Knee Joint Movement Control Using Hybrid Neuro-prosthesis Based on Persistent D-well Time Allocation Strategy with Muscle Fatigue Overcoming: Simulation Approach

Document Type : Original Articles


1 PhD Candidate, Department of Electrical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

2 Associate Professor, Department of Electrical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

3 Associate Professor, Scientific Core of Robotic Rehabilitation and Biofeedback, Mashhad Branch, Islamic Azad University, Mashhad, Iran

4 Professor, Department of Electrical Engineering, Mashhad Branch, Islamic Azad University AND Department of Electrical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran



Introduction: Hybrid neuro-prostheses are used in rehabilitation of individuals with spinal cord injuries. These hybrid neuro-prostheses consist of a robot that moves the knee joint mechanically and a functional electrical stimulation (FES) part that moves the knee joint by electric current stimulation. The main challenge in the use of hybrid neuro-prostheses is muscle fatigue due to electrical stimulation. This study endeavored to reduce muscle fatigue through timing between robot and FES using Persistent D-well Time
Materials and Methods: A mathematical equation was used to model the knee movement in a hybrid neuro-prostheses. A differential equation was used to describe muscle fatigue. The simulation time was determined one hundred seconds and the goal of simulation was considered to regulate knee joint in angle of sixty degrees. Simulation time was divided into stages and a time interval was set for each stage. At each stage, FES was active for a certain time duration. After this duration until the end of the time frame of the stage, switch occurred between the FES and the robot, based on the muscle fatigue value.
Results: At the end of the simulation, the knee was regulated with a root mean square error of 0.79 degree at the reference angle. Using robots in the timing method reduced muscle fatigue and the muscle fatigue value was limited in a bounded range between 0.94 and 0.97.
Conclusion: The timing method simulated in this study can be effective for control of knee movement. Based on the results, it is expected that this method can be used in the control of hybrid neuro-prosthesis in practice during which the exercises prescribed by the therapist are rehearsed and the muscle fatigue increment need to be avoided in the client simultaneously.


