Finite-time control for spacecraft formation with dual-number-based description

This paper investigates the control problem of the dynamical synchronization between two spacecraft in Earth orbit, which will form a leader-follower spacecraft formation.Adynamical synchronization error constructed by the relative translation and rotation between these two spacecraft is first introduced, which is required to track a desired time-varying trajectory given in advance. A six-degrees-of-freedom relative-motion model is proposed by using the dual-quaternion representation, which can describe the coupling effect between the translational motion and the rotational one. A terminal sliding mode-control law is proposed such that the defined dynamical synchronization error can converge to the desired trajectory in finite time, based on which a modified controller is designed to solve the ambiguity problem caused by dual-quaternion representation. To alleviate the chattering phenomenon, a continuous terminal sliding mode-control scheme is furthermore developed, which will enable the tracking errors to converge to a small neighborhood of the origin in finite time. The proposed control strategies are robust to model uncertainties and bounded external disturbances. Finally, numerical simulations are performed to demonstrate the validity of the proposed approaches.