Getting Close without Touching

  • Linda Pagli
  • Giuseppe Prencipe
  • Giovanni Viglietta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7355)


In this paper we study the Near-Gathering problem for a set of asynchronous, anonymous, oblivious and autonomous mobile robots with limited visibility moving in Look-Compute-Move (LCM) cycles: In this problem, the robots have to get close enough to each other, so that every robot can see all the others, without touching (i.e., colliding) with any other robot. The importance of this problem might not be clear at a first sight: Solving the Near-Gathering problem, it is possible to overcome the limitations of having robots with limited visibility, and it is therefore possible to exploit all the studies (the majority, actually) done on this topic, in the unlimited visibility setting. In fact, after the robots get close enough, they are able to see all the robots in the system, a scenario similar to the one where the robots have unlimited visibility. Here, we present a collision-free algorithm for the Near-Gathering problem, the first to our knowledge, that allows a set of autonomous mobile robots to nearly gather within finite time. The collision-free feature of our solution is crucial in order to combine it with an unlimited visibility protocol. In fact, the majority of the algorithms that can be found on the topic assume that all robots occupy distinct positions at the beginning. Hence, only providing a collision-free Near-Gathering algorithm, as the one presented here, is it possible to successfully combine it with an unlimited visibility protocol, hence overcoming the natural limitations of the limited visibility scenario. In our model, distances are induced by the infinity norm. A discussion on how to extend our algorithm to models with different distance functions, including the usual Euclidean distance, is also presented.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ando, H., Oasa, Y., Suzuki, I., Yamashita, M.: A distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Transaction on Robotics and Automation 15(5), 818–828 (1999)CrossRefGoogle Scholar
  2. 2.
    Cieliebak, M.: Gathering Non-oblivious Mobile Robots. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 577–588. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Das, S., Flocchini, P., Prencipe, G., Santoro, N., Yamashita, M.: The power of lights: Synchronizing asynchronoys robots using visibile bits. In: The 32nd International Conference on Distributed Computing Systems, ICDCS (to appear, 2012)Google Scholar
  4. 4.
    Défago, X., Souissi, S.: Non-uniform circle formation algorithm for oblivious mobile robots with convergence toward uniformity. Theoretical Computer Science 396(1-3), 97–112 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Dieudonné, Y., Labbani-Igbida, O., Petit, F.: Circle formation of weak mobile robots. ACM Transactions on Autonomous and Adaptive Systems 3(4) (2008)Google Scholar
  6. 6.
    Dieudonné, Y., Petit, F., Villain, V.: Leader Election Problem versus Pattern Formation Problem. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 267–281. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Efrima, A., Peleg, D.: Distributed Models and Algorithms for Mobile Robot Systems. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds.) SOFSEM 2007. LNCS, vol. 4362, pp. 70–87. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of robots with limited visibility. Theoretical Computer Science 337(1-3), 147–168 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Arbitrary pattern formation by asynchronous oblivious robots. Theoretical Computer Science 407, 412–447 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Katreniak, B.: Convergence with Limited Visibility by Asynchronous Mobile Robots. In: Kosowski, A., Yamashita, M. (eds.) SIROCCO 2011. LNCS, vol. 6796, pp. 125–137. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Pagli, L., Prencipe, G., Viglietta, G.: Getting close without touching. Technical Report TR-12-05, Dipartimento di Informatica, Università di Pisa (2012)Google Scholar
  12. 12.
    Peleg, D.: Distributed Coordination Algorithms for Mobile Robot Swarms: New Directions and Challenges. In: Pal, A., Kshemkalyani, A.D., Kumar, R., Gupta, A. (eds.) IWDC 2005. LNCS, vol. 3741, pp. 1–12. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  13. 13.
    Prencipe, G.: The effect of synchronicity on the behavior of autonomous mobile robots. Theory of Computing Systems (TOCS) 38(5), 539–558 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Souissi, S., Défago, X., Yamashita, M.: Using eventually consistent compasses to gather memory-less mobile robots with limited visibility. ACM Transactions on Autonomous and Adaptive Systems 4(1), 1–27 (2009)CrossRefGoogle Scholar
  15. 15.
    Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. Siam Journal on Computing 28(4), 1347–1363 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Yamashita, M., Suzuki, I.: Characterizing geometric patterns formable by oblivious anonymous mobile robots. Theoretical Computer Science 411(26-28) (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Linda Pagli
    • 1
  • Giuseppe Prencipe
    • 1
  • Giovanni Viglietta
    • 1
  1. 1.Dipartimento di InformaticaUniversità di PisaItaly

Personalised recommendations