Control of a team of car-like robots using abstractions

We present a method to coordinate a large number of under-actuated robots by designing control laws on a small dimensional manifold, independent on the number and ordering of the robots. The small dimensional description of the team has a product structure of a Lie group, which captures the dependence of the ensemble on the world frame, and a shape manifold, which is an intrinsic description of the team. We design decoupled controls for group and shape. The individual control laws which are mapped to the desired collective behavior can be realized by feedback depending only on the current state of the robot and the state on the small dimensional manifold, so that the robots have to broadcast their states and only have to listen to some coordinating agent with small bandwidth.