NeuroHJR: Hamilton-Jacobi Reachability-based Obstacle Avoidance in Complex Environments with Physics-Informed Neural Networks

TL;DR

NeuroHJR introduces a physics-informed neural network approach to approximate Hamilton-Jacobi Reachability, enabling real-time, scalable obstacle avoidance for autonomous ground vehicles in complex, cluttered environments.

Contribution

The paper presents NeuroHJR, a novel neural network framework that embeds system dynamics and safety constraints to efficiently approximate reachability solutions without grid discretization.

Findings

Achieves safety performance comparable to classical HJR methods.

Reduces computational cost significantly in densely cluttered scenarios.

Enables real-time obstacle avoidance in complex environments.

Abstract

Autonomous ground vehicles (AGVs) must navigate safely in cluttered environments while accounting for complex dynamics and environmental uncertainty. Hamilton-Jacobi Reachability (HJR) offers formal safety guarantees through the computation of forward and backward reachable sets, but its application is hindered by poor scalability in environments with numerous obstacles. In this paper, we present a novel framework called NeuroHJR that leverages Physics-Informed Neural Networks (PINNs) to approximate the HJR solution for real-time obstacle avoidance. By embedding system dynamics and safety constraints directly into the neural network loss function, our method bypasses the need for grid-based discretization and enables efficient estimation of reachable sets in continuous state spaces. We demonstrate the effectiveness of our approach through simulation results in densely cluttered scenarios, showing that it achieves safety performance comparable to that of classical HJR solvers while significantly reducing the computational cost. This work provides a new step toward real-time, scalable deployment of reachability-based obstacle avoidance in robotics.