桌球機器人的擊球位置與速度分析

Analysis of Hitting position and racket velocity of table tennis robots

范焜詠(Kun-Yong Fan)

指導教授 ： 劉昭華

淡江大學/工學院/機械與機電工程學系碩士班/碩士(2017年)

https://doi.org/10.6846/TKU.2017.00849

摘要

本論文的目的是假設已經經過攝影機得知對手來球方向、速度、位置後推測乒乓球機器人擊球的位置、方向、擊球後球到對方桌面的預計落點位置與擊球時為了達到擊球後的球速所需要的揮拍角速度並得出球拍的力與力矩。本論文所針對的是三自由度機械手臂，而且假設揮拍是繞垂直地面的軸旋轉，針對各種不同來球位置，來球的球速與方向，且預計擊球後球到對方桌面的落點位置後本文利用線性動量與衝量原理、角動量與角衝量原理、恢復係數估計、尤拉方程式、牛頓第二運動定律、假設球在撞擊球拍面時是以鏡射的方式進行下，可以推測出所需要的揮拍角速度。本論文提出擊球前與擊球後角速度相等的模式、以一點固定之特例情況的模式和估計擊球後球的旋轉方向並運算得知的模式並比較結果。

關鍵字

乒乓球機器人 ； 揮拍角速度 ； 擊球位置

並列摘要

In this thesis we deal with a three-degree-of-freedom spherical table tennis robot. It is assumed that the hitting position, direction and velocity of the coming ball are observed by the camera. The position the ball will drop on the table after the robot hit the ball is also chosen. In this research the hitting position of the robot, hitting direction, and the swing velocity of the paddle so that the ball will fall on the desired location are estimated. Also we may calculate the forces and moments applied to the paddle during swing. The paddle swing is simplified to be a rotation about the axis normal to the ground. Also we assume that rebound of the ball on the paddle is similar to reflection of light from a mirror. The principle of linear impulse and momentum, the principle of angular impulse and momentum, the value of coefficient of restitution, and Newton’s second law of motion are used to estimate the swing velocity of paddle. In this thesis we propose three methods for estimation. The first method is based on the fact that the swing motion is rotation about a fixed-point. In the second method, it is assumed that the swing velocity remains the same after impact. The third method we restrict the resultant moment on the paddle is in the direction of swing. Finally, we compare the results obtained from the three methods.

並列關鍵字

Table Tennis Robot ； Swing velocity ； Hitting position ； Direction of Hitting

參考文獻

[8] 蕭美珠，不同桌球拍膠皮摩擦係數與恢復係數之研究，北體學報，第9期，第45-62頁，2001。

[3] Akira Nakashima., Daigo Ito., Yoshikazu Hayakawa., ‘An online trajectory planning of struck ball with spin by table tennis robot’, 2014 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, July 8-11, Besacon, France, 2014

[6] 邱奕鳴，手眼協調控制之適應性拍球系統, 國立中山大學機械與機電工程學系碩士論文，2013。

[7] 許皓崴，以CUDA技術實現高速視覺系統及具精準動態控制與力感測系統之擊球機器人，國立交通大學電控工程研究所碩士論文，2015。

[11] Nakashima, A., Ogawa, Y., Kobayashi, Y., and Hayakawa, Y., Modeling of rebound phenomenon of a rigid ball with friction and elastic effects. In American Control Conference (ACC), 2010, pages1410.1415. IEEE, 2010.