Improved LQR control for spacecraft formation keeping in elliptical lunar orbits with gravity model uncertainty

Gravity data that measured from lunar back contains errors. Firstly, considering this gravity uncertainty and assuming it as high as 50% of the ideal value, an improved LQR (ILQR) controller is developed in three steps for spacecraft formation-keeping. The first step estimates the upper bound on the gravity error. Then, the auxiliary system, whose solutions are also the solutions to the initial system, is obtained. Finally, using the solutions to the auxiliary, the initial system would be controlled in desired formation-flying. This approach is attractive for two reasons. The process of the ILQR controller preserves the excellent maneuverability belong to the LQR controller. More importantly, the robustness of the initial system is strengthened and the results of the ILQR controller are interference immunity to the gravity uncertainties. The stability of the developed controller is verified by using the Lyapunov stability theorem, and numerical simulations demonstrate the effectiveness of the proposed method in spacecraft formation-keeping problem with high model uncertainty.