Reachability of agents with double integrator dynamics in cyclic pursuit

Some recent work on cyclic pursuit systems with double integrator dynamics has probed the stability of certain proposed laws and investigated the stability of several formations for such a system of agents. Some of these laws use the relative position information of two leading neighbors, instead of one as in case of single integrator dynamics. In some others the relative position of only one leader is used along with its relative velocity and a damping term. In this paper, a new law is proposed which guarantees stability. An algorithm is proposed which enables rendezvous of the agents at any desired point in the two-dimensional space. The gains corresponding to each agent are different and, along with their initial velocities, are considered to be the decision variables. The theoretical results are backed by simulation studies.