Distributed Satellite Formation Control via Feedback Equilibrium Seeking

Spacecraft formation flying refers to the problem of coordinating multiple closely located spacecrafts, in order to make them behave as a cohesive system. In this work, we employ a game-theoretic approach for controlling satellite clusters in a distributed manner. The relative dynamics between satellites are expressed using the Hill-Clohessy-Wiltshire equations of relative motion. A linear-quadratic regulator is implemented locally on each spacecraft as a low-thrust controller in order to stabilize the motion of the satellites, subject to the atmospheric drag, the moon's gravity and the J2 perturbation, and to track the reference orbits commanded by the upper level game-based formation controller. Two coverage coordination games are designed, to model the acquisition and formation-keeping problems in the orbital plane. The (static) games are solved using a distributed generalized Nash equilibrium (GNE) seeking algorithm, and feedback equilibrium seeking (FES) control is implemented for the planar problem.