對於會與人或環境交互作用的機器人而言，良好的人機親和性及人機互動安全性兩者為首要目標，因此機器人如何擁有精準而穩定的勁度控制為一重要課題。為實踐精準的勁度控制，應用於串聯彈性致動器的阻抗控制與導納控制應運而生，與一般常見之剛性致動器不同，串聯彈性致動器為由一馬達與彈簧串聯組成，藉由量測彈簧之變形量以量測力量，藉此方式達成比剛性致動器更精確的力量控制，進而實踐精準的勁度控制以提供虛擬勁度。
　　在人機互動的過程中，環境的不確定性除會影響系統之表現外，其亦會影響系統的耦合穩定性，然而人機互動的安全性比精準的勁度控制更為重要，現今已有許多研究顯示在任意環境下皆能保持穩定的前提下，串聯彈性致動器所能呈現之虛擬勁度在很大程度上受限於其彈簧勁度。為提高串聯彈性致動器所呈現之穩定的虛擬勁度，可藉由增加彈簧勁度以達成此目標，但是相對的其勁度控制之精度便會有所犧牲，而透過添加虛擬阻尼亦可提高其穩定性，但是穩定性範圍在很大程度上仍取決於環境參數。
　　為確切了解環境參數對系統穩定性之影響並克服上述限制，本文首先於考慮環境之情況下建立串聯彈性致動器之模型，接著基於一般的阻抗控制與導納控制，提出一新穎的控制策略，阻抗和導納控制都將基於這種新的控制策略進行修改為混合型阻抗控制與混合型導納控制。由修改後的控制器穩定性分析可知混合型阻抗控制與混合型導納控制的虛擬勁度可以任意選擇，且與串聯彈性致動器本身之彈簧勁度和環境參數無關，因此透過此兩控制方法可使得串聯彈性致動器呈現大範圍且精準的虛擬勁度。此外本文亦以串聯彈性致動器設計一雙軸機器人使其具有良好的力量感測與控制性能，其除可自行運作外，亦可安裝於機械手臂末端以發展其他應用。

Accurate and stable stiffness control is required for robots that need to interact safely with humans or the environment. Accurate stiffness control can be achieved using a series elastic actuators (SEA). A SEA includes an elastic spring in series with an actuator to provide more accurate force control than conventional rigid actuators. Although impedance and admittance controllers have both been developed for series elastic actuators to render virtual stiffness, the stable virtual stiffness is still largely limited by the stiffness of the elastic spring in the SEA. Increasing the stiffness of the spring can allow a larger range of stable virtual stiffness. However, the accuracy of the stiffness control would be compromised. Adding a virtual damper can also improve the stability, but the stability range would highly depend on the environmental parameters. To overcome the limitations, this paper proposes a novel control strategy such that the stable range of the virtual stiffness does not depend on the spring stiffness and the environmental parameters. Both impedance and admittance controllers will be modified based on this new control strategy. The stability analysis of the modified controllers will show that the virtual stiffness can be arbitrarily selected and is unrelated to the spring stiffness and environmental parameters. Experiments will be provided to verify the modified controllers. It is expected that the new control strategy can be used for SEAs when wide-range and accurate virtual stiffness is required.

[1] 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.
[2] Hu, Y., Nori, F., & Mombaur, K. (2016, June). Squat motion generation for the humanoid robot iCub with Series Elastic Actuators. In 2016 6th IEEE International Conference on Biomedical Robotics and Biomechatronics (BioRob) (pp. 207-212). IEEE.
[3] Pratt, G. A., Willisson, P., Bolton, C., & Hofman, A. (2004, June). Late motor processing in low-impedance robots: Impedance control of series-elastic actuators. In Proceedings of the 2004 American control conference (Vol. 4, pp. 3245-3251). IEEE.
[4] Quigley, M., Asbeck, A., & Ng, A. (2011, May). A low-cost compliant 7-DOF robotic manipulator. In 2011 IEEE International Conference on Robotics and Automation (pp. 6051-6058). IEEE.
[5] Zhang, T., Tran, M., & Huang, H. (2019). Admittance shaping-based assistive control of SEA-driven robotic hip exoskeleton. IEEE/ASME Transactions on Mechatronics, 24(4), 1508-1519.
