本研究針對力矩控制下運作的Delta robot提出一種屬於關節級與動力學模型校準級別的校準方法，並以前饋式方法將此兩種校準方法套用至Delta機械手臂進行ISO標準性能驗證定位準確度與定位重複性。量測作業使用單目相機的影像量測技術，利用Levenberg-Marquardt演算法完成相機姿態估測，並透過手眼校正取得座標系之間的關係，以量測機械手臂末端位置。本研究提出之關節校準方法，是以運行軌跡之命令位置識別馬達關節旋轉角度與誤差源之關係，再利用迴歸方法求得擬合曲線方程式作為校準模型。透過校準模型補償馬達旋轉角度命令，進而改善末端平台表現。另一方面，動力學模型校準方法需事先透過最小平方法識別機械手臂系統參數，再透過系統參數補償馬達輸出扭矩使質量矩平穩，達成動態誤差源校準。
本研究在力矩控制下將關節級與動力學模型校準級別的兩種校準方法套用至Delta robot，檢驗其定位準確度與定位重複性。在考慮影像量測誤差情況下，同時使用此兩種方法可將Delta robot之定位準確度由7.766mm降低至1.094mm、定位重複性由1.430mm降低至0.390mm。實驗證明本研究校準方法對於改善機械手臂之定位準確度與定位重複性有明顯的成效。

This research combined the joint-level and non-kinematics-level methods based on feedforward to calibrate the Delta robot under the torque controlled operation, and the ISO standard was used to verify its positioning accuracy and repeatability. The monocular camera was used to perform vision-based measurement; the Levenberg-Marquardt algorithm was applied to estimate the camera’s position, and the relationship between the coordinate systems was obtained from the hand-eye calibration. The joint-level calibration proposed in this research identified the relationship between the motor joint angle error and the command position, and the calibration model was built based on the regression method. The performance of the end platform was improved by the compensation of motor angle through the calibration model. On the other hand, the non-kinematics-level calibration identified the dynamic model parameters of the Delta robot by using the least square method, and then the system parameters were used to compensate the motor output torque to stabilize the moment of mass and achieve dynamic error calibration.
Two calibration methods, joint-level and non-kinematics-level calibrations, were used simultaneously to test the positioning accuracy and repeatability of the Delta robot under the torque controlled operation. Under the limitation of the measurement error, the positioning accuracy was reduced from 7.766 mm to 1.094 mm and the repeatability was reduced from 1.430 mm to 0.390 mm. The results of experiment proved that the calibration methods can improve the performance of Delta Robot effectively.

[1] 黃勇益, 王朝仕, 粘昰薪, and 陳冠叡, "機械手臂資訊擷取與檢測應用," TANET 臺灣網際網路研討會, pp. 1059-1063, 2019.
[2] Y.-L. Kuo and P.-Y. J. I. J. o. A. R. S. Huang, "Experimental and simulation studies of motion control of a Delta robot using a model-based approach," vol. 14, no. 6, p. 1729881417738738, 2017.
[3] V. Nandini, R. D. Vishal, C. A. Prakash, and S. Aishwarya, "A review on applications of machine vision systems in industries," Indian J. Sci. Technol, vol. 9, no. 48, pp. 1-5, 2016.
[4] H. Altaheri, M. Alsulaiman, and G. Muhammad, "Date fruit classification for robotic harvesting in a natural environment using deep learning," IEEE Access, vol. 7, pp. 117115-117133, 2019.
[5] Y.-C. Tang, C. Wang, L. Luo, and X. Zou, "Recognition and localization methods for vision-based fruit picking robots: a review," Frontiers in Plant Science, vol. 11, p. 510, 2020.
[6] H. Alzarok, "A Review on some commonly used sensors for Robotic applications," Intermational Jouranal for Innovative Research in Multidisciplinary Field, vol. 6, no. 9, 2020.
[7] C. Li, "The Review of the Welding Robot’s Precision," Journal of Electronic Research and Application, vol. 5, no. 1, 2021.
[8] M. Peña‐Cabrera, I. Lopez‐Juarez, R. Rios‐Cabrera, and J. Corona‐Castuera, "Machine vision approach for robotic assembly," Assembly Automation, 2005.
[9] C. Li, Y. Ma, S. Wang, and F. Qiao, "Novel industrial robot sorting technology based on machine vision," in International Conference on Modelling, Identification and Control (ICMIC), 2017: IEEE, pp. 902-907.
[10] G. D. Hager, W.-C. Chang, and A. S. Morse, "Robot hand-eye coordination based on stereo vision," IEEE Control Systems Magazine, vol. 15, no. 1, pp. 30-39, 1995.
