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

Granthik Halder, Rudrashis Majumder, Rakshith M R, Rahi Shah, Suresh Sundaram

TL;DR

The paper tackles real-time obstacle avoidance for autonomous ground vehicles in cluttered environments by approximating Hamilton-Jacobi Reachability with Physics-Informed Neural Networks. NeuroHJR embeds system dynamics and safety constraints into the PINN loss, enabling grid-free, scalable estimation of reachable sets. Through simulations, it achieves safety performance comparable to classical HJR while reducing travel time by about 25% and shortening paths, demonstrating potential for real-time robotics deployment. An ablation study on sensor radius highlights a trade-off between sensing range and trajectory efficiency, reinforcing the method's practical relevance for adaptive, safe navigation.

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.

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

TL;DR

The paper tackles real-time obstacle avoidance for autonomous ground vehicles in cluttered environments by approximating Hamilton-Jacobi Reachability with Physics-Informed Neural Networks. NeuroHJR embeds system dynamics and safety constraints into the PINN loss, enabling grid-free, scalable estimation of reachable sets. Through simulations, it achieves safety performance comparable to classical HJR while reducing travel time by about 25% and shortening paths, demonstrating potential for real-time robotics deployment. An ablation study on sensor radius highlights a trade-off between sensing range and trajectory efficiency, reinforcing the method's practical relevance for adaptive, safe navigation.

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.

Paper Structure

This paper contains 21 sections, 26 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Statement
  3. Hamilton-Jacobi Reachability
  4. Forward Reachability Set
  5. Backward Reachability Set
  6. Physics-Informed Neural Networks
  7. Problem Definition
  8. System Model
  9. NeuroHJR Methodology
  10. PDE for Hamilton Jacobi Reachability
  11. NeuroHJR Architecture
  12. Training and Loss Function
  13. PDE Residual Loss
  14. Value Function Loss
  15. Obstacle Avoidance Loss
  16. ...and 6 more sections

Figures (4)

  • Figure 1: NeuroHJR Architecture
  • Figure 2: Obstacle avoidance using NeuroHJR
  • Figure 3: Trajectory Comparison: NeuroHJR vs Conventional HJR
  • Figure 4: Comparison of Trajectories for Different Sensor Radii