[6] Yu, H., Huang, S., Chen, G., Pan, Y., & Guo, Z. (2015). Human–robot interaction control of rehabilitation robots with series elastic actuators. IEEE Transactions on Robotics, 31(5), 1089-1100.
[7] Calanca, A., Muradore, R., & Fiorini, P. (2015). A review of algorithms for compliant control of stiff and fixed-compliance robots. IEEE/ASME Transactions on Mechatronics, 21(2), 613-624.
[8] Raibert, M. H., & Craig, J. J. (1981). Hybrid position/force control of manipulators. Journal of Dynamic Systems, Measurement, and Control, 103(2), 126-133
[9] Ju, M. S., Lin, C. C., Lin, D. H., Hwang, I. S., & Chen, S. M. (2005). A rehabilitation robot with force-position hybrid fuzzy controller: hybrid fuzzy control of rehabilitation robot. IEEE transactions on neural systems and rehabilitation engineering, 13(3), 349-358.
[10] Hogan, N. (1984, June). Impedance control: An approach to manipulation. In 1984 American control conference (pp. 304-313). IEEE.
[11] Keemink, A. Q., van der Kooij, H., & Stienen, A. H. (2018). Admittance control for physical human–robot interaction. The International Journal of Robotics Research, 37(11), 1421-1444.
[12] Yu, W., Rosen, J., & Li, X. (2011, June). PID admittance control for an upper limb exoskeleton. In Proceedings of the 2011 American control conference (pp. 1124-1129). IEEE.
[13] Kim, M. J., Lee, W., Choi, J. Y., Chung, G., Han, K. L., Choi, I. S.,Ott, C., & Chung, W. K. (2019). A passivity-based nonlinear admittance control with application to powered upper-limb control under unknown environmental interactions. IEEE/ASME Transactions on Mechatronics, 24(4), 1473-1484.
[14] Adams, R. J., & Hannaford, B. (1999). Stable haptic interaction with virtual environments. IEEE Transactions on robotics and Automation, 15(3), 465-474.
[15] Ott, C., Mukherjee, R., & Nakamura, Y. (2015). A hybrid system framework for unified impedance and admittance control. Journal of Intelligent & Robotic Systems, 78(3-4), 359-375.
[16] Calanca, A., & Fiorini, P. (2018). A rationale for acceleration feedback in force control of series elastic actuators. IEEE Transactions on Robotics, 34(1), 48-61.
[17] Calanca, A., & Fiorini, P. (2018). Understanding environment-adaptive force control of series elastic actuators. IEEE/ASME Transactions on Mechatronics, 23(1), 413-423.
[18] Tsumugiwa, T., Fuchikami, Y., Kamiyoshi, A., Yokogawa, R., & Yoshida, K. (2007). Stability analysis for impedance control of robot in human-robot cooperative task system. Journal of Advanced Mechanical Design, Systems, and Manufacturing, 1(1), 113-121.
[19] Colgate, J. E. (1988). The Control of dynamically Interacting Systems (Doctoral dissertation, Ph. D., Massachusetts Institute of Technology).
[20] Gallagher, W., Gao, D., & Ueda, J. (2014). Improved stability of haptic human–robot interfaces using measurement of human arm stiffness. Advanced Robotics, 28(13), 869-882.
[21] Tagliamonte, N. L., & Accoto, D. (2014). Passivity constraints for the impedance control of series elastic actuators. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 228(3), 138-153.
[22] Mehling, J. S. (2015). Impedance control approaches for series elastic actuators (Doctoral dissertation).
[23] Vallery, H., Ekkelenkamp, R., Van Der Kooij, H., & Buss, M. (2007, October). Passive and accurate torque control of series elastic actuators. In 2007 IEEE/RSJ international conference on intelligent robots and systems (pp. 3534-3538). IEEE.
[24] Vallery, H., Veneman, J., Van Asseldonk, E., Ekkelenkamp, R., Buss, M., & Van Der Kooij, H. (2008). Compliant actuation of rehabilitation robots. IEEE Robotics & Automation Magazine, 15(3), 60-69.
[25] Lee, C., Kim, D. H., Singh, H., & Ryu J. H. (2020). Successive Stiffness Increment and Time Domain Passivity Approach for Stable High Bandwidth Control of Series Elastic Actuator. In 2020 IEEE International Conference on Robotics and Automation (pp. 4717-4723). IEEE.
