Planning with Learned Dynamics: Probabilistic Guarantees on Safety and Reachability via Lipschitz Constants

• URL: http://arxiv.org/abs/2010.08993v4
• Date: Tue, 19 Oct 2021 18:46:13 GMT
• Title: Planning with Learned Dynamics: Probabilistic Guarantees on Safety and Reachability via Lipschitz Constants
• Authors: Craig Knuth, Glen Chou, Necmiye Ozay, Dmitry Berenson
• Abstract summary: We present a method for feedback motion planning of systems with unknown dynamics. We provide guarantees on safety, reachability, and goal stability. We demonstrate our approach by planning using learned models of a 6D quadrotor and a 7DOF Kuka arm.
• Score: 7.216586291939535
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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