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Robots with Lights

  • Giuseppe Antonio Di LunaEmail author
  • Giovanni Viglietta
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11340)

Abstract

The classic Look-Compute-Move model of oblivious robots has many strengths: algorithms designed for this model are inherently resistant to a large set of failures that can affect the memory of the robots and their communication capabilities.

However, modern technologies allow for cheap and reliable means of communication and memorization. This is especially true if relatively low performances are needed, such as very limited communication bandwidth or constant memory. A theoretical model that expands the classic Look-Compute-Move by adding a minimal ability to communicate and remember is the model of robots with lights. In this model each robot carries a luminous source that it can modify at every cycle. The robot decides the color of its light during its Compute phase, and the light assumes such a color at the beginning of the next Move phase. Other robots can see the color of this light during their Look phases. The light will remain unaltered until the robot that carries it decides to change its color.

Typically, the number of available colors is very limited, i.e., it is constant with respect to the number of robots in the system.

In this chapter we will discuss the hierarchy of \(\mathcal{F}{\textsc {sync}}\), \(\mathcal{S}{\textsc {sync}}\), and \(\mathcal{A}{\textsc {sync}}\) models when lights are present, we call this model \(\mathcal{LUMINOUS}\). Moreover, we will see how lights are applied to solve classic problems such as rendezvous and forming a sequence of patterns. Finally, we will see how lights have been exploited in models where the visibility of robots is limited by the presence of obstructions.

