Geometric pattern formation with coordinated double-integrator agents

This paper deals with the problem of geometric pattern formation by a group of mobile autonomous agents. The patterns are formed by the trajectories of the agents modeled with double integrator dynamics. The patterns can either be closed or can cover the entire space. We build upon an existing consensus law, by introducing self position feedback and study the collective motion of a team of agents. The patterns are not only aesthetically appealing but can also be used in civilian applications like search, exploration and surveillance. There is no restriction on the underlying graph topology. The control law manipulates the location of the eigenvalues of the overall system to achieve the pattern. We present simulation results to validate the developed theory.