2026-07-26T17:25:42Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:15785 2024-03-12T12:00:33Z ddc:004 open_access

Pattern Formation by Robots with Inaccurate Movements Bose, Kaustav Das, Archak Sau, Buddhadeb Distributed Algorithm Mobile Robots Movement Error Approximate Arbitrary Pattern Formation Look-Compute-Move Minimum Enclosing Circle Arbitrary Pattern Formation is a fundamental problem in autonomous mobile robot systems. The problem asks to design a distributed algorithm that moves a team of autonomous, anonymous and identical mobile robots to form any arbitrary pattern F given as input. In this paper, we study the problem for robots whose movements can be inaccurate. Our movement model assumes errors in both direction and extent of the intended movement. Forming the given pattern exactly is not possible in this setting. So we require that the robots must form a configuration which is close to the given pattern F. We call this the Approximate Arbitrary Pattern Formation problem. With no agreement in coordinate system, the problem is unsolvable, even by fully synchronous robots, if the initial configuration 1) has rotational symmetry and there is no robot at the center of rotation or 2) has reflectional symmetry and there is no robot on the reflection axis. From all other initial configurations, we solve the problem by 1) oblivious, silent and semi-synchronous robots and 2) oblivious, asynchronous robots that can communicate using externally visible lights. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Kaustav Bose and Archak Das and Buddhadeb Sau 2022 Is Part Of LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.OPODIS.2021.10 urn:nbn:de:0030-drops-157850 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.10 eng https://creativecommons.org/licenses/by/4.0/legalcode