在遠端與虛擬操作領域中，觸覺回饋裝置作為操作者與遠端或虛擬環境間的溝通橋樑，須具備良好的力量控制性能與能呈現大範圍且精準的虛擬阻抗表現。由於並聯式機構具有高精度與高剛性的優勢，目前被廣泛應用於觸覺回饋裝置的開發中，然而現存並聯式觸覺回饋裝置其雅可比矩陣非定值，除了增添控制的複雜度，亦導致工作空間內各個位置的力量輸出表現與阻抗穩定上限不相同，且為了遷就阻抗表現較弱的區域，使其能呈現的虛擬勁度值受到限制。
本文針對一具有定值雅可比矩陣之3-PRRR平移並聯式機構使用線性串聯彈性致動器進行驅動，令其達成x、y與z方向移動之觸覺回饋控制。串聯彈性致動器運用撓性元件串接馬達與負載，可大幅降低馬達及減速機構之慣性與摩擦對機器末端輸出的影響，因此相較於剛性致動器可達成更精準的輸出力量與勁度控制，此外，輸入與輸出關係為定值的特性，使觸覺回饋裝置整體工作空間的運動呈均勻表現，虛擬勁度的上限亦於工作空間中為一定值，因此可實現大範圍的勁度變化。為了達成大勁度的互動控制，觸覺回饋裝置本身須具備高結構剛性，因此本文首先針對機構原型剛性進行探討，而後在串聯彈性致動器建模中將機構耦合效應納入考量，以求取真實的觸覺回饋裝置動力模型，再根據機器模型設計三維的力量控制器與阻抗控制器，同時以實驗驗證各方向力量與阻抗控制性能，其中，透過虛擬牆控制與各項阻抗指標性實驗證明本文之觸覺回饋裝置於各方向上均有精準且變化廣泛的阻抗表現，使之可與不同勁度大小的環境進行互動。

A haptic device is used to transmit impedance to a human user to mimic the impedance of a virtual or real environment. Existing haptic devices use serial or parallel robots to deliver impedance in multiple dimensions. These robots usually have nonconstant Jacobian matrices that result in poor dynamic properties and low impedance stability limits in certain regions within the workspace. To account for these regions, the range of stiffness rendering is limited. This research presents a three-degrees-of-freedom (DoFs) translational parallel robot with a constant Jacobian matrix in the entire workspace. The consistent dynamic parameters allow a large-range virtual stiffness to be rendered. To provide the accurate and large output force required for high-stiffness rendering, series elastic actuators (SEAs) are used as the input for the parallel robot. SEAs can be used to minimize the geartrain friction and effective inertia to control the output force and impedance more accurately. Design, modeling, and three-dimensional impedance control of the haptic device are presented in this work. Multi-dimensional impedance and virtual-wall control experiments are illustrated to demonstrate the accuracy and rendering range of the haptic device. Since the stable range of virtual stiffness is much larger than existing ones, it is expected that this novel device can be used to render accurate stiffness for both soft and stiff environments.

[1] Goertz, R. C. (1949). Master-slave manipulator (Vol. 2635). Argonne National Laboratory.
[2] Massie, T. H., & Salisbury, J. K. (1994, November). The phantom haptic interface: A device for probing virtual objects. In Proceedings of the ASME winter annual meeting, symposium on haptic interfaces for virtual environment and teleoperator systems (Vol. 55, No. 1, pp. 295-300).
[3] Xiaojun, C., Yanping, L., Chengtao, W., Yiqun, W., Xudong, W., & Guofang, S. (2010, November). An integrated surgical planning and virtual training system using a force feedback haptic device for dental implant surgery. In 2010 International Conference on Audio, Language and Image Processing (pp. 1257-1261). IEEE.
[4] Force Dimension Inc. " Haptic Devices – Omega.x " Available: https://www.forcedime-nsion.com/downloads/specs/specsheet-omega.3.pdf [Accessed: September 11, 2021]
[5] Hannaford, B., & Okamura, A. M. (2016). Haptics. In Springer Handbook of Robotics (pp. 1063-1084). Springer, Cham.
