Pincer Movements are Always Better Than Same-Direction Search

Given a planar circular region, containing an unknown number of smart mobile evaders, our aim is to detect all of them, or at least to confine them by sweeping the region's boundary, using a team of sweeping agents. We assume all sweepers are identical and have line sensors of equal length. By deriving conditions on the speed of the sweepers and their paths, sweepers can ensure the successful completion of the confinement task implying that evaders with a known limit on their speed cannot escape the initial domain. The critical speed is the minimal speed ensuring sweepers confine all evaders to their original domain. If sweepers move at higher speeds, they can succeed in the complete detection task as well. The prevailing idea in multi-agent based search protocols is to distribute sweepers equally across the domain of interest in order to divide the search effort among cooperating sweepers and thereby obtain better performance as the number of sweepers increases. Previous works suggested confinement and complete detection search protocols for groups of agents based on distributing searchers uniformly around the region and having them move in the same (clockwise or counterclockwise) direction. Recent work suggested pincer strategies for the same purpose. However, no sufficient quantitative comparison was done to prove pincer-based strategies are always better in terms of performance metrics such as minimal sweeper speed for confinement, and time of complete detection, for both of which a lower value is better. In this paper we provide a complete analysis of this problem yielding exact results proving pincer-based strategies are always better in all aspects when an even number of sweepers are working together. We do this for the case of sweepers having linear detectors, but we believe similar results can be obtained in general, for any number of sweepers, more general sensor geometries and different environments.