Spacecraft attitude motion planning using GRAFS

The purpose of the present work is to perform spacecraft attitude motion planning using a method designed for optimal control on Lie groups known as “Gradient Ascent in Function Space” (GRAFS). Attitude is globally represented on the Lie group of three dimensional rotations SO(3). The motion planning objective is to determine a rest-to-rest rotation while satisfying pointing constraints and is achieved in two steps. In the first step, path-planning is performed by solving for an appropriate time behavior for the angular rates. The path-planning problem is formulated as an optimal control one in which the objective function can be optimized by gradient ascent algorithms. In the second step, the actual input torque is simply determined by the use of inverse attitude dynamics. Moreover, a time scaling method is introduced to reduce the torque amplitude if required. A numerical example is included to show the effectiveness of the proposed methodology.