Velocity-free fixed-time attitude cooperative control for spacecraft formations under directed graphs

This article addresses the problem of velocity-free fixed-time attitude cooperative control for multiple spacecraft under directed communication graphs and in the presence of bounded disturbances. A distributed fixed-time state observer is designed to estimate the leader's attitude states and a fixed-time extended-state observer is presented to obtain accurate estimates of both unmeasurable angular velocities and bounded disturbances. By use of the fixed-time observers, a distributed fixed-time attitude cooperative control scheme is proposed to make the states of all spacecraft simultaneously track a time-varying reference attitude even when the reference attitude is available only to a subset of the group members. Homogeneous Lyapunov function and homogeneity property are applied to demonstrate that the control scheme can guarantee the attitude tracking errors converging to the neighborhood of the origin in fixed time which is independent of initial conditions. Finally, numerical simulations are presented to show the effectiveness of the control law derived here.