  1. Anaya F, Thangavel P, Yu H. Hybrid FES robotic gait rehabilitation technologies: A review on mechanical design, actuation, and control strategies. Int J Intell Robot Appl 2018; 2(1): 1-28.
  2. Jun D, Wexler AS, Binder-Macleod SA. A predictive fatigue model. II. Predicting the effect of resting times on fatigue. IEEE Trans Neural Syst Rehabil Eng 2002; 10(1): 59-67.
  3. Popoviç DB. Hybrid FES-robot devices for training of activities of daily living. In: Colombo R, Sanguineti V, editors. Rehabilitation robotics. 1st Massachusetts, MA: Academic Press; 2018. p. 277-87.
  4. Baud R, Manzoori AR, Ijspeert A, Bouri M. Review of control strategies for lower-limb exoskeletons to assist gait. J Neuroeng Rehabil 2021; 18(1): 119.
  5. Dodson A. A novel user-controlled assisted standing control system for a hybrid neuroprosthesis [MSc Thesis]. Pittsburgh PA: University of Pittsburgh; 2018.
  6. Voloshina AS, Collins SH. Lower limb active prosthetic systems In: Rosen J, Ferguson PW, editors. Wearable robotics. London, UK: Academic Press; 2020. p. 469-86.
  7. Kirsch NA, Bao X, Alibeji NA, Dicianno BE, Sharma N. Model-based dynamic control allocation in a hybrid neuroprosthesis. IEEE Trans Neural Syst Rehabil Eng 2018; 26(1): 224-32.
  8. Zhang D, Ren Y, Gui K, Jia J, Xu W. Cooperative control for a hybrid rehabilitation system combining functional electrical stimulation and robotic exoskeleton. Front Neurosci 2017; 11: 725.
  9. Tu X, Li J, Li J, Su C, Zhang S, Li H, et al. Model-based hybrid cooperative control of hip-knee exoskeleton and fes induced ankle muscles for gait rehabilitation. Int J Patt Recogn Artif Intell 2017; 31(09): 1759019.
  10. Gil-Castillo J, Alnajjar F, Koutsou A, Torricelli D, Moreno JC. Advances in neuroprosthetic management of foot drop: A review. J Neuroeng Rehabil 2020; 17(1): 46.
  11. Bao X, Kirsch N, Dodson A, Sharma N. Model predictive control of a feedback-linearized hybrid neuroprosthetic system with a barrier penalty. J Comput Nonlinear Dyn 2019; 14(10): 101009-1010097.
  12. Sa-e S, Freeman CT, Yang K. Iterative learning control of functional electrical stimulation in the presence of voluntary user effort. Control Eng Pract 2020; 96: 104303.
  13. Kirsch N, Alibeji N, Sharma N. Nonlinear model predictive control of functional electrical stimulation. Control Eng Pract 2017; 58: 319-31.
  14. Bao X, Sheng Z, Dicianno BE, Sharma N. A tube-based model predictive control method to regulate a knee joint with functional electrical stimulation and electric motor assist. IEEE Trans Control Syst Technol 2021; 29(5): 2180-91.
  15. Bao X, Molazadeh V, Dodson A, Dicianno BE, Sharma N. Using person-specific muscle fatigue characteristics to optimally allocate control in a hybrid exoskeleton - preliminary results. IEEE Trans Med Robot Bionics 2020; 2(2): 226-35.
  16. Sheng Z, Sun Z, Molazadeh V, Sharma N. Switched control of an N-degree-of-freedom input delayed wearable robotic system. Automatica 2021; 125: 109455.
  17. Kirsch NA, Alibeji NA, Sharma N. Model predictive control-based dynamic control allocation in a hybrid neuroprosthesis. Proceedings of the ASME 2014 Dynamic Systems and Control Conference; 2014 Oct 22-24; San Antonio, TX, USA.
  18. Schauer T, Neg+Ñrd NO, Previdi F, Hunt KJ, Fraser MH, Ferchland E, et al. Online identification and nonlinear control of the electrically stimulated quadriceps muscle. Control Eng Pract 2005; 13(9): 1207-19.
  19. Popovic D, Stein RB, Oguztoreli N, Lebiedowska M, Jonic S. Optimal control of walking with functional electrical stimulation: A computer simulation study. IEEE Trans Rehabil Eng 1999; 7(1): 69-79.
  20. Riener R, Quintern J, Schmidt G. Biomechanical model of the human knee evaluated by neuromuscular stimulation. J Biomech 1996; 29(9): 1157-67.
  21. Veltink PH, Chizeck HJ, Crago PE, el-Bialy A. Nonlinear joint angle control for artificially stimulated muscle. IEEE Trans Biomed Eng 1992; 39(4): 368-80.
  22. Behn C, Siedler K. Adaptive PID-tracking control of muscle-like actuated compliant robotic systems with input constraints. Applied Mathematical Modelling 2019; 67: 9-21.
  23. Dorf RC, Bishop RH. Modern control systems. 12th Upper Saddle River, NJ: Pearson; 2010. p. 18-21
  24. Makowski NS, Fitzpatrick MN, Triolo RJ, Reyes RD, Quinn RD, Audu M. Biologically inspired optimal terminal iterative learning control for the swing phase of gait in a hybrid neuroprosthesis: A modeling study. Bioengineering (Basel) 2022; 9(2): 71.
  25. Kirsch NA, Bao X, Alibeji NA, Dicianno BE, Sharma N. Model-based dynamic control allocation in a hybrid neuroprosthesis. IEEE Trans Neural Syst Rehabil Eng 2018; 26(1): 224-32.
  26. Nunes WRBM, Alves UNLT, Sanches MAA, Teixeira MCM, de Carvalho AA. Electrically stimulated lower limb using a Takagi-Sugeno fuzzy model and robust switched controller subject to actuator saturation and fault under nonideal conditions. Int J Fuzzy Syst 2022; 24(1): 57-72.
  27. Bao X, Mao ZH, Munro P, Sun Z, Sharma N. Sub-optimally solving actuator redundancy in a hybrid neuroprosthetic system with a multi-layer neural network structure. Int J Intell Robot Appl 2019; 3(3): 298-313.
  28. Liberzon D. Switching in systems and control. Boston, MA: Birkhauser; 2003. p. 6-7.
  29. Khamar M, Edrisi M, Forghany S. Online usage of biomechanical and simulation software in analysis of rehabilitation robots performances by applying simulation technique. J Res Rehabil Sci 2019; 15(2): 72-8. [In Persian].
  30. Alibeji NA, Molazadeh V, Dicianno BE, Sharma N. A control scheme that uses dynamic postural synergies to coordinate a hybrid walking neuroprosthesis: Theory and experiments. Front Neurosci 2018; 12: 159.
  31. Wang H, Chen X, Wang J. H∞ sliding mode control for PDT-switched nonlinear systems under the dynamic event-triggered mechanism. Appl Math Comput 2022; 412: 126474.
  32. Kirsch N, Alibeji N, Dicianno BE, Sharma N. Switching control of functional electrical stimulation and motor assist for muscle fatigue compensation. Proceedings of the 2016 American Control Conference (ACC); 2016 July 6-8; Boston, MA, USA. p. 4865-70.
  33. Molazadeh V, Zhang Q, Bao X, Sharma N. An iterative learning controller for a switched cooperative allocation strategy during sit-to-stand tasks with a hybrid exoskeleton. IEEE Trans Control Syst Technol 2022; 30(3): 1021-36.
  34. Molazadeh V, Sheng Z, Sharma N. A within-stride switching controller for walking with virtual constraints: Application to a hybrid neuroprosthesis. Proceedings of the 2018 Annual American Control Conference (ACC); 2018 June 27-29; Milwaukee, WI, USA. p. 5286-91.
  35. Molazadeh V, Sheng Z, Bao X, Sharma N. A robust iterative learning switching controller for following virtual constraints: Application to a hybrid neuroprosthesis. IFAC-PapersOnLine 2019; 51(34): 28-33.
  36. Rakhtala SM. Adaptive gain super twisting algorithm to control a knee exoskeleton disturbed by unknown bounds. Int J Dyn Control 2021; 9(2): 711-26.
Volume 18, Issue 1
Pages 12-23
  • Receive Date: 22 July 2022
  • Revise Date: 15 January 2023
  • Accept Date: 02 January 2023
  • First Publish Date: 02 January 2023