Distributionally Robust Model Predictive Control for Trajectory Tracking of Space Manipulator Based on Fully Actuated System Approach

Whether operating autonomously or assisting humans, multi-degree-of-freedom free-flying space manipulator has shown enormous potential in space missions. Leveraging the fully actuated system approach (FASA), this article proposes a distributionally robust model predictive control (MPC) scheme for trajectory tracking issue of space manipulator with stochastic uncertainties and multiple constraints on the angle, angular velocity, and control torque. First, a nominal FASA-based controller is designed to establish a linear second-order fully actuated (SOFA) model with desired eigenstructure assignment. By adopting an exact penalty function, a gradient-based optimization scheme is developed to optimize the FASA-based controller parameters offline, while avoiding violating of multiple constraints on angle, angular velocity, and control torque. Furthermore, a distributionally robust MPC is proposed to enable real-time optimization of auxiliary input, ensuring constraint satisfaction and enhancing performance in the presence of independent stochastic uncertainties. Recursive feasibility and convergence are proven. Monte Carlo numerical simulations are conducted with a planar space robot system to validate the superiority of proposed strategy.