Distributed finite-time tracking for a team of planar flexible spacecraft.

The paper presents a distributed finite-time controller for multiple under-actuated spacecraft with flexible appendages to track a virtual leader with stationary states under an undirected communication graph. Each spacecraft of concern is simplified as a free-floating hub-beam system, which is an under-actuated Euler-Lagrange system by nature since only the hub is driven. In the undirected communication graph, it is assumed that only one spacecraft can receive the information from the virtual leader. A distributed finite-time control law is presented for such a multi-agent system. The closed-loop system is proven to converge to the desired states within a finite time via Lyapunov theory and homogeneous method. Finally, a comparison is made between the proposed controller and the PD controller to show the better performance of the proposed controller.