Finite-Time Control for Spacecraft Formation with Dual-Number-Based Description

Abstract

relativetranslationandrotationbetweenthesetwospacecraftis firstintroduced,whichisrequiredtotrackadesired 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 errorcanconvergetothedesiredtrajectoryin finitetime,basedonwhichamodifiedcontrollerisdesignedtosolvethe ambiguity problem caused by dual-quaternion representation. To alleviate the chattering phenomenon, a continuousterminal sliding mode-control scheme isfurthermore 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.