Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-19T14:55:06.607Z Has data issue: false hasContentIssue false
  • English
  • Français

A robust control scheme for a 2PUS+RR parallel robot for ankle rehabilitation

Published online by Cambridge University Press:  27 July 2023

Erick D. Flores-Salazar ,
Esther Lugo-González Open the ORCID record for Esther Lugo-González [Opens in a new window] ,
Manuel Arias-Montiel Open the ORCID record for Manuel Arias-Montiel [Opens in a new window]  and
Jaime Gallardo-Alvarado Open the ORCID record for Jaime Gallardo-Alvarado [Opens in a new window]
Erick D. Flores-Salazar
Affiliation:
Postgraduate Division, Technological University of Mixteca, Oaxaca, México
Esther Lugo-González*
Affiliation:
Institute of Electronics and Mechatronics, Technological University of Mixteca, Oaxaca, México
Manuel Arias-Montiel
Affiliation:
Institute of Electronics and Mechatronics, Technological University of Mixteca, Oaxaca, México
Jaime Gallardo-Alvarado
Affiliation:
Department of Mechanical Engineering, Technological Institute of Celaya, Guanajuato, México
*
Corresponding author: Esther Lugo-González; Email: elugog@mixteco.utm.mx
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents a robust adaptive controller based on the backstepping technique using an extended state observer (ESO), implemented on a 2PUS+RR parallel robot, to minimize the trajectory tracking error. The proposed backstepping-ESO controller scheme is designed to compensate for the robot’s structured (parametric) and unstructured (nonlinear friction, external disturbances, and dynamics) uncertainties. The overall stability of the controller is guaranteed by the Lyapunov theory. Cosimulation in MATLAB-Simulink and ADAMS View is presented to validate the results of the ESO and backstepping controller implemented in the virtual and physical prototype. For the virtual prototype, it was determined that the system is stable in 2 s and presents a maximum absolute error of 3.5 × $10^{-6}$ m for the actuator position and 2.8 × $10^{-5}$ rad for mobile platform orientation. Regarding the physical robot, a maximum absolute error of 5 × $10^{-4}$ m for the actuator position and 0.0575 rad for the orientation of the robot mobile platform values do not represent a problem for ankle rehabilitation movements. Experimental results were also presented and compared with ankle motion to demonstrate that the applied control system meets the motion requirements of the ankle rehabilitator.

