Relative position fixed-time tracking control of spacecraft

A fixed-time controller is introduced to achieve the relative motion tracking of leader-follower spacecraft within the allotted time. Unlike the existing finite time control scheme, of which settling time can't be determined in advance, a novel fixed-time sliding mode control scheme in conjunction with a time-varying sliding mode surface is proposed. This method can preset desired fixed-values for the relative position tracking error's convergence time according to the task's requirements. Furthermore, the global stability of the whole system is proven to be guaranteed by employing Lyapunov analysis, and fixed-time convergence of the tracking error is ensured based on fixed-time stability theory. Numerical simulations are performed to demonstrate the validity and merit of designed control algorithm.