[6] Tan, H. Z., Srinivasan, M. A., Eberman, B., & Cheng, B. (1994). Human factors for the design of force-reflecting haptic interfaces. Dynamic systems and control, 55(1), 353-359.
[7] Brooks, T. L. (1990, November). Telerobotic response requirements. In 1990 IEEE international conference on systems, man, and cybernetics conference proceedings (pp. 113-120). IEEE.
[8] 3D Systems Inc. " Haptic Devices - Touch " Available: https://www.3dsystems.com/ha-ptics-devices/touch/specifications [Accessed: September 11, 2021]
[9] Haption S.A. Inc. " Virtuose™ 6D " Available: https://www.haption.com/fr/products-fr/virtuose-6d-fr.html [Accessed: September 11, 2021]
[10] Hoshyarmanesh, H., Zareinia, K., Lama, S., & Sutherland, G. R. (2021). Structural design of a microsurgery-specific haptic device: neuroArmPLUSHD prototype. Mechatronics, 73, 102481.
[11] Clavel, R., “A fast robot with parallel geometry” 18th International Symposium on Industrial Robots Sydney, Australia (04 1988) pp. 91–100.
[12] Novint Technologies Inc. " Falcon Haptic Devices " Available: https://hapticshouse.co-m/collections/falcons/products/white-falcon-3d-touch-haptic-controller [Accessed: Se-ptember 11, 2021]
[13] Vulliez, M., Zeghloul, S., & Khatib, O. (2018). Design strategy and issues of the Delthaptic, a new 6-DOF parallel haptic device. Mechanism and Machine Theory, 128, 395-411.
[14] Liu, G., Chen, Y., Xie, Z., & Geng, X. (2018). GASQP optimization for the dimensional synthesis of a delta mechanism based haptic device design. Robotics and Computer-Integrated Manufacturing, 51, 73-84.
[15] Abeywardena, S., & Chen, C. (2017). Implementation and evaluation of a three-legged six-degrees-of-freedom parallel mechanism as an impedance-type haptic device. IEEE/ASME Transactions on Mechatronics, 22(3), 1412-1422.
[16] Kim, K., Chung, W. K., & Youm, Y. (2003, October). Design and analysis of a new 7-DOF parallel type haptic device: PATHOS-II. In Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003)(Cat. No. 03CH37453) (Vol. 3, pp. 2241-2246). IEEE.
[17] Saafi, H., Laribi, M. A., & Zeghloul, S. (2015). Redundantly actuated 3-RRR spherical parallel manipulator used as a haptic device: improving dexterity and eliminating singularity. Robotica, 33(5), 1113-1130.
[18] Force Dimension Inc. " Haptic Devices – delta.6 " Available: https://www.forcedimens-ion.com/downloads/specs/specsheet-delta.6.pdf [Accessed: September 11, 2021]
[19] Chen, Z., Zhang, Y., Wang, D., Li, C., & Zhang, Y. (2012, July). iFeel6-BH1500: A large-scale 6-DOF Haptic Device. In 2012 IEEE International Conference on Virtual Environments Human-Computer Interfaces and Measurement Systems (VECIMS) Proceedings (pp. 121-125). IEEE.
[20] Butterfly Haptics LLC. " Maglev 200™ System " Available: https://butterflyhaptics.co-m/products/system/ [Accessed: September 12, 2021]
[21] ATI Industrial Automation Inc. " Force/Torque Sensors - F/T Models " Available: https://www.ati-ia.com/products/ft/ft_models.aspx?id=Nano25 [Accessed: September 12, 2021]
[22] Pratt, G. A., & Williamson, M. M. (1995, August). Series elastic actuators. In Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots (Vol. 1, pp. 399-406). IEEE.
