Abstract: Focusing on proximity to tumbling target, this paper tries to improve the precision of relative motion model through differential geometric theory. A set of relative motion equations are built in rotating coordinates which solves the coupling between pitch and yaw. A unified frame is established for controller design. Finally a six-degree-of-freedom simulation example is conducted to demonstrate the effectiveness of the relative motion model, which shows robustness, high precision and engineering feasibility.

Key words: Relative motion modeling, Guidance and control, Differential geometric, Decoupling