本論文研究撓性關節機械手臂之系統參數鑑別及控制問題。在本論文中，系統參數鑑別流程可分為三個步驟。首先，將撓性關節機械手臂視為剛體機械手臂，施以剛體機械手臂參數鑑別方法，獲得慣量及摩擦力係數。接著，透過本論文提出之姿態選擇方法，在選定之姿態下掃頻，以雙質量系統進行擬合，進而獲得剛性係數等參數。最後，透過本論文所提出之線性化模型擬合法對實際系統以及模擬系統之頻域誤差以及時域誤差進行最佳化。而系統控制方法為將馬達端以及負載端透過本論文所提出之自適應積分滑動模式控制同時進行控制，並搭配命令整形以及命令前饋。本論文所提出之鑑別方法與輸出誤差比較法(OE)、直接逆向動態模型法(DIDIM)、雙輸入之直接逆向動態模型法(DIDIM2)進行比較，所鑑別出之參數具有最佳之準確性，並於時域以及頻域之誤差表現亦最佳。本論文提出之控制架構與原文獻相比，可提高99% 以上之精度表現，並與PD-Like Controller、Feedback-Feedforward Controller、Decoupling Controller比較，在高轉速以及低轉速命令下，負載端之控制精度具有最好的表現。本論文所提出之鑑別及控制方法均僅使用馬達端之編碼器以及輸入扭矩等資訊，無需外加感測器量測負載端資訊。

This thesis proposes an identification method and control strategy for an n rigid-link flexible-joint (RLFJ) robot manipulator without using additional sensors. The identification approach proposed in this thesis can be divided into three steps. Step 1: The n-RLFJ robot manipulator can be regarded as a rigid manipulator, and the inertia parameters and friction coefficients can be identified. Step 2: Each axis of the n-RLFJ robot manipulator is regarded as a two-inertia model. By using the pose selection method proposed in this thesis, the parameter values of each two-inertia model can be identified. Step 3: Using the linearization model-fitting method proposed in this thesis, the identified system parameters are fine-tuned based on error in the time domain and frequency domain. Compared with the Output Error Method (OE), the Direct Inverse Dynamic Identification Method (DIDIM), and DIDIM2, the system parameters identified using the proposed approach have the best accuracy and performance in both the time domain and frequency domain. To achieve the goal of high tracking precision, an Adaptive Integral Sliding Mode Control (AISMC) scheme with command shaping and command Feedforward is proposed in this thesis. When compared with the PD-Like Controller, the Decoupling Controller and the Feedback-Feedforward Controller, the proposed control strategy exhibits the best control accuracy for the load side of the n-RLFJ robot manipulator. The identification method and control method proposed in this thesis use only the encoder data and input torque on the motor side.

[1] A. Liegeois, E. Dombre, and P. Borrel, "Learning and Control for a compliant Computer-Controlled Manipulator, " IEEE Transactions on Automatic Control, vol. 25, no. 6, pp. 1097-1102, 1980.
[2] S. Nicosia, F. Nicolo, and D. Lentini, "Dynamical Control of Industrial Robots with Elastic and Dissipative Joints, " IFAC VIII Triennial World Congress, 1981.
[3] V. T. Haimo, "Finite Time Controllers," SIAM Journal on Control and Optimization, vol. 24, no. 4, pp.760-770, 1986.
[4] K. S. Fu, R. C. Gonzalez, and C. S. G. Lee, Robotics Control, Sensing, Vision and Intelligence, New York, U.S.A.: McGraw-Hill, 1987.
[5] M. W. Spong, "Modeling and Control of Elastic Joint Robots, " Journal of Dynamic Systems, Measurement and Control, vol. 109, no. 4, pp. 310-319, 1987.
[6] M. Gautier, and W. Khalil, "Direct Calculation of Minimum Inertial Parameters of Serial Robots," IEEE Transactions on Robotics and Automation, vol. 6, no. 3, 1990.
[7] J. J. E. Slotine, and W. Li, Applied Nonlinear Control, New Jersey, U.S.A.: Prentice Hall, 1991.
[8] C. Presse, and M. Gautier, "New Criteria of Exciting Trajectories for Robot Identification," in Proceedings of the IEEE Conference on Robotics and Automation, pp. 907-912, 1993.
[9] J. Y. Hung, W. Gao, and J. C. Hung, "Variable Structure Control: a survey," IEEE Transactions on Industrial Electronics, vol. 40, no. 1, pp. 2-22, 1993.
