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研究生： 歐陽妏青
Wen-ching Ou Yang
論文名稱： 工業機器人之奇異點分析
A Study on the Singularity of Industrial Manipulators
指導教授： 蔡高岳
Kao-yueh Tsai
口試委員: 石伊蓓
Yi-pei Shih
王勵群
Li-chun Wang
學位類別： 碩士
Master
系所名稱： 工程學院 - 機械工程系
Department of Mechanical Engineering
論文出版年： 2011
畢業學年度： 99
語文別： 中文
論文頁數： 86
中文關鍵詞： 奇異點 、賈氏矩陣 、反位移 、螺旋理論
外文關鍵詞： singularity, Jacobian, inverse kinematics, screw theory
相關次數： 點閱：186  下載：1 
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    • 　當機器人在工作空間內之運動路徑接近奇異點時會非常不穩定而造成控制上之問題。目前所使用判斷與奇異點接近程度之方法之計算過程在時間上可能不符合即時控制上之需求。本文首先提出簡化賈氏矩陣行列式值之方法以增加運算速度。計算行列式值時須先利用反位移分析求得各旋轉軸之角位移再代回賈氏矩陣才能判斷是否接近奇異點，本文另外提出一個能夠以反位移分析之二次多項式直接判斷與奇異點接近程度之方法，此方法不須使用到賈氏矩陣因此可大幅提高運算效率。以上兩種方法因牽涉到較複雜之理論而非一般現場工作人員所能瞭解，因此以螺旋理論為基礎提出一個可用目視法大概判斷機器人是否接近奇異點之方法。

    　A manipulator becomes very unstable when its trajectory in task space approaches singular points. Current methods to detect singularity might not meet the time requirement in on-line control. This thesis first employs simplified link parameters to facilitate the computation process for the determinant of the Jacobian. The determinant of the Jacobian cannot be computed unless all joint variables are determined by solving the inverse kinematics. This work proposes a new method that direct employs the coefficients of quadratics used in inverse kinematics to detect singularity. The method is much more efficient because it can evaluate the closeness to singularity without using the Jacobian. The two proposed methods, however, might be too complicated for factory workers to implement, so a simple visual approach, developed from screw theory, is introduced to detect singularity.

    中文摘要-----------------I Abstract-----------------II 誌謝---------------------III 目錄---------------------IV 圖表目錄-----------------VI 第一章 緒論--------------1 1-1 研究動機-------------1 1-2 文獻回顧-------------2 1-3 論文架構-------------4 第二章 理論基礎----------5 2-1 座標系轉換-----------5 2-2 連桿參數定義---------6 2-3 Denavit-Hartenberg齊次轉換矩陣--------7 2-4 單位螺旋與賈氏矩陣---------------------8 第三章 賈氏矩陣法--------------------------14 3-1 行列式值與參考座標系之關係-------------14 3-2 工業用機器人---------------------------18 第四章 反位移分析--------------------------22 4-1 基本方程式-----------------------------23 4-2 五種類型之反位移分析-------------------24 4-3 判別式與奇異點之關係-------------------37 4-4 數值範例-------------------------------52 4-4-1 PUMA構型之反位移分析----------------52 4-4-2 兩判別式之比較----------------------61 第五章 螺旋理論法--------------------------65 5-1 α_2=0°奇異點位置---------------------65 5-2 a_2=0奇異點位置----------------------69 5-3 α_1=0°奇異點位置---------------------72 5-4 a_1=0奇異點位置----------------------75 第六章 研究結果與未來發展------------------81 參考文獻-----------------------------------83 作者簡介-----------------------------------86

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