Tracking control of two holonomic robots in formation without collision

In this paper, we analyze a formation control problem of two disk-shaped holonomic mobile robots without collision each other. We show that the tracking control problem can be reduced to sample stabilization of the origin of the nonlinear system defined on noncontractible manifold by exact linearization via coordinate transformation. We propose a tracking control method which is applying the Rifford-Sontag type controller to the transformed system obtained by the coordinate transformation. The proposed method is a discontinuous time-varying state feedback control. Since our proposed system does not require to design a trajectory for tracking to avoid collision, it is easy to implement to the robot compared to path planning from a current robot´s position to a trajectory given by the formation. It is guaranteed that the robots traces their desired trajectory without collision each other with the proposed method. The performance of the proposed method is confirmed by simulations.