Consensus of a group of mobile agents in three dimensions

This paper investigates the consensus problem of a three dimensional (3D) version of the widely studied Vicsek model, where each member moves in 3D Euclidean space with a constant speed with headings updated according to the average direction of neighbors. In comparison with the original Vicsek model, each agent’s heading is determined by two angle sequences interacting with each other, one of which evolves according to a “linear” non-homogeneous equation, which makes the theoretical analysis quite complicated. By analyzing the underlying structure of the system and relying on estimation of some characteristics concerning the initial states, we will establish consensus results for 3D Vicsek model under random framework without resorting to any a priori connectivity assumption.