Optimal Control of a Spacecraft Orientation Taking into Account the Energy of Rotation

Abstract

The problem of optimal control of the reorientation of a spacecraft as a solid body from an arbitrary initial position into a prescribed final angular position is considered and solved. The construction of an optimal slew control is based on the quaternionic variables and Pontryagin’s maximum principle. The case is investigated when the minimized functional combines, in a given proportion, the integral of the kinetic energy of rotation and the duration of the maneuver. On the basis of necessary optimality conditions, the main properties, laws, and key characteristics (parameters, constants, integrals of motion) of the optimal solution of the control problem, including the maximum kinetic energy for the optimal motion and the turn time, are determined. It is proved that during the optimal rotation, the direction of the kinetic moment is constant in the inertial coordinate system. Formalized equations and expressions for the synthesis of the optimal rotation program are obtained. The optimal solution corresponds to the strategy “acceleration–rotation by inertia–braking”. An assessment is made of the influence of the limiting control moment on the character of the optimal motion and on the quality control indicators. It is shown that the accepted optimality criterion guarantees the motion of a spacecraft with a kinetic rotational energy not exceeding the required value. For dynamically symmetric spacecraft, a complete solution of the reorientation problem in closed form is presented. An example and results of mathematical modeling of the motion of a spacecraft with optimal control are given, demonstrating the practical feasibility of the method for controlling spacecraft spatial orientation.