Document Type : Research Articles


1 Department of Electrical and Robotic Engineering, Shahrood University of Technology, Shahrood, Iran

2 Department of Electrical and Robatic Enbineering ,Shahrood University of Technology,Iran

3 Department of Electrical Engineering, Shahrood University of Technology, Shahrood, Iran


This paper presents a novel optimal impedance voltage-controller for Electrically Driven Lower Limb Rehabilitation Robots (EDLR). To overcome the dynamical complexities, and handle the uncertainties, the proposed method employs an expected forward model of the actuator. The difference between this model’s output and the actual output represents the existing value of lamped uncertainty. A voltage-controller is designed based on this uncertainty estimator, which compensate for the uncertainties. Parameters of the controller have been optimized using genetic algorithms. Key contributions of this paper are I) estimation of the uncertainty by the expected model’s output, II) overcoming the changes in motor parameters, III) introducing a class of closed-loop system termed as “Repeatable”, and IV) designing an optimal impedance voltage-controller that is non-sensitive to the parameter variations. Significant merits of the approach are swift calculations, efficiency, robustness, and guaranteed stability. Furthermore, the simplicity of design, ease of implementation and model-free independent joint structure of the approach are noticeable. The method is compared with an adaptive robust sub-controller and a Taylor-series-based adaptive robust controller, through simulations in passive range of motion and active assistive rehabilitation exercises. The results show the superiority of the proposed method in tracking performance and the time of calculations.


Main Subjects

[1] F. Molteni, G. Gasperini, G. Cannaviello, and E.
Guanziroli, “Exoskeleton and End-Effector Robots for
Upper and Lower Limbs Rehabilitation: Narrative Review,”
PM&R, Vol. 10, No. 9S2, pp. 174-188, Sep. 2018.

[2] JK. Mohanta, S. Mohan, P. Deepasundar, and R .
Kiruba-Shankar, “Development and control of a new
sitting-type lower limb rehabilitation robot,” Comput
Electr Eng, Vol. 67, pp. 330-347, Apr. 2017.

[3] SF. Atashzar, M. Shahbazi, and R. V. Patel,
“Haptics-enabled Interactive NeuroRehabilitation
Mechatronics: Classification, Functionality, Challenges
and Ongoing Research,” Mechatronics, Vol. 57, pp.
001-019, Feb. 2019.

[4] W. Meng, Q. Liu, Z. Zhou, Q. Ai, B. Sheng, and SS. Xie,
“Recent development of mechanisms and control
strategies for robot-assisted lower limb rehabilitation,”
Mechatronics, Vol. 31, pp. 132-145, Oct. 2015.

[5] H. Huang, DL. Crouch, M. Liu, GS. Sawicki, and D.
Wang, “A Cyber Expert System for Auto-Tuning Powered
Prosthesis Impedance Control Parameters,” Ann Biomed
Eng, Vol. 44, pp. 1613-1624, Sep. 2015.

[6] H. Erdogan, Y. Palaska, E. Masazade, D. Erol Barkana,
and HK. Ekenel, “Vision-based game design and
assessment for physical exercise in a robot-assisted
rehabilitation system,” IET Comput Vis, Vol. 12, No. 1,
pp. 059-068, Feb. 2018.

[7] E. Akdoğan, ME. Aktan, AT. Koru, M. Selçuk Arslan, M.
Atlıhan, and B. Kuran, “Hybrid impedance control of a
robot manipulator for wrist and forearm rehabilitation:
Performance analysis and clinical results,” Mechatronics,
Vol. 49, pp. 077-091, Feb. 2018.

[8] SM. Ahmadi, and M. M. Fateh, “Robust control of
electrically driven robots using adaptive uncertainty
estimation,” Comput Electr Eng, Vol. 56, No. C, Nov.

[9] E. Akdoǧan, and MA. Adli, “The design and control of a
therapeutic exercise robot for lower limb rehabilitation:
Physiotherabot,” Mechatronics, Vol. 21, No. 3, pp.
509-522, Apr. 2011.

[10] J. Wu, J. Gao, R. Song, R. Li, Y. Li, and L. Jiang, “The
design and control of a 3DOF lower limb rehabilitation
robot,” Mechatronics, Vol. 33, pp. 013-022, Feb. 2016.

[11] M. M. Fateh, and V. Khoshdel, “Voltage-based adaptive
impedance force control for a lower-limb rehabilitation
robot,” Adv Robot, Vol. 29, No. 15, pp. 961-971, Apr.

[12] S. Mohan, JK. Mohanta, S. Kurtenbach, J. Paris, B. Corves,
and M. Huesing, “Design, development and control of a
2PRP-2PPR planar parallel manipulator for lower limb
rehabilitation therapies,” Mech Mach Theory, Vol. 112, pp.
272-294, Jun. 2017.

[13] M.M. Fateh, “On the Voltage-Based Control of Robot
Manipulators,” Int J Control Autom Syst, Vol. 6, pp.
702-712, 2008.

[14] S. Fateh, and M. M. Fateh, “Adaptive Fuzzy Control of
Robot Manipulators with Asymptotic Tracking
Performance,” J Control Autom Electr Syst, Vol. 31, pp.
052-061, Oct. 2019.

