Nonlinear Optimal Control for Spacecraft Rendezvous and Docking Using Symplectic Numerical Method

This paper addresses the autonomous rendezvous and docking between a chaser spacecraft and a target spacecraft. An optimal control method is employed to plan the rendezvous and docking maneuver, considering various constraints, including force, velocity, field of view, and collision avoidance with a diamond-shaped obstacle. The optimal trajectories are derived using a symplectic algorithm, which ensures high accuracy and enhances computational efficiency. These trajectories serve as the reference for the maneuver. A PD-based tracking control method is proposed to enable real-time feedback control. An air-bearing experimental system, encompassing state measurement, data transmission, and processing, is established to conduct ground-based tracking experiments. Furthermore, specialized simulators for the chaser and target spacecraft, equipped with a docking mechanism, are designed. Experimental results validate both the feasibility of the reference trajectories and the effectiveness of the PD tracking control approach.