{"type":"preprint","publication_status":"submitted","external_id":{"arxiv":["2409.19277"]},"user_id":"32655","abstract":[{"text":"In the general pattern formation (GPF) problem, a swarm of simple autonomous,\r\ndisoriented robots must form a given pattern. The robots' simplicity imply a\r\nstrong limitation: When the initial configuration is rotationally symmetric,\r\nonly patterns with a similar symmetry can be formed [Yamashita, Suzyuki; TCS\r\n2010]. The only known algorithm to form large patterns with limited visibility\r\nand without memory requires the robots to start in a near-gathering (a swarm of\r\nconstant diameter) [Hahn et al.; SAND 2024]. However, not only do we not know\r\nany near-gathering algorithm guaranteed to preserve symmetry but most natural\r\ngathering strategies trivially increase symmetries [Castenow et al.; OPODIS\r\n2022].\r\n  Thus, we study near-gathering without changing the swarm's rotational\r\nsymmetry for disoriented, oblivious robots with limited visibility (the\r\nOBLOT-model, see [Flocchini et al.; 2019]). We introduce a technique based on\r\nthe theory of dynamical systems to analyze how a given algorithm affects\r\nsymmetry and provide sufficient conditions for symmetry preservation. Until\r\nnow, it was unknown whether the considered OBLOT-model allows for any\r\nnon-trivial algorithm that always preserves symmetry. Our first result shows\r\nthat a variant of Go-to-the-Average always preserves symmetry but may sometimes\r\nlead to multiple, unconnected near-gathering clusters. Our second result is a\r\nsymmetry-preserving near-gathering algorithm that works on swarms with a convex\r\nboundary (the outer boundary of the unit disc graph) and without holes (circles\r\nof diameter 1 inside the boundary without any robots).","lang":"eng"}],"date_created":"2024-10-01T13:29:43Z","status":"public","project":[{"_id":"106","grant_number":"453112019","name":"Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme"}],"date_updated":"2024-10-01T13:44:40Z","publication":"arXiv:2409.19277","department":[{"_id":"101"}],"title":"Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility","author":[{"orcid":"0009-0002-4750-2051","id":"32655","first_name":"Raphael","last_name":"Gerlach","full_name":"Gerlach, Raphael"},{"orcid":"0000-0002-8054-2058","first_name":"Sören","full_name":"von der Gracht, Sören","last_name":"von der Gracht","id":"97359"},{"full_name":"Hahn, Christopher","last_name":"Hahn","first_name":"Christopher"},{"id":"47213","first_name":"Jonas","full_name":"Harbig, Jonas","last_name":"Harbig"},{"first_name":"Peter","full_name":"Kling, Peter","last_name":"Kling"}],"oa":"1","year":"2024","keyword":["Swarm Algorithm","Swarm Robots","Distributed Algorithm","Pattern Formation","Limited Visibility","Oblivious"],"citation":{"apa":"Gerlach, R., von der Gracht, S., Hahn, C., Harbig, J., &#38; Kling, P. (n.d.). Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility. In <i>arXiv:2409.19277</i>.","bibtex":"@article{Gerlach_von der Gracht_Hahn_Harbig_Kling, title={Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility}, journal={arXiv:2409.19277}, author={Gerlach, Raphael and von der Gracht, Sören and Hahn, Christopher and Harbig, Jonas and Kling, Peter} }","mla":"Gerlach, Raphael, et al. “Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility.” <i>ArXiv:2409.19277</i>.","ieee":"R. Gerlach, S. von der Gracht, C. Hahn, J. Harbig, and P. Kling, “Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility,” <i>arXiv:2409.19277</i>. .","short":"R. Gerlach, S. von der Gracht, C. Hahn, J. Harbig, P. Kling, ArXiv:2409.19277 (n.d.).","chicago":"Gerlach, Raphael, Sören von der Gracht, Christopher Hahn, Jonas Harbig, and Peter Kling. “Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility.” <i>ArXiv:2409.19277</i>, n.d.","ama":"Gerlach R, von der Gracht S, Hahn C, Harbig J, Kling P. Symmetry Preservation in Swarms of Oblivious Robots with Limited  Visibility. <i>arXiv:240919277</i>."},"_id":"56298","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2409.19277"}],"language":[{"iso":"eng"}]}