Distributed Computing by Mobile Robots: Solving the Uniform Circle Formation Problem

  • Paola Flocchini
  • Giuseppe Prencipe
  • Nicola Santoro
  • Giovanni Viglietta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8878)


Consider a set of n ≠ 4 simple autonomous mobile robots (decentralized, asynchronous, no common coordinate system, no identities, no central coordination, no direct communication, no memory of the past, deterministic) initially in distinct locations, moving freely in the plane and able to sense the positions of the other robots. We study the primitive task of the robots arranging themselves equally spaced along a circle not fixed in advance (Uniform Circle Formation). In the literature, the existing algorithmic contributions are limited to restricted sets of initial configurations of the robots and to more powerful robots. The question of whether such simple robots could deterministically form a uniform circle has remained open. In this paper, we constructively prove that indeed the Uniform Circle Formation problem is solvable for any initial configuration of the robots without any additional assumption. In addition to closing a long-standing problem, the result of this paper also implies that, for pattern formation, asynchrony is not a computational handicap, and that additional powers such as chirality and rigidity are computationally irrelevant.


Mobile Robot Homology Class Intended Behavior Circle Formation Common Coordinate System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chatzigiannakis, I., Markou, M., Nikoletseas, S.: Distributed circle formation for anonymous oblivious robots. In: 3rd Workshop on Efficient and Experimental Algorithms, pp. 159–174 (2004)Google Scholar
  2. 2.
    Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Distributed computing by mobile robots: Gathering. SIAM Journal on Computing 41(4), 829–879 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Cohen, R., Peleg, D.: Convergence properties of the gravitational algorithms in asynchronous robots systems. SIAM Journal on Computing 34, 1516–1528 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Cohen, R., Peleg, D.: Convergence of autonomous mobile robots with inaccurate sensors and movements. SIAM Journal on Computing 38, 276–302 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    S. Das, P. Flocchini, N. Santoro, and M. Yamashita Forming sequences of geometric patterns with oblivious mobile robots. Distributed Computing (to appear, 2014)Google Scholar
  6. 6.
    Défago, X., Konagaya, A.: Circle formation for oblivious anonymous mobile robots with no common sense of orientation. In: 2nd ACM Int. Workshop on Principles of Mobile Computing (POMC), pp. 97–104 (2002)Google Scholar
  7. 7.
    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)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Dieudonné, Y., Labbani-Igbida, O., Petit, F.: Circle formation of weak mobile robots. ACM Trans. on Autonomous and Adaptive Systems 3(4), 16:1–16:20 (2008)Google Scholar
  9. 9.
    Dieudonné, Y., Levé, F., Petit, F., Villain, V.: Deterministic geoleader election in disoriented anonymous systems. Theoretical Computer Science 506, 43–54 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Flocchini, P., Prencipe, G., Santoro, N.: Self-deployment algorithms for mobile sensors on a ring. Theoretical Computer Science 402(1), 67–80 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Flocchini, P., Prencipe, G., Santoro, N.: Distributed Computing by Oblivious Mobile Robots. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool (2012)Google Scholar
  14. 14.
    Flocchini, P., Prencipe, G., Santoro, N., Viglietta, G.: Distributed Computing by Mobile Robots: Solving the Uniform Circle Formation Problem. arXiv:1407.5917 [cs.DC] (2014)Google Scholar
  15. 15.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Arbitrary pattern formation by asynchronous oblivious robots. Theoretical Computer Science 407(1-3), 412–447 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Fujinaga, N., Yamauchi, Y., Kijima, S., Yamashita, M.: Asynchronous pattern formation by anonymous oblivious mobile robots. In: Aguilera, M.K. (ed.) DISC 2012. LNCS, vol. 7611, pp. 312–325. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  17. 17.
    Kamei, S., Lamani, A., Ooshita, F., Tixeuil, S.: Asynchronous mobile robot gathering from symmetric configurations without global multiplicity detection. In: Kosowski, A., Yamashita, M. (eds.) SIROCCO 2011. LNCS, vol. 6796, pp. 150–161. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  18. 18.
    Izumi, T., Souissi, S., Katayama, Y., Inuzuka, N., Défago, X., Wada, K., Yamashita, M.: The gathering problem for two oblivious robots with unreliable compasses. SIAM Journal on Computing 41(1), 26–46 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    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)CrossRefGoogle Scholar
  20. 20.
    Miyamae, T., Ichikawa, S., Hara, F.: Emergent approach to circle formation by multiple autonomous modular robots. J. Robotics and Mechatr. 21(1), 3–11 (2009)Google Scholar
  21. 21.
    Oasa, Y., Suzuki, I., Yamashita, M.: A robust distributed convergence algorithm for autonomous mobile robots. In: IEEE Int. Conference on Systems, Man and Cybernetics, pp. 287–292 (1997)Google Scholar
  22. 22.
    Sugihara, K., Suzuki, I.: Distributed algorithms for formation of geometric patterns with many mobile robots. J. Robot. Syst. 3(13), 127–139 (1996)CrossRefGoogle Scholar
  23. 23.
    Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: Formation of geometric patterns. SIAM Journal on Computing 28(4), 1347–1363 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  24. 24.
    Yamashita, M., Suzuki, I.: Characterizing geometric patterns formable by oblivious anonymous mobile robots. Theoretical Computer Science 411(26-28), 2433–2453 (2010)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Paola Flocchini
    • 1
  • Giuseppe Prencipe
    • 2
  • Nicola Santoro
    • 3
  • Giovanni Viglietta
    • 3
  1. 1.University of OttawaCanada
  2. 2.University of PisaItaly
  3. 3.Carleton UniversityCanada

Personalised recommendations