Sufficient conditions for flocking via graph robustness analysis

In this paper, we consider a multi-agent system consisting of mobile agents with second-order dynamics. The communication network is determined by a standard interaction rule based on the distance between agents. The goal of this paper is to determine practical conditions (on the initial positions and velocities of agents) ensuring that the agents asymptotically agree on a common velocity (i.e. a flocking behavior is achieved). For this purpose, we define a new notion of graph robustness which allows us to establish such conditions, building upon previous work on multi-agent systems with switching communication networks. Though conservative, our approach gives conditions that can be verified a priori. Our result is illustrated through simulations.