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Impedance control based on optimal adaptive high order super twisting sliding mode for a 7-DOF lower limb exoskeleton

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Abstract

In this paper, a novel hybrid optimal Adaptive High-Order Super Twisting Sliding Mode (AHOSTWSM) impedance control is proposed for a lower limb exoskeleton robot with 7 active joints, which takes the interaction forces between the robot and the user into account. First, the dynamic model of the robot is extracted using Lagrange approach. Then, an adaptive super twisting sliding mode controller is designed based on Lyapanov theory. Moreover, the interaction forces are obtained in every time-step and applied to the robot as a compensating torque to guard against disturbances. The desired trajectory of the upper limb joint has been extracted so that the stability of the robot is achieved based on Zero Moment Point (ZMP) criterion at any moment. Moreover, to achieve optimal performance (maximum stability, minimum tracking error, reduced interacting forces, and optimal energy consumption), parameters of the proposed controller, the upper limb desired trajectory, and the impedance system are optimized using Harmony Search Algorithm (HSA). Finally, in order to demonstrate the effectiveness of the proposed controller, optimal sliding mode controller (SMC) is designed and performance of the AHOSTWSM is compared with SMC. The simulation results reveal the superiority of the controller in comparison with SMC.

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References

  1. Banala SK (2009) Robot assisted gaittraining with active leg exoskeleton (ALEX). IEEE Trans Neural Syst Rehabil Eng 17(1):2–8

    Article  Google Scholar 

  2. Shamaei K, Napolitano PC, Dollar AM (2013) A quasi-passive compliant stance control knee-ankle-foot orthosis. Rehabilitation Robotics (ICORR), 2013 IEEE international conference on IEEE

  3. Grabowski AM, Herr HM (2009) Leg exoskeleton reduces the metabolic cost ofhuman hopping. J Appl Physiol 107:670–678

    Article  Google Scholar 

  4. Kerdok AE, Biewener AA, McMahon TA, Weyand PG, Herr HM (2002) Energetics and mechanics of human running on surfaces of different stiffnesses. J Appl Physiol 92:469–478

    Article  Google Scholar 

  5. Herr H (2009) Exoskeletons and orthoses classification design challenges and future directions. J NeuroEng Rehabilit 6(1):1–9

    Article  Google Scholar 

  6. Dollar AM., Herr H (2008) Design of a quasi-passive knee exoskeleton to assist running. In: Intelligent Robots and Systems, 2008. IROS 2008. IEEE/RSJ international conference on IEEE, pp.747–754

  7. Robert B (2009) Exoskeletons and robotic prosthetics: a review of recent developments. Ind Robot Int J 36:421–427. https://doi.org/10.1108/01439910980141

    Article  Google Scholar 

  8. Aaron D, Hugh H (2008) Lower extremity exoskeletons and active orthoses: challenges and state-of-the-art. IEEE Trans Rob 24:144–158. https://doi.org/10.1109/TRO.2008.915453

    Article  Google Scholar 

  9. Vukobratovic M, Borovac B, Surla D, Stokic D (1990) Biped locomotion. Springer-Verlag, Berlin

    Book  Google Scholar 

  10. Kazerooni H, Sreger R, Huang L (2006) Hybrid control of the berkeley lower extremity exoskeleton (BLEEX). Int J Robot Res 25:561–573. https://doi.org/10.1177/0278364906065505

    Article  Google Scholar 

  11. Walsh CJ, Pasch K, Herr H (2006) An autonomous, under actuated exoskeleton for load-carrying augmentation, IEEE/International Conference on Intelligent Robots and. pp.1410–1415. https://doi.org/10.1109/IROS.2006.281932

  12. Banala SK, Kim SH, Agrawal SK, Scholz JP (2009) Robot assisted gait training with active leg exoskeleton (ALEX) IEEETrans. Neural Syst Rehabil 17:2–8. https://doi.org/10.1109/TNSRE.2008.2008280

    Article  Google Scholar 

  13. Herr H (2009) Challenges and state-of-the-art Lower Outhouses extremity exoskeletons and active. J Nero Eng Rehabilit 21:1–9. https://doi.org/10.1186/1743-0003-6-21

    Article  Google Scholar 

  14. Siciliano B, Khatib O (2008) Springer Handbook of Robotics. Springer-Verlag, Berlin, pp 773–793

    Book  Google Scholar 

  15. Jezernik S, Colombo G, Kelly T, Frueh T, Morari M (2003) Robotic Orthosis Lokomat: a rehabilitation and research tool. Neuro Modul 6:108–115. https://doi.org/10.1046/j.1525-1403.2003.3017.x

    Article  Google Scholar 

  16. Mokhtari M, Taghizadeh M, Mazare M (2019) Optimal adaptive high-order super twisting sliding mode control of a lower limb exoskeleton robot. modares mechanical engineering, 19 (3): 777–787. http://journals.modares.ac.ir/article-15-24120-en

  17. Mokhtari M, Taghizadeh M, Mazare M (2020) Hybrid adaptive robust control based on CPG and ZMP for a lower limb exoskeleton. Robotica. https://doi.org/10.1017/S0263574720000260

    Article  Google Scholar 

  18. Mokhtari M, Taghizadeh M, Mazare M (2018) Optimal robust hybrid active force control of a lower limb exoskeleton, Modares Mechanical Engineering. Pp. 342–350. http://journals.modares.ac.ir/article-15-11590-en

  19. Qu Z, Dorsey J (1991) Robust tracking control of robots by a linear feedback law. IEEE Trans Autom Control 36:1081–1084. https://doi.org/10.1109/9.83543

    Article  MathSciNet  MATH  Google Scholar 

  20. Neila M (2011) Adaptive sliding mode control for rigid robotic manipulator. Int J Autom Comput 8:215–220. https://doi.org/10.1007/s1163-0110576-2

    Article  Google Scholar 

  21. Jeong C, Kim J, Han S (2018) Tracking error constrained super-twisting sliding mode control for robotic system. Int J Control Autom Syst 16(804):816. https://doi.org/10.1007/s1255-017-0134-2y

    Article  Google Scholar 

  22. Edwards C, Colet E, Fridman L (2006) Advances in variable structure and sliding mode control. Springer, Berlin

    Book  Google Scholar 

  23. Levant A (1993) Sliding order and sliding accuracy in sliding mode control. Int J Control 58:1247–1263. https://doi.org/10.1080/00207179308923053

    Article  MathSciNet  MATH  Google Scholar 

  24. Liang D, Jian L, Ronghai Q (2016) Super-twisting algorithm based sliding-mode observer with online parameter estimation for sensor less control of permanent magnet synchronous machine. IEEE 53:3672–3682. https://doi.org/10.1109/ECCE.2016.7855479

    Article  Google Scholar 

  25. Goel A, Swarup A (2017) MIMO uncertain nonlinear system control via adaptive high-order super twisting sliding mode and its application to robotic manipulator. J Control Autom Electric Syst 28:36–49. https://doi.org/10.1007/s40313-016-0286-7

    Article  Google Scholar 

  26. Shtessel Y, Taleb M, