Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systems

TL;DR

This paper introduces a contraction-based feedback motion planning approach that uses learned models and probabilistic error bounds to ensure safety and stability in unknown, high-dimensional systems.

Contribution

It develops a method to learn dynamics, estimate model error bounds, and plan trajectories with probabilistic safety guarantees for complex systems.

Findings

Successfully applied to a 4D car, a 6D quadrotor, and a 22D deformable object.

Outperforms baselines that ignore error bounds or trusted domains.

Provides probabilistic safety and reachability guarantees during planning.

Abstract

We present a method for contraction-based feedback motion planning of locally incrementally exponentially stabilizable systems with unknown dynamics that provides probabilistic safety and reachability guarantees. Given a dynamics dataset, our method learns a deep control-affine approximation of the dynamics. To find a trusted domain where this model can be used for planning, we obtain an estimate of the Lipschitz constant of the model error, which is valid with a given probability, in a region around the training data, providing a local, spatially-varying model error bound. We derive a trajectory tracking error bound for a contraction-based controller that is subjected to this model error, and then learn a controller that optimizes this tracking bound. With a given probability, we verify the correctness of the controller and tracking error bound in the trusted domain. We then use the trajectory error bound together with the trusted domain to guide a sampling-based planner to return trajectories that can be robustly tracked in execution. We show results on a 4D car, a 6D quadrotor, and a 22D deformable object manipulation task, showing our method plans safely with learned models of high-dimensional underactuated systems, while baselines that plan without considering the tracking error bound or the trusted domain can fail to stabilize the system and become unsafe.