,” Izv. Akad. Nauk. Teor. Sist. Upr. No. 2, 90–105 (2007) [J. Comp. Sys. Sci. Int. (Engl. Transl.) 46 (2), 310–323 (2007)].
M.V. Levskii, “Use of Universal Variables in Problems of Optimal Control of Orientation of Spacecraft,” Mekh. Avt. Upr. No. 1, 53–59 (2014).
M.V. Levskii, “Use of the Energy Integral in Optimal Control of the Spacecraft Spatial Attitude,” Izv. Akad. Nauk. Mekh. Tv. Tela, No. 2, 7–24 (2009) Mech. Sol. (Engl. Trans.) 44 (4), 502–513 (2009).
M.V. Levskii, RF Patent No. 2 006 431, Byull. Izobret., No. 2 (1994).
M.V. Levskii, “Pontryagin’s Maximum Principle in Optimal Control Problems of Orientation of a Spacecraft,” Izv. Akad. Nauk. Teor. Sist. Upr. No. 6, 144–157 (2008) [J. Comp. Sys. Sci. Int. (Engl. Transl.) 47 (6), 974–986 (2008)].
L. S. Pontryagin, V. G. Boltyanskii, R.V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Wiley-Interscience, New York, 1962; Nauka, Moscow, 1983).
L. Young, Lectures on the Calculus of Variations and Optimal Control Theory (Saunders, Philadelphia, 1969; Mir, Moscow, 1974).
M.V. Levskii, RF Patent No. 2 146 638, Byull. Izobret., No. 8 (2000).
Author information
Authors and Affiliations
Corresponding author
Additional information
Russian Text © The Author(s), 2019, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2019, No. 1, pp. 115–140.
About this article
Cite this article
Levskii, M.V. Optimal Control of Kinetic Moment During the Spatial Rotation of a Rigid Body (Spacecraft). Mech. Solids 54, 92–111 (2019). https://doi.org/10.3103/S0025654419010084
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0025654419010084