References

  1. 1.
    Aljohani, A., Sharma, G.: Complete visibility for mobile robots with lights tolerating a faulty robot. In: Proceedings of the 32nd IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPS Workshops), pp. 834–843 (2017)Google Scholar
  2. 2.
    Aljohani, A., Poudel, P., Sharma, G.: Fault-tolerant complete visibility for asynchronous robots with lights under one-axis agreement. In: Rahman, M.S., Sung, W.-K., Uehara, R. (eds.) WALCOM 2018. LNCS, vol. 10755, pp. 169–182. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-75172-6_15CrossRefGoogle Scholar
  3. 3.
    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
  4. 4.
    Cord-Landwehr, A., et al.: A new approach for analyzing convergence algorithms for mobile robots. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011. LNCS, vol. 6756, pp. 650–661. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-22012-8_52CrossRefGoogle Scholar
  5. 5.
    Czyzowicz, J., Gasieniec, L., Pelc, A.: Gathering few fat mobile robots in the plane. Theor. Comput. Sci. 410, 81–499 (2009)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Das, S., Flocchini, P., Prencipe, G., Santoro, N.: Forming sequences of geometric patterns with oblivious mobile robots. In: Proceedings of the 7th International Conference on FUN with Algorithms (FUN), pp. 113–124 (2014)Google Scholar
  7. 7.
    Das, S., Flocchini, P., Prencipe, G., Santoro, N., Yamashita, M.: The power of lights: synchronizing asynchronous robots using visible bits. In: 32nd IEEE International Conference on Distributed Computing Systems (ICDCS), pp. 506–515 (2012)Google Scholar
  8. 8.
    Das, S., Flocchini, P., Prencipe, G., Santoro, N., Yamashita, M.: Autonomous mobile robots with lights. Theor. Comput. Sci. 609, 171–184 (2016)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Das, S., Flocchini, P., Santoro, N., Yamashita, M.: Forming sequences of geometric patterns with oblivious mobile robots. Distrib. Comput. 28, 131–145 (2015)MathSciNetCrossRefGoogle Scholar
  10. 10.
    D’Emidio, M., Frigoni, D., Navarra, A.: Synchronous robots vs asynchronous lights-enhanced robots on graphs. Electron Notes Theor. Comput. Sci. 322, 169–180 (2016)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Di Luna, G.A., Flocchini, P., Gan Chaudhuri, S., Poloni, F., Santoro, N., Viglietta, G.: Mutual visibility by luminous robots without collisions. Inf. Comput. 254, 392–418 (2017)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Di Luna, G.A., Flocchini, P., Gan Chaudhuri, S., Santoro, N., Viglietta, G.: Robots with lights: overcoming obstructed visibility without colliding. In: Felber, P., Garg, V. (eds.) SSS 2014. LNCS, vol. 8756, pp. 150–164. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-11764-5_11CrossRefGoogle Scholar
  13. 13.
    Di Luna, G.A., Flocchini, P., Poloni, F., Santoro, N., Viglietta, G.: The mutual visibility problem for oblivious robots. In: Proceedings of the 26th Canadian Computational Geometry Conference (CCCG), pp. 348–354 (2014)Google Scholar
  14. 14.
    Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17, 643–644 (1974)CrossRefGoogle Scholar
  15. 15.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Arbitrary pattern formation by asynchronous oblivious robots. Theor. Comput. Sci. 407, 412–447 (2008)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Flocchini, P., Santoro, N., Viglietta, G., Yamashita, M.: Rendezvous with constant memory. Theor. Comput. Sci. 621, 57–72 (2016)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Fujinaga, N., Yamauchi, Y., Ono, H., Kijima, S., Yamashita, M.: Pattern formation by oblivious asynchronous mobile robots. SIAM J. Comput. 44, 740–785 (2015)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Heriban, A., Defago, X., Tixeuil, S.: Optimally gathering two robots. In: Proceedings of the 19th International Conference on Distributed Computing and Networking (ICDCN), pp. 3:1–3:10 (2018)Google Scholar
  19. 19.
    Khan, L.U.: Visible light communication: applications, architecture, standardization and research challenges. Dig. Commun. Netw. 2, 78–88 (2017)CrossRefGoogle Scholar
  20. 20.
    Okumura, T., Wada, K., Katayama, Y.: Optimal asynchronous rendezvous for mobile robots with lights. Arxiv, CoRR abs/1707.04449 (2017)Google Scholar
  21. 21.
    Sharma, G., Alsaedi, R., Bush, C., Mukhopadyay, S.: The complete visibility problem for fat robots with lights. In: Proceedings of the 19th International Conference on Distributed Computing and Networking (ICDCN), pp. 21:1–21:4 (2018)Google Scholar
  22. 22.
    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
  23. 23.
    Sharma, G., Bush, C., Mukhopadyay, S.: Brief announcement: complete visibility for oblivious robots in linear time. In: Proceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 325–327 (2017)Google Scholar
  24. 24.
    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
  25. 25.
    Sharma, G., Vaidyanathan, R., Trahan, J.L., Bush, C., Rai, S.: O(log n)-time complete visibility for asynchronous robots with lights. In: Proceedings of the 32nd IEEE International Parallel and Distributed Processing Symposium (IPDPS), pp. 513–522 (2017)Google Scholar
  26. 26.
    Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28, 1347–1363 (1999)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Vaidyanathan, R., Bush, C., Trahan, J.L., Sharma, G., Rai, S.: Logarithmic-time complete visibility for robots with lights. In: Proceedings of the 29th IEEE International Parallel and Distributed Processing Symposium (IPDPS), pp. 375–384 (2015)Google Scholar
  28. 28.
    Viglietta, G.: Rendezvous of two robots with visible bits. In: Flocchini, P., Gao, J., Kranakis, E., Meyer auf der Heide, F. (eds.) ALGOSENSORS 2013. LNCS, vol. 8243, pp. 291–306. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-45346-5_21CrossRefGoogle Scholar
  29. 29.
    Yamashita, M., Suzuki, I.: Characterizing geometric patterns formable by oblivious anonymous mobile robots. Theor. Comput. Sci. 411, 2433–2453 (2010)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Giuseppe Antonio Di Luna
    • 1
    Email author
  • Giovanni Viglietta
    • 2
  1. 1.Aix-Marseille Université, LIS, CNRS, Université de ToulonToulonFrance
  2. 2.JAISTNomiJapan

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