Document Open Access Logo

𝒪(log{n})-Time Uniform Circle Formation for Asynchronous Opaque Luminous Robots

Authors Caterina Feletti , Carlo Mereghetti , Beatrice Palano

PDF
Thumbnail PDF

File

LIPIcs.OPODIS.2023.5.pdf
  • Filesize: 0.92 MB
  • 21 pages

Document Identifiers

Author Details

Caterina Feletti
  • Dipartimento di Informatica, Università degli Studi di Milano, Italy
Carlo Mereghetti
  • Dipartimento di Informatica, Università degli Studi di Milano, Italy
Beatrice Palano
  • Dipartimento di Informatica, Università degli Studi di Milano, Italy

Cite AsGet BibTex

Caterina Feletti, Carlo Mereghetti, and Beatrice Palano. 𝒪(log{n})-Time Uniform Circle Formation for Asynchronous Opaque Luminous Robots. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.OPODIS.2023.5

Abstract

We study the Uniform Circle Formation (UCF) problem for a distributed system of n robots which are required to displace on the vertices of a regular n-gon. We consider a well-studied model of autonomous, anonymous, mobile robots that act on the plane through Look-Compute-Move cycles. Moreover, robots are unaware of the cardinality of the system, they are punctiform, completely disoriented, opaque, and luminous. Collisions among robots are not tolerated. In the literature, the UCF problem has been solved for such a model by a deterministic algorithm in the asynchronous mode, using a constant amount of light colors and 𝒪(n) epochs in the worst case. In this paper, we provide an improved algorithm for solving the UCF problem for asynchronous robots, which uses 𝒪(log n) epochs still maintaining a constant amount of colors.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Computing methodologies → Mobile agents
  • Computing methodologies → Robotic planning
Keywords
  • Autonomous mobile robots
  • Opaque robots
  • Luminous robots
  • Pattern formation

