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𝒪(log{n})-Time Uniform Circle Formation for Asynchronous Opaque Luminous Robots

Authors Caterina Feletti , Carlo Mereghetti , Beatrice Palano

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Caterina Feletti
  • Dipartimento di Informatica, Università degli Studi di Milano, Italy
Carlo Mereghetti
  • Dipartimento di Informatica, Università degli Studi di Milano, Italy
Beatrice Palano
  • Dipartimento di Informatica, Università degli Studi di Milano, Italy

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Caterina Feletti, Carlo Mereghetti, and Beatrice Palano. 𝒪(log{n})-Time Uniform Circle Formation for Asynchronous Opaque Luminous Robots. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.OPODIS.2023.5

Abstract

We study the Uniform Circle Formation (UCF) problem for a distributed system of n robots which are required to displace on the vertices of a regular n-gon. We consider a well-studied model of autonomous, anonymous, mobile robots that act on the plane through Look-Compute-Move cycles. Moreover, robots are unaware of the cardinality of the system, they are punctiform, completely disoriented, opaque, and luminous. Collisions among robots are not tolerated. 
In the literature, the UCF problem has been solved for such a model by a deterministic algorithm in the asynchronous mode, using a constant amount of light colors and 𝒪(n) epochs in the worst case. In this paper, we provide an improved algorithm for solving the UCF problem for asynchronous robots, which uses 𝒪(log n) epochs still maintaining a constant amount of colors.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Computing methodologies → Mobile agents
  • Computing methodologies → Robotic planning
Keywords
  • Autonomous mobile robots
  • Opaque robots
  • Luminous robots
  • Pattern formation

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