[10] A. D. Luca, and P. Tomei, Theory of Robot Control, London, U.K.:Springer-Verlag, pp. 179-218, 1996.
[11] E. Walter, and L. Pronzato, "Identification of Parametric Models from Experimental Data, " Springer, 1997.
[12] J. Swevers, C. Ganseman, D. B. Tukel, J. D. Schutter, and H. V. Brussel, "Optimal Robot Excitation and Identification," IEEE Transactions on Robotics and Automation, vol. 13, no. 5, pp. 730-740, 1997.
[13] W. Khalil, and D. Creusot, "SYMORO: A System for the Symbolic Modelling of Robots, " Robotica, vol. 15, no. 2, pp. 153-161, 1997.
[14] G. Antonelli, F. Caccavale, and P. Chiacchio, "A Systematic Procedure for the Identification of Dynamic Parameters of Robot Manipulators," Robotica, vol. 17, no, 4, pp. 427-435, 1999.
[15] I. D. Landau, B. D. O. Anderson, and F. De Bruyne, "Closed-Loop Output Error Identification Algorithms for Nonlinear Plants," in Proceedings of the 38th IEEE Conference on Decision and Control, pp. 606-611, 1999.
[16] E. Berglund, and G. E. Hovland, "Automatic Elasticity Tuning of Industrial Robot Manipulators," in Proceedings of the 39th IEEE Conference on Decision and Control, vol.5, pp. 5091-5096, 2000.
[17] J. T. Huang, "A New Approach to Parametric Identification of a Single-Link Flexible-Joint Manipulator," Journal of Intelligent and Robotic Systems, vol. 37, pp. 273-284, 2003.
[18] M. Östring, S. Gunnarsson, and M. Norrlöf, "Closed-Loop Identification of an Industrial Robot Containing Flexibilities, " Control Engineering Practice, vol. 11, no. 3, pp. 291-300, 2003.
[19] E. Wernholt, and S. Gunnarsson, "Nonlinear Identification of a Physically Parameterized Robot Model, " 14th IFAC Symposium on System Identification, pp. 143-148, 2006.
[20] A. Albu-Schäffer, C. Ott, and G. Hirzinger, "A Unified Passivity Based Control Framework for Position, Torque and Impedance Control of Flexible Joint Robots, " International Journal of Robotics Research, vol. 26, no. 1, pp. 23-39, 2007.
[21] C. Lightcap, and S. Banks, "Dynamic Identification of a Mitsubishi pa10-6ce Robot Using Motion Capture," in Proceedings of the 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3860-3865, 2007.
[22] J. Swevers, W. Verdonck, and J. D. Schutter, "Dynamic Model Identification for Industrial Robots, " IEEE Control Systems, vol. 27, no. 5, pp. 58-71, 2007.
[23] M. C. Chien, and A. C. Huang, "Adaptive Control for Flexible-Joint Electrically Driven Robot with Time-Varying Uncertainties," IEEE Transactions on Industrial Electronics, vol. 54, no. 2, pp. 1032-1038, 2007.
[24] T. Dobrowiecki, and S. Johan, "Measuring a Linear Approximation to Weakly Nonlinear MIMO systems." Automatica, vol. 43, no.10, pp.1737-1751, 2007.
[25] C. Ott, and Y. Nakamura, Cartesian Impedance Control of Redundant and Flexible-Joint Robots, New Yor, U.S.A.: Springer, pp. 28-38, 2008.
[26] S. Moberg, and S. Hanssen, "On Feedback Linearization for Robust Tracking Control of Flexible Joint Robots," in Proceedings of the 17th World Congress the International Federation of Automatic Control, vol. 41, pp. 12218-12223, 2008.
[27] J. J. Craig, Introduction to Robotics: Mechanics and Control, U.S.A: Pearson Prentice-Hall, 2009.
[28] J. Oaki, and S. Adachi, "Decouple Identification for Serial Two-Link Robot Arm with Elastic Joints, " 15th IFAC Symposium on System Identification, vol. 1, pp. 1417-1422, 2009.
[29] N. Ghahramani, and F. Towhidkhah, "Constrained Incremental Predictive Controller Design for a Flexible Joint Robot, " ISA Transactions, vol. 48, pp. 321-326, 2009.
[30] I. H. Chan, "Swept Sine Chirps for Measuring Impulse Response," Power, vol. 50, no. 40, pp. 30, 2010.
[31] S. Moberg, "Modeling and Control of Flexible Manipulators, " Ph.D. dissertation, Department Electronic English, Linköping University., Linköping, Sweden, 2010.
