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Review Article Volume 11 Issue 2
Optimal control of a spacecraft based on the combined criteria of quality related to the energy costs
Levskii MV
Received: May 20, 2025 | Published: June 25, 2025
Citation: Levskii MV. Optimal control of a spacecraft based on the combined criteria of quality related to the energy costs. Int Rob Auto J. 2025;11(2):33-38. DOI: 10.15406/iratj.2025.11.00298
Abstract
Solution of optimal control problem of spacecraft reorientation using the combined indicator (in sense of energy consumptions and time for rotation) and quaternion models is presented in analytical form. The minimized functional combines in a given proportion the contribution of control forces and the integral of rotary energy, as well as maneuver’s duration. The construction of optimal turn control is based on a differential equation relating the attitude quaternion and angular momentum of a spacecraft. Analytical solution is obtained using the Pontryagin’s maximum principle. The properties of optimal rotation are studied in detail. Formalized equations and computational formulas are written to construct the optimal rotation program. Analytical equations and relations for finding the optimal control are presented. Key relations that determine the optimal values of the parameters of rotation control algorithm are given. The made numerical experiments confirm the analytical conclusions. In the case of a dynamically symmetric solid body, the problem of spatial reorientation with minimum energy and time consumption is completely solved (in closed form).
Keywords: spacecraft attitude, quaternion, the combined criteria of optimality, maximum principle, optimal control, the boundary-value problem
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