A kinematic swarm model for vortex-like behavior around an uncertain target

This paper proposes a kinematic model for a swarm of agents able to exhibit the formation of vortices around a given reference trajectory and to deal with uncertainty in the reference information. One of the main novelties of this model is the use of two coordinates coupling matrices that weight the attraction to a given reference trajectory and the interaction among agents. Each agent may exchange information with all the other agents in its neighbourhood and this neighbourhood is described by a detection range related to the proximity sensor that each agent is equipped with. The communication topology graph evolution is studied too and sufficient conditions to ensure both the persistence of connections between the agents and the achievement of a complete graph are provided. Moreover the swarm aggregation and steady-state properties are described. Numerical simulations illustrate the obtained results.