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Consensus reaching in swarms ruled by a hybrid metric-topological distance

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Abstract

Recent empirical observations of three-dimensional bird flocks and human crowds have challenged the long-prevailing assumption that a metric interaction distance rules swarming behaviors. In some cases, individual agents are found to be engaged in local information exchanges with a fixed number of neighbors, i.e. a topological interaction. However, complex system dynamics based on pure metric or pure topological distances both face physical inconsistencies in low and high density situations. Here, we propose a hybrid metric-topological interaction distance overcoming these issues and enabling a real-life implementation in artificial robotic swarms. We use network- and graph-theoretic approaches combined with a dynamical model of locally interacting self-propelled particles to study the consensus reaching process for a swarm ruled by this hybrid interaction distance. Specifically, we establish exactly the probability of reaching consensus in the absence of noise. In addition, simulations of swarms of self-propelled particles are carried out to assess the influence of the hybrid distance and noise.

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Authors and Affiliations

  1. Singapore University of Technology and Design, 20 Dover Drive, 138682, Singapore, Singapore

    Yilun Shang & Roland Bouffanais

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  1. Yilun Shang
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  2. Roland Bouffanais
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Correspondence to Roland Bouffanais.

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Shang, Y., Bouffanais, R. Consensus reaching in swarms ruled by a hybrid metric-topological distance. Eur. Phys. J. B 87, 294 (2014). https://doi.org/10.1140/epjb/e2014-50094-4

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  • DOI: https://doi.org/10.1140/epjb/e2014-50094-4

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