Some generalizations of linear cyclic pursuit

In this paper, the behaviour of a group of autonomous mobile agents under cyclic pursuit is studied. Cyclic pursuit is a simple distributed control law, in which the agent i pursues agent i+1 modulo n. The agents are assumed to be linear and identical, with no kinematic constraints on motion. It is shown here that the point of convergence of the system of agents is a function of the controller gain. The bounds on the controller gain for convergence to occur is also studied. The results generalize available results in the literature.