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

TL;DR

This paper introduces a hybrid metric-topological interaction model for swarming behavior, addressing physical inconsistencies of pure metric or topological models and analyzing consensus reaching in such systems.

Contribution

It proposes a novel hybrid interaction distance for swarms, combining metric and topological features, and studies its impact on consensus dynamics through theoretical and simulation methods.

Findings

Exact probability of consensus without noise derived

Hybrid distance improves consensus robustness

Simulations confirm theoretical predictions

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 pro- cess 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.