Dual-quaternion-based finite-time control for spacecraft tracking in six degrees of freedom

This article investigates the tracking control problem for the six-degree-of-freedom motion of a follower spacecraft relative to a leader spacecraft. Employing dual quaternion representation, the model of the six-degree-of-freedom relative motion between the two spacecraft is derived. Taking into account the model uncertainties and external disturbances, two robust fast sliding mode control laws are proposed to guarantee the finite-time convergence of the tracking errors, where the second control law can solve the dual-equilibrium problem that exists in the first one. In order to alleviate chattering phenomenon, continuous saturation function is introduced into the controller and a softening control strategy is developed. It is worth pointing out that the convergence rate of the proposed fast sliding mode control is faster than that of the linear sliding mode control and terminal sliding mode control. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed approaches.