Finite-time control of underactuated spacecraft hovering

Finite-time controllers are proposed in this paper for underactuated spacecraft hovering in the absence of the radial or in-track thrust. The indirect method, which is generally adopted to solve the singularity problem in the conventional terminal sliding mode, is modified to ensure the continuity of the high-order time derivative of the sliding surface at the switch points. Rigorous proofs via the Lyapunov-based approaches verify the finite-time stability of the closed-loop system. By comparisons with the asymptotic controllers, the advantages of the finite-time ones in faster convergence rate and enhanced control precision have also been substantiated.