Robust Path-following for Keplerian Orbits

This work introduces a novel path-following control strategy inspired by the famous two-body problem, aiming to stabilize any Keplerian orbit. Utilizing insights from the mathematical structure of the two-body problem, we derive a robust path-following law adopting sliding mode control theory to achieve asymptotic convergence to bounded disturbances. The resulting control law is demonstrated to be asymptotically stable. Illustrative examples showcase its applicability, including orbiting an accelerated moving point, patching Keplerian trajectories for complex patterns, and orbital maintenance around the asteroid Itokawa. The proposed control law offers a significant advantage for the orbital station-keeping problem, as its sliding surface is formulated based on variables commonly used to define orbital dynamics. This inherent alignment facilitates easy application to orbital station-keeping scenarios.