Certifiable Reachability Learning Using a New Lipschitz Continuous Value Function

TL;DR

This paper introduces a novel reachability learning framework for high-dimensional nonlinear systems, utilizing a Lipschitz continuous value function and certification methods to ensure safety in reach-avoid problems, validated on drone and highway scenarios.

Contribution

The paper presents a new Lipschitz continuous reach-avoid value function and certification methods, enhancing learning performance and providing deterministic safety guarantees.

Findings

Validated on 12D drone racing hardware

Demonstrated in 10D highway take-over simulation

Achieved improved learning performance and safety guarantees

Abstract

We propose a new reachability learning framework for high-dimensional nonlinear systems, focusing on reach-avoid problems. These problems require computing the reach-avoid set, which ensures that all its elements can safely reach a target set despite disturbances within pre-specified bounds. Our framework has two main parts: offline learning of a newly designed reachavoid value function, and post-learning certification. Compared to prior work, our new value function is Lipschitz continuous and its associated Bellman operator is a contraction mapping, both of which improve the learning performance. To ensure deterministic guarantees of our learned reach-avoid set, we introduce two efficient post-learning certification methods. Both methods can be used online for real-time local certification or offline for comprehensive certification. We validate our framework in a 12-dimensional crazyflie drone racing hardware experiment and a simulated 10-dimensional highway take-over example.