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研究生：	黃子源 Huang, Tzu-Yuan
論文名稱：	基於運動學與動力學物理限制之工業用機械手臂運動規劃研究 Study on Motion Planning for Industrial Manipulators based on Kinematic Constraints and Dynamic Constraints
指導教授：	鄭銘揚 Cheng, Ming-Yang
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 電機工程學系 Department of Electrical Engineering
論文出版年：	2020
畢業學年度：	108
語文別：	中文
論文頁數：	163
中文關鍵詞：	運動規劃、機器人控制、雙向掃描、進給率最佳化
外文關鍵詞：	motion Planning, robot Control, bidirectional scan algorithm, feedrate optimization
相關次數：	點閱：96 下載：2
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隨著各國人力成本增加與工業4.0 的興起，工業用機械手臂之需求與日俱
增，其應用相較於以前更加多元，從原本執行取放、插件等任務，到今日許多工業應用如：焊接、表面加工、金屬加工等。這些應用中，機械手臂的精度與工作效率非常重要，然而機械手臂為高度非線性系統，若在卡式空間為追求效率而提高進給率將導致關節空間的物理量有飽和現象進而影響精度。此外，多數研究並未討論只有機械手臂姿態(orientation)有變化但其末端效應器位置不動之軌跡，本論文發展一套完整之技術，從工業用機械手臂之順逆向運動學關係建立、動力學模型建立，並考慮運動學與動力學等物理限制，在預覽階段完成機械手臂之進給率限制以及卡氏空間加速度限制之規劃，並建立一套前加減速演算法依照預覽階段規劃之限制進行加減速，最後於插值器進行細插值。本論文提出之規劃方法經由數學推導，證明其求解進給率與加速度限制時必定有解，相較於傳統進給率需花費計算資源尋找切換點，本論文提出之方法較為節省資源，且具備完整性(cpmpletness)，適合應用於控制器產品。此外，本論文亦針對只有機械手臂姿態有變化但其末端效應器位置不動之軌跡進行討論，並利
用四元數建立旋轉關係以及微分運動學關係式，完成角速度、角加速度與關節空間物理量之推導，最後進行角速度規劃。本論文藉由提出之運動規劃演算法，考量關節速度、關節加速度、關節轉矩等物理限制，分別對機械手臂只有位置變化但無姿態變化、只有姿態變化但機械手臂末端點不動和機械手臂末端點位置與姿態皆有變化等三種工作軌跡進行模擬驗證與機台實作，由模擬與實驗結果可以得知演算法能夠在不違反機械手臂物理限制之下，達到接近時間最佳化之效果，適用於機械手臂產品且符合其高速高精之需求。

With increasing Labor costs and the popularity of Industry 4.0, the requirements of industrial manipulators have risen gradually since 2009, with its application fields become more and more wide-ranging, such as welding, surface machining, and metal machining. In addition, it is necessary to increase the processing efficiency and the accuracy of robots. The main purpose of this thesis is to develop a motion planning algorithm for industrial manipulators based on kinematic constraints and dynamic constraints so that the joint velocity, joint acceleration and joint torque of manipulators will not exceed their limits. The motion planning approach proposed in this thesis is mathematically proven to be robust, as it does not need to find switch points, a process which is time comsuming in conventional methods. In contrast to conventional methods which only discuss the case that the total arc length of a work path does not equal zero, the proposed approach can plan the angular velocity of the manipulators in which only the orientation of the end-effector changes by partial differentiating the inverse kinematics equation and quaternion. Moreover, the motion planning technique developed in this thesis covers many topics, including forward kinematics, inverse kinematics of a robot, robot dynamics, system identification, acceleration/deceleration algorithm and axis command interpolation. The simulations and experiments of motion planning carried out on a 6-DOF industrial manipulator. Simulation and experimental results show that the joint velocity, joint acceleration and joint torque do not violate the physical constraints, and the work efficiency is near time optimal, meeting the requirement of high speed and high accuracy.

