Discrete-Time Backstepping Sliding Mode Control for a 2-DOF PAM-Based Exoskeleton
Main Article Content
Abstract
The objective of this study is to propose a discrete-time backstepping sliding mode control technique (BSMC) for regulating a pneumatic artificial muscle (PAM)-based exoskeleton used in rehabilitating human lower extremities. The PAM system is challenging to control due to its high nonlinearity, parameter uncertainty, and significant delay resulting from the use of compressed air. The backstepping control method is a recursive approach that systematically designs control laws for nonlinear and complicated systems. This technique ensures stable and robust system control, even in uncertain circumstances. Furthermore, the backstepping controller is capable of handling high-order systems and guaranteeing high-precision tracking of a desired trajectory. The incorporation of sliding mode control is aimed at enhancing the performance of the robot PAM system by reducing chattering and reaching time. The algorithm employs Lyapunov functions and sliding surfaces to design the control signal for operating the system. The study concludes with experimental scenarios demonstrating the effectiveness of the proposed approach.
Keywords
Pneumatic Artificial Muscle, Backstepping, Sliding Mode Control
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
[1] M. al Kouzbary, N. A. Abu Osman, A. K. Abdul Wahab, Sensorless control system for assistive robotic ankle-foot, Int J Adv Robot Syst, vol. 15, no. 3, May 2018, https://doi.org/10.1177/1729881418775854.
[2] Z. Wang, L. Quan, and X. Liu, Sensorless SPMSM position estimation using position estimation error suppression control and EKF in wide speed range, Math Probl Eng, vol. 2014, 2014, https://doi.org/10.1155/2014/480640.
[3] M. G. Antonelli, P. Beomonte Zobel, A. De Marcellis, and E. Palange, Design and characterization of a mckibben pneumatic muscle prototype with an embedded capacitive length transducer, Machines, vol. 10, no. 12, Dec. 2022, https://doi.org/10.3390/machines10121156.
[4] S. M. Mirvakili, I. W. Hunter, Artificial muscles: mechanisms, applications, and challenges, Advanced Materials, vol. 30, no. 6. Wiley-VCH Verlag, Feb. 2018, https://doi.org/10.1002/adma.201704407.
[5] J. Zhong, J. Fan, Y. Zhu, J. Zhao, and W. Zhai, One nonlinear pid control to improve the control performance of a manipulator actuated by a pneumatic muscle actuator, Advances in Mechanical Engineering, vol. 2014, 2014, https://doi.org/10.1155/2014/172782.
[6] G. Andrikopoulos, G. Nikolakopoulos and S. Manesis, Non-linear control of Pneumatic Artificial Muscles, 21st Mediterranean Conference on Control and Automation, Platanias, Greece, 2013, pp. 729-734, https://doi.org/10.1109/MED.2013.6608804.
[7] J. Wu, J. Huang, Y. Wang, K. Xing and Q. Xu, Fuzzy PID control of a wearable rehabilitation robotic hand driven by pneumatic muscles, 2009 International Symposium on Micro-NanoMechatronics and Human Science, Nagoya, Japan, 2009, pp. 408-413, https://doi.org/10.1109/MHS.2009.5352012.
[8] A. Koohestani and E. A. Moghadam, Controlling muscle-joint system by functional electrical stimulation using combination of PID and fuzzy controller, APCBEE Procedia, vol. 7, pp. 156-162, 2013, https://doi.org/10.1016/j.apcbee.2013.08.027.
[9] J. Zhao, J. Zhong, and J. Fan, Position control of a pneumatic muscle actuator using RBF neural network tuned PID controller, Math Probl Eng, vol. 2015, 2015, https://doi.org/10.1155/2015/810231.
[10] P. Pathak, S. B. Panday, and J. Ahn, Artificial neural network model effectively estimates muscle and fat mass using simple demographic and anthropometric measures, Clinical Nutrition, vol. 41, no. 1, pp. 144-152, Jan. 2022, https://doi.org/10.1016/j.clnu.2021.11.027.
