A model for swarm formation with reference tracking

This paper proposes a continuous-time model for aggregating a team of agents in k-dimensional space and for establishing a reference tracking. Since the model is of kinematic nature, each agent is considered as an ideal point communicating without delay with the other components of the team. The proposed model ensures that the agents centroid path converges in finite-time to the imposed trajectory while the agents aggregate in finite-time in a hyper-ball moving around the reference path. The dimension of the hyper-ball is modulated by varying one of the free parameters of the model. This fact guarantees that the swarm can reduce or enlarge its dimension according to the environment in which it moves. Conditions are also provided to guarantee absence of agents clashes and static swarm configuration around the performed path.