Abstract
In this paper, an integrated human-in-the-loop simulation paradigm for the design and performance analysis of a 6 DOF lower extremity exoskeleton is presented. An adaptive Super Twisting Sliding Mode Controller (ASTSMC) is designed for the trajectory tracking control of the exoskeleton by considering the human motion as reference trajectory. The dynamic model, that include linear and rotational displacement of hip, knee and ankle joints of both the legs is developed using Lagrange energy formulation. The position and angular velocity error of the wearer and the exoskeleton are being considered to establish the control law. Super twisting SMC is a robust control scheme that works effectively in the presence of external disturbances and parameter variations. However, the STSMC introduces chattering in the closed loop because of its high gain, to overcome this drawback, an adaptive STSMC is proposed for the control of exoskeleton against unknown disturbances without chattering. An adaptation scheme using Lyapunov criterion is derived that ensures the stability of the system in closed loop. The performance of the proposed control strategy is verified by implementing on the integrated CAD model of the exoskeleton along with the wearer. The effectiveness of the controller is tested under wind disturbance of varying velocity and direction. The results demonstrate improved tracking performance of the proposed control scheme with least error and less control effort compared to constant gain STSMC in normal and uneven terrain.
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Huang, L., Steger, J. R., & Kazerooni, H. (2005). Hybrid control of the Berkeley lower extremity exoskeleton (BLEEX). ASME International Mechanical Engineering Congress and Exposition, 23, 1429–1436. https://doi.org/10.1115/IMECE2005-80109
Zoss, A. B., Kazerooni, H., & Chu, A. (2006). Biomechanical design of the Berkeley lower extremity exoskeleton (BLEEX). IEEE/ASME Transactions on Mechatronics, 11(2), 128–138. https://doi.org/10.1109/TMECH.2006.871087
Yan, L. J., Shen, Q. M., Yang, D., Qiao, J. M., & Datseris, P. (2019). Kinematic and dynamic modeling and analysis of a lower extremity exoskeleton. In 16th International conference on ubiquitous robots (IEEE) Jeju, Korea, June 24–27 (Vol. 7, pp. 625–630). https://doi.org/10.1109/URAI.2019.8768556.
Yanbei, L., Lei, Y., Hua, Q., Jian, W., Sen, M., & Na, L. (2014). Dynamics and kinematics analysis and simulation of lower extremity power-assisted exoskeleton. Journal of Vibroengineering, 16(2), 781–791. https://www.jvejournals.com/article/14857/pdf
Zhang, M., Guo, Y., & He, M. (2019). Dynamic analysis of lower extremity exoskeleton of rehabilitation robot. Proceedings of the 2019, 4th international conference on robotics, control and automation, ICRCA, (pp 128–131). https://doi.org/10.1145/3351180.3351207.
Mokhtaria, M., Taghizadehb, M., & Mazarea, M. (2018). Optimal adaptive super-twisting sliding mode control of a lower limb exoskeleton. Amirkabir Journal of Mechanical Engineering, 50(4):1–3. https://mej.aut.ac.ir/?_action=showPDF&sc=1&article=3631&_ob=2a6045c7bb60786b611bf1f86e291bdc&fileName=full_text.pdf
Zhanga, X., Jianga, W., Li, Z., & Song, S. (2019). A hierarchical Lyapunov-based cascade adaptive control scheme for lower-limb exoskeleton. European Journal of Control, 50, 198–208. https://doi.org/10.1016/j.ejcon.2019.06.003
Zhu, S., Jin, X., Yao, B., Chen, Q., Pei, X., & Pan, Z. (2016). Non-linear sliding mode control of the lower extremity exoskeleton based on human–robot cooperation. International Journal of Advanced Robotic Systems, 13(5), 1–10. https://doi.org/10.1177/1729881416662788
Zoss, A. B., Kazerooni, H., & Chu, A. (2005). On the mechanical design of the Berkeley lower extremity exoskeleton (BLEEX). IEEE/ASME Transactions on Mechatronics, 11(2), 128–138.
