Hierarchy for Circular Orbit Stabilization of Underactuated Satellites with Application to Distributed Formations

The paper addresses circular orbits stabilization for a class of thrust-underactuated satellites, utilizing smooth feedbacks. The problem is first solved in a path-following sense which is pertinent to stabilization of distributed formations. Two orthogonal thrusts are used where, broadly, one is used to stabilize the satellite to the desired orbital plane, and the second is used to stabilize the desired orbit on that plane. Control design follows a five-step hierarchy of stabilizing five nested sets. A main advantage of the approach is its amenability to modification. By redesigning only the last step of the hierarchy, the result is extended to stabilizing time parametrized orbits, i.e. trajectory tracking, and distributed formations of not necessarily co-planar orbits with or without temporal requirements. The results are illustrated through simulations.