A new algorithm for the control of vehicle platooning is proposed and tested on a robot-soccer test bed. We considered decentralized platooning, i.e., a virtual train of vehicles, where each vehicle is autonomous and decides on its motion based on its own perceptions. The platooning vehicles have non-holonomic constraints. The following vehicle only has information about its own orientation and about its distance and azimuth to the leading vehicle. Its position is determined using odometry and a compass. The reference position and the orientation of the following vehicle are determined by the estimated path of the leading vehicle in a parametric polynominal form. The parameters of the polynominals are determined using the least-squares method. This parametric reference path is also used to determine the feed-forward part of the applied control algorithm. The feed-back control consists of a state controller with three inputs: the longitudinal and lateral position errors and the orientation error. The results of the experiments demonstrate the applicability of the proposed algorithm for vehicle platoons.