[23] Zinn, M., Khatib, O., Roth, B., & Salisbury, J. K. (2008, March). Large workspace haptic devices-a new actuation approach. In 2008 Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems (pp. 185-192). IEEE.
[24] Basafa, E., Sheikholeslami, M., Mirbagheri, A., Farahmand, F., & Vossoughi, G. R. (2009, September). Design and implementation of series elastic actuators for a haptic laparoscopic device. In 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society (pp. 6054-6057). IEEE.
[25] Zhang, S., Guo, S., Gao, B., Hirata, H., & Ishihara, H. (2015). Design of a novel telerehabilitation system with a force-sensing mechanism. Sensors, 15(5), 11511-11527.
[26] Katsura, S., Irie, K., & Ohishi, K. (2008). Wideband force control by position-acceleration integrated disturbance observer. IEEE Transactions on Industrial Electronics, 55(4), 1699-1706.
[27] Gupta, A., & O’Malley, M. K. (2011). Disturbance-observer-based force estimation for haptic feedback.
[28] Tobergte, A., & Helmer, P. (2013, November). A disturbance observer for the sigma. 7 haptic device. In 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (pp. 4964-4969). IEEE.
[29] Hogan, N. (1984, June). Impedance control: An approach to manipulation. In 1984 American control conference (pp. 304-313). IEEE.
[30] Van der Linde, R. Q., Lammertse, P., Frederiksen, E., & Ruiter, B. (2002, July). The HapticMaster, a new high-performance haptic interface. In Proc. Eurohaptics (pp. 1-5). Edinburgh University.
[31] Peer, A., & Buss, M. (2008). A new admittance-type haptic interface for bimanual manipulations. IEEE/ASME Transactions on mechatronics, 13(4), 416-428.
[32] Zhang, H., Zhang, Y., Wang, D., & Lu, L. (2017, June). Dentaltouch: A haptic display with high stiffness and low inertia. In 2017 IEEE World Haptics Conference (WHC) (pp. 388-393). IEEE.
[33] 黃聖元 (2020)。「新型平移式並聯機構之設計與分析」，成功大學機械工程學系碩士學位論文
[34] THK Inc. " 交叉滾柱軸環 綜合產品目錄 " Available: http://tech.thk.com/cs/produ-cts/pdf_download.php?file=510C_18_CrossRollerRing.pdf [Accessed: June 15, 2021]
[35] MISUMI Group Inc. "小徑滾珠軸承 兩側密封式" Available: https://tw.misumi-ec.c-om/vona2/detail/110300107560/?KWSearch=%e5%b0%8f%e5%be%91%e6%bb%be%e7%8f%a0%e8%bb%b8%e6%89%bf%20%e5%85%a9%e5%81%b4%e5%af%86-%e5%b0%81%e5%bc%8f&searchFlow=results2products [Accessed: June 15, 2021]
[36] THK Inc. " Dimensional Drawing, Dimensional Table - Model RU " Available: https://tech.thk.com/en/products/pdf/en_a18_022.pdf [Accessed: June 15, 2021]
[37] OPTEX FA Co., LTD " FASTUS CD22 Series " Available: http://www.optex-fa.com/p-roducts/dsp_sensor/cd22/index4.html [Accessed: June 15, 2021]
[38] KEYENCE Inc. " CCD Laser Displacement Sensor LK Series " Available: https://www.keyence.com.tw/products/measure/laser-1d/lk/models/lk-081/?search_dl=1 [Accessed:June 15, 2021]
[39] OP MOUNT Inc. " M-MTP90-100-C7 " Available: http://www.opmount.com.tw/cht/P-oduct_detail/487/289.html [Accessed: June 15, 2021]
[40] FUTEK Inc. " LSB200 Series – FSH00107 " Available: https://www.futek.com/store/l-egacy-sensors-and-instruments/miniature-s-beam-LSB200/FSH00107 [Accessed: Ju-ne 15, 2021]
[41] 卓孟寬 (2020)。「平移式並聯工具機之運動與動力分析」，成功大學機械工程學系碩士學位論文
[42] 徐嘉佑 (2012)。「具兩共置撓性驅動軸機器手腕之動力與控制」，成功大學機械工程學系碩士學位論文。
[43] Dombre, E., Duchemin, G., Poignet, P., & Pierrot, F. (2003). Dermarob: A safe robot for reconstructive surgery. IEEE Transactions on Robotics and Automation, 19(5), 876-884.
