Document Open Access Logo

Forming Large Patterns with Local Robots in the OBLOT Model

Authors Christopher Hahn , Jonas Harbig , Peter Kling

PDF
Thumbnail PDF

File

LIPIcs.SAND.2024.14.pdf
  • Filesize: 1.04 MB
  • 20 pages

Document Identifiers

Author Details

Christopher Hahn
  • Universität Hamburg, Germany
Jonas Harbig
  • Paderborn University, Germany
Peter Kling
  • Universität Hamburg, Germany

Funding

  • Harbig, Jonas: This work was partially supported by the German Research Foundation(DFG) under the project number ME 872/14-1.

Cite AsGet BibTex

Christopher Hahn, Jonas Harbig, and Peter Kling. Forming Large Patterns with Local Robots in the OBLOT Model. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SAND.2024.14

Abstract

In the arbitrary pattern formation problem, n autonomous, mobile robots must form an arbitrary pattern P ⊆ R². The (deterministic) robots are typically assumed to be indistinguishable, disoriented, and unable to communicate. An important distinction is whether robots have memory and/or a limited viewing range. Previous work managed to form P under a natural symmetry condition if robots have no memory but an unlimited viewing range [Masafumi Yamashita and Ichiro Suzuki, 2010] or if robots have a limited viewing range but memory [Yukiko Yamauchi and Masafumi Yamashita, 2013]. In the latter case, P is only formed in a shrunk version that has constant diameter. Without memory and with limited viewing range, forming arbitrary patterns remains an open problem. We provide a partial solution by showing that P can be formed under the same symmetry condition if the robots' initial diameter is ≤ 1. Our protocol partitions P into rotation-symmetric components and exploits the initial mutual visibility to form one cluster per component. Using a careful placement of the clusters and their robots, we show that a cluster can move in a coordinated way through its component while "drawing" P by dropping one robot per pattern coordinate.

Subject Classification

ACM Subject Classification
  • Theory of computation → Self-organization
Keywords
  • Swarm Algorithm
  • Swarm Robots
  • Distributed Algorithm
  • Pattern Formation
  • Limited Visibility
  • Oblivious

