本研究設計一關節式六軸機械手臂，在機械結構上使用兩種平衡系統以減輕馬達負載，以基於Arm晶片架構的Arduino開發板做為機械手臂之控制核心，機械手臂利用Denavit-Hartenberg（D-H）建立機械手臂之理想運動學模型並利用順逆運動學來推導各軸角度與機械手臂終端器空間位置的關係，以透過背隙校正來補償實際運動學模型與理想運動學模型之差異，提高機械手臂定位精度。本研究中導入模糊滑動控制、以函數近似法為基礎之兩種適應性控制器做為各軸馬達定位，以機械手臂之運動控制探討各控制器之特性；並在最後結合以質量彈簧阻尼系統做為力量控制的控制律，實現人機互動與兩台機械手臂合作搬運物體之阻抗控制。
關鍵字：六軸機械手臂控制、平衡機構設計、背隙補償、FSMC、FAT適應性控制、力回饋控制

In this thesis, a six-axis manipulator was designed. Two kinds of counterbalance mechanism are used to reduce the loading of motors.The overall control system was constructed on three Arduino develpoment board which is based on a 32-bit ARM core microcontroller. The Denavit-Hartenberg matrix was employed to build the ideal kinematics model of this manipulator. The forward and inverse kinematics is used to derive the relationship between the angle of each axis and the spatial position of the end-effector of the manipulator. Backlash calibration is adopted to improve the positioning accuracy of the manipulator. In addition, fuzzy-sliding mode controller and two kinds of adaptive controllers based on function approximation technique are employed to monitor the motion trajectory of this manipulator. The experimental result are used to evaluate and compare the performance of these controller. Finally, the mass-spring-damping system is introduced as the control law for interaction force control to accomplish the operation of human-machine interaction and cooperating handle object by two manipulators.
Keywords: Six-axis manipulator control, counterbalance mechanism design, backlash calibration, FSMC, FAT adaptive control, force control

【1】 Ciupitu, L. and L. Vladareanu. “Adaptive Balancing by Counterweights of Robots and Mechatronic Systems.” International Journal of Modeling and Optimization 8, pp.178-182, 2018.
【2】 K. Ahn, W. Lee and J. Song, “Reduction in gravitational torques of an industrial robot equipped with 2 DOF passive counterbalance mechanisms,” 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 4344-4349, 2016.
【3】 W. Lee, S. Lee and J. Song, “Design of a 6-DOF collaborative robot arm with counterbalance mechanisms,” 2017 IEEE International Conference on Robotics and Automation (ICRA), pp. 3696-3701, 2017.
【4】 H. Kim, J. Min and J. Song, "Multi-DOF counterbalance mechanism for low-cost, safe and easy-usable robot arm," 2014 11th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), pp. 185-188, 2014.
【5】 Mooring BW, Roth ZS, Driels MR. Fundamentals of manipulator calibration. New York: Wiley; 1991.
【6】 F. Xi, “Effect of non-geometric errors on manipulator inertial calibration,” Proceedings of 1995 IEEE International Conference on Robotics and Automation, pp. 1808-1813 vol.2, 1995.
【7】 J. H. Jang, S. H. Kim, and Y. K. Kwak, “Calibration of geometric and non-geometric errors of an industrial robot,” Robotica, vol. 19, no. 3, pp. 311–321, 2001.
【8】 L. A. Zadeh, “Fuzzy sets,” Information and Control, Vol.8, pp. 338-353, 1965.
【9】 E. H. Mamdani, “Application of Fuzzy Algorithms for control a Simple Dynamic Plants,” Proc. of IEEE, Vol.121, No.12, pp. 1585-11588, 1974.
【10】 G. C. Hung, and S.C Lin, “A Stability Approach to Fuzzy Control Design for Nonlinear System,” Fuzzy Set and System, Vol. 48, Issue 3, pp.279-287,1992.
【11】 楊宗賢, “輪轂馬達電動車之墊子差速與速度控制,” 碩士論文, 國立臺灣科技大學機械工程系, 2012
【12】 賴柏儒, “以FPGA嵌入式系統為控制核心應用在五自由度機械手臂之機構設計與控制,” 碩士論文, 國立臺灣科技大學機械工程系, 2014
【13】 A.-C. Huang and Y.-S. Kuo, “Sliding control ofnon-linear systems containing time-varying uncer-tainties with unknown bounds,” International Jour-nal of Control, vol. 74, no. 3, pp. 252–264, 2001.
【14】 M. H. Raibert & J.J. Craig, “Hybrid Positon-Force Control of Manipulators,” ASME, J. Dyn. Syst., Meas., Contr., vol. 103, pp. 126-133, June 1981.
【15】 游喬焜, “以系統晶片結合力量感測器發展具軌跡與力量控制功能之機械手臂,” 碩士論文, 國立臺灣科技大學機械工程系, 2009.
【16】 G. Field and Y. Stepanenko, "Model reference impedance control of robotic manipulators," Proceedings of IEEE Pacific Rim Conference on Communications Computers and Signal Processing, vol.2, pp. 614-617, 1993.
【17】 S. A. Schneider and R. H. Cannon, “Object impedance control for cooperative manipulation: theory and experimental results,” in IEEE Transactions on Robotics and Automation, vol. 8, no. 3, pp. 383-394, June 1992.
【18】 D. Williams and O. Khatib, “The virtual linkage: a model for internal forces in multi-grasp manipulation,” [1993] Proceedings IEEE International Conference on Robotics and Automation, pp. 1025-1030 vol.1, 1993.
【19】 O. Khatib, K. Yokoi, K. Chang, D. Ruspini, R. Holmberg and A. Casal, “Vehicle/arm coordination and multiple mobile manipulator decentralized cooperation,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. IROS '96, pp. 546-553 vol.2, 1996.
【20】 K. Kosuge, H. Yoshida and T. Fukuda, “Dynamic control for robot-human collaboration,” Proceedings of 1993 2nd IEEE International Workshop on Robot and Human Communication, pp. 398-401, 1993.
【21】 O. M. Al-Jarrah and Y. F. Zheng, “Arm-manipulator coordination for load sharing using variable compliance control,” Proceedings of International Conference on Robotics and Automation, pp. 895-900 vol.1, 1997.
【22】 J. Denavit, and R. S. Hartenberg, “A Kinematics Notation for Lower Pair Mechanisms Based on Matrices,” ASME.,J.of Applied Mechanics 22, 1995
【23】 C. s. g. Lee and M. Ziegler, "Geometric Approach in Solving Inverse Kinematics of PUMA Robots," in IEEE Transactions on Aerospace and Electronic Systems, vol. AES-20, no. 6, pp. 695-706, Nov. 1984.
【24】 F. C. Park, K. M. Lynch, “Introduction to Robotics: Mechanics, Planning, and Control”, 2015.
【25】 李佑琳, “嵌入式觸覺感測夾爪與機械手臂之整合,” 碩士論文, 國立臺灣科技大學機械工程系, 2014.
【26】 劉浩德, “機械手臂手端位置與力量之遠端遙控,” 碩士論文, 國立臺灣科技大學機械工程系, 2015.
【27】 陳柏璋, “以函數近似為基礎之適應控制研究及其於主動式懸吊系統之應用”
【28】 陳名裕, “管道聲場之主動噪音控制,” 碩士論文, 國立臺灣科技大學機械工程系, 2004