Chance-constrained model predictive control for spacecraft rendezvous with disturbance estimation

Abstract

A robust Model Predictive Controller (MPC) is used to solve the problem of spacecraft rendezvous, using the Hill–Clohessy–Wiltshire model with additive disturbances and line-of-sight constraints. Since a standard (non-robust) MPC is not able to cope with disturbances, a robust MPC is designed using a chance-constrained approach for robust satisfaction of constraints in a probabilistic sense. Disturbances are modeled as Gaussian allowing for an explicit transformation of the probabilistic constraints into simple algebraic constraints. To estimate the distribution parameters a predictor of disturbances is proposed. Both robust and non-robust MPC control laws are compared using the Monte Carlo method, which shows the superiority of the robust MPC.