{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T11:41:21Z","timestamp":1770291681859,"version":"3.49.0"},"reference-count":17,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,7,31]],"date-time":"2022-07-31T00:00:00Z","timestamp":1659225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"JSPS KAKENHI","award":["22H01440"],"award-info":[{"award-number":["22H01440"]}]},{"name":"JSPS KAKENHI","award":["22J22440"],"award-info":[{"award-number":["22J22440"]}]},{"name":"SSUP program of Sony Semiconductor Solutions Corporation","award":["22H01440"],"award-info":[{"award-number":["22H01440"]}]},{"name":"SSUP program of Sony Semiconductor Solutions Corporation","award":["22J22440"],"award-info":[{"award-number":["22J22440"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>For a robotic swarm system composed of autonomous mobile robots, controlling and using asymmetric global geometric states promotes the task performance of the swarm. This paper presents a systematic method for estimating asymmetric global geometric states over a swarm system. To overcome the limitations of local observation or communication ability, we propose a wave-type interaction among neighboring robots. We assume that each robot has a scalar state variable called a phase, which is manipulated through interactions. Through the analysis of eigenvalues of a graph Laplacian matrix corresponding to a local communication network of robots, we show that a robot can estimate global states, such as the size of an entire swarm, by frequency analysis of its phase. We also analyzed the stability of the wave-type interaction based on von-Neumann stability. We verified the proposed method by computer simulations, in which robots in a swarm detected the deformation in the shape of the swarm when the swarm was passing through a narrow area. The result will contribute to building a control system for swarms that can manipulate their shape or characteristics to adapt themselves based on tasks or environmental requirements.<\/jats:p>","DOI":"10.3390\/sym14081578","type":"journal-article","created":{"date-parts":[[2022,8,1]],"date-time":"2022-08-01T23:49:27Z","timestamp":1659397767000},"page":"1578","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Wave-Type Interaction within a Robotic Swarm System for Decentralized Estimation of Global Geometric States"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3048-6606","authenticated-orcid":false,"given":"Yuki","family":"Origane","sequence":"first","affiliation":[{"name":"Department of Systems and Control Engineering, School of Engineering, Tokyo Institute of Technology, Tokyo 152-8550, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3186-6531","authenticated-orcid":false,"given":"Daisuke","family":"Kurabayashi","sequence":"additional","affiliation":[{"name":"Department of Systems and Control Engineering, School of Engineering, Tokyo Institute of Technology, Tokyo 152-8550, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11721-012-0075-2","article-title":"Swarm robotics: A review from the swarm engineering perspective","volume":"7","author":"Brambilla","year":"2013","journal-title":"Swarm Intell."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.neucom.2015.05.116","article-title":"A review of swarm robotics tasks","volume":"172","author":"Bayindir","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"124172","DOI":"10.1109\/ACCESS.2020.3006096","article-title":"Multi-Robot Control Inspired by Bacterial Chemotaxis: Coverage and Randezvous vi Networking of Chemotaxis Controllers","volume":"8","author":"Izumi","year":"2020","journal-title":"IEEE Access"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3870","DOI":"10.1103\/PhysRevLett.76.3870","article-title":"Collective Motion in a System of Motile Elements","volume":"76","author":"Shimoyama","year":"1996","journal-title":"Phys. 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