Reachability Barrier Networks: Learning Hamilton-Jacobi Solutions for Smooth and Flexible Control Barrier Functions

TL;DR

This paper introduces reachability barrier networks (RBNs), a neural network approach using Hamilton-Jacobi solutions to generate smooth, accurate, and scalable control barrier functions for safety-critical autonomous systems, with probabilistic safety guarantees.

Contribution

The paper presents a novel physics-informed neural network method to generate high-dimensional, smooth control barrier functions with post-training tunability and probabilistic safety assurances.

Findings

RBNs outperform neural CBFs in high-dimensional safety tasks.

RBNs are highly accurate in low dimensions.

Empirical safety improvements in a 9D multi-vehicle scenario.

Abstract

Recent developments in autonomous driving and robotics underscore the necessity of safety-critical controllers. Control barrier functions (CBFs) are a popular method for appending safety guarantees to a general control framework, but they are notoriously difficult to generate beyond low dimensions. Existing methods often yield non-differentiable or inaccurate approximations that lack integrity, and thus fail to ensure safety. In this work, we use physics-informed neural networks (PINNs) to generate smooth approximations of CBFs by computing Hamilton-Jacobi (HJ) optimal control solutions. These reachability barrier networks (RBNs) avoid traditional dimensionality constraints and support the tuning of their conservativeness post-training through a parameterized discount term. To ensure robustness of the discounted solutions, we leverage conformal prediction methods to derive probabilistic safety guarantees for RBNs. We demonstrate that RBNs are highly accurate in low dimensions, and safer than the standard neural CBF approach in high dimensions. Namely, we showcase the RBNs in a 9D multi-vehicle collision avoidance problem where it empirically proves to be 5.5x safer and 1.9x less conservative than the neural CBFs, offering a promising method to synthesize CBFs for general nonlinear autonomous systems.