氣壓肌肉致動器（PMAs) 因其高能重比、可撓曲的結構設計和易於維護而受到重視，並使其適用於需要與人體緊密互動的機器人應用。本研究中，藉由比例方向控制閥，透過調節雙氣壓肌肉致動器的壓力來控制單自由度機械臂的旋轉運動。為了確保多層非線性動態的穩定性，我們選擇了逆步控制器，並加入了積分狀態以減少穩態追跡誤差。此外，還添加了適應性控制器來補償系統中的時變不確定性，例如氣壓肌肉致動器的彈性等，以實現不同追跡頻率下一致且準確的性能。不同於傳統的逆步控制器通常應用於嚴格回授形式的系統，在本研究中，由於單一比例控制閥之控制命令同時影響到兩組氣壓肌肉致動器的壓力狀態，因此在加入積分狀態的逆步控制器的推導中，兩個壓力狀態的收斂必須在同一層之中處理。最後，我們對不同的適應性參數組合進行了測試，以在 0.1 Hz 到 1 Hz 追跡頻率下達成最佳的追踪性能。具體來說，實驗結果顯示適應性積分逆步控制器在追踪 1 Hz 弦波參考軌跡時，能夠達成 0.738◦ 的均方根誤差（RMSE）和 1.765◦ 的最大誤差。

Pneumatic muscle actuators (PMAs) are highly regarded for their high power-to-weight ratio, flexible structural design, and ease of maintenance, making it suitable for robot applications that require close interaction with human bodies. In this study, the rotating motion of a 1 DOF manipulator actuated by dual PMAs is controlled by a proportional control valve through regulation of the pressure of dual PMAs. For stability of various layers of nonlinear dynamics, a backstepping controller is chosen and an integral state is augmented to reduce steady-state tracking error. Moreover, an adaptive controller is added to compensate for the time-varying uncertainties in the system such as the flexibility of the PMAs so as to achieve consistent and accurate performance tracking trajectories of various frequencies. Different from the traditional backstepping controller which is typically applied to systems of strict feedback form, in this research, the dual PMA actuated manipulator is in a non-strict feedback form as the single control command to the proportional control valve simultaneously affects both pressure states of the dual PMAs. Therefore, the convergence of the two pressure states is rendered in the same layer in derivation of the integral state augmented backstepping controller. In the end, various combinations of adaptive parameters are examined for optimum tracking performance from 0.1 Hz to 1 Hz. Specifically, the experimental results show that the adaptive integral backstepping controller achieves an average root mean square error (RMSE) of 0.738◦ and a maximum error of 1.765◦ tracking a sinusoidal reference trajectory of 1 Hz.

[1] C.-P. Chou and B. Hannaford, “Measurement and modeling of mckibben pneumatic artificial muscles,” IEEE Transactions on robotics and automation, vol. 12, no. 1, pp. 90–102, 1996.
[2] D. Reynolds, D. Repperger, C. Phillips, and G. Bandry, “Modeling the dynamic characteristics of pneumatic muscle,” Annals of biomedical engineering, vol. 31, pp. 310–317, 2003.
[3] C.-M. Chang, “Real-time adaptive integral backstepping control of a 1-dof manipulator driven by dual pneumatic muscle actuators,” Master’s thesis, National Taiwan University of Science and Technology, Taipei, 8 2022.
[4] 中華民國人口推估（2022 年至 2070 年）. 國家發展委員會, 2022, 臺灣.
[5] F. Daerden, D. Lefeber, et al., “Pneumatic artificial muscles: actuators for robotics and automation,” European Journal of Mechanical and Enviromental Engineering, vol. 47, no. 1, pp. 11–22, 2002.
[6] C.-P. Chou and B. Hannaford, “Static and dynamic characteristics of mckibben pneumatic artificial muscles,” in Proceedings of the 1994 IEEE international conference on robotics and automation, pp. 281–286, IEEE, 1994.
[7] B. Coetzee, Z. Hweju, and K. Abou-El-Hossein, “Development of a pneumatic muscle actuator system for a robotic hand,” International Journal of Mechanical Engineering and Robotics Research, vol. 11, no. 9, 2022.
[8] A. D. D. R. Carvalho, N. Karanth, and V. Desai, “Characterization of pneumatic muscle actuators and their implementation on an elbow exoskeleton with a novel hinge design,” Sensors and Actuators Reports, vol. 4, p. 100109, 2022.
[9] S. A. Al-Ibadi, L. A. Al-Abeach, and M. A. Al-Ibadi, “Experimental modeling of pneumatic muscle actuator,” in 2022 Iraqi International Conference on Communication and Information Technologies (IICCIT), pp. 153–158, IEEE, 2022.
