Mixed-Integer Linear Programming Models for Multi-Robot Non-Adversarial Search

TL;DR

This paper introduces novel MILP models for multi-robot search path planning in graph environments, enabling optimal solutions with improved computational efficiency and adaptability for online deployment.

Contribution

First MILP models for MESPP that handle multiple searchers, capture ranges, and false negatives, improving solution quality and computational performance.

Findings

Achieved 98% reduction in computational time compared to previous methods.

Distributed approach performs within 6% of centralized solutions.

Models enable longer planning horizons and practical online adaptation.

Abstract

In this letter, we consider the Multi-Robot Efficient Search Path Planning (MESPP) problem, where a team of robots is deployed in a graph-represented environment to capture a moving target within a given deadline. We prove this problem to be NP-hard, and present the first set of Mixed-Integer Linear Programming (MILP) models to tackle the MESPP problem. Our models are the first to encompass multiple searchers, arbitrary capture ranges, and false negatives simultaneously. While state-of-the-art algorithms for MESPP are based on simple path enumeration, the adoption of MILP as a planning paradigm allows to leverage the powerful techniques of modern solvers, yielding better computational performance and, as a consequence, longer planning horizons. The models are designed for computing optimal solutions offline, but can be easily adapted for a distributed online approach. Our simulations show that it is possible to achieve 98% decrease in computational time relative to the previous state-of-the-art. We also show that the distributed approach performs nearly as well as the centralized, within 6% in the settings studied in this letter, with the advantage of requiring significant less time - an important consideration in practical search missions.