Fixed-time position coordinated tracking control for spacecraft formation flying with collision avoidance

In this paper, the fixed-time stability of spacecraft formation reconfiguration (position tracking) is studied. Firstly, a novel nonsingular terminal sliding mode surface is designed and based on which a fixed-time coordinated controller is designed to keep the closed-loop system states have a finite settling time bounded by some predefined constants. Secondly, another nonsingular terminal sliding mode surface is designed by combining the artificial potential function and the aforementioned sliding surface, which can meet the mutual distance constraint during transition process among spacecraft when it is bounded. Then another coordinated controller with fixed-time observer considering mutual distance constraint is presented, which can guarantee the closed-loop system states stable also in bounded settling time. Finally, simulation results are shown to validate the correctness of the proposed theorems. It is worth mentioning that the control schemes can also work even though there is a properly limit on the control input.