A Hamilton-Jacobi Reachability-Guided Search Framework for Efficient and Safe Indoor Planar Robot Navigation

2026-04-19

AI Summary

This work addresses the challenge of balancing safety and real-time planning efficiency in robot navigation within complex, dynamic indoor environments, where conventional graph-search methods often suffer from the curse of dimensionality. The authors propose a novel framework that integrates offline Hamilton-Jacobi (HJ) reachability analysis with online graph search. By leveraging precomputed HJ value functions to encode safety constraints and provide heuristic guidance, the approach ensures collision avoidance while significantly accelerating the search process. This method represents the first effective incorporation of HJ reachability into online graph-based planning, thereby mitigating HJ’s reliance on fully known environments and substantially reducing computational overhead. Extensive simulations and real-world experiments demonstrate that the proposed approach consistently outperforms existing baselines across diverse indoor scenarios—both with and without human presence—achieving simultaneous improvements in planning speed and safety.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Intelligent Robots: Motion and Path Planning
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation

Abstract

Autonomous navigation requires planning to reach a goal safely and efficiently in complex and potentially dynamic environments. Graph search-based algorithms are widely adopted due to their generality and theoretical guarantees when equipped with admissible heuristics. However, the computational complexity of graph search grows rapidly with the dimensionality of the search space, often making real-time planning in dynamic environments intractable. In this paper, we combine offline Hamilton-Jacobi (HJ) reachability with online graph search to leverage the complementary strengths of both. Precomputed HJ value functions, used as informative heuristics and proactive safety constraints, amortize online computation of the graph search process. At the same time, graph search enables reachability-based reasoning to be incorporated into online planning, overcoming the long-standing challenge of HJ reachability requiring full knowledge of the environment. Extensive simulation studies and real-world experiments demonstrate that the proposed approach consistently outperforms baseline methods in terms of planning efficiency and navigation safety, in environments with and without human presence.

Problem

• autonomous navigation
• Hamilton-Jacobi reachability
• graph search
• real-time planning
• navigation safety

Innovation

• Hamilton-Jacobi reachability
• graph search
• informative heuristics
• proactive safety constraints
• autonomous navigation