Fixed-time coordination control for 6-DOF attitude-orbit coupled spacecraft formation flying

This paper presents a distributed fixed-time control protocol for 6-DOF(degree-of-freedom) attitude-orbit coupled spacecraft formation flying with external disturbances. Firstly, the 6-DOF attitude-orbit coupled dynamics is established. The communication topology between the spacecraft in the formation is described by a directed graph. Secondly, a fixed-time disturbance observer (FxTDO) is designed to ensure that the estimation errors of the unknown external disturbances can converge to zero in fixed time. Thirdly, based on non-singular fixed-time terminal sliding mode (NFFTSM) surface, the fixed-time coordination control protocol is proposed combined with the fixed-time disturbance observer, which can guarantee that each spacecraft can track their desirable positions and attitudes in fixed time. The stability of the closed-loop system is proved through Lyapunuov method. Finally, simulation results for a formation with one virtual leader and five followers demonstrate the effectiveness of the proposed control scheme.