Optimal control design of nonlinear spacecraft rendezvous system with collision avoidance constraint

This paper investigates the optimal control design problem of spacecraft rendezvous system with collision avoidance constraint. A new nonlinear spacecraft rendezvous model is established. Based on this model, an optimal control problem is formulated, which is subject to a collision avoidance constraint on the path of the chaser spacecraft. By using the control parametrization technique, the constrained optimal control problem is approximated by a sequence of constrained parameter selection problems. Furthermore, an exact penalty function method is introduced to transform these constrained parameter selection problems into approximate unconstrained optimization problems. It is shown that the solutions of these approximate unconstrained optimization problems converge to the solution of the original problem. Comparing with other methods, the effectiveness of method proposed in this paper is demonstrated through solving two minimum fuel consumption spacecraft rendezvous problems.