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Space and Move-Optimal Arbitrary Pattern Formation on Infinite Rectangular Grid by Oblivious Robot Swarm

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

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Author Details

Avisek Sharma
  • Department of Mathematics, Jadavpur University, India
Satakshi Ghosh
  • Department of Mathematics, Jadavpur University, India
Pritam Goswami
  • Department of Mathematics, Jadavpur University, India
Buddhadeb Sau
  • Department of Mathematics, Jadavpur University, India

Funding

The first and the third authors are supported by the University Grants Commission (UGC), India. The second author is supported by the West Bengal State Government Fellowship Scheme. The fourth author is supported by the Science and Engineering Research Board (SERB), India

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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)
https://doi.org/10.4230/LIPIcs.SAND.2024.20

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Distributed algorithms
  • Oblivious robots
  • Optimal algorithms
  • Swarm robotics
  • Space optimization
  • and Rectangular grid

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References

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