Learning Provably Robust Motion Planners Using Funnel Libraries

TL;DR

This paper introduces a method for learning motion planners with probabilistic success guarantees in uncertain environments by combining robust control and generalization theory, validated through simulated autonomous vehicle and drone navigation tasks.

Contribution

The paper develops a novel approach that integrates funnel libraries with PAC-Bayes bounds to create motion planners with formal robustness guarantees.

Findings

Successfully guarantees motion planning success under disturbances in simulations.

Demonstrates robustness in autonomous vehicle navigation on a five-lane highway.

Shows effective drone navigation through obstacle fields with wind disturbances.

Abstract

This paper presents an approach for learning motion planners that are accompanied with probabilistic guarantees of success on new environments that hold uniformly for any disturbance to the robot's dynamics within an admissible set. We achieve this by bringing together tools from generalization theory and robust control. First, we curate a library of motion primitives where the robustness of each primitive is characterized by an over-approximation of the forward reachable set, i.e., a "funnel". Then, we optimize probably approximately correct (PAC)-Bayes generalization bounds for training our planner to compose these primitives such that the entire funnels respect the problem specification. We demonstrate the ability of our approach to provide strong guarantees on two simulated examples: (i) navigation of an autonomous vehicle under external disturbances on a five-lane highway with multiple vehicles, and (ii) navigation of a drone across an obstacle field in the presence of wind disturbances.