Tracking Mobile Intruders in an Art Gallery: Guard Deployment Strategies, Fundamental Limitations, and Performance Guarantees
Guillermo J. Laguna, Sourabh Bhattacharya

TL;DR
This paper investigates guard deployment strategies for tracking mobile intruders in polygonal environments, formulates the problem as a multi-robot task allocation challenge, and proposes algorithms with performance guarantees, addressing both simple and complex polygons.
Contribution
It introduces a novel approach to guard deployment and tracking in polygonal environments, including NP-hardness analysis, partition-based algorithms, and extensions to multiple intruders and non-simple polygons.
Findings
NP-hardness of minimum guard speed problem
Partition-based guard allocation algorithm
Effective strategies for multiple intruders
Abstract
This paper addresses the problem of tracking mobile intruders in a polygonal environment. We assume that a team of diagonal guards is deployed inside the polygon to provide mobile coverage. First, we formulate the problem of tracking a mobile intruder inside a polygonal environment as a multi-robot task allocation (MRTA) problem. Leveraging on guard deployment strategies in art gallery problems for mobile coverage, we show that the problem of finding the minimum speed of guards to persistently track a single mobile intruder is NP-hard. Next, for a given maximum speed of the intruder and the guards, we propose a technique to partition a polygon, and compute a feasible allocation of guards to the partitions. We prove the correctness of the proposed algorithm, and show its completeness for a specific class of inputs. We classify the guards based on the structural properties of the…
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Taxonomy
TopicsRobotic Path Planning Algorithms · Computational Geometry and Mesh Generation · Optimization and Search Problems
