Kinematically optimal spacecraft attitude control

Abstract

The problem of optimal control of a spacecraft reorientation from an arbitrary initial position into a prescribed final angular position is studied. The reorientation time is minimized. The case when the velocity parameters are limited is investigated. On the basis of necessary optimality conditions in the form of Pontryagin's maximum principle and using quaternion variables for the control problems of the spacecraft motion, an analytical solution of the stated problem is obtained. The kinematic problem of spacecraft reorientation is solved completely. Formal equations are derived and computational expressions for constructing the optimal control program are obtained. For the symmetric form of constraints on the angular velocity vector, the optimal reorientation problem is solved analytically (the result is obtained in terms of elementary functions). Results of the mathematical simulation of the spacecraft motion under the optimal control are presented that demonstrate the practical usefulness of the proposed algorithm for the spacecraft attitude control.