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Decentralized Progressive Shape Formation with Robot Swarms

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Distributed Autonomous Robotic Systems

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 6))

Abstract

We tackle the problem of achieving any given shape defined as a point cloud in a distributed manner with a swarm of robots. The contributions of this paper are (i) An algorithm that transforms a point cloud into a acyclic directed graph; (ii) A motion control law that, from the acyclic directed graph, allows a swarm of robots to achieve the target shape in a decentralized manner; and (iii) A theoretical model, which provides sufficient conditions on the convergence of the control law. The key idea of our approach is to achieve the target shape progressively by inducing an ordering among the robots. More precisely, we construct an acyclic directed graph so that any free robot (i.e., not part of the shape) finds its location with respect to the already placed robots. We prove that, for a 2D shape, it is sufficient for a free robot to calculate its location with respect to two already placed robots to achieve this objective. We validate our method through accurate physics-based simulations of non-holonomic robots.

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Notes

  1. 1.

    In our experiments we set \(Z=2^{16}-1\). With this value, 302 robots must simultaneously request the same label i to have a probability \(>0.5\) that at least two robots choose the same value for z. We observed that, on average, a robot has only about 8 neighbors; assuming that all of them request the same i simultaneously, the probability that at least two requests have the same value for z is \({\approx }4.27 \cdot 10^{-4}\).

  2. 2.

    http://www.argos-sim.info/.

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Author information

Authors and Affiliations

  1. Worcester Polytechnic Institute, Worcester, MA, USA

    Carlo Pinciroli

  2. Università Roma Tre, Rome, Italy

    Andrea Gasparri

  3. Université Libre de Bruxelles, Bruxelles, Belgium

    Emanuele Garone

  4. Polytechnique Montréal, Montreal, QC, Canada

    Giovanni Beltrame

Authors
  1. Carlo Pinciroli
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  2. Andrea Gasparri
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  3. Emanuele Garone
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  4. Giovanni Beltrame
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Corresponding author

Correspondence to Carlo Pinciroli .

Editor information

Editors and Affiliations

  1. Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, UK

    Roderich Groß

  2. Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, UK

    Andreas Kolling

  3. School for Engineering of Matter, Transport and Energy (SEMTE), Arizona State University, Tempe, AZ, USA

    Spring Berman

  4. Massachusetts Institute of Technology, Cambridge, MA, USA

    Emilio Frazzoli

  5. ENAC, IIE, DIAL, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

    Alcherio Martinoli

  6. Department of Mechanical Engineering and Science, Kyoto University, Kyoto, Japan

    Fumitoshi Matsuno

  7. Wyss Institute for Biologically Inspired Engineering, Harvard University Wyss Institute for Biologically Inspired, Cambridge, MA, USA

    Melvin Gauci

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Pinciroli, C., Gasparri, A., Garone, E., Beltrame, G. (2018). Decentralized Progressive Shape Formation with Robot Swarms. In: Groß, R., et al. Distributed Autonomous Robotic Systems. Springer Proceedings in Advanced Robotics, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-73008-0_30

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  • DOI: https://doi.org/10.1007/978-3-319-73008-0_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73006-6

  • Online ISBN: 978-3-319-73008-0

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