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Algorithmic Foundations of Robotics XI pp 1–17Cite as

Efficient Multi-robot Motion Planning for Unlabeled Discs in Simple Polygons

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Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 107))

Abstract

We consider the following motion-planning problem: we are given \(m\) unit discs in a simple polygon with \(n\) vertices, each at their own start position, and we want to move the discs to a given set of \(m\) target positions. Contrary to the standard (labeled) version of the problem, each disc is allowed to be moved to any target position, as long as in the end every target position is occupied. We show that this unlabeled version of the problem can be solved in \(O\left( n\log n+mn+m^2\right) \) time, assuming that the start and target positions are at least some minimal distance from each other. This is in sharp contrast to the standard (labeled) and more general multi-robot motion planning problem for discs moving in a simple polygon, which is known to be strongly np-hard.

The work has been carried out in part during Aviv Adler’s visit to Tel Aviv University, enabled by the generous Melvin M. Goldberg Fellowship for Research in Israel.

Work by D.H. and K.S. has been supported in part by the 7th Framework Programme for Research of the European Commission, under FET-Open grant number 255827 (CGL—Computational Geometry Learning), by the Israel Science Foundation (grant no. 1102/11), by the German-Israeli Foundation (grant no. 1150-82.6/2011), and by the Hermann Minkowski–Minerva Center for Geometry at Tel Aviv University.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Princeton University, New Jersey, USA

    Aviv Adler

  2. Department of Mathematics and Computing Science, Tu Eindhoven, Eindhoven, The Netherlands

    Mark de Berg

  3. Blavatnik School of Computer Science, Tel-Aviv University, Tel Aviv-Yafo, Israel

    Dan Halperin & Kiril Solovey

Authors
  1. Aviv Adler
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  2. Mark de Berg
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  3. Dan Halperin
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  4. Kiril Solovey
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Corresponding author

Correspondence to Kiril Solovey .

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Editors and Affiliations

  1. Department of Computer Engineering, Bogazici University, Istanbul, Turkey

    H. Levent Akin

  2. Department of Computer Science and Engineering, Texas A&M University, College Station, Texas, USA

    Nancy M. Amato

  3. Department of Computer Science and Engineering, University of Minnesota, Minneapolis, Minnesota, USA

    Volkan Isler

  4. Department of Information and Computing Sciences, Utrecht University, Utrecht, Utrecht, The Netherlands

    A. Frank van der Stappen

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Adler, A., de Berg, M., Halperin, D., Solovey, K. (2015). Efficient Multi-robot Motion Planning for Unlabeled Discs in Simple Polygons. In: Akin, H., Amato, N., Isler, V., van der Stappen, A. (eds) Algorithmic Foundations of Robotics XI. Springer Tracts in Advanced Robotics, vol 107. Springer, Cham. https://doi.org/10.1007/978-3-319-16595-0_1

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  • DOI: https://doi.org/10.1007/978-3-319-16595-0_1

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  • Online ISBN: 978-3-319-16595-0

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