Synchronization control of relative motion for spacecraft with screw theory-based description

For the approaching operations with intensity coupling between position and attitudes, precise synchronization control of relative translation and rotation is one of the essentials to be solved. Traditionally, translation and rotation motion are modeled and controlled separately, in which the coupling between relative position and attitudes is ignored, so the control period is long and the synchronization cannot be guaranteed. This paper investigates the synchronization control problem of spacecraft relative motion. A six-degree-of-freedom relative motion model is proposed using the dual-number representation of screw theory, which can not only describe the coupling effect between the translational movement and the rotational one, but also make the model of translation and rotation in the same style to the benefits of designing controller easy. The causes of couple forming are presented after analyzing the coupling term of the relative motion model. A synchronization error constructed by the relative translation and rotation is introduced. A synchronization control law is designed based on nonlinear feedback to eliminate the error, and its stability is proved by Lyapunov methods. Choosing the final approaching phase of docking and rendezvous to make numerical simulation, the results demonstrate the validity of the proposed method by comparing with PD controller. Meanwhile, it is proved that the proposed method can achieve synchronous convergence of the attitudes and orbit control, which has important implications for the required attitudes and orbit synchronization operations.