Robust control of spacecraft formation flying

In this paper, a robust control scheme for two spacecraft in formation subjected to time-variant external disturbances in the space environment was developed. The proposed controller consists of two parts, the first part is for the nominal system without disturbances and the second part is to compensate for effects of system disturbances. A dynamic relative motion error model was established to design the second part of the controller and to analyze the stability of the closed-loop system using Lyapunov stability theory. Furthermore, the robustness of proposed control method to the system disturbances is analyzed based on robust control theory. It is proven that the relative motion error of two spacecraft in formation is uniformly ultimately bounded under the proposed controller for the assumed disturbances in the dynamic model.