The research on the collision between a spinning ball and a table, as a general issue for the trajectory analysis of the spinning-flying objects, is important but complicated. Traditionally, it is studied either by simplifying the collision process as a black box in which the ball’s motion state changes abruptly before and after collision, or by assuming that the coefficient of restitution and the coefficient of friction are simply piecewise linear or even constant during the whole collision process. In this paper, we first analyze the mechanism of the collision dynamics and conclude from mathematical derivations that the collision between a ping-pong ball and a table is a continuous transition process and its collision duration is a constant irrelevant to the ball’s motion state. These two conclusions are also verified by the visual measurement using an ultrahigh-speed camera. Then, we propose a novel rebound model using the mean value theorem, momentum theorem, and angular momentum theorem. The novelty of the proposed model is that the forces and the parameters in it are formulated as the continuous functions related to the ball’s motion state, which is more accurate, rather than as constants. The integrations of these functions over time can be formulated by using the mean value theorem, and their expressions are learned using multilayer perception with a large data set collected by the position vision system and the pan-tilt vision system. The experimental results verify the effectiveness and accuracy of the proposed model.
['Yongsheng Zhao', 'Rong Xiong', 'Yifeng Zhang']
Rebound Modeling of Spinning Ping-Pong Ball Based on Multiple Visual Measurements