Optimal control of loose spacecraft formations near libration points with collision avoidance

Abstract

This paper investigates the optimal control of loose leader-following spacecraft formations near libration points. The formation reconfigurations and keepings can be applied at the same time for the loose formations. A loose sphere leader-following formation, i.e., the leader spacecraft moves along the reference Halo orbits while the motions of all follower spacecrafts are restricted to a sphere formation with its center located at the leader, is explored in this study carefully. Collision avoidances among follower spacecrafts are taken into consideration since there are no constraints between followers and then the formation for all followers is loose. A symplectic penalty iteration algorithm is proposed to obtain the optimal solutions with minimization of energy cost. An effective penalty function to avoid collision is developed, and a high efficiency and structure-preserving symplectic method is introduced in the iteration algorithm. Several optimal control problems including formation reconfigurations and formation keepings are solved to show the effectiveness of the proposed algorithm. Numerical results show that errors of formations can be reduced to millimeters or smaller only by few control input and the collision can be avoided successfully by the developed penalty function.