Vortex formation in a Swarm of Agents with a Coordinates Mixing Matrix-based Model

In this letter a kinematic model is proposed to explain the formation of vortices in a swarm of agents. The main characteristic of this model is the introduction of two coordinates coupling matrices weighting both the attractive term to a given target reference trajectory and the interaction term among agents. These matrices, on which the stability properties of the swarm depend, allow to obtain a rotational behaviour of the agents around the target. Each agent may exchange information with all the other agents in its neighbourhood. This neighbourhood is considered to be a circle of a certain radius that depends on the characteristics of the proximity sensor that each agent is equipped with. The communication topology graph evolution is studied providing sufficient conditions to ensure both the persistence of connections between the agents and the achievement of a fully connected graph in finite-time. Moreover the swarm aggregation and steady-state properties are described. Numerical simulations are provided to illustrate the obtained results.