Taking Advantage of Symmetries: Gathering of Asynchronous Oblivious Robots on a Ring

  • Ralf Klasing
  • Adrian Kosowski
  • Alfredo Navarra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5401)


One of the recently considered models of robot-based computing makes use of identical, memoryless mobile units placed in nodes of an anonymous graph. The robots operate in Look-Compute-Move cycles; in one cycle, a robot takes a snapshot of the current configuration (Look), takes a decision whether to stay idle or to move to one of the nodes adjacent to its current position (Compute), and in the latter case makes an instantaneous move to this neighbor (Move). Cycles are performed asynchronously for each robot.

In such a restricted scenario, we study the influence of symmetries of the robot configuration on the feasibility of certain computational tasks. More precisely, we deal with the problem of gathering all robots at one node of the graph, and propose a solution based on a symmetry-preserving strategy. When the considered graph is an undirected ring and the number of robots is sufficiently large (more than 18), such an approach is proved to solve the problem for all starting situations, as long as gathering is feasible. In this way we also close the open problem of characterizing symmetric situations on the ring which admit a gathering [R. Klasing, E. Markou, A. Pelc: Gathering asynchronous oblivious mobile robots in a ring, Theor. Comp. Sci. 390(1), 27-39, 2008].

The proposed symmetry-preserving approach, which is complementary to symmetry-breaking techniques found in related work, appears to be new and may have further applications in robot-based computing.


Asynchronous system Mobile robots Oblivious robots  Gathering problem Ring 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Agmon, N., Peleg, D.: Fault-Tolerant Gathering Algorithms for Autonomous Mobile Robots. SIAM Journal on Computing 36(1), 56–82 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Alpern, S., Gal, S.: The Theory of Search Games and Rendezvous. Kluwer Academic Publishers, Dordrecht (2002)zbMATHGoogle Scholar
  3. 3.
    Ando, H., Oasa, Y., Suzuki, I., Yamashita, M.: Distributed Memoryless Point Convergence Algorithm for Mobile Robots with Limited Visibility. IEEE Transactions on Robotics and Automation 15(5), 818–828 (1999)CrossRefGoogle Scholar
  4. 4.
    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
  5. 5.
    Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Solving the Robots Gathering Problem. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 1181–1196. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Cohen, R., Peleg, D.: Robot Convergence via Center-of-Gravity Algorithms. In: Kralovic, R., Sýkora, O. (eds.) SIROCCO 2004. LNCS, vol. 3104, pp. 79–88. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Cohen, R., Peleg, D.: Convergence of Autonomous Mobile Robots with Inaccurate Sensors and Movements. SIAM Journal on Computing 38(1), 276–302 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    De Marco, G., Gargano, L., Kranakis, E., Krizanc, D., Pelc, A., Vaccaro, U.: Asynchronous deterministic rendezvous in graphs. Theoretical Computer Science 355, 315–326 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Dessmark, A., Fraigniaud, P., Kowalski, D., Pelc, A.: Deterministic rendezvous in graphs. Algorithmica 46, 69–96 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Flocchini, P., Ilcinkas, D., Pelc, A., Santoro, N.: Computing without communicating: ring exploration by asynchronous oblivious robots. In: Tovar, E., Tsigas, P., Fouchal, H. (eds.) OPODIS 2007. LNCS, vol. 4878, pp. 105–118. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Flocchini, P., Ilcinkas, D., Pelc, A., Santoro, N.: Remembering without Memory: Tree Exploration by Asynchronous Oblivious Robots. In: Shvartsman, A.A., Felber, P. (eds.) SIROCCO 2008. LNCS, vol. 5058, pp. 33–47. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Flocchini, P., Kranakis, E., Krizanc, D., Santoro, N., Sawchuk, C.: Multiple Mobile Agent Rendezvous in a Ring. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 599–608. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of Asynchronous Robots with Limited Visibility. Theoretical Computer Science 337(1-3), 147–168 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Gąsieniec, L., Kranakis, E., Krizanc, D., Zhang, X.: Optimal Memory Rendezvous of Anonymous Mobile Agents in a Unidirectional Ring. In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds.) SOFSEM 2006. LNCS, vol. 3831, pp. 282–292. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Haba, K., Izumi, T., Katayama, Y., Inuzuka, N., Wada, K.: On the Gathering Problem in a Ring for 2n Autonomous Mobile Robots, Technical Report COMP2008-30, IEICE, Japan (2008)Google Scholar
  16. 16.
    Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. Theoretical Computer Science 390(1), 27–39 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Kowalski, D., Pelc, A.: Polynomial deterministic rendezvous in arbitrary graphs. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 644–656. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  18. 18.
    Lynch, N.: Distributed Algorithms. Morgan Kaufmann, San Francisco (1996)zbMATHGoogle Scholar
  19. 19.
    Prencipe, G.: CORDA: Distributed Coordination of a Set of Autonomous Mobile Robots. In: Proceedings of the European Research Seminar on Advances in Distributed Systems (ERSADS), pp. 185–190 (2001)Google Scholar
  20. 20.
    Prencipe, G.: On the Feasibility of Gathering by Autonomous Mobile Robots. In: Pelc, A., Raynal, M. (eds.) SIROCCO 2005. LNCS, vol. 3499, pp. 246–261. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  21. 21.
    Suzuki, I., Yamashita, M.: Distributed Anonymous Mobile Robots: Formation of Geometric Patterns. SIAM Journal on Computing 28(4), 1347–1363 (1999)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ralf Klasing
    • 1
  • Adrian Kosowski
    • 1
    • 2
  • Alfredo Navarra
    • 3
  1. 1.LaBRI - Université Bordeaux 1 - CNRS, 351 cours de la LiberationTalence cedexFrance
  2. 2.Department of Algorithms and System ModelingGdańsk University of TechnologyGdańskPoland
  3. 3.Dipartimento di Matematica e InformaticaUniversità degli Studi di PerugiaPerugiaItaly

Personalised recommendations