Plane Formation by Semi-synchronous Robots in the Three Dimensional Euclidean Space

  • Taichi Uehara
  • Yukiko Yamauchi
  • Shuji Kijima
  • Masafumi Yamashita
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10083)

Abstract

We consider the plane formation problem that requires a set of autonomous mobile robots initially placed in the three-dimensional space to land on a common plane that is not defined a priori. The problem was first introduced for fully-synchronous (FSYNC) robots with rigid movement (i.e., the robots always reach the next position) and solvable instances are characterized in terms of the symmetry among the robots, i.e., the rotation group of the initial configuration of robots (Yamauchi et al. DISC 2015). We consider the plane formation problem for semi-synchronous (SSYNC) robots with non-rigid movement. We present a plane formation algorithm for oblivious SSYNC robots, and show that the SSYNC robots with non-rigid movement have the same plane formation power as the FSYNC robots with rigid movement.

Keywords

Mobile robots The plane formation problem Semi-synchronous model Non-rigid movement Symmetry breaking 

References

  1. 1.
    Cromwell, P.: Polyhedra. University Press, Cambridge (1997)MATHGoogle Scholar
  2. 2.
    Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Distributed computing by mobile robots: gathering. SIAM J. of Comput. 41(4), 829–879 (2012)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Dijkstra, E.W.: Self stabilizing systems in spite of distributed control. Comm. ACM 17, 643–644 (1974)CrossRefMATHGoogle Scholar
  4. 4.
    Flocchini, P., Prencipe, G., Santoro, N.: Distributed Computing by Oblivious Mobile Robots. Morgan & Claypool, San Rafeal (2012)MATHGoogle Scholar
  5. 5.
    Flocchini, P., Prencipe, G., Santoro, N., Viglietta, G.: Distributed computing by mobile robots: Solving the uniform circle formation problem. In: Proceedings OPODIS 2014, pp. 217–232 (2014)Google Scholar
  6. 6.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Arbitrary pattern formation by asynchronous, anonymous, oblivious robots. Theor. Comput. Sci 407, 412–447 (2008)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Fujinaga, N., Yamauchi, Y., Ono, H., Kijima, S., Yamashita, M.: Pattern formation by oblivious asynchronous mobile robots. SIAM J. Comput. 44(3), 740–785 (2015)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: Formation of geometric patterns. SIAM J. on Comput. 28(4), 1347–1363 (1999)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Yamashita, M., Suzuki, I.: Characterizing geometric patterns formable by oblivious anonymous mobile robots. Theor. Comput. Sci. 411, 2433–2453 (2010)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Yamauchi, Y., Uehara, T., Kijima, S., Yamashita, M.: Plane formation by synchronous mobile robots in the three dimensional euclidean space. In: Moses, Y. (ed.) DISC 2015. LNCS, vol. 9363, pp. 92–106. Springer, Heidelberg (2015). doi:10.1007/978-3-662-48653-5_7 CrossRefGoogle Scholar
  11. 11.
    Yamauchi, Y., Uehara, T., Yamashita, M.: Brief announcement: pattern formation problem for synchronous mobile robots in the three dimensional euclidean space. In: Proceedings of PODC 2016, pp. 447–449 (2016)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Taichi Uehara
    • 1
  • Yukiko Yamauchi
    • 1
  • Shuji Kijima
    • 1
  • Masafumi Yamashita
    • 1
  1. 1.Kyushu UniversityFukuokaJapan

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