Research on Chance-Constrained Robust MPC Method for Rendezvous with Space Tumbling Targets

The robust trajectory planning and control of service spacecraft is a key issue in rendezvous and capture operations for space tumbling targets. Considering the constraints of line-of-sight, approach velocity, control saturation, etc., as well as random uncertain disturbances during the rendezvous process, this paper proposes a probabilistic-constrained robust model predictive control (MPC) method for rendezvous control to solve the complex multi-constraint and uncertain space tumbling target rendezvous problem. First, uncertain disturbances are treated as unbounded Gaussian-distributed noises, and probabilistic constraints are transformed into simple deterministic algebraic constraints based on the equivalence principle. Then, a tracking-type robust MPC rendezvous controller is designed based on the linearized Clohessy-Wiltshire equations. The objective function penalizes the distance between the evolution of the nominal system and the virtual equilibrium point, the distance from the virtual equilibrium point to the target docking point, and the energy consumption during this process. In terms of constraints, the minimum robust positively invariant set is calculated to achieve constraint tightening and obtain tighter constraints for the nominal system. This controller can effectively handle unbounded random disturbances and complete the rendezvous task with a smaller prediction horizon, thus offering advantages of real-time performance, autonomy, and high efficiency. Finally, simulations verify the effectiveness of the proposed control method and strategy.