Robust Variable Horizon Model Predictive Control for Rendezvous with Rotating Target

This paper presents a new robust model predictive control (MPC) scheme for rendezvous and docking of a servicer spacecraft with a rotating noncooperative target. The main feature of the proposed solution is that the prediction horizon is included among the optimization variables. Robustness against model uncertainty is achieved by applying a tube-based control approach. Finite completion time of the variable horizon tube MPC algorithm is guaranteed, thanks to a suitable adaptive choice of the terminal constraint. The latter is also instrumental to promote a close proximity approach to the docking point. Efficient solutions are presented to limit the computational burden of the variable horizon optimization problem and of the set computations required by tube MPC. The approach is validated on two simulation benchmarks: a Monte Carlo study of a rendezvous with a rotating object in low-Earth orbit and a mission setting involving the capture of the nonoperational EnviSat spacecraft. The results demonstrate the advantages of the proposed technique with respect to both a tube-based optimal control law and a variable horizon MPC law without adaptation of the terminal constraint.