Navigation and obstacle avoidance via backstepping for mechanical systems with drift in the closed loop

We study backstepping controllers whose goal it is to navigate a mechanical system to a submanifold of its generalized positions under the circumstance that a drift vector field appears in the closed loop due to unmodeled dynamics. We not only derive conditions under which the desired submanifold remains asymptotically stable despite drift, but also provide results on overestimating the navigation function along solutions, such that obstacle avoidance can be guaranteed despite drift.