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This work proposes a novel path-following control inspired by the famoustwo-body problem. In recognizing the mathematical structure of the two-bodyproblem, we derive a robust path-following law that can stabilize in anyKeplerian orbit. We use the sliding mode control theory framework to achievethat, which is only possible after we propose and prove asymptotic convergenceof a new kind of sliding surface, especially suitable for this path-followingproblem. We can derive our control law with this new sliding surface, showingthat it is asymptotically stable. The applicability of this new path-followingis exemplified for three examples. In a moving path-following problem, aparticle is requested to orbit an accelerated moving point. A patchedhyperboles example shows the possibility of patching Keplerian trajectories forobtaining a whole complex trajectory. Lastly, an orbital maintenance problemaround the asteroid Itokawa is shown.

A Novel Robust 3-D Path Following Control for Keplerian Orbits