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Arbitrary Pattern Formation by Asynchronous Opaque Robots with Lights

  • Kaustav BoseEmail author
  • Manash Kumar Kundu
  • Ranendu Adhikary
  • Buddhadeb Sau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11639)

Abstract

The Arbitrary Pattern Formation problem asks for a distributed algorithm that moves a set of autonomous mobile robots to form any arbitrary pattern given as input. The robots are assumed to be autonomous, anonymous and identical. They operate in Look-Compute-Move cycles under a fully asynchronous scheduler. The robots do not have access to any global coordinate system. The existing literature that investigates this problem, considers robots with unobstructed visibility. This work considers the problem in the more realistic obstructed visibility model, where the view of a robot can be obstructed by the presence of other robots. The robots are assumed to be punctiform and equipped with visible lights that can assume a constant number of predefined colors. We have studied the problem in two settings based on the level of consistency among the local coordinate systems of the robots: two axis agreement (they agree on the direction and orientation of both coordinate axes) and one axis agreement (they agree on the direction and orientation of only one coordinate axis). In both settings, we have provided a full characterization of initial configurations from where any arbitrary pattern can be formed.

Keywords

Distributed algorithm Arbitrary pattern formation Leader election Autonomous robots Opaque robots Luminous robots Obstructed visibility Asynchronous scheduler Look-compute-move cycle 

Notes

Acknowledgements

The first three authors are supported by NBHM, DAE, Govt. of India, UGC, Govt. of India and CSIR, Govt. of India, respectively. We would like to thank the anonymous reviewers for their valuable comments which helped us improve the quality and presentation of the paper.