[32] 李宗憲，撓性關節機械臂之回饋線性化控制，碩士論文，國立中興大學機械工程研究所，中華民國，2010。
[33] E. Wernholt, and S. Moberg, "Nonlinear Gray-Box Identification Using Local Models Applied to Industrial Robots, " Automatica, vol. 47, no. 4, pp. 650-660, 2011.
[34] J. Oaki, and A. Shuichi, "Grey-box Modeling of Elastic-joint Robot with Harmonic Drive and Timing Belt," International Federation of Automatic Control(IFAC), vol. 45, pp. 1401-1406, 2012.
[35] W. Rackl, R. Lampariello, and G. Hirzinger, "Robot Excitation Trajectories for Dynamic Parameter Estimation Using Optimized B-Splines," in Proceedings of the 2012 IEEE International Conference on Robotics and Automation, pp. 2042-2047, 2012.
[36] A. Janot, P. O. Vandanjon, and M. Gautier, "Identification of Physical Parameters and Instrumental Variables Validation with Two-stage Least Squares Estimator, " IEEE Transactions on Control Systems Technology, vol. 21, no. 4, pp. 1386-1393, 2013.
[37] M. Gautier, A. Janot, and P. Vandanjon, "A New Closed-Loop Output Error Method for Parameter Identification of Robot Dynamics," IEEE Transactions on Control Systems Technology, vol. 21, no. 2, pp. 428-444, 2013.
[38] M. Gautier, A. Jubien, A. Janot, and P. Robet, "Dynamic Identification of Flexible Joint Manipulators with an Efficient Closed Loop Output Error Method Based on Motor Torque Output Data," in Proceedings of the 2013 IEEE International Conference on Robotics and Automation, pp. 2949-2955, 2013.
[39] P. Robet, M. Gautier, A. Jubien, and A. Janot, "Global Identification of Mechanical and Electrical Parameters of DC motor Driven Joint with a Fast CLOE method," in Proceedings of the 2013 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp.1205-1210, 2013.
[40] 甘國毅，撓性關節平面雙機械臂之階層式適應位置與力量控制，碩士論文，國立中興大學機械工程研究所，中華民國，2013。
[41] 李承燁，撓性關節平面雙機械臂之階層式計算力矩法位置力量控制，碩士論文，國立中興大學機械工程研究所，中華民國，2013。
[42] A. Janot, P. O. Vandanjon, and M. Gautier, "A Generic Instrumental Variable Approach for Industrial Robot Identification," IEEE Transactions on Control Systems Technology, vol. 22, no. 1, pp. 132-145, 2014.
[43] C. Gaz, F. Flacco, and A. D. Luca, "Identifying the Dynamic Model Used by the KUKA LWR: A Reverse Engineering Approach," in Proceedings of the 2014 IEEE International Conference on Robotics and Automation (ICRA), pp. 1386-1392, 2014.
[44] J. Oaki, and S. Adachi, "Plug-in Feedback Using Physically Parameterized Observer for Vibration-Suppression Control of Elastic-Joint Robot," in Proceedings of the 2014 European Control Conference (ECC), pp. 2058-2065, 2014.
[45] M. A. Khosravi, and H. D. Taghirad, "Dynamic Modeling and Control of Parallel Robots with Elastic Cables: Singular Perturbation Approach, " IEEE Transactions on Robotics, vol. 30, no. 3, pp. 694-704, 2014.
[46] S. Moberg, and E. Wernholt, "Modeling and Parameter Estimation of Robot Manipulators Using Extended Flexible Joint Models, " Journal of Dynamic Systems Measurement and Control, vol. 136, no. 3, 2014.
[47] W. Khalil, A. Vijayalingam, B. Khomutenko, I. Mukhanov, P. Lemoine, and G. Ecorchard, "OpenSYMORO: An Open-Source Software Package for Symbolic Modelling of Robots," in Proceedings of the 2014 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp. 1206-1211, 2014.
[48] A. Jubien, M. Gautier, and A. Janot, "DIDIM-CLIE Method for Dynamic Parameter Identification of Flexible Joint Robots," in Proceedings of the 2015 IEEE International Conference on Advanced Intelligent Mechatronics, pp. 226-231, 2015.
[49] F. Petit, A. Daasch, and A. A. Schäffer, "Backstepping Control of Variable Stiffness Robots, " IEEE Transactions on Control Systems Technology, vol. 23, no. 6, pp. 2195-2202, 2015.
