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Randomized Pattern Formation Algorithm for Asynchronous Oblivious Mobile Robots

  • Yukiko Yamauchi
  • Masafumi Yamashita
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8784)

Abstract

We present a randomized pattern formation algorithm for asynchronous oblivious (i.e., memory-less) mobile robots that enables formation of any target pattern. As for deterministic pattern formation algorithms, the class of patterns formable from an initial configuration I is characterized by the symmetricity (i.e., the order of rotational symmetry) of I, and in particular, every pattern is formable from I if its symmetricity is 1. The randomized pattern formation algorithm ψ PF we present in this paper consists of two phases: The first phase transforms a given initial configuration I into a configuration I′ such that its symmetricity is 1, and the second phase invokes a deterministic pattern formation algorithm ψ CWM by Fujinaga et al. (DISC 2012) for asynchronous oblivious mobile robots to finally form the target pattern.

There are two hurdles to overcome to realize ψ PF . First, all robots must simultaneously stop and agree on the end of the first phase, to safely start the second phase, since the correctness of ψ CWM is guaranteed only for an initial configuration in which all robots are stationary. Second, the sets of configurations in the two phases must be disjoint, so that even oblivious robots can recognize which phase they are working on. We provide a set of tricks to overcome these hurdles.

Keywords

Mobile robot pattern formation randomized algorithm 

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References

  1. 1.
    Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Distributed computing by mobile robots: Gathering. SIAM J. of Comput. 41(4), 829–879 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    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
  3. 3.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Arbitrary pattern formation by asynchronous, anonymous, oblivious robots. Theor. Comput. Sci. 407, 412–447 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    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
  6. 6.
    Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: Formation of geometric patterns. SIAM J. on Comput. 28(4), 1347–1363 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Yamashita, M., Suzuki, I.: Characterizing geometric patterns formable by oblivious anonymous mobile robots. Theor. Comput. Sci 411, 2433–2453 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Yamauchi, Y., Yamashita, M.: Pattern formation by mobile robots with limited visibility. In: Moscibroda, T., Rescigno, A.A. (eds.) SIROCCO 2013. LNCS, vol. 8179, pp. 201–212. Springer, Heidelberg (2013)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Yukiko Yamauchi
    • 1
  • Masafumi Yamashita
    • 1
  1. 1.Faculty of Information Science and Electrical EngineeringKyushu UniversityJapan

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