桌球飛行狀態估測與碰撞模型之建立

Abstract

本研究使用高速雙眼視覺系統辨識發球者所發的桌球，並估測球體在空中飛行時的速度和轉速，以及建立球體在碰撞前後速度和轉速變化的關係式。 在高速雙眼視覺系統中，透過相機校正和立體視覺，可將球體位置從二維影像平面轉換到三維空間。在球體轉速估測方面，考慮了加入球體轉速影響的球體飛行模型，藉由影像抓取到的球體飛行軌跡，使用反覆求解微分方程的方法來求得與地面碰撞前後的速度和轉速。 在碰撞關係式的建構方面，首先分析之前研究的碰撞模型的誤差，並提出修正後的碰撞模型，在球體飛行方向的速度，提出了物理模型和類神經網路學習的方法來估測反彈後的速度和轉速，並藉由預測球體碰撞後的飛行軌跡來驗證建立的碰撞關係式的準確度。

This thesis is dedicated to estimating the velocity and spin rate of a flying table tennis ball, and establishing a collision model that characterizes the variation of velocity and spin rate after collision. A high-speed binocular vision system is used to identify the position of a ball in the 3D space. A flight model which takes into account the influence of the spin rate to the ball’s flying trajectory are used to estimate the state of the flying table tennis ball by repeatedly solving the governing differential equations. We analyze the experimental data and modify the commonly used collision model in the literature. Two types of modifications are proposed. One is based on the physical laws, and the other applies the neural network. Finally we verify the accuracy of the modified models by comparing the experimental data and the predicted flying trajectory from the modified models. Improvement of the accuracy in predicting the flying trajectory of a ball is achieved by both methods.