Keywords

adaptable controlextended state observerparallel robotpassive rehabilitationmovement control
Type
Research Article
Information
Robotica , Volume 41 , Issue 11 , November 2023 , pp. 3296 - 3313
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Mazare, M. and Taghizadeh, M., “Adaptive back-stepping robust control of a 3-[P2(US)] parallel robot on optimal trajectory,” Int. Robot. Autom. J. 5(3), 101–110 (2019).CrossRefGoogle Scholar
Alyoussef, F. and Kaya, I., “A Review on Nonlinear Control Approaches: Sliding Mode Control, Back-Stepping Control and Feedback linearization Control,” In: International Engineering and Natural Sciences Conference (IENSC 2019), Diyarbakır, Turkey (2019).Google Scholar
Zeinali, M. and Notash, L., “Adaptive sliding mode control with uncertainty estimator for robot manipulators,” Mech. Mach. Theory 45(1), 80–90 (2010).CrossRefGoogle Scholar
Dachang, Z., Baolin, D., Puchen, Z. and Wu, W., “Adaptive backstepping sliding mode control of trajectory tracking for robotic manipulators,” Complexity 2020(1), 1–11 (2020).Google Scholar
Yu, J., Shi, P. and Zhao, L., “Finite-time command filtered backstepping control for a class of nonlinear systems,” Automatica 92(1), 173–180 (2018).CrossRefGoogle Scholar
Coutinho, A. and Hess-Coelho, T., “Improving the performance of parallel robots by applying distinct hybrid control techniques,” Robotica 40(4), 951–975 (2022).CrossRefGoogle Scholar
Wang, Y., Lin, Q., Zhou, L., Shi, X. and Wang, L., “Backstepping sliding mode robust control for a wire-driven parallel robot based on a nonlinear disturbance observer,” Math. Probl. Eng. 2020(1), 1–17 (2020).Google Scholar
Azcaray, H., Blanco, A., García, C., Adam, M., Reyes, J., Guerrero, G. and Guzmán, G., “Robust GPI control of a new parallel rehabilitation robot of lower extremities,” Int. J. Control Autom. Syst. 16(5), 2384–2392 (2018).CrossRefGoogle Scholar
Guzmán-Valdivia, C. H., Carrera-Escobedo, J. L., Blanco-Ortega, A., Oliver-Salazar, M. A. and Gómez-Becerra, F. A., “Diseño y control de un sistema interactivo para la rehabilitación de tobillo: TobiBot,” Ingenier. Mecáni. Tecnolog. Desarroll. 5(1), 255–264 (2014).Google Scholar
Sinasi-Ayas, M., Hakki-Altas, I. and Sahin, E., “Fractional order-based trajectory tracking control of an ankle rehabilitation robot,” Trans. Inst. Meas. Control 40(2), 550–564 (2018).CrossRefGoogle Scholar
Magadán, A., Blanco, A., Gama, K. and Abúndez, A., “Mechatronic Integral Ankle Rehabilitation System: Ankle Rehabilitation Robot, Serious Game, and Facial Expression Recognition System,” In: Advanced Topics on Computer Vision, Control and Robotics in Mechatronics (Springer, Cham, 2018).Google Scholar
Chen, G., Zhou, Z., Vanderborght, B., Wang, N. and Wang, Q., “Proxy-based sliding mode control of a robotic ankle-foot system for post-stroke rehabilitation,” Adv. Robot. 30(15), 992–1003 (2016).CrossRefGoogle Scholar
Li, J., Zuo, S., Zhang, L., Dong, M., Zhang, Z., Tao, C. and Ji, R., “Mechanical design and performance analysis of a novel parallel robot for ankle rehabilitation,” ASME. J. Mech. Robot. 12(5), 1–17 (2020).CrossRefGoogle Scholar
Wang, L., Chang, Y. and Zhu, H., “Internal model control and experimental study of ankle rehabilitation robot,” Robotica 38(5), 940–956 (2020).CrossRefGoogle Scholar
Dong, M., Wenpei, F., Jianfeng, L., Xiaodong, Z., Xi, R., Yuan, K. and Yu, Z., “A new ankle robotic system enabling whole-stage compliance rehabilitation training,” IEEE/ASME Trans. Mechatron. 26(3), 1490–1500 (2021).CrossRefGoogle Scholar
Zhang, M., Mcdaid, A., Veale, A. J., Peng, Y. and Xie, S. Q., “Adaptive trajectory tracking control of a parallel ankle rehabilitation robot with joint-space force distribution,” IEEE Access. 7(1), 85812–85820 (2019).CrossRefGoogle Scholar
Qingsong, A., Chengxiang, Z., Jie, Z., Meng, W., Liu, Q., Xie, S. Q. and Yang, M., “Disturbance estimated adaptive backstepping sliding mode control of a pneumatic muscles-driven ankle rehabilitation robot,” Sensors (Basel) 18(66), 1–21 (2018).Google Scholar
Salimi-Lafmejani, A., Tale-Masouleh, M. and Kalhor, A., “Trajectory tracking control of a pneumatically actuated 6-DOF Gough-Stewart parallel robot using Backstepping-Sliding Mode controller and geometry-based quasi forward kinematic method,” Robot. Comput. Integr. Manuf. 54(1), 96–114 (2018).CrossRefGoogle Scholar
Mohanta, J. K., Mohan, S., Takeda, Y. and Corves, B., “Adaptive Backstepping Motion Control of a New Sitting-type Lower Limb Rehabilitation Robot,” In: Advances in Mechanism and Machine Science. IFToMM WC 2019. Mechanisms and Machine Science, IFToMM, Krakow, Poland (Uhl, T., ed.) (2019).Google Scholar
Shi, G., Wu, Z., He, T., Li, D., Ding, Y. and Liu, S., “Decentralized active disturbance rejection control design for the gas turbine,” Meas. Control 53(9-10), 1589–1601 (2020).CrossRefGoogle Scholar
Linares, J., Hernández, A., Guerrero, J. F., Mino, G., Espinosa, E. and Zurita, E. W., “Decentralized ADR Angular Speed Control for Load Sharing in Servomechanisms,” In: 2018 IEEE Power and Energy Conference at Illinois, PECI, Champaign, IL, USA (2018).Google Scholar
Flores-Salazar, E. D., Arias-Montiel, M., Lugo-González, E., Gallardo-Alvarado, J. and Tapia Herrera, R., “Alternative Methods for Direct Kinematic Analysis of a Parallel Robot for Ankle Rehabilitation,” In: New Trends in Medical and Service Robotics, MESROB 2020, Mechanisms and Machine Science (Uhl, T., ed.) (Springer, Cham, 2021).Google Scholar
Flores-Salazar, E. D., Garcí-Murillo, M. A., Lugo-González, E., Gallardo-Alvarado, J. and Arias-Montiel, M., “Análisis cinemático de un robot paralelo 2-PUS+RR aplicado a un rehabilitador de tobillo,” In: Modelación Matemática III, Biomatemáticas e Ingeniería (Barrangan-Mendoza, F., Palafox-Delgado, S. and Santiago Santos, A., eds.) (Universidad Tecnológica de la Mixteca, Oaxaca, 2019).Google Scholar
Garcia-Murillo, M. A., Takeda, Y., Castillo-Castaneda, E., Matsuura, D., Kawasumi, S. and Gallardo-Alvarado, J., “Kinematics and Dynamics of a 3-RPSR Parallel Robot Used as a Pipe-Bending Machine,” In: Advances in Robot Kinematics 2014 (Springer, Cham, 2014).Google Scholar
Khalil, H. K., Nonlinear Systems (Prentice Hall, New York, 2002).Google Scholar
Blanco, A., Gomez, F., Vela, L. and Delgado, R., “A Generalized Proportional Integral Controller for an Ankle Rehabilitation Machine Based on an XY Table,” In: Proceedings of 2013 International Conference on Mechatronics, Electronics and Automotive Engineering, ICMEAE, Morelos, México (2013).Google Scholar
Lippert, L., Clinical Kinesiology and Anatomy (F.A. Davis Company, Philadelphia, PA, 2006).Google Scholar
McConville, J., “Elementary Adams Theory,” In: Introduction to Mechanical Systems Simulation Using Adams (SDC Publications, Kansas, 2015).Google Scholar
Moore, H., “Acerca de Matlab,” In: MATLAB Para Ingenieros (Prentice Hall, Naucalpan de Juárez, 2009).Google Scholar
Andrade, R. J., Lacourpaille, L., Freitas, S. R., Mcnair, P. J. and Nordez, A., “Effects of hip and head position on ankle range of motion, ankle passive torque, and passive gastrocnemius tension,” Scand. J. Med. Sci. Sports 1(4), 1–7 (2016).Google Scholar