In this paper, we present a method for table tennis ball trajectory filtering and prediction. Our gray-box approach builds on a physical model. At the same time, we use data to learn parameters of the dynamics model, of an extended Kalman filter, and of a neural model that infers the ball's initial condition. We demonstrate superior prediction performance of our approach over two black-box approaches, which are not supplied with physical prior knowledge. We demonstrate that initializing the spin from parameters of the ball launcher using a neural network drastically improves long-time prediction performance over estimating the spin purely from measured ball positions. An accurate prediction of the ball trajectory is crucial for successful returns. We therefore evaluate the return performance with a pneumatic artificial muscular robot and achieve a return rate of 29/30 (97.7%).

翻译：本文提出了一种乒乓球轨迹滤波与预测方法。我们的灰盒方法基于物理模型构建，同时通过数据学习动力学模型参数、扩展卡尔曼滤波器参数以及推断球初始状态的神经模型参数。我们证明了该方法在预测性能上优于两种未配备物理先验知识的黑盒方法。研究表明，利用神经网络从发球器参数中初始化旋转状态，相比仅从测量得到的球位置估计旋转，能显著提升长时间预测性能。精确的球轨迹预测对成功回球至关重要。为此，我们使用气动人工肌肉机器人评估回球性能，实现了29/30（97.7%）的回球成功率。