Uniform Circle Formation

  • Giovanni Viglietta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11340)


We treat the second of the two patterns that are formable in the \(\mathcal{OBLOT}\) model from every initial configuration of n robots: Uniform Circle, i.e., the pattern where the robots are located at the vertices of a regular n-gon. The algorithm presented in this chapter solves the Uniform Circle Formation Problem in the standard \(\mathcal{OBLOT}\) model under the \(\mathcal{A}\textsc {sync}\) scheduler.


Uniform Circle Formation 


  1. 1.
    Bhagat, S., Mukhopadhyaya, K.: Optimum circle formation by autonomous robots. In: Chaki, R., Cortesi, A., Saeed, K., Chaki, N. (eds.) Advanced Computing and Systems for Security. AISC, vol. 666, pp. 153–165. Springer, Singapore (2018). Scholar
  2. 2.
    Chatzigiannakis, I., Markou, M., Nikoletseas, S.: Distributed circle formation for anonymous oblivious robots. In: Ribeiro, C.C., Martins, S.L. (eds.) WEA 2004. LNCS, vol. 3059, pp. 159–174. Springer, Heidelberg (2004). Scholar
  3. 3.
    Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Distributed computing by mobile robots: gathering. SIAM J. Comput. 41(4), 829–879 (2012)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Défago, X., Konagaya, A.: Circle formation for oblivious anonymous mobile robots with no common sense of orientation. In: Proceedings of the ACM International Workshop on Principles of Mobile Computing (POMC), pp. 97–104 (2002)Google Scholar
  5. 5.
    Défago, X., Souissi, S.: Non-uniform circle formation algorithm for oblivious mobile robots with convergence toward uniformity. Theor. Comput. Sci. 396(1–3), 97–112 (2008)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Dieudonné, Y., Labbani-Igbida, O., Petit, F.: Circle formation of weak mobile robots. ACM Trans. Auton. Adapt. Syst. 3(4), 16:1–16:20 (2008)CrossRefGoogle Scholar
  7. 7.
    Dieudonné, Y., Petit, F.: Swing words to make circle formation quiescent. In: Prencipe, G., Zaks, S. (eds.) SIROCCO 2007. LNCS, vol. 4474, pp. 166–179. Springer, Heidelberg (2007). Scholar
  8. 8.
    Dieudonné, Y., Petit, F.: Squaring the circle with weak mobile robots. In: Hong, S.-H., Nagamochi, H., Fukunaga, T. (eds.) ISAAC 2008. LNCS, vol. 5369, pp. 354–365. Springer, Heidelberg (2008). Scholar
  9. 9.
    Feletti, C., Mereghetti, C., Palano, B.: Uniform circle formation for swarms of opaque robots with lights. In: Izumi, T., Kuznetsov, P. (eds.) Stabilization, Safety, and Security of Distributed Systems. LNCS, vol. 11201, pp. 317–332. Springer, Cham (2018). Scholar
  10. 10.
    Flocchini, P., Prencipe, G., Santoro, N.: Self-deployment algorithms for mobile sensors on a ring. Theor. Comput. Sci. 402(1), 67–80 (2008)CrossRefGoogle Scholar
  11. 11.
    Flocchini, P., Prencipe, G., Santoro, N., Viglietta, G.: Distributed computing by mobile robots: solving the uniform circle formation problem. In: Aguilera, M.K., Querzoni, L., Shapiro, M. (eds.) OPODIS 2014. LNCS, vol. 8878, pp. 217–232. Springer, Cham (2014). Scholar
  12. 12.
    Flocchini, P., Prencipe, G., Santoro, N., Viglietta, G.: Distributed computing by mobile robots: uniform circle formation. Distrib. Comput. 30(6), 413–457 (2017)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Fujinaga, N., Yamauchi, Y., Kijima, S., Yamashita, M.: Asynchronous pattern formation by anonymous oblivious mobile robots. SIAM J. Comput. 44(3), 740–785 (2015)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Katreniak, B.: Biangular circle formation by asynchronous mobile robots. In: Pelc, A., Raynal, M. (eds.) SIROCCO 2005. LNCS, vol. 3499, pp. 185–199. Springer, Heidelberg (2005). Scholar
  15. 15.
    Mamino, M., Viglietta, G.: Square formation by asynchronous oblivious robots. In: Proceedings of the 28th Canadian Conference on Computational Geometry (CCCG), pp. 1–6 (2016)Google Scholar
  16. 16.
    Miyamae, T., Ichikawa, S., Hara, F.: Emergent approach to circle formation by multiple autonomous modular robots. J. Robot. Mechatron. 21(1), 3–11 (2009)CrossRefGoogle Scholar
  17. 17.
    Mondal, M., Chaudhuri, S.G.: Uniform circle formation by mobile robots. In: Proceedings of the Workshop Program of the 19th International Conference on Distributed Computing and Networking (ICDCN), pp. 20:1–20:2 (2018)Google Scholar
  18. 18.
    Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.JAISTNomiJapan

Personalised recommendations