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Coordinated Particle Relocation with Global Signals and Local Friction (Media Exposition)

Authors Victor M. Baez , Aaron T. Becker , Sándor P. Fekete , Arne Schmidt

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LIPIcs.SoCG.2020.72.pdf
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Victor M. Baez
  • Department of Electrical and Computer Engineering, University of Houston, TX, USA
Aaron T. Becker
  • Department of Electrical and Computer Engineering, University of Houston, TX, USA
Sándor P. Fekete
  • Department of Computer Science, TU Braunschweig, Germany
Arne Schmidt
  • Department of Computer Science, TU Braunschweig, Germany

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Victor M. Baez, Aaron T. Becker, Sándor P. Fekete, and Arne Schmidt. Coordinated Particle Relocation with Global Signals and Local Friction (Media Exposition). In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 72:1-72:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.SoCG.2020.72

Abstract

In this video, we present theoretical and practical methods for achieving arbitrary reconfiguration of a set of objects, based on the use of external forces, such as a magnetic field or gravity: Upon actuation, each object is pushed in the same direction. This concept can be used for a wide range of applications in which particles do not have their own energy supply or in which they are subject to the same global control commands.
A crucial challenge for achieving any desired target configuration is breaking global symmetry in a controlled fashion. Previous work (some of which was presented during SoCG 2015) made use of specifically placed barriers; however, introducing precisely located obstacles into the workspace is impractical for many scenarios. In this paper, we present a different, less intrusive method: making use of the interplay between static friction with a boundary and the external force to achieve arbitrary reconfiguration. Our key contributions are theoretical characterizations of the critical coefficient of friction that is sufficient for rearranging two particles in triangles, convex polygons, and regular polygons; a method for reconfiguring multiple particles in rectangular workspaces, and deriving practical algorithms for these rearrangements. Hardware experiments show the efficacy of these procedures, demonstrating the usefulness of this novel approach.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Computer systems organization → Embedded and cyber-physical systems
Keywords
  • Global control
  • reconfiguration
  • geometric algorithms
  • friction

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