隨著科技的快速發展，機械手臂的應用已越來越成熟，而在加工方
面更是可以取代傳統加工機台或是需要手工人力的作業，現今之機械手
臂擁有很好重複精度和足夠之精確度來應用於自動化產業中，如自動化
中的上下料、機械手臂自動焊接、噴漆…等等。
而在多數機械手臂工業加工應用中，手臂工具末端於加工路徑中所
產生的誤差與振動容易導致整體加工精度和工件表面粗糙度的表現不
佳，為避免上述情形的發生，本研究提出一種以物理分析進行振動預測
並進行改善控制的方式來降低其振動所造成的影響，於本研究中最後將
以金屬工件去毛邊任務之情境來呈現出本文在抑振控制上之研究。
相較於一般市售之機械手臂控制，本研究將著重於振動模型，齒輪
箱模型之分析與應用基因演算法輔助物理模型的建立，最後達成單純以
上層控制命令補償的方式來進行振動抑制的目的，此做法不僅在最終實
際應用時不需外加額外之感測器、亦不用直接改變原先機構，故在對於
市售一般機械手臂的應用上可以降低開發之成本，並且提升機械手臂應
用於路徑加工之表現。

The overwhelming manufacturing process with robotic arm has replaced
human labors in handling and manufacturing work-pieces in factories. In these years, higher accuracy and repeatability are required for robotic manipulators to perform processes such as welding, deburring and grinding in factories. In these path-following processes, the manipulator’s end-effector often encounter position error caused by its vibrating structures. Therefore, the quality of machining accuracy and surface roughness becomes unstable and unsatisfied. For the purpose of avoiding the vibrations while the robotic manipulator is working, this study aims to design a feedback control strategy to reduce vibrations which is divided into two parts, namely (1) dynamic
modeling the robot arm by applying modified mass-spring-damper model to
each joints and links of the robot arm, and (2) realizing the control of the robot arm’s vibration resistance with predicated dynamics to compensate for the undesired dynamics, respectively. Through the proposed model, the response of each joints in different postures and different payloads applied at the end effector can be fully analyzed and the vibrations can be predicted and compensated.
The realization method of this study can promote the performance of the
robotic manipulator without adding extra sensors or changing the original mechanism structure.

摘要 ................ I
Abstract ............ II
致謝 ................ III
目錄 ................ IV
第一章 緒論 ......... 1
1.1 前言 ............ 1
1.2 研究動機 ........ 2
1.3 文獻回顧 ........ 2
1.4 研究目標與方法 .................................. 7
1.5 預期結果 ........................................ 8
第二章 機械手臂加工應用之理論建構 ................... 9
2.1 物理模型建立 .................................... 9
2.1.1 雙自由度彈簧阻尼旋轉系統 ...................... 9
2.1.2 齒輪箱系統之物理模型 .......................... 11
2.2 機械手臂之運動學 ................................ 13
2.2.1 Denavit-Hartenberg參數 ........................ 13
2.2.2 逆向運動學 .................................... 15
2.2.3 機械手臂動力學與路徑規劃 ...................... 17
2.2.4 路徑規劃....................................... 17
2.2.5 牛頓歐拉方程(Newton's Euler Equation) ......... 19
2.3 磨削理論 ........................................ 20
2.4 基因演算法 ...................................... 22
2.4.1 基因演算法中之專有名詞 ........................ 22
2.4.2 基因演算法的工作步驟 .......................... 23
2.4.3 基因演算法之完整流程：......................... 25
第三章 物理建模與分析 ............................... 27
3.1 系統硬體設計 .................................... 27
3.1.1 四軸機械手臂 .................................. 27
3.1.2 四軸實驗平台結合量測系統之工具末端 ............ 29
3.1.3 UR5 六軸機器手臂與切削工具 .................... 30
3.1.4 毛邊路徑採集相機系統 .......................... 32
3.2 理論模型 ........................................ 33
3.2.1 四軸機械手臂系統之物理建模 .................... 33
3.2.2 使用基因演算法輔助UR5 之物理建模 .............. 35
3.2.3 相機之毛邊路徑擷取與建模 ...................... 38
第四章 抑振演算法設計與手臂控制 ..................... 41
4.1 四軸機械手臂控制 ................................ 41
4.1.1 四軸手臂軌跡規劃控制與實現 .................... 41
4.1.2 模擬實時控制系統之演算法 ...................... 42
4.2 六軸機械手臂路徑控制與切削控制 .................. 44
4.2.1 六軸手臂加工軌跡規劃 .......................... 44
4.2.2 六軸手臂加工軌跡之控制與實現 .................. 46
4.2.3 毛邊路徑採集與力量換算 ........................ 48
4.3 抑振演算法設計 .................................. 48
4.3.1 演算法設計流程 ................................ 49
第五章 實驗與結果 ................................... 56
5.1 四軸機械手臂實驗設計與結果量測 .................. 56
5.2 六軸機械手臂於去毛邊任務實驗設計與結果量測 ...... 60
第六章 總結與未來工作 ............................... 71
6.1 總結 ............................................ 71
6.2 本文貢獻 ........................................ 72
6.3 未來展望 ........................................ 73
參考文獻 ............................................ 74