[50] J. Jingfu, and G. Nicholas, "Parameter Identification for Industrial Robots with a Fast and Robust Trajectory Design Approach," Robotics and Computer-Integrated Manufacturing, no. 31, pp. 21-29, 2015.
[51] J. Oaki, and S. Adachi, "Vibration-Suppression and Fast-Positioning Control of Elastic-Joint Robot Arm Utilizing Nonlinear-Model-Based Phase-Lead Compensator," in Proceedings of the 2015 IEEE Conference on Control Applications (CCA), pp. 281-287, 2015.
[52] K. Ito, and M. Iwasaki, "State Feedback-Based Vibration Suppression for Multi-Axis Industrial Robot with Posture Change," in Proceedings of the IECON 2016 - 42nd Annual Conference of the IEEE Industrial Electronics Society, pp. 5119-5124, 2016.
[53] 莊閔皓，六軸工業用機械手臂之系統鑑別與順應控制研究，碩士論文，國立成功大學電機工程研究所，中華民國，2016。
[54] M. Jin, J. Lee, and N. G. Tsagarakis, "Model-Free Robust Adaptive Control of Humanoid Robots with Flexible Joints," IEEE Transactions on Industrial Electronics, vol. 64, no. 2, pp. 1706-1715, 2017.
[55] 王智陞，工業用機械手臂之動態系統鑑別方法研究，碩士論文，國立成功大學電機工程研究所，中華民國，2017。
[56] A. Asgharnia, R. Shahnazi, and A. Jamali, "Performance and Robustness of Optimal Fractional Fuzzy PID Controllers for Pitch Control of a Wind Turbine Using Chaotic Optimization Algorithms, " ISA Transactions, vol. 79, pp. 27-44, 2018.
[57] H. Jin, Z. Liu, H. Zhang, Y. Liu, and J. Zhao, "A Dynamic Parameter Identification Method for Flexible Joints Based on Adaptive Control, " IEEE ASME Transactions on Mechatronics, vol. 23, no. 6, pp. 2896-2908, 2018.
[58] J. Oaki, "Physical Parameter Estimation for Feedforward and Feedback Control of a Robot Arm with Elastic Joints, " 2018 International Federation of Automatic, vol. 51, no. 15, pp. 425-430, 2018.
[59] L. Zhang, L. Liu, Z. Wang, Y. Xia, "Continuous Finite-Time Control for Uncertain Robot Manipulators with Integral Sliding Mode, " IET Control Theory and Applications, vol. 12, no. 11, 2018.
[60] R. M. Colorado, and J. M. Valenzuela, "Experimental Parameter Identification of Flexible Joint Robot Manipulators," Robotica, vol. 36, no. 3, pp. 313-332, 2018.
[61] D. P. Nam, P. T. Loc, N. Huong, and D. T. Tan, "A Finite-Time Sliding Mode Controller Design for Flexible Joint Manipulator Systems Based on Disturbance Observer," International Journal of Mechanical Engineering and Robotics Research, vol. 8, no. 4, pp. 619-625, 2019.
[62] H. P. Ni, C. R. Zhang, T. L. Hu, T. Wang, Q. Z. Chen, and C. Chen, "A Dynamic Parameter Identification Method of Industrial Robots Considering Joint Elasticity, " International Journal of Advanced Robotic Systems, vol. 16, no. 1, 2019.
[63] H. Wang, Y. Pan, S. Li, and H. Yu, "Robust Sliding Mode Control for Robots Driven by Compliant Actuators," IEEE Transactions on Control Systems Technology, vol. 27, no. 3, pp. 1259-1266, 2019.
[64] J. Kim, and E. A. Croft, "Full-State Tracking Control for Flexible Joint Robots with Singular Perturbation Techniques," IEEE Transactions on Control Systems Technology, vol. 27, no. 1, pp. 63-73, 2019.
[65] S. Zaare, M. R. Soltanpour, and M. Moattari, "Adaptive Sliding Mode Control of N Flexible-Joint Robot Manipulators in the Presence of Structured and Unstructured Uncertainties," Multibody System Dynamics, vol.47, pp. 397-434, 2019.
[66] T. C. Wesselink, P. Borja, and J. M. A. Scherpen, "saturated Control without Velocity Measurements for Planar Robots with Flexible Joints, " in Proceedings of the IEEE 58th Conference on Decision and Control, pp. 7093-7098, 2019.
[67] Y. Fang, J. Hu, W. Liu, Q. Shao, J. Qi, and Y. Peng, "Smooth and Time-Optimal S-curve Trajectory Planning for Automated Robots and Machines, " Mechanism and Machine Theory, vol. 137, pp. 127-153, 2019.