中文摘要 ................................................ I
EXTENDED ABSTRACT ....................... II
誌謝 .............................................. X
目錄 ................................................. XIII
表目錄 ................................................ XVI
圖目錄 ........................................... XVII
第一章、緒論 ................................. 1
1 研究動機 .................................... 1
2 文獻回顧 .................................... 2
3 論文貢獻與架構 .......................... 7
第二章、順逆向運動學與運動學限制 ............................................ 10
1 順向運動學MDH 模型 .............................. 10
2 尤拉角表示法與四元數表示法 .......................... 14
3 逆向運動學求解 ........................................ 22
4 運動學與進給率關係 .............................. 26
5 本章小結 ................................ 29
第三章、動力學模型與限制 ....................................................................... 30
1 Lagrange Euler 法與進給率關係 .......................................................... 30
2 Newton Euler 法與進給率關係 ............................................................ 32
3 系統鑑別之動力學模型與進給率關係................................................ 36
4 本章小結 ................................................................................................ 37
第四章、進給率限制與卡氏空間加速度限制之規劃 ............................... 38
XIV
1 初始進給率上限 .................................................................................... 38
2 雙向掃描法 ............................................................................................ 39
3 方法之存在解證明 ................................................................................ 49
3.1 方法有解證明步驟一 ................................................................ 51
3.2 方法有解證明步驟二 ................................................................ 54
3.3 方法有解證明步驟三 ................................................................ 58
4 本章小結 ................................................................................................ 59
第五章、插值與加減速 ............................................................................... 60
1 粗插值 .................................................................................................... 60
1.1 直線與四元數球面線性插值 .................................................... 61
1.2 位移粗插值法 ............................................................................. 65
1.3 姿態粗插值法 ............................................................................. 66
1.4 綜合粗插值法 ............................................................................. 68
2 4 Block 梯形加減速法 ......................................................................... 69
3 細插值器 ................................................................................................ 74
4 本章小結 ................................................................................................ 77
第六章、模擬與實驗 ................................................................................... 78
1 模擬介紹 ................................................................................................ 79
2 位移插值法模擬 .................................................................................... 80
2.1 基於軸速度與軸加速度之限制模擬 ........................................ 81
2.2 基於軸速度與關節轉矩之限制模擬 ........................................ 86
2.3 基於軸速度、軸加速度與關節轉矩模擬 ................................ 90
3 姿態插值法模擬 .................................................................................... 95
3.1 基於軸速度與軸加速度之限制模擬 ........................................ 97
3.2 基於軸速度與關節轉矩之限制模擬 ...................................... 101
XV
3.3 基於軸速度、軸加速度與關節轉矩模擬 .............................. 106
4 綜合插值法模擬 .................................................................................. 111
4.1 基於軸速度與軸加速度之限制模擬 ...................................... 112
4.2 基於軸速度與關節轉矩之限制模擬 ...................................... 117
4.3 基於軸速度、軸加速度與關節轉矩模擬 .............................. 122
5 實驗環境與介紹 .................................................................................. 127
6 位移插值法實驗 .................................................................................. 130
6.1 基於軸速度與軸加速度之限制實驗 ...................................... 130
6.2 基於軸速度與關節轉矩之限制實驗 ...................................... 133
6.3 基於軸速度、軸加速度與關節轉矩實驗 .............................. 136
7 姿態插值法實驗 .................................................................................. 138
7.1 基於軸速度與軸加速度之限制實驗 ...................................... 139
7.2 基於軸速度與關節轉矩之限制實驗 ...................................... 141
7.3 基於軸速度、軸加速度與關節轉矩實驗 .............................. 144
8 綜合插值法實驗 .................................................................................. 146
8.1 基於軸速度與軸加速度之限制實驗 ...................................... 147
8.2 基於軸速度與關節轉矩之限制實驗 ...................................... 149
8.3 基於軸速度、軸加速度與關節轉矩實驗 .............................. 152
9 本章小結 .............................................................................................. 155
第七章、結論與建議 ................................................................................. 157
1 結論 ...................................................................................................... 157
2 未來展望與建議 .................................................................................. 158
參考文獻 ..................................................................................................... 159
                                    

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校內：2025-07-08公開
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