Pattern Formation

  • Giuseppe PrencipeEmail author
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11340)


The Pattern Formation problem is one of the most important coordination problem for robotic systems. Initially the entities are in arbitrary positions; within finite time they must arrange themselves in the space so to form a pattern given in input. In this chapter, we will mainly deal with the problem in the \(\mathcal{OBLOT}\) model.


Pattern formation Agreement Multiplicity detection 


  1. 1.
    Ando, H., Suzuki, I., Yamashita, M.: Formation and agreement problems for synchronous mobile robots with limited visibility. In: Proceedings of the 1995 IEEE Symposium on Intelligent Control, pp. 453–460 (1995)Google 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.
    Défago, X., Konagaya, A.: Circle formation for oblivious anonymous mobile robots with no common sense of orientation. In: Proceedings of 2nd Workshop on Principles of Mobile Computing, pp. 97–104 (2002)Google Scholar
  4. 4.
    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
  5. 5.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Arbitrary pattern formation by asynchronous oblivious robots. Theor. Comput. Sci. 407(1–3), 412–447 (2008)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Kasuya, M., Ito, N., Inuzuka, N., Wada, K.: A pattern formation algorithm for a set of autonomous distributed robots with agreement on orientation along one axis. Syst. Comput. Jpn. 37(10), 89–100 (2006)CrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    Sugihara, K., Suzuki, I.: Distributed algorithms for formation of geometric patterns with many mobile robots. J. Robot. Syst. 13, 127–139 (1996)CrossRefGoogle Scholar
  9. 9.
    Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Tanaka, O.: Forming a circle by distributed anonymous mobile robots. Master’s thesis, Department of Electrical Engineering (1992)Google Scholar
  11. 11.
    Wang, P.K.C.: Navigation strategies for multiple autonomous mobile robots moving in formation. J. Robot. Syst. 8(2), 177–195 (1991)CrossRefGoogle Scholar
  12. 12.
    Yamauchi, Y., Uehara, T., Kijima, S., Yamashita, M.: Plane formation by synchronous mobile robots in the three-dimensional euclidean space. J. ACM 64(3), 16:1–16:43 (2017)MathSciNetCrossRefGoogle Scholar
  13. 13.
    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). Scholar
  14. 14.
    Fujinaga, N., Ono, H., Kijima, S., Yamashita, M.: Pattern formation through optimum matching by oblivious CORDA robots. In: Lu, C., Masuzawa, T., Mosbah, M. (eds.) OPODIS 2010. LNCS, vol. 6490, pp. 1–15. Springer, Heidelberg (2010). Scholar
  15. 15.
    Yamashita, M., Suzuki, I.: Characterizing geometric patterns formable by oblivious anonymous mobile robots. Theor. Comput. Sci. 411(26–28), 2433–2453 (2010)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Fujinaga, N.: Oblivious pattern formation algorithms for asynchronous mobile robots based on bipartite matching approach. Master’s thesis, Department of Informatics, Kyushu University (2012)Google Scholar
  17. 17.
    Das, S., Flocchini, P., Santoro, N., Yamashita, M.: On the computational power of oblivious robots: forming a series of geometric patterns. In: Proceedings of 29th Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 267–276 (2010)Google Scholar
  18. 18.
    Bouzid, Z., Lamani, A.: Robot networks with homonyms: the case of patterns formation. In: Défago, X., Petit, F., Villain, V. (eds.) SSS 2011. LNCS, vol. 6976, pp. 92–107. Springer, Heidelberg (2011). Scholar

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Authors and Affiliations

  1. 1.University of PisaPisaItaly

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