Multi-Robot Motion Planning of k-Colored Discs Is PSPACE-Hard

Authors Thomas Brocken, G. Wessel van der Heijden, Irina Kostitsyna, Lloyd E. Lo-Wong, Remco J. A. Surtel

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Author Details

Thomas Brocken
  • TU Eindhoven, The Netherlands
G. Wessel van der Heijden
  • TU Eindhoven, The Netherlands
Irina Kostitsyna
  • TU Eindhoven, The Netherlands
Lloyd E. Lo-Wong
  • TU Eindhoven, The Netherlands
Remco J. A. Surtel
  • TU Eindhoven, The Netherlands

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Thomas Brocken, G. Wessel van der Heijden, Irina Kostitsyna, Lloyd E. Lo-Wong, and Remco J. A. Surtel. Multi-Robot Motion Planning of k-Colored Discs Is PSPACE-Hard. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


In the problem of multi-robot motion planning, a group of robots, placed in a polygonal domain with obstacles, must be moved from their starting positions to a set of target positions. We consider the specific case of unlabeled disc robots of two different sizes. That is, within one class of robots, where a class is given by the robots' size, any robot can be moved to any of the corresponding target positions. We prove that the decision problem of whether there exists a schedule moving the robots to the target positions is PSPACE-hard.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Disc-robot motion planning
  • algorithmic complexity
  • PSPACE-hard


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