[11] 蔡銘浩 and 連豊力, "驅控整合模組機械手臂與機械視覺整合技術開發," 機械工業雜誌, no. 436, pp. 18-26, 2019.
[12] G. Du and P. Zhang, "Online robot calibration based on vision measurement,"Robotics Computer-Integrated Manufacturing, vol. 29, no. 6, pp. 484-492, 2013.
[13] B. P. Larouche and Z. H. Zhu, "Autonomous robotic capture of non-cooperative target using visual servoing and motion predictive control," Autonomous Robots, vol. 37, no. 2, pp. 157-167, 2014.
[14] R. C. Luo, C.-H. Hsieh, and S. C. Chou, "Effective visual calibration system for
107
parallel robot using decision tree with cooperative coevolution network approach," in 2015 IEEE International Conference on Industrial Technology (ICIT) IEEE, pp. 198-203, 2015
[15] A. Traslosheros, J. M. Sebastián, J. Torrijos, R. Carelli, and E. Castillo, "An inexpensive method for kinematic calibration of a parallel robot by using one hand-held camera as main sensor," Sensors, vol. 13, no. 8, pp. 9941-9965, 2013.
[16] A. Angelidis and G.-C. Vosniakos, "Prediction and compensation of relative position error along industrial robot end-effector paths," International journal of precision engineering manufacturing, vol. 15, no. 1, pp. 63-73, 2014.
[17] M.-H. Chiang, H.-T. Lin, and C.-L. Hou, "Development of a stereo vision measurement system for a 3D three-axial pneumatic parallel mechanism robot arm," Sensors, vol. 11, no. 2, pp. 2257-2281, 2011.
[18] M. Dehghani, M. Ahmadi, A. Khayatian, M. Eghtesad, and M. Yazdi, "Vision-based calibration of a Hexa parallel robot," Industrial Robot: An International Journal, 2014.
[19] H. Li, X. Zhang, L. Zeng, and H. Wu, "Vision-aided online kinematic calibration of a planar 3RRR manipulator," in Mechanism and Machine Science: Springer, pp. 963-972, 2016.
[20] Z. Zhang, "A flexible new technique for camera calibration," IEEE Transactions on pattern analysis machine intelligence, vol. 22, no. 11, pp. 1330-1334, 2000.
[21] X. X. Lu, "A review of solutions for perspective-n-point problem in camera pose estimation," in Journal of Physics: Conference Series, vol. 1087, no. 5: IOP Publishing, p. 052009, 2018
[22] Y. Xu and J. M. Brownjohn, "Review of machine-vision based methodologies for displacement measurement in civil structures," Journal of Civil Structural Health Monitoring, vol. 8, no. 1, pp. 91-110, 2018.
[23] Y. Zheng, Y. Kuang, S. Sugimoto, K. Astrom, and M. Okutomi, "Revisiting the pnp problem: A fast, general and optimal solution," in Proceedings of the IEEE International Conference on Computer Vision, pp. 2344-2351, 2013
[24] J. L. Crassidis and J. L. Junkins, Optimal estimation of dynamic systems. CRC press, 2011.
[25] I. S. Organization, "ISO 9283:1998 Manipulating industrial robots Performance criteria and related test methods.."
[26] L. Wu and H. Ren, "Finding the kinematic base frame of a robot by hand-eye calibration using 3D position data," IEEE Transactions on Automation Science and Engineering, vol. 14, no. 1, pp. 314-324, 2016.
[27] M. Shah, R. D. Eastman, and T. Hong, "An overview of robot-sensor calibrationmethods for evaluation of perception systems," in Proceedings of the Workshop on Performance Metrics for Intelligent Systems, pp. 15-20, 2012
[28] W. Li, M. Dong, N. Lu, X. Lou, and P. Sun, "Simultaneous robot–world and hand–eye calibration without a calibration object," Sensors, vol. 18, no. 11, p. 3949, 2018.
[29] 江宗錡, "六軸關節型機械手臂之手眼校正研究," 成功大學電機工程學系學位論文, pp. 1-66, 2014.
[30] J. Fu, Y. Ding, T. Huang, and X. Liu, "Hand-eye calibration method with a three-dimensional-vision sensor considering the rotation parameters of the robot pose," International Journal of Advanced Robotic Systems, vol. 17, no. 6, p. 1729881420977296, 2020.
[31] X. Zhi and S. Schwertfeger, "Simultaneous hand-eye calibration and reconstruction," in 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) IEEE, pp. 1470-1477, 2017
[32] M. Abderrahim, A. Khamis, S. Garrido, and L. Moreno, "Accuracy and calibration issues of industrial manipulators," Industrial robotics: programming, simulation application, pp. 131-146, 2004.
