Gathering on a Circle with Limited Visibility by Anonymous Oblivious Robots

Authors Giuseppe A. Di Luna, Ryuhei Uehara, Giovanni Viglietta, Yukiko Yamauchi



PDF
Thumbnail PDF

File

LIPIcs.DISC.2020.12.pdf
  • Filesize: 0.51 MB
  • 17 pages

Document Identifiers

Author Details

Giuseppe A. Di Luna
  • DIAG, Sapienza University of Rome, Italy
Ryuhei Uehara
  • School of Information Science, JAIST, Ishikawa, Japan
Giovanni Viglietta
  • School of Information Science, JAIST, Ishikawa, Japan
Yukiko Yamauchi
  • Department of Informatics, Graduate School of ISEE, Kyushu University, Japan

Acknowledgements

The authors would like to thank the anonymous reviewers for greatly improving the readability of this paper.

Cite As Get BibTex

Giuseppe A. Di Luna, Ryuhei Uehara, Giovanni Viglietta, and Yukiko Yamauchi. Gathering on a Circle with Limited Visibility by Anonymous Oblivious Robots. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.DISC.2020.12

Abstract

A swarm of anonymous oblivious mobile robots, operating in deterministic Look-Compute-Move cycles, is confined within a circular track. All robots agree on the clockwise direction (chirality), they are activated by an adversarial semi-synchronous scheduler (SSYNCH), and an active robot always reaches the destination point it computes (rigidity). Robots have limited visibility: each robot can see only the points on the circle that have an angular distance strictly smaller than a constant ϑ from the robot’s current location, where 0 < ϑ ≤ π (angles are expressed in radians).
We study the Gathering problem for such a swarm of robots: that is, all robots are initially in distinct locations on the circle, and their task is to reach the same point on the circle in a finite number of turns, regardless of the way they are activated by the scheduler. Note that, due to the anonymity of the robots, this task is impossible if the initial configuration is rotationally symmetric; hence, we have to make the assumption that the initial configuration be rotationally asymmetric.
We prove that, if ϑ = π (i.e., each robot can see the entire circle except its antipodal point), there is a distributed algorithm that solves the Gathering problem for swarms of any size. By contrast, we also prove that, if ϑ ≤ π/2, no distributed algorithm solves the Gathering problem, regardless of the size of the swarm, even under the assumption that the initial configuration is rotationally asymmetric and the visibility graph of the robots is connected.
The latter impossibility result relies on a probabilistic technique based on random perturbations, which is novel in the context of anonymous mobile robots. Such a technique is of independent interest, and immediately applies to other Pattern-Formation problems.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Distributed algorithms
  • Theory of computation → Self-organization
Keywords
  • Mobile robots
  • Gathering
  • limited visibility
  • circle

Metrics

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

References

  1. N. Agmon and D. Peleg. Fault-tolerant gathering algorithms for autonomous mobile robots. SIAM Journal on Computing, 36(1):56-82, 2006. Google Scholar
  2. H. Ando, Y. Oasa, I. Suzuki, and M. Yamashita. Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Transactions on Robotics and Automation, 15(5):818-838, 1999. Google Scholar
  3. S. Bhagat, K. Mukhopadhyaya, and S. Mukhopadhyaya. Computation under restricted visibility. In Distributed Computing by Mobile Entities: Current Research in Moving and Computing, pages 134-183. Springer, 2019. Google Scholar
  4. M. Cieliebak, P. Flocchini, G. Prencipe, and N. Santoro. Distributed computing by mobile robots: gathering. SIAM Journal on Computing, 41(2):829-879, 2012. Google Scholar
  5. P. Courtieu, L. Rieg, S. Tixeuil, and X. Urbain. Impossibility of gathering, a certification. Information Processing Letters, 115(3):447-452, 2015. Google Scholar
  6. G. D'Angelo, G. Di Stefano, and A. Navarra. Gathering on rings under the Look-Compute-Move model. Distributed Computing, 27(4):255-285, 2014. Google Scholar
  7. G. D'Angelo, A. Navarra, and N. Nisse. A unified approach for gathering and exclusive searching on rings under weak assumptions. Distributed Computing, 30(1):17-48, 2017. Google Scholar
  8. S. Das, G.A. Di Luna, P. Flocchini, N. Santoro, G. Viglietta, and M. Yamashita. Oblivious permutations on the plane. In 23rd International Conference on Principles of Distributed Systems, pages 24:1-24:16, 2019. Google Scholar
  9. X. Défago, M. Gradinariu, S. Messika, P. Raipin-Parvédy, and S. Dolev. Fault-tolerant and self-stabilizing mobile robots gathering. In 20th International Symposium on Distributed Computing, pages 46-60, 2006. Google Scholar
  10. B. Degener, B. Kempkes, P. Kling, F. Meyer auf der Heide, P. Pietrzyk, and R. Wattenhofer. A tight runtime bound for synchronous gathering of autonomous robots with limited visibility. In 23rd ACM Symposium on Parallelism in Algorithms and Architectures, pages 139-148, 2011. Google Scholar
  11. G.A. Di Luna, P. Flocchini, L. Pagli, G. Prencipe, N. Santoro, and G. Viglietta. Gathering in dynamic rings. Theoretical Computer Science, 811:79-98, 2020. Google Scholar
  12. G.A. Di Luna, P. Flocchini, N. Santoro, and G. Viglietta. TuringMobile: a turing machine of oblivious mobile robots with limited visibility and its applications. In 32nd International Symposium on Distributed Computing, pages 19:1-19:18, 2018. Google Scholar
  13. G.A. Di Luna, P. Flocchini, N. Santoro, G. Viglietta, and M. Yamashita. Meeting in a polygon by anonymous oblivious robots. Distributed Computing (to appear), 2019. Google Scholar
  14. G.A. Di Luna and G. Viglietta. Robots with lights. In Distributed Computing by Mobile Entities, Current Research in Moving and Computing, pages 252-277. Springer, 2019. Google Scholar
  15. P. Flocchini. Gathering. In Distributed Computing by Mobile Entities: Current Research in Moving and Computing, pages 63-82. Springer, 2019. Google Scholar
  16. P. Flocchini, G. Prencipe, and N. Santoro. Self-deployment of mobile sensors on a ring. Theoretical Computer Science, 402(1):67-80, 2008. Google Scholar
  17. P. Flocchini, G. Prencipe, and N. Santoro. Distributed Computing by Oblivious Mobile Robots. Morgan & Claypool, 2012. Google Scholar
  18. P. Flocchini, G. Prencipe, and N. Santoro, editors. Distributed Computing by Mobile Entities, Current Research in Moving and Computing. Springer, 2019. Google Scholar
  19. P. Flocchini, G. Prencipe, N. Santoro, and G. Viglietta. Distributed computing by mobile robots: uniform circle formation. Distributed Computing, 30(6):413-457, 2017. Google Scholar
  20. P. Flocchini, G. Prencipe, N. Santoro, and P. Widmayer. Gathering of asynchronous robots with limited visibility. Theoretical Computer Science, 337(1-3):147-168, 2005. Google Scholar
  21. N. Fujinaga, Y. Yamauchi, S. Kijima, and M. Yamahista. Pattern formation by oblivious asynchronous mobile robots. SIAM Journal on Computing, 44(3):740-785, 2015. Google Scholar
  22. S. Kamei, A. Lamani, F. Ooshita, S. Tixeuil, and K. Wada. Gathering on rings for myopic asynchronous robots with lights. In 23rd International Conference on Principles of Distributed Systems, pages 27:1-27:17, 2019. Google Scholar
  23. E. Kranakis, D. Krizanc, and E. Markou. The Mobile Agent Rendezvous Problem in the Ring. Morgan and Claypool, 2010. Google Scholar
  24. A. Monde, Y. Yamauchi, S. Kijima, and M. Yamashita. Self-stabilizing localization of the middle point of a line segment by an oblivious robot with limited visibility. In 19th International Symposium on Stabilization, Safety, and Security of Distributed Systems, pages 172-186, 2017. Google Scholar
  25. L. Pagli, G. Prencipe, and G. Viglietta. Getting close without touching: near-gathering for autonomous mobile robots. Distributed Computing, 28(5):333-349, 2015. Google Scholar
  26. P. Poudel and G. Sharma. Universally optimal gathering under limited visibility. In 19th International Symposium on Stabilization, Safety, and Security of Distributed Systems, pages 323-340, 2017. Google Scholar
  27. S. Souissi, X. Défago, and M. Yamashita. Using eventually consistent compasses to gather memory-less mobile robots with limited visibility. ACM Transactions on Autonomous and Adaptive Systems, 4(1):9:1-9:27, 2009. Google Scholar
  28. I. Suzuki and M. Yamashita. Distributed anonymous mobile robots: formation of geometric patterns. SIAM Journal on Computing, 28(4):1347-1363, 1999. Google Scholar
  29. Y. Yamauchi. Symmetry of anonymous robots. In Distributed Computing by Mobile Entities, Current Research in Moving and Computing, pages 109-133. Springer, 2019. Google Scholar
  30. Y. Yamauchi, T. Uehara, S. Kijima, and M. Yamashita. Plane formation by synchronous mobile robots in the three-dimensional euclidean space. Journal of the ACM, 64(3):16:1-16:43, 2017. Google Scholar
  31. Y. Yamauchi and M. Yamashita. Pattern formation by mobile robots with limited visibility. In 20th International Colloquium on Structural Information and Communication Complexity, pages 201-212, 2013. Google Scholar
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