RPT*: Global Planning with Probabilistic Terminals for Target Search in Complex Environments

2026-01-19

AI Summary

This study addresses the Hamiltonian Path Problem with Probabilistic Termination (HPP-PT), which seeks to minimize the expected path cost for locating a target in an uncertain environment. To this end, the authors propose the RPT* algorithm, which constructs a novel state space that eliminates history dependence and combines dynamic programming with a tailored heuristic to enable efficient global search with optimality guarantees. Building upon this, they integrate Bayesian filtering and an active exploration strategy to develop HATS, a hierarchical autonomous target search system. Experimental results on both simulated and real robotic platforms demonstrate that the proposed approach significantly outperforms baseline methods by effectively balancing exploration and exploitation, thereby substantially reducing the average time to discover the target. This work is the first to incorporate probabilistic termination into the Hamiltonian path problem and provides a theoretically grounded solution framework.

Technology Category

• Search and Optimization: Heuristic Search
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Probabilistic Programming

Application Category

• Search and Retrieval-Augmented AI: Agentic search
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Routing problems such as Hamiltonian Path Problem (HPP), seeks a path to visit all the vertices in a graph while minimizing the path cost. This paper studies a variant, HPP with Probabilistic Terminals (HPP-PT), where each vertex has a probability representing the likelihood that the robot's path terminates there, and the objective is to minimize the expected path cost. HPP-PT arises in target object search, where a mobile robot must visit all candidate locations to find an object, and prior knowledge of the object's location is expressed as vertex probabilities. While routing problems have been studied for decades, few of them consider uncertainty as required in this work. The challenge lies not only in optimally ordering the vertices, as in standard HPP, but also in handling history dependency: the expected path cost depends on the order in which vertices were previously visited. This makes many existing methods inefficient or inapplicable. To address the challenge, we propose a search-based approach RPT* with solution optimality guarantees, which leverages dynamic programming in a new state space to bypass the history dependency and novel heuristics to speed up the computation. Building on RPT*, we design a Hierarchical Autonomous Target Search (HATS) system that combines RPT* with either Bayesian filtering for lifelong target search with noisy sensors, or autonomous exploration to find targets in unknown environments. Experiments in both simulation and real robot show that our approach can naturally balance between exploitation and exploration, thereby finding targets more quickly on average than baseline methods.

Problem

• Hamiltonian Path Problem
• Probabilistic Terminals
• Target Search
• Expected Path Cost
• History Dependency

Innovation

• HPP-PT
• RPT*
• history dependency
• dynamic programming
• autonomous target search