Fixed-Time Coordinated Control of Relative Positions in Spacecraft Formation Based on Homogeneity Theory

In this paper, a cooperative control law for fixed-time relative position coordination of spacecraft formation was designed based on the homogeneity theory. The control law includes a new type of integral sliding mode that is initialized at the origin. The designed control law ensures that once the system state leaves the sliding mode surface, it will return to the sliding mode surface within a fixed time. The fixed-time convergence of the system was proven based on the homogeneity theory.