Novel Coordinate Transformation and Robust Cooperative Formation Control for Swarms of Spacecraft

This paper presents a new coordinate transformation method for controlling a large number of spacecraft moving in elliptical orbits. A new coordinate transformation method for phase synchronization of spacecraft in relative elliptical orbits is introduced to effectively maintain desired formation patterns. The proposed controller, which employs both the adaptive graph Laplacian matrix and the distance-based connectivity rule, synchronizes the relative motions of spacecraft with a guaranteed property of robustness. A complex time-varying network topology, constructed by the proposed controller, relaxes the standard requirement of consensus stability, even permitting stabilization on an arbitrary unbalanced graph. A challenging example of reconfiguring swarms of spacecraft shows the reliability of the coordinate transformation method and the effectiveness of the proposed phase synchronization controller.