[11] P. V. Kokotovic, The joy of feedback: nonlinear and adaptive, in IEEE Control Systems Magazine, vol. 12, no. 3, pp. 7-17, June 1992, http://doi.org/10.1109/37.165507.
[12] Y. Kim, T. H. Oh, T. Park, and J. M. Lee, Backstepping control integrated with Lyapunov-based model predictive control, J Process Control, vol. 73, pp. 137-146, Jan. 2019, https://doi.org/10.1016/j.jprocont.2018.12.007.
[13] T. Liard, I. Ismaıla Balogoun, S. Marx, and F. Plestan, Boundary sliding mode control of a system of linear hyperbolic equations: a Lyapunov approach, 2021.
[14] J. Wang, J. Liu, G. Zhang, and S. Guo, Periodic event-triggered sliding mode control for lower limb exoskeleton based on human-robot cooperation, ISA Trans, vol. 123, pp. 87-97, Apr. 2022, https://doi.org/10.1016/j.isatra.2021.05.039.
[15] L. Melkou and M. Hamerlain, High Order Homogeneous Sliding Mode Control for a Robot Arm with Pneumatic Artificial Muscles, IECON 2019 - 45th Annual Conference of the IEEE Industrial Electronics Society, Lisbon, Portugal, 2019, pp. 394-399, https://doi.org/10.1109/IECON.2019.8927339.
[16] L. Zhao, H. Cheng, and T. Wang, Sliding mode control for a two-joint coupling nonlinear system based on extended state observer, ISA Trans, vol. 73, pp. 130-140, Feb. 2018, https://doi.org/10.1016/j.isatra.2017.12.027.
[17] D. B. Reynolds, D. W. Repperger, C. A. Phillips, and G. Bandry, Modeling the dynamic characteristics of pneumatic muscle, Ann Biomed Eng, vol. 31, no. 3, pp. 310-317, 2003, https://doi.org/10.1114/1.1554921.
[18] T. Y. Choi and J. J. Lee, Control of manipulator using pneumatic muscles for enhanced safety, IEEE Transactions on Industrial Electronics, vol. 57, no. 8, pp. 2815-2825, Aug. 2010, https://doi.org/10.1109/TIE.2009.2036632.
[19] C. Schreiber, F. Moissenet, A multimodal dataset of human gait at different walking speeds established on injury-free adult participants, Sci Data, vol. 6, no. 1, Dec. 2019, https://doi.org/10.1038/s41597-019-0124-4.
[20] D. A. Winter, Biomechanics and Motor Control of Human Movement, John Wiley & Sons, 2009. https://doi.org/10.1002/9780470549148
[2] Z. Wang, L. Quan, and X. Liu, Sensorless SPMSM position estimation using position estimation error suppression control and EKF in wide speed range, Math Probl Eng, vol. 2014, 2014, https://doi.org/10.1155/2014/480640.
[3] M. G. Antonelli, P. Beomonte Zobel, A. De Marcellis, and E. Palange, Design and characterization of a mckibben pneumatic muscle prototype with an embedded capacitive length transducer, Machines, vol. 10, no. 12, Dec. 2022, https://doi.org/10.3390/machines10121156.
[4] S. M. Mirvakili, I. W. Hunter, Artificial muscles: mechanisms, applications, and challenges, Advanced Materials, vol. 30, no. 6. Wiley-VCH Verlag, Feb. 2018, https://doi.org/10.1002/adma.201704407.
[5] J. Zhong, J. Fan, Y. Zhu, J. Zhao, and W. Zhai, One nonlinear pid control to improve the control performance of a manipulator actuated by a pneumatic muscle actuator, Advances in Mechanical Engineering, vol. 2014, 2014, https://doi.org/10.1155/2014/172782.
[6] G. Andrikopoulos, G. Nikolakopoulos and S. Manesis, Non-linear control of Pneumatic Artificial Muscles, 21st Mediterranean Conference on Control and Automation, Platanias, Greece, 2013, pp. 729-734, https://doi.org/10.1109/MED.2013.6608804.
