A smoothed exact penalty function method for the optimal-fuel spacecraft rendezvous problem with the collision avoidance constraint

This paper studies the minimum-fuel rendezvous problem subject to collision avoidance constraint. A new spacecraft rendezvous model is established. Based on this model, a state-constrained optimal control problem is formulated. A smoothed exact penalty function method is used to transform the constrained optimal control problem into a sequence of approximate unconstrained optimization problems. It is shown that the solutions of these approximate unconstrained optimization problems converge to the solution of the original problem. Finally, the effectiveness of the proposed approach is demonstrated through numerical simulation in the case of spacecraft rendezvous on a highly elliptical orbit.