Novel Vehicular Trajectories for Collective Motion from Coupled Oscillator Steering Control

We consider a model for vehicle motion coordination for three vehicles that uses coupled oscillator steering control. Prior work on such models has focused primarily on sinusoidal coupling functions, which typically give behavior in which individual vehicles move either in straight lines or in circles. We show that other, more exotic trajectories are possible when more general coupling functions are considered. Such trajectories are associated with periodic orbits in the steering control subsystem. The proximity of these periodic orbits to heteroclinic bifurcations allows for a detailed characterization of the properties of the vehicular trajectories.