Hybrid Systems Approach to Autonomous Rendezvous and Docking of an Underactuated Satellite

This work examines the autonomous rendezvous, proximity operations, and docking (ARPOD) problem wherein a "deputy" spacecraft must maneuver and dock with a "chief" spacecraft. This problem is challenging in that the deputy is modeled to be underactuated; thrust is only allowable along a single axial direction (its local x axis) and rotation is only allowed about its local z axis. Furthermore, the deputy's coupled translational and attitudinal dynamics (modeled via the Clohessy-Wiltshire equations with inputs) do not allow local controllability about the equilibrium point when linearized. To solve this underactuated ARPOD problem, we design a periodic bimodal switching control law that drives the deputy to a docking configuration with the chief. We model the system to have hybrid (i.e., continuous and discrete) dynamics and recast the docking objective as a set stabilization problem. The main result of this work is a rigorous proof that leverages properties of geometric control, Floquet theory, and homogeneity to show that the switching control law renders the objective set to be locally asymptotically stable. Numerical simulations are provided to illustrate the main result.