[26] Isik, K., Thomas, G. C., & Sentis, L. (2019). A Fixed Structure Gain Selection Strategy for High Impedance Series Elastic Actuator Behavior. Journal of Dynamic Systems, Measurement, and Control, 141(2).
[27] Roozing, W., Malzahn, J., Kashiri, N., Caldwell, D. G., & Tsagarakis, N. G. (2017). On the stiffness selection for torque-controlled series-elastic actuators. IEEE Robotics and Automation Letters, 2(4), 2255-2262.
[28] Lee, H., Jinoh, L., Jee-Hwan, R., & Oh, S. (2019, November). Relaxing the Conservatism of Passivity Condition for Impedance Controlled Series Elastic Actuators. In 2019 IEEE/RSJ International Conference on Intelligent Robotics and Systems (pp. 7610-7615). IEEE.
[29] Calanca, A., Muradore, R., & Fiorini, P. (2017). Impedance control of series elastic actuators: Passivity and acceleration-based control. Mechatronics, 47, 37-48.
[30] Haninger, K., Asignacion, A., & Oh, S. (2019). Safe rendering of high impedance on a series-elastic actuator with disturbance observer-based torque control. arXiv preprint arXiv:1912.01355.
[31] Siciliano, B., Sciavicco, L., Villani, L., & Oriolo, G. (2010). Robotics: modeling, planning and control. Springer Science & Business Media.
[32] 張宇翔 (2020)。「用於宏微機器人冗餘操作之新型端效器模組設計與分析」，成功大學機械工程學系碩士學位論文。
[33] 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.
[34] 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。
[35] Oriental motor USA Corp. "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: September 3, 2020]
[36] 尤應龍 (2018)。「開發微型串聯彈性致動器於遠端操作機器人的精準力感知與控制」，成功大學機械工程學系碩士學位論文。
[37] Newshiki Enterprise CO., LTD. "Harmonic Drive精密控制用減速機 綜合型錄" Available:https://www.newshiki.com.tw/%e5%9e%8b%e9%8c%84%e4%b8%8b%e8%bc%89/ [Accessed: September 3, 2020]
[38] 黃彥霖 (2020)。「步進馬達扭矩控制方法之研究」，成功大學機械工程學系碩士學位論文。
[39] RLS. (1989) "RM08超小型非接觸式磁旋轉編碼器" Available: https://www.rls.si/cn/rm08-super-small-non-contact-rotary-encoder [Accessed: September 3, 2020]
[40] 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。
[41] AL-CHARM Enterprise CO., LTD. "SG系列 滾珠螺桿" Available: https://www.al-charm.com.tw/products/SG%E7%B3%BB%E5%88%97 [Accessed: September 3, 2020]
[42] KSS CO., LTD. "Q&A Ball Screws" Available: https://www.kssballscrew.com/us/product/qa.html [Accessed: September 3, 2020]
[43] Renishaw, Inc. "ATOM™編碼器系列" Available: https://www.renishaw.com.tw/tw/atom-encoder-series--37564 [Accessed: September 3, 2020]
[44] THK CO., LTD. "交叉滾柱軸承 綜合產品目錄" Available: https://www.thk.com/catalog/?lang=ct [Accessed: September 3, 2020]
[45] 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 [Ac-cessed: September 3, 2020]
[46] Stutts, D. S. (1995). Analytical Dynamics: Lagrange’s Equation and its Application–A Brief Introduction. Missouri University of Science and Technology, Rolla, MO, accessed Aug, 28, 2017.
[47] 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。
[48] 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。
[49] 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.
[50] 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.
[51] 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.
[52] 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.
[53] MISUMI Group Inc." 聯軸器 十字形 固定螺絲型" Available: https://tw.misumi-ec.com/vona2/detail/110300607630/?PNSearch=MCO10-3-4&HissuCode=MCO10-3-4&searchFlow=suggest2products&Keyword=MCO10-3-4 [Accessed: September 3, 2020]
[54] 許登傑、陳文瑞、麥朝創與蔡孟勳 (2017)。「系統頻譜分析於工具機上的應用」，機械工業雜誌。
[55] Lee, Y. S., & Lan, C. C. (2020, July). Rendering of Arbitrary and Stable Stiffness Using a Series Elastic Actuator. In 2020 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM) (pp. 960-965). IEEE.
[56] 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。
[57] 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.