Consensus of the 3-dimensional Vicsek model

This paper investigates the consensus problem of a 3-dimensional (3D for short) version of the widely studied Vicsek model. The 3D Vicsek model is composed of a large number of autonomous agents, all moving in the 3D Euclidean space with a constant speed and with headings updated according to the average directions of neighbors. Compared with the Vicsek model, each agent´s heading is determined by two angles interacting with each other, and one of the two angles evolves according to the non-homogeneous linear equation, which make the theoretical analysis quite complicated. By analyzing the underlying structure of the system and estimating some characteristics concerned with the initial states, we will prove that the system can reach consensus for large population.