[15] M. M. Fateh, and S. Khorashadizadeh, “Optimal robust
voltage control of electrically driven robot manipulators,”
Nonlinear Dyn, Vol. 70, No. 2, pp. 1445-1458, Oct. 2012.

[16] S. Khorashadizadeh, and M. M. Fateh, “Uncertainty
estimation in robust tracking control of robot manipulators
using the Fourier series expansion,” Robotica, Vol. 35, No.
2, pp. 310-336, Feb. 2017.

[17] R. Shanmugasundram, K. M. Zakaraiah, and N. Yadaiah,
“Effect of parameter variations on the performance of
direct current (DC) servomotor drives,” JVC/Journal Vib
Control, Vol. 19, No. 10, pp. 1575-1586, Jul. 2013.

[18] S. Khorashadizadeh, and M. Sadeghijaleh, “Adaptive
fuzzy tracking control of robot manipulators actuated by
permanent magnet synchronous motors,” Comput Electr
Eng, Vol. 72, pp. 100-111, Nov. 2018.
[19] M. M. Fateh, and S. Khorashadizadeh, “Robust control of
electrically driven robots by adaptive fuzzy estimation of
uncertainty,” Nonlinear Dyn, Vol. 69, No. 3, pp.
1465-1477, Aug. 2012.

[20] A. Izadbakhsh, P. Kheirkhahan, and S. Khorashadizadeh,
“FAT-Based Robust Adaptive Control of Electrically
Driven Robots in Interaction with Environment,” Robotica,
Vol. 37, No. 5, pp. 779-800, May. 2019.

[21] S. M. Ahmadi, and M.M. Fateh, “On the Taylor series
asymptotic tracking control of robots,” Robotica, Vol. 37,
No. 3, pp. 405-427, Mar. 2019.

[22] L. Wang, Z. Du, W. Dong, Y. Shen, and G. Zhao,
“Intrinsic sensing and evolving internal model control of
compact elastic module for a lower extremity exoskeleton,”
Sensors (Switzerland), Vol. 18, No. 3, Mar. 2018.

[23] S. M. Hashem Zadeh, S. Khorashadizadeh, M. M. Fateh,
and M. Hadadzarif. “Optimal sliding mode control of a
robot manipulator under uncertainty using PSO,”
Nonlinear Dyn, Vol. 84, No. 4, Feb. 2016.

[24] M. M. Fateh, “Robust control of flexible-joint robots using
voltage control strategy,” Nonlinear Dyn, Vol. 67, pp.
15251537, Jan. 2012.

[25] M. Jalaeian-F, M. M. Fateh, and M. Rahimiyan,
“Optimal Predictive Impedance Control in the Presence of
Uncertainty for a Lower Limb Rehabilitation Robot,” J
Syst Sci Complex, Vol. 33, No. 3, Jun. 2020.

[26] M. Jalaeian-F, M. M. Fateh, and M. Rahimiyan,
Bi-Level Adaptive Computed-Current Impedance
Controller for Electrically Driven Robots,” Robotica,
Published online, 28 May 2020, pp. 1-17.

[27] C. Guo, S. Guo, J. Ji, and F. Xi, “Iterative Learning
Impedance for Lower Limb Rehabilitation Robot,” J
Healthc Eng, Vol. 2017, Article ID 6732459, 9 pages, Aug.

[28] J. F. Veneman , R. Kruidhof, E. E. G. Hekman, R.
Ekkelenkamp, E. H. F. Van Asseldonk, and H. Van Der
Kooij, “Design and evaluation of the LOPES exoskeleton
robot for interactive gait rehabilitation,” IEEE Trans
Neural Syst Rehabil Eng, Vol. 15, No. 3, pp. 379-386, Sep.

[29] G. A. Turley, M.A. Williams, R.M. Wellings, and D.R.
Griffin, “Evaluation of range of motion restriction within
the hip joint,” Med Biol Eng Comput, Vol. 51, No. 4, pp.
467-477, Dec. 2012.

[30] H. Fasih, S. Tavakoli, J. Sadeghi, and H. Torabi, “Kalman
Filter-Smoothed Random Walk Based Centralized
Controller for Multi-Input Multi-Output Processes,” Int J
Ind Electron Control Optim, Vol. 2, No. 2, pp. 155-166,
Spr. 2019.

[31] M. Jalaeian-F, M.M. Fateh, and M Rahimiyan, “Internal
Model Impedance Control for a Lower Limb
Rehabilitation Robot in the Presence of Uncertainty,” 26th
Iran. Conf. Electr. Eng. ICEE 2018, Mashhad, Iran: IEEE,
Vol. 2018, pp. 930-935, 2018.

[32] M. Jalaeian-F, M. M. Fateh, and M. Rahimiyan,
“Dynamic-Growing Fuzzy-Neural Acceleration-Based
Impedance Controller for a Lower Limb Rehabilitation
Robot,” Electr Eng (ICEE), Iran Conf 2018, Vol. 2018, pp.
1000-1004, 2018