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

2025-05-16

AI Summary

Constructing control barrier functions (CBFs) for high-dimensional nonlinear autonomous systems remains challenging due to difficulties in analytical derivation, non-differentiability, excessive conservatism, and lack of completeness. Method: This paper proposes Reachability Barrier Networks (RBNs), a novel CBF synthesis framework based on physics-informed neural networks (PINNs) that solve the discounted Hamilton–Jacobi (HJ) equation. RBNs parameterize the discount factor to enable post-training adjustment of safety conservatism and integrate conformal prediction to yield probabilistic safety guarantees. Results: Evaluated on a 9D multi-vehicle collision avoidance task, RBNs improve safety by 5.5× and reduce conservatism by 1.9× compared to neural CBFs, while maintaining high accuracy in low-dimensional settings. RBNs thus overcome fundamental limitations of conventional CBFs—namely, non-differentiability, inaccuracy, and poor scalability to high dimensions—enabling rigorous, adaptable, and scalable safety-critical control.

Technology Category

• Natural Language Processing: Safety and Robustness
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Security and Privacy: Large-scale security measurements

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.

Problem

• Generating smooth Control Barrier Functions (CBFs) for safety-critical controllers
• Overcoming dimensionality constraints in Hamilton-Jacobi (HJ) solutions
• Ensuring probabilistic safety guarantees for autonomous systems

Innovation

• Physics-informed neural networks approximate CBFs smoothly
• Parameterized discount term adjusts conservativeness post-training
• Conformal prediction ensures probabilistic safety guarantees