1] M. W. Spong, S. Hutchinson, and M. Vidyasagar, Robot modeling and
control. wiley New York, 2006.
[2] R. Featherstone and D. Orin, "Robot dynamics: equations and
algorithms," in Proceedings 2000 ICRA. Millennium Conference. IEEE
International Conference on Robotics and Automation. Symposia
Proceedings (Cat. No. 00CH37065), 2000, vol. 1, pp. 826-834: IEEE.
[3] K. P. Hawkins, "Analytic inverse kinematics for the universal robots ur-
5/ur-10 arms," Georgia Institute of Technology2013.
[4] P. M. Kebria, S. Al-Wais, H. Abdi, and S. Nahavandi, "Kinematic and
dynamic modelling of UR5 manipulator," in 2016 IEEE international
conference on systems, man, and cybernetics (SMC), 2016, pp. 004229-
004234: IEEE.
[5] W. Bartelmus, "Gearbox dynamic modelling," Journal of Theoretical and
Applied Mechanics, vol. 39, pp. 989-999, 2001.
[6] J. Zhou, W. Sun, and Q. Tao, "Gearbox low-noise design method based
on panel acoustic contribution," Mathematical Problems in Engineering,
vol. 2014, 2014.
[7] KISSsoft, "KISSsoft Software."
[8] RomaxTech, "RomaxDESIGNER."
[9] W. R. Finley, M. M. Hodowanec, and W. G. Holter, "An analytical
approach to solving motor vibration problems," in Industry Applications
Society 46th Annual Petroleum and Chemical Technical Conference (Cat.
No. 99CH37000), 1999, pp. 217-232: IEEE.
[10] J. B. Jonker, R. Waiboer, and R. Aarts, "Modelling of joint friction in
robotic manipulators with gear transmissions," in Multibody Dynamics:
Springer, 2007, pp. 221-243.
[11] M. Itoh and H. Yoshikawa, "Vibration suppression control for an
articulated robot: Effects of model-based control applied to a waist axis,"
International Journal of Control, Automation, and Systems, vol. 1, no. 3,
pp. 263-270, 2003.
[12] A. Jubien, M. Gautier, and A. Janot, "Dynamic identification of the Kuka
LWR robot using motor torques and joint torque sensors data," IFAC
Proceedings Volumes, vol. 47, no. 3, pp. 8391-8396, 2014.
[13] G. Testa, "Experimental stiffness identification in the joints of a
lightweight robotThe UR5 Manipulator as a Case Study," Master thesis
of Universitat Politècnica de Catalunya, 2017.
[14] C. Dumas, S. Caro, C. Mehdi, S. Garnier, and B. Furet, "Joint stiffness
identification of industrial serial robots," 2011.
[15] D. Whitley, "A genetic algorithm tutorial," Statistics and computing, vol.
4, no. 2, pp. 65-85, 1994.
[16] D. Tsetserukou, N. Kawakami, and S. Tachi, "Vibration damping control
of robot arm intended for service application in human environment," in
Humanoids 2008-8th IEEE-RAS International Conference on Humanoid
Robots, 2008, pp. 441-446: IEEE.
[17] L. Lichun, F. Jizai, and J. Peklenik, "A study of grinding force
mathematical model," CIRP Annals, vol. 29, no. 1, pp. 245-249, 1980.
[18] C. Yao, T. Wang, W. Xiao, X. Huang, and J. Ren, "Experimental study
on grinding force and grinding temperature of Aermet 100 steel in surface
grinding," Journal of Materials Processing Technology, vol. 214, no. 11,
pp. 2191-2199, 2014.
[19] D. J. Inman and R. C. Singh, Engineering vibration. Prentice Hall
Englewood Cliffs, NJ, 1994.
[20] R. b. J. M. Mistakes., "DYNAMIXEL e-Manual."
[21] murata, "SCL3300-D01 Manual."
[22] Panasonic, "HG-C1030 manual."