Robust model predictive control for multi-step short range spacecraft rendezvous

Abstract

This work presents a robust model predictive control (MPC) approach for the multi-step short range spacecraft rendezvous problem. During the specific short range phase concerned, the chaser is supposed to be initially outside the line-of-sight (LOS) cone. Therefore, the rendezvous process naturally includes two steps: the first step is to transfer the chaser into the LOS cone and the second step is to transfer the chaser into the aimed region with its motion confined within the LOS cone. A novel MPC framework named after Mixed MPC (M-MPC) is proposed, which is the combination of the Variable-Horizon MPC (VH-MPC) framework and the Fixed-Instant MPC (FI-MPC) framework. The M-MPC framework enables the optimization for the two steps to be implemented jointly rather than to be separated factitiously, and its computation workload is acceptable for the usually low-power processors onboard spacecraft. Then considering that disturbances including modeling error, sensor noise and thrust uncertainty may induce undesired constraint violations, a robust technique is developed and it is attached to the above M-MPC framework to form a robust M-MPC approach. The robust technique is based on the chance-constrained idea, which ensures that constraints can be satisfied with a prescribed probability. It improves the robust technique proposed by Gavilan et al., because it eliminates the unnecessary conservativeness by explicitly incorporating known statistical properties of the navigation uncertainty. The efficacy of the robust M-MPC approach is shown in a simulation study.