Flocking motion of multi-agent systems: A proximity digraph case

Abstract

We investigate the coordinated motion of a multi-agent system with heterogeneous distance-dependent communication constraints. In this setup, the underlying interaction network is dynamic since edges appear or disappear as the agents navigate their workspace. Inspired by the gradient-descent method, we provide a distributed controller which preserves the position-dependent communication network connectivity properties. We use a distributed connectivity measure based on the entries of the first-left eigenvector of the network's associated Laplacian matrix to provide the agents with local knowledge of the overall network topology and reveal its dynamics properties. We illustrate our result with a numerical simulation.