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Pattern Formation by Robots with Inaccurate Movements
Authors
Kaustav Bose 
,
Archak Das ,
Buddhadeb Sau
-
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Volume:
25th International Conference on Principles of Distributed Systems (OPODIS 2021)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Principles of Distributed Systems (OPODIS) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2022-02-28
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Author Details
- Advanced Computing and Microelectronics Unit, Indian Statistical Institute, Kolkata, India
Acknowledgements
We would like to thank the anonymous reviewers for their comments and suggestions which helped us to improve the presentation of the paper.
Cite AsGet BibTex
Kaustav Bose, Archak Das, and Buddhadeb Sau. Pattern Formation by Robots with Inaccurate Movements. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.OPODIS.2021.10
https://doi.org/10.4230/LIPIcs.OPODIS.2021.10
Abstract
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.
Subject Classification
ACM Subject Classification
- Theory of computation → Distributed algorithms
- Theory of computation → Computational geometry
- Computing methodologies → Distributed algorithms
- Computing methodologies → Robotic planning
Keywords
- Distributed Algorithm
- Mobile Robots
- Movement Error
- Approximate Arbitrary Pattern Formation
- Look-Compute-Move
- Minimum Enclosing Circle
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References
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