[44] 吳冠毅 (2018)。「肘外甲機器之串聯彈性致動機構與驅動控制器設計」，成功大學機械工程學系碩士學位論文。
[45] 蘇胤毓 (2019)。「具串聯彈性致動與錯位適應之前臂復健機器人設計」，成功大學機械工程學系碩士學位論文。
[46] Orientalmotor Co., LTD " Stepper Motors (Motor Only) - PKP Series 2-Phase " Available: https://www.orientalmotor.com.tw/products/st/list/detail/?product_name=PKP214D06A-R2EL%2BLCE08A-006&brand_tbl_code=ST&series_code= GCG0& type_code=2%E7%9B%B8_%E6%A8%99%E6%BA%96%E5%9E%8B_%E9%99%84%E7%B7%A8%E7%A2%BC%E5%99%A8_s [Accessed: June 15, 2021]
[47] Orientalmotor Co., LTD " Stepper Motors (Motor Only) - PKP Series 2-Phase " Available: https://www.orientalmotor.com.tw/products/st/list/detail/?product_name=PKP225D15A2-R2EL-L&brand_tbl_code=ST&series_code=GC00&type_code= [Ac-cessed: June 15, 2021]
[48] Maxon Group " DC motors - RE Program " Available: https://www.maxongroup.com/maxon/view/product/273752 [Accessed: June 15, 2021]
[49] MISUMI Group Inc. "滾珠螺桿選定指南" Available: https://tw.misumi-ec.com/pdf/fa/2019/p489_p2955.pdf [Accessed: June 15, 2021]
[50] Renishaw Inc. " ATOMTM光學尺系列" Available: https://www.renishaw.com.tw/tw/atom-encoder-series—37564 [Accessed: June 15, 2021]
[51] HIWIN Inc. " MG系列 微小型線性滑軌" Available: https://www.hiwin.tw/products/linear_guideway/mg.aspx [Accessed: June 15, 2021]
[52] MISUMI Group Inc. "迷你線性滑軌 標準滑塊/輕預壓･微小間隙" Available: https://tw.misumi-ec.com/vona2/detail/110302586530/ [Accessed: June 15, 2021]
[53] MISUMI Group Inc. "迷你線性滑軌 短滑塊/輕預壓･微小間隙" Available: https://t-w.misumi-ec.com/vona2/detail/110300042210/ [Accessed: June 15, 2021]
[54] 郭彧伶 (2019)。「具兩維可調式定力輸出之力量控制機構設計」，成功大學機械工程學系碩士學位論文。
[55] Lan, C. C., & Cheng, Y. J. (2008). Distributed shape optimization of compliant mechanisms using intrinsic functions. Journal of Mechanical Design, 130(7).
[56] Lan, C. C., & Lee, K. M. (2006). Generalized shooting method for analyzing compliant mechanisms with curved members. Journal of Mechanical Design 128.4 (2006): 765-775.
[57] Bodson, M., Chiasson, J. N., Novotnak, R. T., & Rekowski, R. B. (1993). High-performance nonlinear feedback control of a permanent magnet stepper motor. IEEE Transactions on Control Systems Technology, 1(1), 5-14.
[58] Nollet, F., Floquet, T., & Perruquetti, W. (2008). Observer-based second order sliding mode control laws for stepper motors. Control engineering practice, 16(4), 429-443.
[59] Ohmae, T., Matsuda, T., Kamiyama, K., & Tachikawa, M. (1982). A microprocessor-controlled high-accuracy wide-range speed regulator for motor drives. IEEE Transactions on Industrial Electronics, (3), 207-211.
