Directed coordinated orbit-tracking control of second-order nonlinear satellites in three-dimensional space

This paper deals with the three-dimensional (3D) coordinated control of satellites formation motion along a set of given closed orbits, where each satellite has intrinsic second-order Lipchitz nonlinear dynamics and the commutation topology among satellites is directed. A projection-based orbit extension method is presented by extending our previous concentric compressing method. The control for the orbit-tracking subsystem and the formation motion subsystem are designed respectively at first, and then the overall closed-loop coordinated orbit-following system is regarded as a cascade system. By using tools from Input-to-State stability (ISS) theory and the extension of Barbalat´s lemma, it is shown the closed-loop coordinated orbit-tracking system is asymptotic stability if the directed communication topology contains a directed spanning tree. The effectiveness of the analytical results is verified by Satellite Tool Kit (STK).