Time-optimal reorientation of the rigid spacecraft using a pseudospectral method integrated homotopic approach

Abstract

This paper proposes a robust algorithm for time-optimal rigid spacecraft reorientation trajectory generation. Based on the Pontryagin's maximum principle, the first-order necessary optimality conditions are derived. These optimality conditions are numerically satisfied by adopting a pseudospectral method integrated homotopic approach to solve the associated shooting functions. First, the energy-optimal reorientation solution is obtained using the Radau pseudospectral method, which has a spectral convergence speed and can give a precise estimation of the initial costates used to start the homotopic approach. Then, a modified homotopy scheme is given to deform the associated energy-optimal solution to the desired time-optimal solution continuously. Finally, for the inertially symmetric spacecraft reorientation problem, the newly found time-optimal solutions are presented. The performance of the algorithm is illustrated by simulating a general asymmetric rigid spacecraft time-optimal reorientation problem. Copyright © 2014 John Wiley & Sons, Ltd.