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Chase Your Farthest Neighbour

A Simple Gathering Algorithm for Anonymous, Oblivious and Non-communicating Agents

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Distributed Autonomous Robotic Systems

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 6))

Abstract

We consider a group of mobile robotic agents, identical and indistinguishable, having no memory (oblivious) and no common frame of reference (neither absolute location nor a common orientation). Furthermore, these agents are assumed to posses only rudimentary sensing and computational capabilities (limited visibility and basic geometric sorting). We prove that, such robots, implementing a “Chase the farthest neighbour” policy, preform the task of gathering to a point within a finite time or a finite expected number of time steps. In continuous time, preforming such a gathering task is rather straightforward, while in the discrete time, we prove that a randomized semi-synchronised timing model leads to gathering within a finite expected number of time-steps.

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References

  1. Agmon, N., Peleg, D.: Fault-tolerant gathering algorithms for autonomous mobile robots. SIAM J. Comput. 36(1), 56–82 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ando, H., Oasa, Y., Suzuki, Y., Yamashita, Y.: Distributed memory less point convergence algorithm for mobile robots with limited visibility. In: IEEE Transactions on Robotics and Automation, vol. 15(5), pp. 818–828 (1999)

    Article  Google Scholar 

  3. Bellaiche, L.I., Bruckstein, A.: Continuous time gathering of agents with limited visibility and bearing-only sensing. Technical report, CIS Technical report, TASP (2015)

    Google Scholar 

  4. Bruckstein, A., Zeitouni, O.: A puzzling feedback quantizer. Technical report 879, EE Department Technion IIT (1993)

    Google Scholar 

  5. Cortes, J.: Discontinuous dynamical systems. IEEE control Syst. 28(3), 36–73 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gauci, M., Chen, J., Dodd, T.J., Gross, R.: Evolving aggregation behaviors in multi-robot systems with binary sensors. Distributed Autonomous Robotic Systems, pp. 355–367. Springer, Berlin (2014)

    Google Scholar 

  7. Gauci, M., Chen, J., Li, W., Dodd, T.J., Gross, R.: Self-organized aggregation without computation. Int. J. Robot. Res. (2014). https://doi.org/10.1177/0278364914525244

    Article  Google Scholar 

  8. Gordon, N., Wagner, I., Bruckstein, A.: Gathering multiple robotic a(ge)nts with limited sensing capabilities. Ant Colony Optimization and Swarm Intelligence. Lecture Notes in Computer Science, p. 142–153. Springer, Berlin (2004)

    Chapter  Google Scholar 

  9. Gordon, N., Wagner, I., Bruckstein, A.: A randomized gathering algorithm for multiple robots with limited sensing capabilities. In: Proceedings of MARS 2005 workshop at ICINCO Barcelona (2005)

    Google Scholar 

  10. Gordon, N., Elor, Y., Bruckstein, A.: Gathering multiple robotic agents with crude distance sensing capabilities. Ant Colony Optimization and Swarm Intelligence. Lecture Notes in Computer Science, pp. 72–83. Springer, Berlin (2008)

    Google Scholar 

  11. Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control 48(6), 988–1001 (2003)

    Article  MathSciNet  Google Scholar 

  12. Manor, R., Bruckstein, A.: Chase Your Farthest Neighbour: A simple gathering algorithm for anonymous, oblivious and non-communicating agents. Technical report CIS-2016-01 (2016)

    Google Scholar 

  13. Moreau, L.: Stability of continuous-time distributed consensus algorithms. In: Proceedings of the 43rd IEEE Conference on Decision and Control, 2004. CDC. vol. 4, p. 3998–4003 (2004)

    Google Scholar 

  14. Moreau, L.: Stability of multi-agent systems with time-dependent communication links. IEEE Trans. Autom. Control 50, 169–182 (2005)

    Article  MATH  Google Scholar 

  15. Suzuki, I., Yamashita, M.: A theory of distributed anonymous mobile robots formation and agreement problems. Technical report, DTIC Document (1994)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Technion, Haifa, Israel

    Rotem Manor & Alfred M. Bruckstein

Authors
  1. Rotem Manor
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  2. Alfred M. Bruckstein
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Corresponding author

Correspondence to Rotem Manor .

Editor information

Editors and Affiliations

  1. Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, UK

    Roderich Groß

  2. Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, UK

    Andreas Kolling

  3. School for Engineering of Matter, Transport and Energy (SEMTE), Arizona State University, Tempe, AZ, USA

    Spring Berman

  4. Massachusetts Institute of Technology, Cambridge, MA, USA

    Emilio Frazzoli

  5. ENAC, IIE, DIAL, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

    Alcherio Martinoli

  6. Department of Mechanical Engineering and Science, Kyoto University, Kyoto, Japan

    Fumitoshi Matsuno

  7. Wyss Institute for Biologically Inspired Engineering, Harvard University Wyss Institute for Biologically Inspired, Cambridge, MA, USA

    Melvin Gauci

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Manor, R., Bruckstein, A.M. (2018). Chase Your Farthest Neighbour. In: Groß, R., et al. Distributed Autonomous Robotic Systems. Springer Proceedings in Advanced Robotics, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-73008-0_8

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  • DOI: https://doi.org/10.1007/978-3-319-73008-0_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73006-6

  • Online ISBN: 978-3-319-73008-0

  • eBook Packages: EngineeringEngineering (R0)

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