Metrics

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

Related Versions

References

  1. Kaustav Bose, Ranendu Adhikary, Manash Kumar Kundu, and Buddhadeb Sau. Arbitrary pattern formation on infinite grid by asynchronous oblivious robots. Theor. Comput. Sci., 815:213-227, 2020. URL: https://doi.org/10.1016/J.TCS.2020.02.016.
  2. 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.
  3. Jannik Castenow, Matthias Fischer, Jonas Harbig, Daniel Jung, and Friedhelm Meyer auf der Heide. Gathering anonymous, oblivious robots on a grid. Theor. Comput. Sci., 815:289-309, 2020. URL: https://doi.org/10.1016/J.TCS.2020.02.018.
  4. Jannik Castenow, Jonas Harbig, Daniel Jung, Peter Kling, Till Knollmann, and Friedhelm Meyer auf der Heide. A unifying approach to efficient (near)-gathering of disoriented robots with limited visibility. In OPODIS 2022, December 13-15, 2022, Brussels, Belgium, volume 253 of LIPIcs, pages 15:1-15:25. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPICS.OPODIS.2022.15.
  5. Serafino Cicerone, Gabriele Di Stefano, and Alfredo Navarra. Asynchronous arbitrary pattern formation: the effects of a rigorous approach. Distributed Comput., 32(2):91-132, 2019. URL: https://doi.org/10.1007/S00446-018-0325-7.
  6. Reuven Cohen and David Peleg. Convergence properties of the gravitational algorithm in asynchronous robot systems. SIAM J. Comput., 34(6):1516-1528, 2005. URL: https://doi.org/10.1137/S0097539704446475.
  7. Shantanu Das, Paola Flocchini, Nicola Santoro, and Masafumi Yamashita. Forming sequences of geometric patterns with oblivious mobile robots. Distributed Comput., 28(2):131-145, 2015. URL: https://doi.org/10.1007/S00446-014-0220-9.
  8. Bastian Degener, Barbara Kempkes, Tobias Langner, Friedhelm Meyer auf der Heide, Peter Pietrzyk, and Roger Wattenhofer. A tight runtime bound for synchronous gathering of autonomous robots with limited visibility. In SPAA 2011, San Jose, CA, USA, June 4-6, 2011 (Co-located with FCRC 2011), pages 139-148. ACM, 2011. URL: https://doi.org/10.1145/1989493.1989515.
  9. Paola Flocchini, Giuseppe Prencipe, and Nicola Santoro, editors. Distributed Computing by Mobile Entities, Current Research in Moving and Computing, volume 11340. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-11072-7.
  10. Paola Flocchini, Giuseppe Prencipe, and Nicola Santoro. Moving and computing models: Robots. In Distributed Computing by Mobile Entities, Current Research in Moving and Computing, volume 11340, pages 3-14. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-11072-7_1.
  11. 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.
  12. Paola Flocchini, Giuseppe Prencipe, Nicola Santoro, and Peter Widmayer. Arbitrary pattern formation by asynchronous, anonymous, oblivious robots. Theor. Comput. Sci., 407(1-3):412-447, 2008. URL: https://doi.org/10.1016/J.TCS.2008.07.026.
  13. Nao Fujinaga, Yukiko Yamauchi, Hirotaka Ono, Shuji Kijima, and Masafumi Yamashita. Pattern formation by oblivious asynchronous mobile robots. SIAM J. Comput., 44(3):740-785, 2015. URL: https://doi.org/10.1137/140958682.
  14. Christopher Hahn, Jonas Harbig, and Peter Kling. Forming large patterns with local robots in the OBLOT model (arXiv-version with extended appendix). arXiv. URL: https://arxiv.org/abs/2404.02771.
  15. Chang-kwon Kang, Farbod Fahimi, Rob Griffin, D Brian Landrum, Bryan Mesmer, Guangsheng Zhang, Taeyoung Lee, Hikaru Aono, Jeremy Pohly, Jesse McCain, et al. Marsbee-swarm of flapping wing flyers for enhanced mars exploration. Technical report, NASA, 2019. Google Scholar
  16. David G. Kirkpatrick, Irina Kostitsyna, Alfredo Navarra, Giuseppe Prencipe, and Nicola Santoro. Separating bounded and unbounded asynchrony for autonomous robots: Point convergence with limited visibility. In PODC 2021, Italy, July 26-30, 2021, pages 9-19. ACM, 2021. URL: https://doi.org/10.1145/3465084.3467910.
  17. Giuseppe Antonio Di Luna, Paola Flocchini, Nicola Santoro, and Giovanni Viglietta. Turingmobile: a turing machine of oblivious mobile robots with limited visibility and its applications. Distributed Comput., 35(2):105-122, 2022. URL: https://doi.org/10.1007/S00446-021-00406-6.
  18. Moumita Mondal and Sruti Gan Chaudhuri. Uniform circle formation by swarm robots under limited visibility. In ICDCIT 2020, Bhubaneswar, India, January 9-12, 2020, volume 11969, pages 420-428. Springer, 2020. URL: https://doi.org/10.1007/978-3-030-36987-3_28.
  19. Fernando Soto, Jie Wang, Rajib Ahmed, and Utkan Demirci. Medical Micro/Nanorobots in Precision Medicine. Advanced Science, 7(21), November 2020. URL: https://doi.org/10.1002/advs.202002203.
  20. 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.
  21. Yuko Ulrich, Mari Kawakatsu, Christopher K. Tokita, Jonathan Saragosti, Vikram Chandra, Corina E. Tarnita, and Daniel J. C. Kronauer. Response thresholds alone cannot explain empirical patterns of division of labor in social insects. PLOS Biology, 19(6):e3001269, June 2021. URL: https://doi.org/10.1371/journal.pbio.3001269.
  22. Giovanni Viglietta. Uniform circle formation. In Distributed Computing by Mobile Entities, Current Research in Moving and Computing, volume 11340, pages 83-108. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-11072-7_5.
  23. 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.
  24. Yukiko Yamauchi. A survey on pattern formation of autonomous mobile robots: asynchrony, obliviousness and visibility. Journal of Physics: Conference Series, 473:012016, December 2013. URL: https://doi.org/10.1088/1742-6596/473/1/012016.
  25. Yukiko Yamauchi, Taichi Uehara, and Masafumi Yamashita. Brief announcement: Pattern formation problem for synchronous mobile robots in the three dimensional euclidean space. In PODC 2016, Chicago, IL, USA, July 25-28, 2016, pages 447-449. ACM, 2016. URL: https://doi.org/10.1145/2933057.2933063.
  26. Yukiko Yamauchi and Masafumi Yamashita. Pattern formation by mobile robots with limited visibility. In SIROCCO 2013, Ischia, Italy, July 1-3, 2013, volume 8179 of Lecture Notes in Computer Science, pages 201-212. Springer, 2013. URL: https://doi.org/10.1007/978-3-319-03578-9_17.
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact