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Advanced Computing and Systems for Security pp 153–165Cite as

Optimum Circle Formation by Autonomous Robots

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 666))

Abstract

This paper considers a constrained version of the circle formation problem for a set of asynchronous, autonomous robots on the Euclidean plane. The circle formation problem asks a set of autonomous, mobile robots, initially having distinct locations, to place themselves, within finite time, at distinct locations on the circumference of a circle (not defined a priori), without colliding with each other. The constrained circle formation problem demands that in addition the maximum distance moved by any robot to solve the problem should be minimized. A basic objective of the optimization constrain is that it implies energy savings of the robots. This paper presents results in two parts. First, it is shown that the constrained circle formation problem is not solvable for oblivious asynchronous robots under ASYNC model even if the robots have rigid movements. Then the problem is studied for robots which have O(1) bits of persistent memory. The initial robot configurations, for which the problem is not solvable in this model, are characterized. For other configurations, a distributed algorithm is presented to solve the problem for asynchronous robots. Only one bit of persistent memory is needed in the proposed algorithm.

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Authors and Affiliations

  1. Advanced Computing and Microelectronics Unit, Indian Statistical Institute, Kolkata, India

    Subhash Bhagat & Krishnendu Mukhopadhyaya

Authors
  1. Subhash Bhagat
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  2. Krishnendu Mukhopadhyaya
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Corresponding author

Correspondence to Subhash Bhagat .

Editor information

Editors and Affiliations

  1. A. K. Choudhury School of Information Technology, University of Calcutta, Kolkata, West Bengal, India

    Rituparna Chaki

  2. Dipartimento di Scienze Ambientali, Informatica e Statistica, Università Ca’ Foscari, Venice, Italy

    Agostino Cortesi

  3. Faculty of Computer Science, Bialystok University of Technology, Bialystok, Poland

    Khalid Saeed

  4. Computer Science and Engineering, University of Calcutta, Kolkata, West Bengal, India

    Nabendu Chaki

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Bhagat, S., Mukhopadhyaya, K. (2018). Optimum Circle Formation by Autonomous Robots. In: Chaki, R., Cortesi, A., Saeed, K., Chaki, N. (eds) Advanced Computing and Systems for Security. Advances in Intelligent Systems and Computing, vol 666. Springer, Singapore. https://doi.org/10.1007/978-981-10-8180-4_10

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  • DOI: https://doi.org/10.1007/978-981-10-8180-4_10

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-8179-8

  • Online ISBN: 978-981-10-8180-4

  • eBook Packages: EngineeringEngineering (R0)

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