Relative coupled dynamics and control using dual number

Control of relative position and orientation are usually split into two parts in rendezvous and docking missions. It is simple but not precise enough. Based on dual number, this paper derives coupled dynamics equations of two spacecrafts in which the coupling effect of relative position and orientation is indicated. Furthermore, an incremental PID control law is designed to control the coupled system. And a simulation of coupled dynamics and control for the rendezvous problem during final approach phrase is done. The simulation results show that the coupled system can satisfy the accuracy and security requirements.