Finite-time control for spacecraft body-fixed hovering over an asteroid

A finite-time control scheme for autonomous body-fixed hovering of a rigid spacecraft over a tumbling asteroid is presented. The relative configuration between the spacecraft and asteroid is described in terms of exponential coordinates on the Lie group SE(3), which is the configuration space for the spacecraft. With a Lyapunov stability analysis, the finite-time convergence of the proposed control scheme for the closed-loop system is proved. Numerical simulations validate the performance of the proposed control scheme.