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

TL;DR

This paper introduces RPT*, a novel search-based algorithm with optimality guarantees for solving the probabilistic Hamiltonian Path Problem variant, enabling efficient target search in uncertain and complex environments.

Contribution

It presents RPT*, a new dynamic programming-based method that handles history dependency and uncertainty in routing problems, along with HATS for autonomous target search.

Findings

RPT* achieves optimal solutions with efficiency improvements.

HATS effectively balances exploration and exploitation.

Approach outperforms baseline methods in simulations and real robots.

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.