Eur. Phys. J. B (2014) 87: 294
https://doi.org/10.1140/epjb/e2014-50094-4

Regular Article

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

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

^a e-mail: bouffanais@sutd.edu.sg

Received: 10 February 2014
Received in final form: 2 October 2014
Published online: 8 December 2014

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.