References

  1. 1.
    Adhikary, R., Bose, K., Kundu, M.K., Sau, B.: Mutual visibility by asynchronous robots on infinite grid. In: Gilbert, S., Hughes, D., Krishnamachari, B. (eds.) ALGOSENSORS 2018. LNCS, vol. 11410, pp. 83–101. Springer, Cham (2019).  https://doi.org/10.1007/978-3-030-14094-6_6CrossRefGoogle Scholar
  2. 2.
    Agathangelou, C., Georgiou, C., Mavronicolas, M.: A distributed algorithm for gathering many fat mobile robots in the plane. In: Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing, pp. 250–259. ACM (2013)Google Scholar
  3. 3.
    Bhagat, S., Chaudhuri, S.G., Mukhopadhyaya, K.: Gathering of opaque robots in 3D space. In: Proceedings of the 19th International Conference on Distributed Computing and Networking, ICDCN 2018, pp. 2:1–2:10, Varanasi, India, 4–7 January 2018.  https://doi.org/10.1145/3154273.3154322
  4. 4.
    Bhagat, S., Mukhopadhyaya, K.: Optimum algorithm for mutual visibility among asynchronous robots with lights. In: Spirakis, P., Tsigas, P. (eds.) SSS 2017. LNCS, vol. 10616, pp. 341–355. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-69084-1_24CrossRefGoogle Scholar
  5. 5.
    Bose, K., Adhikary, R., Kundu, M.K., Sau, B.: Arbitrary pattern formation on infinite grid by asynchronous oblivious robots. In: Das, G.K., Mandal, P.S., Mukhopadhyaya, K., Nakano, S. (eds.) WALCOM 2019. LNCS, vol. 11355, pp. 354–366. Springer, Cham (2019).  https://doi.org/10.1007/978-3-030-10564-8_28CrossRefGoogle Scholar
  6. 6.
    Bose, K., Kundu, M.K., Adhikary, R., Sau, B.: Arbitrary pattern formation by asynchronous opaque robots with lights. CoRR abs/1902.04950 (2019). http://arxiv.org/abs/1902.04950
  7. 7.
    Bramas, Q., Tixeuil, S.: Arbitrary pattern formation with four robots. In: Izumi, T., Kuznetsov, P. (eds.) SSS 2018. LNCS, vol. 11201, pp. 333–348. Springer, Cham (2018).  https://doi.org/10.1007/978-3-030-03232-6_22CrossRefGoogle Scholar
  8. 8.
    Cicerone, S., Di Stefano, G., Navarra, A.: Asynchronous arbitrary pattern formation: the effects of a rigorous approach. Distrib. Comput. 32(2), 1–42 (2018).  https://doi.org/10.1007/s00446-018-0325-7MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Cicerone, S., Di Stefano, G., Navarra, A.: Embedded pattern formation by asynchronous robots without chirality. Distrib. Comput. 1–25 (2018).  https://doi.org/10.1007/s00446-018-0333-7CrossRefGoogle Scholar
  10. 10.
    Das, S., Flocchini, P., Santoro, N., Yamashita, M.: Forming sequences of geometric patterns with oblivious mobile robots. Distrib. Comput. 28(2), 131–145 (2015).  https://doi.org/10.1007/s00446-014-0220-9MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Di Luna, G.A., Flocchini, P., Chaudhuri, S.G., Poloni, F., Santoro, N., Viglietta, G.: Mutual visibility by luminous robots without collisions. Inf. Comput. 254, 392–418 (2017)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Dieudonné, Y., Petit, F., Villain, V.: Leader election problem versus pattern formation problem. CoRR abs/0902.2851 (2009). http://arxiv.org/abs/0902.2851
  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).  https://doi.org/10.1007/978-3-642-15763-9_26CrossRefGoogle Scholar
  14. 14.
    Feletti, C., Mereghetti, C., Palano, B.: Uniform circle formation for swarms of opaque robots with lights. In: Izumi, T., Kuznetsov, P. (eds.) SSS 2018. LNCS, vol. 11201, pp. 317–332. Springer, Cham (2018).  https://doi.org/10.1007/978-3-030-03232-6_21CrossRefGoogle Scholar
  15. 15.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Arbitrary pattern formation by asynchronous, anonymous, oblivious robots. Theor. Comput. Sci. 407(1–3), 412–447 (2008).  https://doi.org/10.1016/j.tcs.2008.07.026MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    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).  https://doi.org/10.1137/140958682MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Lukovszki, T., Meyer auf der Heide, F.: Fast collisionless pattern formation by anonymous, position-aware robots. In: Aguilera, M.K., Querzoni, L., Shapiro, M. (eds.) OPODIS 2014. LNCS, vol. 8878, pp. 248–262. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-14472-6_17CrossRefGoogle Scholar
  18. 18.
    Peleg, D.: Distributed coordination algorithms for mobile robot swarms: new directions and challenges. In: Pal, A., Kshemkalyani, A.D., Kumar, R., Gupta, A. (eds.) IWDC 2005. LNCS, vol. 3741, pp. 1–12. Springer, Heidelberg (2005).  https://doi.org/10.1007/11603771_1CrossRefGoogle Scholar
  19. 19.
    Sharma, G., Busch, C., Mukhopadhyay, S.: Mutual visibility with an optimal number of colors. In: Bose, P., Gąsieniec, L.A., Römer, K., Wattenhofer, R. (eds.) ALGOSENSORS 2015. LNCS, vol. 9536, pp. 196–210. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-28472-9_15CrossRefGoogle Scholar
  20. 20.
    Sharma, G., Vaidyanathan, R., Trahan, J.L., Busch, C., Rai, S.: Complete visibility for robots with lights in O(1) time. In: Bonakdarpour, B., Petit, F. (eds.) SSS 2016. LNCS, vol. 10083, pp. 327–345. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-49259-9_26CrossRefGoogle Scholar
  21. 21.
    Sharma, G., Vaidyanathan, R., Trahan, J.L., Busch, C., Rai, S.: O(log n)-time complete visibility for asynchronous robots with lights. In: IEEE International 2017 Parallel and Distributed Processing Symposium (IPDPS), pp. 513–522. IEEE (2017)Google Scholar
  22. 22.
    Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots. In: SIROCCO 1996, The 3rd International Colloquium on Structural Information & Communication Complexity, pp. 313–330, Siena, Italy, 6–8 June 1996Google Scholar
  23. 23.
    Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999).  https://doi.org/10.1137/S009753979628292XMathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Vaidyanathan, R., Sharma, G., Trahan, J.L.: On fast pattern formation by autonomous robots. In: Izumi, T., Kuznetsov, P. (eds.) SSS 2018. LNCS, vol. 11201, pp. 203–220. Springer, Cham (2018).  https://doi.org/10.1007/978-3-030-03232-6_14CrossRefGoogle Scholar
  25. 25.
    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, Cham (2013).  https://doi.org/10.1007/978-3-319-03578-9_17CrossRefGoogle Scholar
  26. 26.
    Yamauchi, Y., Yamashita, M.: Randomized pattern formation algorithm for asynchronous oblivious mobile robots. In: Kuhn, F. (ed.) DISC 2014. LNCS, vol. 8784, pp. 137–151. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-45174-8_10CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsJadavpur UniversityKolkataIndia

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