Hierarchical sliding-mode control for attitude stabilization of an underactuated spacecraft

For an underactuated spacecraft with two control actuators, an attitude controller is proposed based on hierarchical sliding-mode control. Firstly, attitude dynamics and kinematics models are introduced and analyzed. Secondly, the first-layer sliding surface is defined by the state variables of the underactuated system, and the equivalent controller is obtained by Filippov equivalent theorem. Then, the second-layer sliding surface and the third-layer sliding surface are constructed in sequence, and the switching controller is derived by using the sliding-mode control theory. Thus the total controller is deduced by the equivalent and switching controller. The global asymptotic stability of all sliding surfaces is proved by using Lyapunov stability theory and Barbalat theory. The simulation results illustrate the feasibility of the proposed control algorithm.