Shepherding and herdability in complex multiagent systems

Abstract

We study the shepherding control problem where a group of “herders” need to orchestrate their collective behavior in order to steer the dynamics of a group of “target” agents towards a desired goal. We relax the assumptions, often made in the existing literature, of targets showing cohesive collective behavior in the absence of the herders, and herders owning global sensing capabilities. We find scaling laws linking the number of targets with the minimum number of herders needed to shepherd them, and we unveil the existence of a critical threshold of the density of the targets, below which the number of herders needed for success significantly increases. We explain the existence of such a threshold in terms of the percolation of a suitably defined herdability graph and support our numerical evidence by analyzing a partial differential equation describing the herders dynamics in a simplified one-dimensional setting. Extensive numerical experiments validate our methodology.