The strategy for the control of vehicle platooning is proposed and tested on different mobile robot platforms. The decentralized platooning is considered, i.e. a virtual train of vehicles where each vehicle is autonomous and decides on its motion based on its own perceptions. The following vehicle only has information about its distance and azimuth to the leading vehicle. Its position is determined using odometry. The reference position and the orientation of the following vehicle are determined by the estimated path of the leading vehicle in a parametric polynomial form. The parameters of the polynomials are determined using the least-squares method. This parametric reference path is also used to determine the feed-forward part and to suppress tracking errors by a feed-back part of the applied globally stable nonlinear control law. The results of the experiment and simulations demonstrate the applicability of the proposed algorithm for vehicle platoons.