The present paper deals with an online approach to learn the inverse dynamics of any robot. This is realized by the use of Gaussian Processes drifting parallel along the system data. An extension by a database enables the efficient use of data points from the past. The central component of this work is the implementation of such a method in a controller in order to achieve the actual goal: the feedforward control of an industrial robot by means of machine learning. This is done by splitting the procedure into two threads running parallel so that the prediction is decoupled from the computing-intensive training of the models. Experiments show that the method reduces the tracking errors more clearly than an elaborately identified rigid body model including friction. For a defined trajectory, the squared areas of the tracking errors of all axes are reduced by more than 54% compared to motion without pre-control. In addition, a highly dynamic pick-and-place experiment is used to investigate the possible changes in system dynamics. Compared to an offline trained model, the approximation error of the proposed online approach is smaller for the remaining time of the experiment after an initial phase. Furthermore, this error is smaller throughout the experiment for online learning with parallel drifting Gaussian Processes than when using a single one.