Comparative Study of Pseudospectral Methods for Spacecraft Optimal Attitude Maneuvers

Abstract

This paper presents a comparative study of six common pseudospectral (PS) methods for solving optimal spacecraft attitude control problems. The problems of minimum time, minimum control effort, and the linear combination thereof are considered here, for a rest-to-rest spacecraft slew maneuver. In this study, three traditional PS methods (Gauss, Legendre, and Chebyshev) and three variations of the novel Birkhoff PS method (Legendre–Gauss, Legendre–Gauss–Lobatto, and Chebyshev–Gauss–Lobatto) are used. The Wilcoxon rank sum test is used to perform statistical analysis to compare results between traditional and Birkhoff PS results. Accuracy, computational efficiency, and robustness to initial conditions are used as performance metrics for each PS method. The results show that for all three optimal control problems, the Birkhoff Legendre–Gauss method is more accurate than the traditional Gauss PS method. Furthermore, the results show that the Birkhoff variants could in some cases find the minimum cost using fewer iterations compared with traditional PS methods. The Birkhoff PS methods also are less susceptible to initial guesses for solutions that could cause the results to reach infeasible points or become trapped in local minimums.