A Generalized Gazi-Passino Model with Coordinate-coupling Matrices for Swarm Formation with Rotation Behaviour

Abstract

In this paper a kinematic continuous time swarm model is considered by extending the results in [1]. The extension regards a more general class of attraction/repulsion functions that can be used to explain the formation of rotational patterns in a swarm of agents. The main characteristic of this model is the introduction of two coordinates coupling matrices weighting both the attractive and the repulsive interactions among the agents. A stability analysis is presented to characterize the swarm in terms of size and cohesiveness. Moreover, a class of attraction/repulsion functions is presented to guarantee the cohesiveness of the swarm in a polytopic region and a steady-state motion of the agents in a rotational frame around the swarm centroid. Numerical simulations are provided to illustrate the obtained results. IEEE