A Generalized Gazi–Passino Model With Coordinate-Coupling Matrices for Swarm Formation With Rotation Behavior

Abstract

In this article, a kinematic continuous time swarm model is considered by extending the results in the paper “A class of attractions/repulsion functions for stable swarm aggregations” (as shown in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">International Journal of Control</i> , vol. 77, pages 1567–1579). 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 coordinate-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.