Chase Your Farthest Neighbour

A Simple Gathering Algorithm for Anonymous, Oblivious and Non-communicating Agents
  • Rotem Manor
  • Alfred M. Bruckstein
Part of the Springer Proceedings in Advanced Robotics book series (SPAR, volume 6)


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.


  1. 1.
    Agmon, N., Peleg, D.: Fault-tolerant gathering algorithms for autonomous mobile robots. SIAM J. Comput. 36(1), 56–82 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 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)Google Scholar
  3. 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. 4.
    Bruckstein, A., Zeitouni, O.: A puzzling feedback quantizer. Technical report 879, EE Department Technion IIT (1993)Google Scholar
  5. 5.
    Cortes, J.: Discontinuous dynamical systems. IEEE control Syst. 28(3), 36–73 (2008)MathSciNetCrossRefGoogle Scholar
  6. 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. 7.
    Gauci, M., Chen, J., Li, W., Dodd, T.J., Gross, R.: Self-organized aggregation without computation. Int. J. Robot. Res. (2014).
  8. 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)Google Scholar
  9. 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. 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. 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)Google Scholar
  12. 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. 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. 14.
    Moreau, L.: Stability of multi-agent systems with time-dependent communication links. IEEE Trans. Autom. Control 50, 169–182 (2005)CrossRefzbMATHGoogle Scholar
  15. 15.
    Suzuki, I., Yamashita, M.: A theory of distributed anonymous mobile robots formation and agreement problems. Technical report, DTIC Document (1994)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.TechnionHaifaIsrael

Personalised recommendations