{"type":"ScholarlyArticle","title":"Multi-Robot Adversarial Patrolling Strategies via Lattice Paths","authors":[{"name":"Jan Buermann","slug":"jan-buermann","given":"Jan","family":"Buermann","affiliation":"University of Southampton , UK"},{"name":"Jie Zhang","slug":"jie-zhang","given":"Jie","family":"Zhang","affiliation":"University of Southampton , UK"}],"abstract":"In full-knowledge multi-robot adversarial patrolling, a group of robots have to detect an adversary who knows the robots' strategy. The adversary can easily take advantage of any deterministic patrolling strategy, which necessitates the employment of a randomised strategy. While the Markov decision process has been the dominant methodology in computing the penetration detection probabilities, we apply enumerative combinatorics to characterise the penetration detection probabilities. It allows us to provide the closed formulae of these probabilities and facilitates characterising optimal random defence strategies. Comparing to iteratively updating the Markov transition matrices, our methods significantly reduces the time and space complexity of solving the problem. We use this method to tackle four penetration configurations.","doi":"10.24963/ijcai.2020/582","url":"https://ijcai.org/proceedings/2020/582","pdf":"https://ijcai.org/proceedings/2020/0582.pdf","markdown":"https://ijcai.org/proceedings/2020/582.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/582","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Planning and Scheduling","track":"Main track","number":582,"pages":{"first":4213,"last":4219},"keywords":["Planning and Scheduling: Planning under Uncertainty","Planning and Scheduling: Theoretical Foundations of Planning","Planning and Scheduling: Robot Planning"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25398/file_25398.m3u8","length_sec":286,"provider":"hls"}],"references":[{"position":1,"raw":"[Agmon et al., 2008] Noa Agmon, Vladimir Sadov, Gal A. 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