Finite-Time Attitude Control of Underactuated Spacecraft with a Hierarchical Sliding Mode Control Approach

In this paper, a finite-time three-axis stabilization controller for an underactuated rigid spacecraft is proposed based on well-designed hierarchical terminal sliding mode surfaces to handle the insufficiency of control effort and disturbances. Firstly, the attitude kinematic of an underactuated rigid spacecraft is parameterized by the w-z representation and the dynamic model with only two orthogonal torque inputs are presented. Secondly, based on the terminal sliding mode theory, a three-hierarchized sliding surface is established. A finite-time stable control law is derived by the Filippov equivalence theorem and the principle of sliding mode control. The finite-time stability is proved by the Lyapunov theory. Finally, the high performance of the proposed control approach is verified through numerical simulations and comparisons with state-of-the-art studies.