Optimal Control of Kinetic Moment During the Spatial Rotation of a Rigid Body (Spacecraft)

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.