Flocking algorithm for multiple nonholonomic cars

In this paper, a flocking control algorithm for multiple nonholonomic cars is proposed. First, it is shown that the nonholonomic car is linearized by using a virtual vehicle. Second, we define a metric and topological neighborhood set in order to decide which cars to be next to the other car. Control objectives consist of three rules in boids model as separation, alignment, and cohesion, which is a well-known framework of emerging flock, advocated by Reynolds in 1986. Using the neighborhood set, we show the formation of flocking corresponds to the model. These cars are supposed to be on a straight highway, which enables us to set an assumption that each car heads to the same direction and reaches the same velocity eventually. The input for a car consists of the artificial potential method and LaSalle's invariance principle is utilized to prove the convergence of the entire vehicle system. Finally, the effectiveness of the presented method is examined through simulation.