[33] 中華民國國家標準, "CNS 14491: 工業用機器人性能準則與相關試驗法."
[34] A. Elatta, L. P. Gen, F. L. Zhi, Y. Daoyuan, and L. J. I. T. J. Fei, "An overview of robot calibration," vol. 3, no. 1, pp. 74-78, 2004.
[35] R. Bernard and S. Albright, Robot calibration. Springer Science & Business Media, 1993.
[36] Z. Roth, B. Mooring, B. Ravani, and Automation, "An overview of robot calibration," IEEE Journal on Robotics, vol. 3, no. 5, pp. 377-385, 1987.
[37] T. Bentaleb and J. Iqbal, "On the improvement of calibration accuracy ofparallel robots–modeling and optimization," Journal of Theoretical Applied Mechanics, vol. 58, 2020.
[38] M. Gaudreault, A. Joubair, and I. Bonev, "Self-calibration of an industrial robot using a novel affordable 3D measuring device," Sensors, vol. 18, no. 10, p. 3380, 2018.
[39] R. Kelaiaia, "Improving the pose accuracy of the Delta robot in machining operations," The International Journal of Advanced Manufacturing Technology, vol. 91, no. 5, pp. 2205-2215, 2017.
[40] D. Yu, "A new pose accuracy compensation method for parallel manipulators based on hybrid artificial neural network," Neural Computing Applications, vol. 33, no. 3, pp. 909-923, 2021.
[41] R. Pagani, C. Nuzzi, M. Ghidelli, A. Borboni, M. Lancini, and G. Legnani, "Cobot User Frame Calibration: Evaluation and Comparison between Positioning Repeatability Performances Achieved by Traditional and Vision-Based Methods," Robotics, vol. 10, no. 1, p. 45, 2021.
[42] Y. Guo, B. Song, X. Tang, X. Zhou, and Z. Jiang, "A calibration method of non-contact R-test for error measurement of industrial robots," Measurement, vol. 173, p. 108365, 2021.
[43] J.-W. Lee, G.-T. Park, J.-S. Shin, and J.-W. Woo, "Industrial robot calibration method using denavit—Hatenberg parameters," in 2017 17th International Conference on Control, Automation and Systems (ICCAS) IEEE, pp. 1834-1837, 2017
[44] H. Liu, "Environment for Industrial RobotPerformance Evaluation," ed, 2015.
[45] J. Semjon et al., "Comparison of the delta robot ABB IRB 360 properties after collisions," Communications-Scientific letters of the University of Zilina, vol. 20, no. 1, pp. 42-46, 2018.
[46] V. Schmidt and A. Pott, "Implementing extended kinematics of a cable-driven parallel robot in real-time," in Cable-driven parallel robots: Springer, pp. 287-298, 2013
[47] A. Joubair, M. Slamani, and I. A. Bonev, "Kinematic calibration of a 3‐DOF planar parallel robot," Industrial Robot: An International Journal, 2012.
[48] A. Codourey, "Dynamic modeling of parallel robots for computed-torque control implementation," The International Journal of Robotics Research, vol. 17, no. 12, pp. 1325-1336, 1998.
[49] R. T. Arrazate, "Development of a URDF file for simulation and programming of a delta robot using ROS," 2017.
[50] 蔡高岳教授, "機器人學," 課程內容 Chapter 5.
[51] 王謙, "基於無感測器之 模型式Delta機械手臂故障偵測," 碩士, 機械工程系, 國立臺灣科技大學, 台北市, 2019.
[52] 郭翰, "無感測器之阻抗控制 應用於Delta機械臂," 碩士, 機械工程系, 國立臺灣科技大學, 台北市, 2019.
[53] E. G. Papadopoulos and G. C. J. J. D. S. Chasparis, Meas., Control, "Analysis and model-based control of servomechanisms with friction," vol. 126, no. 4, pp. 911-915, 2004.
[54] MATLAB, "Computer Vision Toolbox ,What Is Camera Calibration?," https://www.mathworks.com/help/, 2020.
[55] L. Ma, Y. Chen, and K. L. J. a. p. c. Moore, "A family of simplified geometric distortion models for camera calibration," 2003.
[56] N. Andreff, R. Horaud, and B. Espiau, "Robot hand-eye calibration using structure-from-motion," The International Journal of Robotics Research, vol. 20, no. 3, pp. 228-248, 2001.
[57] 陳弘洋, "使用 LEAP MOTION 感測器於工業機械手臂機構參數誤差校正之研究," 中興大學機械工程學系所學位論文, pp. 1-109, 2015.
[58] 李勇志, "三維雷射量測儀之研發及在工業機器人校正之應用," 碩士, 機械工程學研究所, 國立臺灣大學, 台北市, 1999.