[10] B. Tondu, “Static modeling of pneumatic artificial muscle actuator,” in 2022 IEEE 5th International Conference on Soft Robotics (RoboSoft), pp. 364–369, IEEE, 2022.
[11] M.-K. Chang and J.-C. Wu, “Tracking control of a 2-dof arm actuated by pneumatic muscle actuators using adaptive fuzzy sliding mode control,” Journal of System Design and Dynamics, vol. 1, no. 2, pp. 257–269, 2007.
[12] T.-C. Tsai and M.-H. Chiang, “Design and control of a 1-dof robotic lower-limb system driven by novel single pneumatic artificial muscle,” Applied Sciences, vol. 10, no. 1, p. 43, 2019.
[13] L.-W. Lee, L.-Y. Lu, I.-H. Li, C.-W. Lee, and T.-J. Su, “Design and control of 6-dof robotic manipulator driven by pneumatic muscles and motor,” Sens. Mater, vol. 33, pp. 3081–3100, 2021.
[14] F.-G. Zhang, “Adaptive backstepping control for a pneumatic muscle actuated 1-dof manipulator,” Master’s thesis, National Taiwan University of Science and Technology, Taipei, 2020.
[15] C.-W. Chiang, “Real-time adaptive integral backstepping control of a single pneumatic muscle actuated 1-dof manipulator,” Master’s thesis, National Taiwan University of Science and Technology, Taipei, 8 2021.
[16] Y.-H. Hsieh, “Design and fabrication of pneumatic muscle lower back support wear,” Master’s thesis, National Taiwan University of Science and Technology, Taipei, 8 2019.
[17] P.-Y. Ou, “Model-based design and fabrication of pneumatic muscle actuators,” Master’s thesis, National Taiwan University of Science and Technology, Taipei, 8 2018.
[18] S.-Y. Luo, “Ukf pressure observer based adaptive integral backstepping control of a single pneumatic muscle actuated 1-dof manipulator,” Master’s thesis, National Taiwan University of Science and Technology, Taipei, 8.
[19] G. Andrikopoulos, G. Nikolakopoulos, and S. Manesis, “Advanced nonlinear pid-based antagonistic control for pneumatic muscle actuators,” IEEE Transactions on Industrial Electronics, vol. 61, no. 12, pp. 6926–6937, 2014.
[20] H. A. Al-Mosawi, A. Al-Ibadi, and T. Y. Abdalla, “An adaptive parallel fuzzy and proportional integral controller (apfpic) for the contractor pneumatic muscle actuator position control,” in 2022 International Conference on Electrical, Computer, Communications and Mechatronics Engineering (ICECCME), pp. 1–6, IEEE, 2022.
[21] H. Al-Mosawi, A. Al-Ibadi, and T. Abdalla, “A comprehensive comparison of different control strategies to adjust the length of the soft contractor pneumatic muscle actuator,” Iraqi J. Electr. Electron. Eng., vol. 18, no. 2, pp. 101–109, 2022.
[22] C.-J. Chiang and Y.-C. Chen, “Incremental fuzzy sliding mode control of pneumatic muscle actuators,” Int. J. Innov. Comput. Inf. Control, vol. 14, pp. 1917–1928, 2018.
[23] C.-J. Chiang and Y.-C. Chen, “Neural network fuzzy sliding mode control of pneumatic muscle actuators,” Engineering Applications of Artificial Intelligence, vol. 65, pp. 68–86, 2017.
[24] P. Carbonell, Z. Jiang, and D. Repperger, “Nonlinear control of a pneumatic muscle actuator: backstepping vs. sliding-mode,” in Proceedings of the 2001 IEEE International Conference on Control Applications (CCA’01)(Cat. No. 01CH37204), pp. 167–172, IEEE, 2001.
[25] P. Ioannou and B. Fidan, Adaptive control tutorial. SIAM, 2006.
[26] P. V. Kokotovic, “The joy of feedback: nonlinear and adaptive,” IEEE Control Systems Magazine, vol. 12, no. 3, pp. 7–17, 1992.
[27] M. Smaoui, X. Brun, and D. Thomasset, “A study on tracking position control of an electropneumatic system using backstepping design,” Control Engineering Practice, vol. 14, no. 8, pp. 923–933, 2006.
[28] D. Meng, B. Lu, C. Tang, and Q. Li, “Disturbance-observer-based backstepping controller for position tracking error constrained electro-pneumatic servo systems,” in 2018 37th Chinese Control Conference (CCC), pp. 3687–3692, IEEE, 2018.