Variable Impedance Control for Rehabilitation Robot using Interval Type-2 Fuzzy Logic

Document Type : Original Article


Center of Excellence on Soft Computing and Intelligent Information Processing, Mechanical Engineering Department, Ferdowsi University of Mashhad, Iran


In this study, a novel variable impedance control for a lower-limb rehabilitation robotic system using voltage control strategy is presented. The majority of existing control approaches are based on control torque strategy, which require the knowledge of robot dynamics as well as dynamic of patients. This requires the controller to overcome complex problems such as uncertainties and nonlinearities involved in the dynamic of the system, robot and patients. On the other hand, how impedance parameters must be selected is a serious question in control system design for rehabilitation robots. To resolve these problems this paper, presents a variable impedance control based on the voltage control strategy. In contrast to the usual current-based (torque mode) the use of motor dynamics lees to a computationally faster and more realistic voltage-base controller. The most important advantage of the proposed control strategy is that the nonlinear dynamic of rehabilitation robot is handled as an external load, hence the control law is free from robot dynamic and the impedance controller is computationally simpler, faster and more robust with negligible tracking error. Moreover, variable impedance parameters based on Interval Type-2 Fuzzy Logic (IT2Fl) is proposed to evaluate impedance parameters. The proposed control is verified by a stability analysis. To illustrate the effectiveness of the control approach, a 1-DOF lower-limb rehabilitation robot is designed. Voltage-based impedance control are simulated through a therapeutic exercise consist of Isometric and Isotonic exercises. Simulation results show that the proposed voltage-based variable impedance control is superior to voltage-based impedance control in therapeutic exercises.


[1]     E. Akdogan and M. Arif Adli. “The design and control of a therapeutic exercise robot for lower limb rehabilitation: Physiotherabot”, Mechatronics, Vol. 21, (2011), pp. 509–522.
[2]     M. S. Ju, C. C. K. Lin, D. H. Lin, I. S. Hwang and S. M. Chen, “A rehabilitation robot with force-position hybrid fuzzy controller: Hybrid fuzzy control of rehabilitation robot”, IEEE Transactions on Neural Systems and Rehabilitation Engineering, Vol. 13(3), (2005), pp. 349–358.
[3]     PA. Houglum, “Therapeutic exercises for musculoskeletal injuries”, ThomsonShore, 2009.
[4]     M. Bernhardt, M. Frey, G. Colombo, and R. Riener,“Hybrid force-position control yields cooperative behaviour of the rehabilitation robot LOKOMAT”, In 9th International Conference on Rehabilitation Robotics, ICORR2005, (2005), pp. 536–539.
[5]     H. I. Krebs, N. Hogan, M. L. Aisen, and B. T. Volpe, “Robot aided neurorehabilitation”, IEEE Transactions on Rehabilitation Engineering, 6(1), (1998), pp. 75–87.
[6]     R. Richardson, M. Brown, M. Bhakta and M. C. Levesley, “Design and control of a three degree of freedom pneumatic physiotherapy robot”. Robotica, 21, (2003), pp. 589–604.
[7]     T. Tsuji, and Y. Tanaka, “On-line learning of robot arm impedance using neural networks” Robot. Auton. Syst. Vol. 52, (2005), pp. 257–271.
[8]     T. Tsuji and Y. Tanaka, “Tracking control properties of human-robotic systems based on impedance control”, IEEE Trans. Syst. Man Cybern., Vol. 35, (2005), pp. 523–535.
[9]     C. Yueyan, Z. Ji, W. Bidou and H. Shuang, “High-Precision Fuzzy Impedance Control Algorithm and Application in Robotic Arm”, International Conference on Advanced Intelligent Mechatronic Monterey, Colifornia, USA, (2005), pp. 24-28.
[10]  M. M Fateh and V. Khoshdel, “Voltage-Based Adaptive Impedance Force Control for a Lower-Limb Rehabilitation Robot”, Advanced Robotic, Vol. 12, (2015), pp. 1-15.
[11]  R. Z. Stanisic and A. V. Fernandez, “Adjusting the Parameters of the mechanical impedance for Velocity, impact and force control”, Robotica, Vol. 30, (2012), pp. 583-597.
[12]  S. Kizir and Z. bingul, “Fuzzy Impedance and Force Control of Stewart Platform”, Journal of Electrical Engineering & Computer Sciences, (2013).
[13]  G. Xu, A. Song and H. Li, “Control System Design for an Upper-Limb Rehabilitation Robot”, Advanced Robotics, Vol. 25, pp. 229-251.
[14]  G. Xu, A. Song and H. Li, “Adaptive Impedance Control for Upper-Limb Rehabilitation Robot Using Evolutionary Dynamic Recurrent Fuzzy Neural Network”, Journal of Intelligent Robot System, Vol. 62, (2011), pp. 501–525.
[15]  L. Huanga, S. S. Geb and T. H. Leeb, “Fuzzy unidirectional force control of constrained robotic manipulators”, Fuzzy Sets and Systems, Vol. (134), (2003), pp. 135–146.
[16]  D. Surdilovic and Z. Cojbasic, “Robust Robot Compliant Motion Control Using Intelligent Adaptive Impedance Approach”, International Conference on Robotics & Automation Detroit, Michigan, May 1999.
[17]  M. M. Fateh, “On the voltage-based control of robot manipulators”, International Journal of Control, Automation, and Systems, Vol. 6(5), (2008), pp. 702–712.
[18]  J. M. Mendel. “Uncertain Rule-based Fuzzy Logic Systems: Introduction and New Directions”, Upper Saddle River, N. J: Prentice-Hall, 2001.
[19]  H. A. Hagras, “A hierarchical type-2 fuzzy logic control architecture for autonomous mobile Robots”, IEEE Transactions on Fuzzy Systems, Vol. 12(4), (2004), pp. 524-539.
[20]  L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning”, Information Sciences, Vol. 8(3), (1975), pp. 199-249.
[21]  V. Khoshdel and A. Akbarzadeh, “Robust Impedance Control for Rehabilitation Robot”, Modares Mechanical Engineering Vol.15(8), (2015), pp.429-437 (In Persian).
[22]  Q. L. Liang and J. M. Mendel, “Interval type-2 fuzzy logic systems: Theory and design”, IEEE Transactions on Fuzzy Systems, Vol. 8(5), (2000), pp. 535-550.
[23]  M. Biglarbegian, W. W. Melek and J. M. Mendel, “On the stability of interval type-2 TSK fuzzy logic control systems”, IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, Vol. 40(3), (2010), pp. 798-818.
[24]  L. X. Wang, “A Course in Fuzzy Systems and Control”, NewYork: Prentice Hall, (1996).