Robust control of spacecraft rendezvous on elliptical orbits: Optimal sliding mode and backstepping sliding mode approaches

The problem of relative motion control of spacecraft rendezvous process on elliptical orbit is considered in this paper. Due to the presence of nonlinear dynamics and external disturbances, two robust controllers are developed based on sliding mode control theory. The first one is an optimal sliding mode controller; in which optimal control theory is used to reduce the tracking error and fuel cost, and then integral sliding mode control technique is applied to robustify optimal controller. The other controller is a backstepping sliding mode one that is developed based on nonlinear dynamics of spacecraft rendezvous; having applied the backstepping method to synthesis the tracking errors and Lyapunov functions, a sliding mode controller is developed to guarantee the Lyapunov stability, handling of all nonlinearities, robustness against uncertainties as well as tracking the desired position. It is assumed that the chaser and target spacecraft are in a low Earth orbit and subject to the perturbing effects of J2 and atmospheric drag. In addition, two fault tolerant scenarios, i.e. thruster degradation and short thruster failure are also considered to verify the robustness and efficacy of the control approaches. Simulation results confirm the effectiveness of the proposed controllers in reaching to the desired position in case of actuator fault-free and fault tolerant situations.