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In this paper, we present a method for table tennis ball trajectory filteringand prediction. Our gray-box approach builds on a physical model. At the sametime, we use data to learn parameters of the dynamics model, of an extendedKalman filter, and of a neural model that infers the ball's initial condition.We demonstrate superior prediction performance of our approach over twoblack-box approaches, which are not supplied with physical prior knowledge. Wedemonstrate that initializing the spin from parameters of the ball launcherusing a neural network drastically improves long-time prediction performanceover estimating the spin purely from measured ball positions. An accurateprediction of the ball trajectory is crucial for successful returns. Wetherefore evaluate the return performance with a pneumatic artificial muscularrobot and achieve a return rate of 29/30 (97.7%).

Black-Box vs. Gray-Box: A Case Study on Learning Table Tennis Ball Trajectory Prediction with Spin and Impacts