Optimal sliding mode control for spacecraft formation flying

In this paper, in order to control the relative motion for spacecraft formation flying, an optimal sliding mode controller has been proposed. This controller is designed based on the linearized equations of relative motion under two-body dynamics or Hill´s equations and applied to nonlinear system that is subjected to external disturbances. Firstly, an augmented system composed of the original system and the desired condition is used to transform the optimal tracking issue into the linear quadratic regulator (LQR) problem. Then the integral sliding mode control is used to robustify the optimal LQR against the uncertainties and disturbances. Due to moving the satellites in low earth orbits, J₂ perturbation and atmospheric drag are considered as external disturbances and the stability of the close-loop system is guaranteed by Lyapunov second method. The performance of the proposed controller in tracking the desired trajectory is compared to optimal controller and simulation results have been presented.