Adaptive sliding mode controller design for on-orbit servicing to uncontrollable spacecraft

A relative position and attitude coupled adaptive controller is designed on the basis of second-order sliding mode control algorithm. It is proposed for on-orbit servicing on the free tumbling uncontrollable target spacecraft. Considering the coupled effect of relative rotation on relative translation, a relative position and attitude coupled dynamic model is derived for two docking ports on different spacecraft. Based on this coupled relative motion model, an adaptive super twisting controller is proposed to attenuate the chattering phenomenon caused by bounded perturbation with known upper bound. It makes the closed-loop system converge to the equilibrium point in finite time. Under the condition of limited disturbances, the closed-loop system is proved to be steady by Lyapunov method and the supremum of convergence time is estimated. By comparison with the super twisting method, numerical simulations are performed to validate strong robustness of the designed adaptive second-order sliding mode controller for parameter uncertainty and linearly growing bounded disturbances. The control accuracy is high enough for the requirement of on-orbit servicing mission.