Quadratic Optimal Control in Reorienting a Spacecraft in a Fixed Time Period in a Dynamic Problem Statement

Abstract

A dynamic problem of a spacecraft (SC) turning from an arbitrary initial angular position to the required final angular position is considered and solved. The termination time of the maneuver is known. To optimize the turn control program, the quadratic criterion of quality is used; the minimized functional characterizes the energy consumption. The construction of the optimal control of the turn is based on quaternion variables and Pontryagin’s maximum principle. It is shown that during the optimal turn, the moment of forces is parallel to a straight line immobile in space and the angular momentum direction in the rotation process of the SC is constant relative to the inertial coordinate system. The formalized equations and calculation expressions to determine the optimal turn program are obtained. For a dynamically symmetric SC, a complete solution to the reorientation problem in the closed form is given. An example and results of the mathematical simulation of the dynamics of the SC’s motion under the optimal control are presented, which demonstrate the practical feasibility of the developed method to control the SC’s attitude.