[7] J. Wu, J. Huang, Y. Wang, K. Xing and Q. Xu, Fuzzy PID control of a wearable rehabilitation robotic hand driven by pneumatic muscles, 2009 International Symposium on Micro-NanoMechatronics and Human Science, Nagoya, Japan, 2009, pp. 408-413, https://doi.org/10.1109/MHS.2009.5352012.
[8] A. Koohestani and E. A. Moghadam, Controlling muscle-joint system by functional electrical stimulation using combination of PID and fuzzy controller, APCBEE Procedia, vol. 7, pp. 156-162, 2013, https://doi.org/10.1016/j.apcbee.2013.08.027.
[9] J. Zhao, J. Zhong, and J. Fan, Position control of a pneumatic muscle actuator using RBF neural network tuned PID controller, Math Probl Eng, vol. 2015, 2015, https://doi.org/10.1155/2015/810231.
[10] P. Pathak, S. B. Panday, and J. Ahn, Artificial neural network model effectively estimates muscle and fat mass using simple demographic and anthropometric measures, Clinical Nutrition, vol. 41, no. 1, pp. 144-152, Jan. 2022, https://doi.org/10.1016/j.clnu.2021.11.027.
[11] P. V. Kokotovic, The joy of feedback: nonlinear and adaptive, in IEEE Control Systems Magazine, vol. 12, no. 3, pp. 7-17, June 1992, http://doi.org/10.1109/37.165507.
[12] Y. Kim, T. H. Oh, T. Park, and J. M. Lee, Backstepping control integrated with Lyapunov-based model predictive control, J Process Control, vol. 73, pp. 137-146, Jan. 2019, https://doi.org/10.1016/j.jprocont.2018.12.007.
[13] T. Liard, I. Ismaıla Balogoun, S. Marx, and F. Plestan, Boundary sliding mode control of a system of linear hyperbolic equations: a Lyapunov approach, 2021.
[14] J. Wang, J. Liu, G. Zhang, and S. Guo, Periodic event-triggered sliding mode control for lower limb exoskeleton based on human-robot cooperation, ISA Trans, vol. 123, pp. 87-97, Apr. 2022, https://doi.org/10.1016/j.isatra.2021.05.039.
[15] L. Melkou and M. Hamerlain, High Order Homogeneous Sliding Mode Control for a Robot Arm with Pneumatic Artificial Muscles, IECON 2019 - 45th Annual Conference of the IEEE Industrial Electronics Society, Lisbon, Portugal, 2019, pp. 394-399, https://doi.org/10.1109/IECON.2019.8927339.
[16] L. Zhao, H. Cheng, and T. Wang, Sliding mode control for a two-joint coupling nonlinear system based on extended state observer, ISA Trans, vol. 73, pp. 130-140, Feb. 2018, https://doi.org/10.1016/j.isatra.2017.12.027.
[17] D. B. Reynolds, D. W. Repperger, C. A. Phillips, and G. Bandry, Modeling the dynamic characteristics of pneumatic muscle, Ann Biomed Eng, vol. 31, no. 3, pp. 310-317, 2003, https://doi.org/10.1114/1.1554921.
[18] T. Y. Choi and J. J. Lee, Control of manipulator using pneumatic muscles for enhanced safety, IEEE Transactions on Industrial Electronics, vol. 57, no. 8, pp. 2815-2825, Aug. 2010, https://doi.org/10.1109/TIE.2009.2036632.
[19] C. Schreiber, F. Moissenet, A multimodal dataset of human gait at different walking speeds established on injury-free adult participants, Sci Data, vol. 6, no. 1, Dec. 2019, https://doi.org/10.1038/s41597-019-0124-4.
[20] D. A. Winter, Biomechanics and Motor Control of Human Movement, John Wiley & Sons, 2009. https://doi.org/10.1002/9780470549148