[60] Tsuji, T., Hashimoto, T., Kobayashi, H., Mizuochi, M., & Ohnishi, K. (2008). A wide-range velocity measurement method for motion control. IEEE Transactions on industrial electronics, 56(2), 510-519.
[61] 林靜慧 (2020)。「使用按需輔助控制器於機器人輔助之完整前臂復健訓練」，成功大學機械工程學系碩士學位論文。
[62] Lee, S. H., & Song, J. B. (2001). Acceleration estimator for low-velocity and low-acceleration regions based on encoder position data. IEEE/ASME transactions on mechatronics, 6(1), 58-64.
[63] 李育昇 (2020)。「以串聯彈性致動器呈現任意穩定虛擬勁度」，成功大學機械工程學系碩士學位論文。
[64] Texas Instruments Inc. " OPA548 High-Voltage, High-Current, Wide-Output-Voltage-Swing Power Operational Amplfier " Available: https://www.ti.com/product/ OPA548? keyMatch=OPA548&tisearch=Search-EN-everything&usecase=GPN [Accessed: Jun-e 15, 2021]
[65] WACOH-TECH Inc. " Capacitive 6-axis force sensor " Available: https://wacohtech.com/en/products/dynpick/200n_500n_rcdb.html [Accessed: June 15, 2021]
[66] 林奎佑 (2019)。「使用步進馬達於直線串聯彈性致動器的準確力量及阻抗控制」，成功大學機械工程學系碩士學位論文
[67] Chandler, R. F., Clauser, C. E., McConville, J. T., Reynolds, H. M., & Young, J. W. (1975). Investigation of inertial properties of the human body. Air Force Aerospace Medical Research Lab Wright-Patterson AFB OH.
[68] Oriental motor Co., LTD " PKP214D06A-R2EL轉速–轉矩特性圖" Available: https://www.orientalmotor.com.tw/products_file/st/image/tct_pkp214d06a-r2el_d.gif [Acces- sed: June 15, 2021]
[69] Oriental motor Co., LTD " PKP225D15A2-R2EL轉速–轉矩特性圖" Available: https://www.orientalmotor.com.tw/products_file/st/image/tct_pkp225d15a2-r2el_d.gif [Ac- cessed: June 15, 2021]
[70] De Keyser, R., Ionescu, C. M., & Festila, C. (2011, December). A one-step procedure for frequency response estimation based on a Switch-Mode Transfer Function Analyzer. In 2011 50th IEEE Conference on Decision and Control and European Control Conference (pp. 1189-1194). IEEE.
[71] Kwon, D. S., & Woo, K. Y. (2000, November). Control of the haptic interface with friction compensation and its performance evaluation. In Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000)(Cat. No. 00CH37113) (Vol. 2, pp. 955-960). IEEE.
[72] Olsson, H., Åström, K. J., De Wit, C. C., Gäfvert, M., & Lischinsky, P. (1998). Friction models and friction compensation. Eur. J. Control, 4(3), 176-195.
[73] Kumičáková, D., Tlach, V., & Císar, M. (2016). Testing the performance characteristics of manipulating industrial robots.
[74] ISO 9283:1998 "Manipulating industrial robots - Performance criteria and related test methods" Available: https://www.iso.org/standard/22244.html [Accessed: June 15, 20-21]
[75] Orientalmotor Co., LTD " Linear actuators (with absolute sensor) - DRSⅡ Series " Available: https://www.orientalmotor.com.tw/products/limo/list/detail/?product_name=DRSM42LG-04B2AZAK%2BAZD-K%2BCC010VZR2&brand_tbl_code= LM&s-eries_code =SO00&type_code=component&driver_type=%E8%84%88%E6%B3%A2%E5%88%97%E8%BC%B8%E5%85%A5%E5%9E%8B [Accessed: July 25, 2021]
[76] Mehling, J. S. (2015). Impedance control approaches for series elastic actuators (Doctoral dissertation, Rice University).