Bkekri, R., Benamor, A., Alouane, M. A., Fried, G., & Messaoud, H. (2018). Robust adaptive sliding mode control for a human-driven knee joint orthosis. Industrial Robot: An International Journal, 45(3), 379–389. https://doi.org/10.1108/IR-11-2017-0205
Rahmani, M., & Rahman, M. H. (2018). Novel robust control of a 7-DOF exoskeleton robot. PLoS ONE, 13(9), 1–18. https://doi.org/10.1371/journal.pone.0203440
Liu, J., Zhang, Y., Wang, J., & Chen, W. (2018). Adaptive sliding mode control for a lower-limb exoskeleton rehabilitation robot. 13th IEEE conference on industrial electronics and applications (ICIEA), (pp 1481–1486). https://doi.org/10.1109/ICIEA.2018.8397943(978-1-5386-6/18)
Yihao, D., Wang, H., Qiu, S., Yao, W., Xie, P., & Chen, X. (2018). An advanced adaptive control of lower limb rehabilitation robot. Frontiers in Robotics and AI, 5(116), 1–11. https://doi.org/10.3389/frobt.2018.00116
Islam, M. R., Rahmani, M., & Rahman, M. H. (2020). A novel exoskeleton with fractional sliding mode control for upper limb rehabilitation. Robotica, 38(11), 2099–2120. https://doi.org/10.1017/S0263574719001851
Amiri, M. S., Ramli, R., & Ibrahim, M. F. (2019). Initialized model reference adaptive control for lower limb exoskeleton. IEEE Transactions and Journals, 7, 167210–167220. https://doi.org/10.1109/Access.2019.2954110
Souza, R. S., de Castro, M. T., Furtado, G. P., & Forner-Cordero, A. (2018). Model reference adaptive impedance controller design for modular exoskeleton. International Federation of Automatic Control, 51(27), 345–349. https://doi.org/10.1016/j.ifacol.2018.11.616
Yun, D., Khan, A. M., Yan, R. J., Ji, Y., Jang, H., Iqbal, J., Zuhaib, K. M., Ahn, J. Y., Han, J., & Han, C. (2016). Handling subject arm uncertainties for upper limb rehabilitation robot using robust sliding mode control. International Journal of Precision Engineering and Manufacturing, 17(3), 355–362.
Chen, C., Zhang, S., Zhu, X., Shen, J., & Zhiyao, X. (2020). Disturbance observer-based patient-cooperative control of a lower extremity rehabilitation exoskeleton. International Journal of Precision Engineering and Manufacturing, 21(3), 957–968. https://doi.org/10.1007/s12541-019-00312-9
Li, Y., Guan, X., Tong, Y., et al. (2015). Design and simulation study of the translational-knee lower extremity exoskeleton. Mechanics, 21(3), 207–213
Bkekri, R., Benamor, A., Alouane, M. A., Fried, G., & Messaoud, H. (2018). Robust adaptive sliding mode control for a human-driven knee joint orthosis. Journal of Industrial Robot, 45(3), 379–389. https://doi.org/10.1108/IR-11-2017-0205
Rahmani, M., & Rahman, M. H. (2019). Adaptive neural network fast fractional sliding mode control of a 7-DOF exoskeleton robot. International Journal of Control, Automation and Systems, 18(10), 1–10. https://doi.org/10.1007/s12555-019-0155-1
Choo, J., & Park, J. H. (2017). Increasing payload capacity of wearable robots employing linear actuators and elastic mechanism. International Journal of Precision Engineering and Manufacturing, 18(5), 661–671.
Huang, G., Zhang, W., Meng, F., Zhangguo, Yu., Chen, X., Ceccarelli, M., & Huang, Q. (2018). Master–slave control of an intention-actuated exoskeletal robot for locomotion and lower extremity rehabilitation. International Journal of Precision Engineering and Manufacturing, 19(7), 983–991.
Hyun, D. J., Lim, H., Park, S., & Jung, K. (2017). Development of ankle-less active lower-limb exoskeleton controlled using finite leg function state machine. International Journal of Precision Engineering and Manufacturing, 18(6), 803–811.
Din, S. U., Khan, Q., Rehman, F. U., & Akmeliawanti, R. (2017). A comparative experimental study of robust sliding mode control strategies for under actuated systems. IEEE Access, 6, 1927–1939. https://doi.org/10.1109/ACCESS.2017.2780889
David, A. (2009). Biomechanics and motor control of human movement (4th ed.). Hoboken,NJ,USA: Wiley. https://doi.org/10.1002/9780470549148
Spong, M. W., Hutchinson, S., & Vidyasagar, M. (2000). Robot dynamics and control, 2nd Edition.
