Extended state observer–based finite-time controller design for coupled spacecraft formation with actuator saturation

This article investigates the consensus tracking control problem of the leader–follower spacecraft formation system in the presence of model uncertainties, external disturbances, and actuator saturation, where the relative motion of the leader and the follower need to track a desired time-varying trajectory given in advance. First, the six-degree-of-freedom relative-coupled translational and rotational dynamics models are derived using the exponential coordinates on the Lie group SE(3). Then, a fast terminal sliding mode control law is proposed to guarantee the tracking control objective come true in finite time robust against all the aforementioned drawbacks. As a stepping stone, an extended state observer is designed to estimate and compensate the total composed disturbances of the system, and it is proved that the estimate errors can converge to a really small neighborhood of the origin in finite time. Based on the observer information, a less-conservative modified controller is furthermore developed to eliminate the chattering caused by the signum function. The stability of the closed-loop system is shown by theoretical analysis. Finally, the validity of the proposed schemes is illustrated through numerical simulations.