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Ranendu Adhikary, Manash Kumar Kundu, and Buddhadeb Sau. Circle formation by asynchronous opaque robots on infinite grid. Comput. Sci., 22(1), 2021. URL: https://doi.org/10.7494/CSCI.2021.22.1.3840.
  2. Kálmán Bolla, Tamás Kovács, and Gábor Fazekas. Gathering of fat robots with limited visibility and without global navigation. In International Symposium on Swarm and Evolutionary Computation, SIDE 2012, pages 30-38. Springer, 2012. URL: https://doi.org/10.1007/978-3-642-29353-5_4.
  3. Kaustav Bose, Manash Kumar Kundu, Ranendu Adhikary, and Buddhadeb Sau. Arbitrary pattern formation by asynchronous opaque robots with lights. Theor. Comput. Sci., 849:138-158, 2021. URL: https://doi.org/10.1016/J.TCS.2020.10.015.
  4. Kevin Buchin, Paola Flocchini, Irina Kostitsyna, Tom Peters, Nicola Santoro, and Koichi Wada. Autonomous mobile robots: Refining the computational landscape. In 35th International Parallel and Distributed Processing Symposium Workshops, IPDPS Workshops 2021, pages 576-585. IEEE, 2021. URL: https://doi.org/10.1109/IPDPSW52791.2021.00091.
  5. Sruti Gan Chaudhuri and Krishnendu Mukhopadhyaya. Leader election and gathering for asynchronous fat robots without common chirality. J. Discrete Algorithms, 33:171-192, 2015. URL: https://doi.org/10.1016/J.JDA.2015.04.001.
  6. Mark Cieliebak and Giuseppe Prencipe. Gathering autonomous mobile robots. In 9th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2002, pages 57-72. Carleton Scientific, 2002. Google Scholar
  7. James D. Currie and D. Sean Fitzpatrick. Circular words avoiding patterns. In 6th International Conference on Developments in Language Theory, DLT 2002, pages 319-325. Springer, 2002. URL: https://doi.org/10.1007/3-540-45005-X_28.
  8. Shantanu Das, Paola Flocchini, Giuseppe Prencipe, Nicola Santoro, and Masafumi Yamashita. Autonomous mobile robots with lights. Theor. Comput. Sci., 609:171-184, 2016. URL: https://doi.org/10.1016/J.TCS.2015.09.018.
  9. Suparno Datta, Ayan Dutta, Sruti Gan Chaudhuri, and Krishnendu Mukhopadhyaya. Circle formation by asynchronous transparent fat robots. In 9th International Conference on Distributed Computing and Internet Technology, ICDCIT 2013, pages 195-207. Springer, 2013. URL: https://doi.org/10.1007/978-3-642-36071-8_15.
  10. Xavier Défago and Akihiko Konagaya. Circle formation for oblivious anonymous mobile robots with no common sense of orientation. In Workshop on Principles of Mobile Computing, POMC 2002, pages 97-104. ACM, 2002. URL: https://doi.org/10.1145/584490.584509.
  11. Mattia D'Emidio, Daniele Frigioni, and Alfredo Navarra. Characterizing the computational power of anonymous mobile robots. In 36th International Conference on Distributed Computing Systems, ICDCS 2016, pages 293-302. IEEE Computer Society, 2016. URL: https://doi.org/10.1109/ICDCS.2016.58.
  12. Yoann Dieudonné and Franck Petit. Circle formation of weak robots and lyndon words. Inf. Process. Lett., 101(4):156-162, 2007. URL: https://doi.org/10.1016/J.IPL.2006.09.008.
  13. Yoann Dieudonné and Franck Petit. Swing words to make circle formation quiescent. In 14th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2007, pages 166-179. Springer, 2007. URL: https://doi.org/10.1007/978-3-540-72951-8_14.
  14. Yoann Dieudonné and Franck Petit. Squaring the circle with weak mobile robots. In 19th International Symposium on Algorithms and Computation, ISAAC 2008, pages 354-365. Springer, 2008. URL: https://doi.org/10.1007/978-3-540-92182-0_33.
  15. Caterina Feletti, Carlo Mereghetti, and Beatrice Palano. Uniform circle formation for swarms of opaque robots with lights. In 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2018, pages 317-332. Springer, 2018. URL: https://doi.org/10.1007/978-3-030-03232-6_21.
  16. Caterina Feletti, Carlo Mereghetti, and Beatrice Palano. Uniform circle formation for fully, semi-, and asynchronous opaque robots with lights. Applied Sciences, 13(13), 2023. URL: https://doi.org/10.3390/app13137991.
  17. Caterina Feletti, Carlo Mereghetti, Beatrice Palano, and Priscilla Raucci. Uniform circle formation for fully semi-, and asynchronous opaque robots with lights. In 23rd Italian Conference on Theoretical Computer Science, ICTCS 2022, pages 207-221. CEUR-WS.org, 2022. URL: https://ceur-ws.org/Vol-3284/8511.pdf.
  18. Paola Flocchini, Giuseppe Prencipe, and Nicola Santoro. Distributed Computing by Oblivious Mobile Robots. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool Publishers, 2012. URL: https://doi.org/10.2200/S00440ED1V01Y201208DCT010.
  19. Paola Flocchini, Giuseppe Prencipe, and Nicola Santoro, editors. Distributed Computing by Mobile Entities, Current Research in Moving and Computing, volume 11340 of Lecture Notes in Computer Science. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-11072-7.
  20. Paola Flocchini, Giuseppe Prencipe, Nicola Santoro, and Giovanni Viglietta. Distributed computing by mobile robots: uniform circle formation. Distributed Comput., 30(6):413-457, 2017. URL: https://doi.org/10.1007/S00446-016-0291-X.
  21. László Hegedüs and Benedek Nagy. Representations of circular words. In 14th International Conference on Automata and Formal Languages, AFL 2014, pages 261-270, 2014. URL: https://doi.org/10.4204/EPTCS.151.18.
  22. Manash Kumar Kundu, Pritam Goswami, Satakshi Ghosh, and Buddhadeb Sau. Arbitrary pattern formation by opaque fat robots on infinite grid. Int. J. Parallel Emergent Distributed Syst., 37(5):542-570, 2022. URL: https://doi.org/10.1080/17445760.2022.2088750.
  23. Giuseppe Antonio Di Luna, Paola Flocchini, Sruti Gan Chaudhuri, Nicola Santoro, and Giovanni Viglietta. Robots with lights: Overcoming obstructed visibility without colliding. In 16th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2014, pages 150-164. Springer, 2014. URL: https://doi.org/10.1007/978-3-319-11764-5_11.
  24. R.C. Lyndon and M.P. Schützenberger. The equation a^M = b^N c^P in a free group. Michigan Math. J., 9:289-298, 1962. URL: https://doi.org/10.1307/mmj/1028998766.
  25. Moumita Mondal and Sruti Gan Chaudhuri. Uniform circle formation by mobile robots. In 19th International Conference on Distributed Computing and Networking, ICDCN 2018, pages 20:1-20:2. ACM, 2018. URL: https://doi.org/10.1145/3170521.3170541.
  26. Moumita Mondal and Sruti Gan Chaudhuri. Uniform circle formation by swarm robots under limited visibility. In 16th International Conference Distributed Computing and Internet Technology, ICDCIT 2020, pages 420-428. Springer, 2020. URL: https://doi.org/10.1007/978-3-030-36987-3_28.
  27. Gokarna Sharma, Ramachandran Vaidyanathan, and Jerry L. Trahan. Constant-time complete visibility for asynchronous robots with lights. In 19th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2017, pages 265-281. Springer, 2017. URL: https://doi.org/10.1007/978-3-319-69084-1_18.
  28. Gokarna Sharma, Ramachandran Vaidyanathan, Jerry L. Trahan, Costas Busch, and Suresh Rai. Complete visibility for robots with lights in O(1) time. In 18th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2016, pages 327-345, 2016. URL: https://doi.org/10.1007/978-3-319-49259-9_26.
  29. Yossi Shiloach. Fast canonization of circular strings. J. Algorithms, 2(2):107-121, 1981. URL: https://doi.org/10.1016/0196-6774(81)90013-4.
  30. Kazuo Sugihara and Ichiro Suzuki. Distributed algorithms for formation of geometric patterns with many mobile robots. J. Field Robotics, 13(3):127-139, 1996. URL: https://doi.org/10.1002/(SICI)1097-4563(199603)13:3%3C127::AID-ROB1%3E3.0.CO;2-U.
  31. Ichiro Suzuki and Masafumi Yamashita. Distributed anonymous mobile robots: Formation of geometric patterns. SIAM J. Comput., 28(4):1347-1363, 1999. URL: https://doi.org/10.1137/S009753979628292X.
  32. Giovanni Viglietta. Uniform circle formation. In Distributed Computing by Mobile Entities, Current Research in Moving and Computing, pages 83-108. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-11072-7_5.
  33. Masafumi Yamashita and Ichiro Suzuki. Characterizing geometric patterns formable by oblivious anonymous mobile robots. Theor. Comput. Sci., 411(26-28):2433-2453, 2010. URL: https://doi.org/10.1016/J.TCS.2010.01.037.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact