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International Symposium on Stabilization, Safety, and Security of Distributed Systems

SSS 2017: Stabilization, Safety, and Security of Distributed Systems pp 172–186Cite as

Self-stabilizing Localization of the Middle Point of a Line Segment by an Oblivious Robot with Limited Visibility

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10616))

Abstract

This paper poses a question about a simple localization problem, which is arisen from self-stabilizing location problems by oblivious mobile autonomous robots with limited visibility. The question is if an oblivious mobile robot on a line-segment can localize the middle point of the line-segment in finite steps observing the direction (i.e., Left or Right) and distance to the nearest end point. This problem is also akin to (a continuous version of) binary search, and could be closely related to computable real functions. Contrary to appearances, it is far from trivial if this simple problem is solvable or not, and unsettled yet. This paper is concerned with three variants of the original problem, minimally relaxing, and presents self-stabilizing algorithms for them. We also show an easy impossibility theorem for bilaterally symmetric algorithms.

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Notes

  1. 1.

    We conjecture that Problem 1 is unsolvable. To avoid ambiguity, especially for an impossibility proof (in the future), we give there a formal description of the problem.

  2. 2.

    Here, \(x \mapsto f(\phi (D,x))\) represents a transition of the robot on the interval \([-D,D]\).

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Acknowledgement

This work is partly supported by JSPS KAKENHI Grant Numbers 15K15938 and 17K19982.

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Authors and Affiliations

  1. Graduate School of Information Science and Electrical Engineering, Kyushu University, Fukuoka, 819-0395, Japan

    Akihiro Monde, Yukiko Yamauchi, Shuji Kijima & Masafumi Yamashita

Authors
  1. Akihiro Monde
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  2. Yukiko Yamauchi
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  3. Shuji Kijima
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  4. Masafumi Yamashita
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Corresponding author

Correspondence to Akihiro Monde .

Editor information

Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Paul Spirakis

  2. Chalmers University of Technology, Gothenburg, Sweden

    Philippas Tsigas

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Monde, A., Yamauchi, Y., Kijima, S., Yamashita, M. (2017). Self-stabilizing Localization of the Middle Point of a Line Segment by an Oblivious Robot with Limited Visibility. In: Spirakis, P., Tsigas, P. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2017. Lecture Notes in Computer Science(), vol 10616. Springer, Cham. https://doi.org/10.1007/978-3-319-69084-1_12

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  • DOI: https://doi.org/10.1007/978-3-319-69084-1_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-69083-4

  • Online ISBN: 978-3-319-69084-1

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