Feasibility analysis and saturation control for underactuated spacecraft formation reconfiguration in elliptic orbits

This work proposes a saturation control scheme for underactuated spacecraft formation reconfiguration in elliptic orbits without radial or along-track thrust. Firstly, the rank criterion method is applied to analyze the controllability and feasibility of formation reconfiguration by linearizing the linear time-varying dynamics to linear time-invariant ones. Based on the inherent coupling of the linear time-varying system, the underactuated error dynamics are presented for either underactuated case. Subsequently, the developed underactuated saturation controller can ensure that the time-varying system trajectory asymptotically converges to the specified configuration. The Lyapunov-based analysis presents the constraint conditions of controller parameters and the stable reconfiguration accuracy of the system states. Finally, numerical simulations for both underactuated scenarios are performed in the environment with J2 perturbation to verify the validity of the proposed underactuated control scheme.