Feasibility Analysis and Synchronization Control for Underactuated Spacecraft Formation Hovering

This brief develops a synchronization control scheme for underactuated spacecraft formation hovering in the case without along-track thrust. The feasible sets of initial positions for this underactuated case are derived based on the nonlinear and linear relative orbital dynamics. Then, a nonpreset parameter underactuated controller is designed to deal with the unmatched disturbances caused by the loss of along-track control. Moreover, a synchronization item is added to the above controller to synchronize the hovering motion between the follower spacecraft. The Lyapunov-based analysis indicates that the minimum nonzero eigenvalue of the Laplace matrix corresponding to the synchronization item determines the stable hovering accuracy of the system states. Numerical simulations also demonstrate the validity of the presented underactuated synchronization controller (SC).