Skip to main content
SpringerLink
Log in

Uniform Circle Formation

  • Chapter
  • First Online:
Distributed Computing by Mobile Entities

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11340))

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    A similar concept has been used in [3], with some technical differences.

References

  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). https://doi.org/10.1007/978-981-10-8180-4_10

    Chapter  Google Scholar 

  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). https://doi.org/10.1007/978-3-540-24838-5_12

    Chapter  Google Scholar 

  3. Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Distributed computing by mobile robots: gathering. SIAM J. Comput. 41(4), 829–879 (2012)

    Article  MathSciNet  Google Scholar 

  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. 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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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). https://doi.org/10.1007/978-3-540-72951-8_14

    Chapter  Google Scholar 

  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). https://doi.org/10.1007/978-3-540-92182-0_33

    Chapter  Google Scholar 

  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). https://doi.org/10.1007/978-3-030-03232-6_21

    Chapter  Google Scholar 

  10. Flocchini, P., Prencipe, G., Santoro, N.: Self-deployment algorithms for mobile sensors on a ring. Theor. Comput. Sci. 402(1), 67–80 (2008)

    Article  Google Scholar 

  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). https://doi.org/10.1007/978-3-319-14472-6_15

    Chapter  Google Scholar 

  12. Flocchini, P., Prencipe, G., Santoro, N., Viglietta, G.: Distributed computing by mobile robots: uniform circle formation. Distrib. Comput. 30(6), 413–457 (2017)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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). https://doi.org/10.1007/11429647_16

    Chapter  Google Scholar 

  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. Miyamae, T., Ichikawa, S., Hara, F.: Emergent approach to circle formation by multiple autonomous modular robots. J. Robot. Mechatron. 21(1), 3–11 (2009)

    Article  Google Scholar 

  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. Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. JAIST, Nomi, Japan

    Giovanni Viglietta

Authors
  1. Giovanni Viglietta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giovanni Viglietta .

Editor information

Editors and Affiliations

  1. University of Ottawa, Ottawa, ON, Canada

    Paola Flocchini

  2. University of Pisa, Pisa, Italy

    Giuseppe Prencipe

  3. Carleton University, Ottawa, ON, Canada

    Nicola Santoro

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Viglietta, G. (2019). Uniform Circle Formation. In: Flocchini, P., Prencipe, G., Santoro, N. (eds) Distributed Computing by Mobile Entities. Lecture Notes in Computer Science(), vol 11340. Springer, Cham. https://doi.org/10.1007/978-3-030-11072-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-11072-7_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11071-0

  • Online ISBN: 978-3-030-11072-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation