Spacecraft attitude motion planning using rotation matrices and gradient-based optimization

The purpose of the present work is to perform spacecraft attitude motion plan ning so that a rest-to-rest rotation is achieved while satisfying pointing con straints. Attitude is represented on the group of three dimensional rotations SO(3). The motion planning is executed in two steps. In the first step, path planning is performed by searching for a time behavior for the angular rates through the formulation of an optimal control problem solved with a gradient based algorithm. In the second step, the actual input torque is simply determined by the use of inverse attitude dynamics. A numerical example is included to show the effectiveness of the method. From a practical point of view, the control torque resulting from the proposed approach is continuously differentiable and vanishes at its endpoints.