In table tennis, developing a precise ball-racket rebound model is crucial for predicting the trajectory and spin of a ball after it hits the racket, which is instrumental in racket design and enhancing the capabilities of table tennis robots. To this end, accuracy and computational efficiency are two challenges to overcome, which has not been perfectly handled using existing methods such as finite element (FE) and simplified rigid-body models. This article introduces a new model that calculates ball-racket rebounds in two orthogonal directions. Vertically, the collision dynamics are analyzed with the Kelvin–Voigt model, revealing that the contact duration is independent of the incoming ball’s velocity. Horizontally, we establish that the restitution coefficient varies as a function of the incident velocity, based on a continuous contact force model and momentum conservation principles. High-speed camera data corroborate these findings and confirm the model’s efficacy across diverse conditions. Compared to an established representative model, our method not only maintains high computational efficiency but also improves the accuracy of predicting the ball’s linear and angular velocities by an average of 42.72% and 33.77%, respectively, as evidenced by our experimental data.

中文翻译：

---

基于连续接触力的乒乓球机器人球拍回弹模型

在乒乓球运动中，开发精确的球拍反弹模型对于预测球击中球拍后的轨迹和旋转至关重要，这有助于球拍设计和增强乒乓球机器人的能力。为此，精度和计算效率是需要克服的两个挑战，而有限元（FE）和简化刚体模型等现有方法尚未完美解决这一问题。本文介绍了一种计算两个正交方向上的球拍反弹的新模型。在垂直方向上，使用 Kelvin-Voigt 模型对碰撞动力学进行了分析，结果表明接触持续时间与来球速度无关。在水平方向上，我们基于连续接触力模型和动量守恒原理，确定恢复系数随入射速度变化。高速摄像机数据证实了这些发现，并证实了该模型在不同条件下的有效性。与已建立的代表性模型相比，我们的方法不仅保持了较高的计算效率，而且根据实验数据，预测球的线速度和角速度的准确性分别平均提高了 42.72% 和 33.77%。