Ezhilarasi, D., & Nair, A. S. (2020). Performance analysis of super twisting sliding mode controller by ADAMS–MATLAB co-simulation in lower extremity exoskeleton. International Journal of Precision Engineering and Manufacturing-Green Technology, 7, 743–754.
Frdman, L., & Levant, A. (2002) Higher order sliding modes. In Sliding mode control in engineering (pp 53–101). Marcel Dekker.
Bartolini, G., Pisano, E., & Usai, E. (2003). A survey of application of second order sliding mode control to mechanical systems. International Journal of Control, 76(9), 875–892. https://doi.org/10.1080/0020717031000099010
Yue, C., Lin, X., Zhang, X., Qiu, J., & Cheng, H. (2018). Design and performance evaluation of a wearable sensing system for lower-limb exoskeleton, Applied Bionics and Biomechanics, 2018, 8610458. https://doi.org/10.1155/2018/8610458
Moreno, J. A., & Osorio, M. (2008). A lyapunov approach to second-order sliding mode controllers and observers. In Proceedings of 47th IEEE conference on decision and control (CDC 2008), Mexico (pp. 2856–2861). https://doi.org/10.1109/CDC.2008.4739356(978-1-4244-3124-3/08).
Moreno, J. A. (2009). A linear frame work for the robust stability of a generalized super-twisting algorithm. In Proceedings of sixth IEEE conference on electrical engineering, computing science and automatic control (CCE 2009), Toluca, Mexico, November 10–13, 2009. https://doi.org/10.1109/ICEEE.2009.5393477.
Avila, A. D., Moreno, J. A., & Fridman, L. (2009). Optimal lyapunov function selection for reaching time estimation of super twisting algorithm. Proceedings of 48thIEEE conference on decision and control (CDC2009) (pp 8405–8410). https://doi.org/10.1109/CDC.2009.5400466(978-1-4244-3872-3/09).
Levant, A. (2007). Principles of 2-sliding mode design. Automatica, 80(43), 576–586.
Shtessel, Y. B., Moreno, J. A., Plestan, F., Fridman, L. M., & Poznyak, A. S. (2010). Super-twisting adaptive sliding mode control: a Lyapunov design. 49th IEEE conference on decision and control (pp 5109–5113). https://doi.org/10.1109/CDC.2010.5717908(978-1-4244-7746-3/10).
Zakeri, E., Moezi, S. A., & Eghtesad, M. (2019). Optimal interval type-2 fuzzy fractional order super twisting algorithm: a second order sliding mode controller for fully-actuated and under-actuated nonlinear systems. ISA Transactions, 85(4), 13–32.
Utkin, V. I. (1992). Sliding modes in control and optimization, 1st edition, Springer-Verlag. ISBN 3-540-53516-0.
Yali, H., Aiquo, S., Haitao, G., & Songqing, Z. (2015). The muscle activation patterns of the lower limb during stair climbing at different backpack load. Acta of Bioengineering and Biomechanics., 17, 13–20. https://doi.org/10.5277/ABB-00155-2014-06
Sachs, P. (1972). Wind forces in engineering (1st ed.). Oxford: Pergamon Press.
Guoa, J., Li, W., Dinga, L., Guo, T., Gao, H., Huanga, B., & Denga, Z. (2020). High–slip wheel–terrain contact modelling for grouser–wheeled planetary rovers traversing on sandy terrains. Mechanism and Machine Theory, 153, 104032. https://doi.org/10.1016/j.mechmachtheory.2020.104032
Kumar, P., & Kumar, A. (2014) Human induced vibration in structures. National Conference on “Recent Advances in Mechanical Engineering”. International Journal of Mechanical Engineering and Robotic Design, Special Issue, 1(1), 44–54. http://www.ijmerr.com/uploadfile/2015/0828/20150828054606377.pdf
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Ezhilarasi, D., Nair, A.S. Modeling and Evaluation of Adaptive Super Twisting Sliding Mode Control in Lower Extremity Exoskeleton. Int. J. of Precis. Eng. and Manuf.-Green Tech. 8, 901–915 (2021). https://doi.org/10.1007/s40684-021-00335-6
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DOI: https://doi.org/10.1007/s40684-021-00335-6