Modelling, Analysis, and Optimization of Three-Dimensional Restricted Visual Field Metric-Free Swarms

Abstract

Models of collective behaviour have been proved helpful in revealing what mechanism may underlie characteristics of a flock of birds, a school of fish, and a swarm of herds. Recently, the metric-free model gradually occupies a dominant position in the research field of collective intelligence. Most of these models endow every single individual with the ability of a global visual field, which can offer each particle sufficient external information. In this paper, we mainly focus on whether the global visual field is necessary to form a consistent and cohesive group or not. Inspired by the biological characteristic of starlings, we develop a three-dimensional restricted visual field metric-free(RVFMF) model based on Pearce and Turner's previous work. We further investigate several vital factors governing the convergent consistency of the RVFMF model with the assistance of extensive numerical simulations. According to the simulation results, we conclude that the best view angle of each particle in a swarm increases with the expansion of the population size. Besides, the best view angle gradually becomes stable around 155 degrees when the population size is larger than 1000. We also offer quantitative analysis data to prove that a flock of birds could obtain better consistency under optimal restricted visual field than under global visual field.