We present an approach for feedback motion planning of systems with unknown dynamics which provides  guarantees on safety, reachability, and stability about the goal . Given a learned control-affine approximation of the true dynamics  , we estimate the Lipschitz constant of the difference between the true and learned dynamics to determine a trusted domain for our learned model . Provided the system has at least as many controls as states, we further derive the conditions under which a one-step feedback law exists. This allows fora small bound on the tracking error when the trajectory is executed on the real system . Our method imposes a check for the existence of the feedback law as constraints in a sampling-based planner, which returns a feedback policy ensuring that under the true dynamics, the goal is reachable, the path is safe in execution, and the closed-loop system is invariant in a small set about the goal. We demonstrate our approach by planning using learned models of a 6D quadrotor and a 7DOF Kuka arm. We show that a baseline which plans using the same learned dynamics without considering the error bound or the existence of the feedback law can fail to stabilize around the plan and become unsafe.
We present a method for feedback motion planning of systems with unknown dynamics which provides probabilistic guarantees on safety, reachability, and goal stability. To find a domain in which a learned control-affine approximation of the true dynamics can be trusted , we estimate the Lipschitz constant of the difference between the true and learned dynamics , and ensure the estimate is valid with a given probability . Provided the system has at least as many controls as states, we also derive existence conditions for a one-step feedback law which can keep the real system within a small bound of a nominal trajectory planned with the learned dynamics . Our method imposes the feedback law existence as a constraint in a sampling-based planner, which returns a feedback policy around a nominal plan ensuring that, if the Lipschitz constant estimate is valid, the true system is safe during plan execution, reaches the goal, and is ultimately invariant in a small set about the goal. We demonstrate our approach by planning using learned models of a 6D quadrotor and a 7DOF Kuka arm. We show that a baseline which plans using the same learned dynamics without considering the error bound or the existence of the feedback law can fail to stabilize around the plan and become unsafe.
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