[68] J. Oaki, "Rigid-Joint-Model Feedforward with Elastic-Joint-Model Feedback for Motion Control of a 6-DOF Industrial Robot," 2020 International Federation of Automatic Control, vol.53, no.2, pp. 8462-8469, 2020.
[69] M. Bottin, S. Cocuzza, N. Comand, and A. Doria, "Modeling and Identification of an Industrial Robot with a Selective Modal Approach," Applied Sciences, vol. 10, no. 13, pp. 4619, 2020.
[70] M. Hong, W. Yao, Z. Zhu, and Y. Guo, "A Hybrid PID Controller for Flexible Joint Manipulator Based on State Observer and Singular Perturbation Approach," in Proceedings of the 2020 39th Chinese Control Conference, pp. 3599-3603, 2020.
[71] M. R. Soltanpour, S. Zaare, and M. Haghgoo, "Free-Chattering Fuzzy Sliding Mode Control of Robot Manipulators with Joints Flexibility in Presence of Matched and Mismatched Uncertainties in Model Dynamic and Actuators, " Journal of Intelligent & Robotic Systems, vol. 100, pp. 47-69, 2020.
[72] S. Zaare, and M. R. Soltanpour, "Continuous Fuzzy Nonsingular Terminal Sliding Mode Control of Flexible Joints Robot Manipulators Based on Nonlinear Finite Time Observer in the Presence of Matched and Mismatched Uncertainties, " Journal of the Franklin Institute, vol. 357, pp. 6539-6570, 2020.
[73] T. V. Trung, and M. Iwasaki, " High-Performance Positioning using Decoupling Controllers for Flexible Two-Link Robots with Strain Wave Gears," IEEJ Journal of Industry Applications, vol. 9, no. 4, pp. 408-417, 2020.
[74] Y. L. Wang, Y. Wang, Q. Wang, and H. B.Wang, "Dynamic Parameter Identification of Flexible Joint Robot Based on Adaptive Particle Swarm Optimization-Genetic Algorithm, " Acta Metrologica Sinica, vol. 41, no. 1, pp. 60-66, 2020.
[75] 2021/2022產業技術白皮書，經濟部技術處，2021。
[76] J. Jia, M. Zhang, and C. Li, "Improved Dynamic Parameter Identification Method Relying on Proprioception for Manipulators," Nonlinear Dynamics, no. 105, pp. 1373-1388, 2021.
[77] Q. Leboutet, J. Roux, A. Janot, J. R. G. Olvera, and G. Cheng, "Inertial Parameter Identification in Robotics: A Survey, " Applied Sciences, vol. 11, no. 9, pp. 4303, 2021.
[78] X. Cheng, H. Liu, and W. Lu, "Chattering-Suppressed Sliding Mode Control for Flexible-Joint Robot Manipulators, " Actuators, vol. 10, no. 288, 2021.
[79] 蔡靚萱，《一次搞懂元宇宙》它是下世代的網路！臉書、Nvidia、微軟、Visa全力投入，商業周刊，2021。
[80] D. T. Trung, V. V. Hung, and L. Zhaoheng, "Linearization of Dynamic Equations for Vibration and Modal Analysis of Flexible Joint Manipulators, " Mechanism and Machine Theory, vol. 167, 2022.
[81] H. H. Lin, M. Y. Cheng, Y. T. Chen, and C. Y. Huang, "Contour Following Accuracy Improvement—A Dynamic Fast Nonsingular Terminal Sliding Mode Control Approach," IEEE Access, vol. 10, pp. 34185-34195, 2022.
[82] H. M. Tuan, F. Sanfilippo, and N. V. Hao, "A Novel Adaptive Sliding Mode Controller for a 2-DOF Elastic Robotic Arm, " Robotics, vol. 11, no. 47, 2022.
[83] Kyle 科技產業資訊室 (iKnow)。IFR公布2022年機器人五大趨勢。檢索日期2022年5月3日，取自https://iknow.stpi.narl.org.tw/Post/Rea d.aspx?PostID=18861.
[84] The Math Works, Optimization Toolbox for Use with MATLAB, The Math Works, 2022.
[85] 涂翠珊。協作機器人疫情期間吸企業投資 2030市場規模上看80億美元。檢索日期2022年5月3日，取自https://www.digitimes.com.tw /iot/article.asp?cat=158&cat1=20&cat2=11&id=0000612456_PNX5OSW04ATJ8E7ASJLME.