Spacecraft attitude motion planning using gradient-based optimization

The purpose of the present work is to perform spacecraft attitude motion planning so that a rest-to-rest rotation is achieved while satisfying pointing constraints. Atti- tude 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.