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研究生:戴天祥
研究生(外文):Tien-Hsiang Tai
論文名稱:利用光學三維量測原理之機械手臂校正
論文名稱(外文):Robot Calibration using 3-D Optical Measurement Principle
指導教授:陳亮嘉
指導教授(外文):Liang-Chia Chen
口試委員:劉正良林志哲何昭慶
口試委員(外文):Cheng-Liang LiuChih-Che LinChao-Ching Ho
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:機械工程學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2020
畢業學年度:108
語文別:中文
論文頁數:101
中文關鍵詞:機械手臂校正手眼校正光學量測DH轉換
外文關鍵詞:Robot calibrationHand-Eye calibrationOptical MeasurementDH Transformation
DOI:10.6342/NTU201902044
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隨著自動化工業的發展,機械手臂被廣泛應用於各種產業之中。由於機械手臂的工作能力將影響產品的品質,機械手臂的校正是必不可少的。本研究之主要目的在於利用光學量測系統,進行手眼校正與對機械手臂參數的補償,完成對機械手臂的校正,提升機械手臂在校正範圍之內的定位精度。
本研究的手眼校正為利用32個不同的手臂姿態,針對同一量測目標,找到做為「手」的機械手臂末端效應器與做為「眼」的量測系統之間的手眼轉換關係,然後結合由24個DH參數所描述的六軸機械手臂運動學模型,建立七軸機械手臂運動學模型。通過利用90個不同的手臂姿態,對在校正空間內的校正模型進行量測,而校正空間範圍結合單軸位移平台以及校正模型達到至少312×240×200 mm3之大小。接著分別計算出手臂第七軸理想中與實際上的位置與方向,即公稱(nominal)姿態與實際姿態,並利用兩種姿態之間的差距計算機械手臂公稱參數與實際參數之間的誤差。最後,將該參數誤差補償於公稱參數上,使機械手臂的實際姿態能夠趨近於所欲到達的目的姿態。
為了驗證機械手臂校正的演算法與實驗結果,分別利用模擬數據與實驗數據計算校正前後機械手臂的公稱姿態與實際姿態之間的誤差。在模擬實驗之中,探頭量測與手臂定位的誤差利用標準差為0.1 mm的高斯分布噪音替代,結果顯示手臂姿態的平均位置體積誤差在校正前為0.5558 mm,經過校正後下降至0.0677 mm,誤差降低了87.8%。而在實際的實驗中,手臂姿態的平均位置體積誤差在校正前為6.0242 mm,經過校正後下降至2.0803 mm,誤差降低了65.5%。通過結合光學量測系統與機械手臂,建立七軸機械手臂運動學模型,本研究達成了手眼校正以及對機械手臂的校正。
With the development of automatic technology, robot arms are widely applied in kinds of different industrials. The performance of robot arms will decide the production quality in manufacturing. Therefore, robot calibration is indispensable in automatic applications. This study aims to utilize the Hand-Eye calibration and the robot calibration to improve the positioning accuracy in the calibration space.
In this study, the Hand-Eye calibration uses 32 different robot configurations to find the transformation between the end-effector of the robot arm and the measurement system by measuring the same target. Then combing the six-axis robot arm’s kinematics model described by 24 DH parameters and Hand-Eye transformation to establish the 7-axis robot kinematics model. With the integration of the linear stage and calibration model, the calibration space reaches a size of at least 312×240×200 mm3. After that, estimating the ideal and real position and orientation of the 7th axis of the robot arm, namely the nominal pose and the real pose, with 90 different robot configurations. using the difference between two poses to calculate the parameter errors between the nominal parameters and the real parameters of the robot arm. Finally, the calibrated parameters, which are compensated by the parameter errors, are applied so that the real pose of the robot arm can approach the desired pose.
In order to verify the algorithm and the experiment result of the robot calibration, the errors between the nominal pose and the real pose of the robot arm before and after the calibration are calculated by using simulation data and experimental data, respectively. In the simulation, the measurement error of the measurement system and the positioning error of the robot arm are set as a Gaussian noise with standard deviation of 0.1 mm. The result shows that the average volumetric error of the robot position was reduced from 0.5558 mm to 0.0677 mm after the calibration, and the error was decreased about 87.8%. In the experiment, the result shows that the average volumetric error of the robot position was reduced from 6.0242 mm to 2.0803 mm after the calibration, and the error was decreased about 65.5%. By the integration of the optical measurement system and the robot arm, and the 7-axis robot kinematics model, this study achieved the Hand-Eye calibration and the robot calibration.
中文摘要 iii
Abstract iv
目錄 vi
圖目錄 ix
表目錄 xii
Chapter 1 緒論 1
1.1 研究背景 1
1.2 研究動機 2
1.3 研究目的 3
1.4 論文架構 5
Chapter 2 文獻回顧 6
2.1 三維轉換矩陣 6
2.1.1 齊次轉換矩陣 6
2.1.2 Denavit-Hartenberg轉換矩陣 8
2.2 最小平方法 9
2.2.1 線性最小平方法 9
2.2.2 非線性最小平方法 10
2.3 手眼校正 12
2.3.1 AX=XB的求解方法 14
2.3.2 AX=ZB的求解方法 15
2.4 運動學 15
2.4.1 順向運動學 15
2.4.2 逆向運動學 16
2.5 相移法 17
2.6 機械手臂校正相關文獻 19
2.6.1 雷射追蹤量測法 19
2.6.2 結構光量測法 21
2.6.3 建立資料庫 23
2.7 文獻總結 25
Chapter 3 研究方法 26
3.1 建立世界座標系 27
3.2 光學三維量測探頭 31
3.2.1 球心座標 31
3.2.2 矩陣計算 33
3.3 手眼校正 35
3.4 機械手臂校正 38
Chapter 4 實驗與結果分析 45
4.1 實驗架構 45
4.1.1 光學三維量測探頭 46
4.1.2 六軸機械手臂 47
4.1.3 校正模型 48
4.1.4 單軸位移平台 50
4.2 光學三維量測探頭精度驗證 51
4.2.1 探頭景深之量測精度實驗 52
4.2.2 球心距離準確度驗證 57
4.2.3 重覆度驗證 59
4.2.4 座標系轉換關係準確度驗證 61
4.3 手眼校正實驗 64
4.3.1 實驗內容 64
4.3.2 模擬實驗 64
4.3.3 實際實驗與結果分析 68
4.4 機械手臂校正實驗 76
4.4.1 實驗內容 76
4.4.2 模擬實驗 76
4.4.3 實際實驗 78
4.4.4 校正結果驗證 88
Chapter 5 結論與未來展望 92
5.1 結論 92
5.2 未來展望 93
REFERENCE 95
符號彙編 99
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