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Documents authored by Sau, Buddhadeb

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DOI: 10.4230/LIPIcs.SAND.2024.20
Space and Move-Optimal Arbitrary Pattern Formation on Infinite Rectangular Grid by Oblivious Robot Swarm

Authors: Avisek Sharma, Satakshi Ghosh, Pritam Goswami, and Buddhadeb Sau

Published in: LIPIcs, Volume 292, 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)

Abstract
Arbitrary Pattern Formation (APF) is a fundamental coordination problem in swarm robotics. It requires a set of autonomous robots (mobile computing units) to form an arbitrary pattern (given as input) starting from any initial pattern. This problem has been extensively investigated in continuous and discrete scenarios, with this study focusing on the discrete variant. A set of robots is placed on the nodes of an infinite rectangular grid graph embedded in the euclidean plane. The movements of each robot is restricted to one of the four neighboring grid nodes from its current position. The robots are autonomous, anonymous, identical, and homogeneous, and operate Look-Compute-Move cycles. In this work, we adopt the classical OBLOT robot model, meaning the robots have no persistent memory or explicit communication methods, yet they possess full and unobstructed visibility. This work proposes an algorithm that solves the APF problem in a fully asynchronous scheduler assuming the initial configuration is asymmetric. The considered performance measures of the algorithm are space and number of moves required for the robots. The algorithm is asymptotically move-optimal. Here, we provide a definition of space complexity that takes the visibility issue into consideration. We observe an obvious lower bound 𝒟 of the space complexity and show that the proposed algorithm has the space complexity 𝒟+4. On comparing with previous related works, we show that this is the first proposed algorithm considering OBLOT robot model that is asymptotically move-optimal and has the least space complexity which is almost optimal.
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Avisek Sharma, Satakshi Ghosh, Pritam Goswami, and Buddhadeb Sau. Space and Move-Optimal Arbitrary Pattern Formation on Infinite Rectangular Grid by Oblivious Robot Swarm. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{sharma_et_al:LIPIcs.SAND.2024.20,
  author =	{Sharma, Avisek and Ghosh, Satakshi and Goswami, Pritam and Sau, Buddhadeb},
  title =	{{Space and Move-Optimal Arbitrary Pattern Formation on Infinite Rectangular Grid by Oblivious Robot Swarm}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{20:1--20:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.20},
  URN =		{urn:nbn:de:0030-drops-198989},
  doi =		{10.4230/LIPIcs.SAND.2024.20},
  annote =	{Keywords: Distributed algorithms, Oblivious robots, Optimal algorithms, Swarm robotics, Space optimization, and Rectangular grid}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2021.10
Pattern Formation by Robots with Inaccurate Movements

Authors: Kaustav Bose, Archak Das, and Buddhadeb Sau

Published in: LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021)

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.
Cite as

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)

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@InProceedings{bose_et_al:LIPIcs.OPODIS.2021.10,
  author =	{Bose, Kaustav and Das, Archak and Sau, Buddhadeb},
  title =	{{Pattern Formation by Robots with Inaccurate Movements}},
  booktitle =	{25th International Conference on Principles of Distributed Systems (OPODIS 2021)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-219-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{217},
  editor =	{Bramas, Quentin and Gramoli, Vincent and Milani, Alessia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.10},
  URN =		{urn:nbn:de:0030-drops-157850},
  doi =		{10.4230/LIPIcs.OPODIS.2021.10},
  annote =	{Keywords: Distributed Algorithm, Mobile Robots, Movement Error, Approximate Arbitrary Pattern Formation, Look-Compute-Move, Minimum Enclosing Circle}
}
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