Abstract
This paper focuses on the trajectory tracking problem for a swarm of mobile agents. A kinematic model describing the interactions and evolutions of the swarm members is proposed and its main properties are analyzed emphasizing that the agents centroid is ensured to track in finite-time a given reference trajectory and that the agents reach an aggregation in finite-time in a hyper-ball moving around the centroid path. One of the main characteristics of the model is the presence of an interaction matrix, between agents coordinates, which allows to define some properties of the swarm allowing the creation of different forms of agents aggregations, i.e., spheres, ellipsoids, straight lines, etc. Indeed swarm properties related to the agents configuration around the performed path along with agents interactions and absence of collisions are analyzed depending on the chosen interaction matrix.
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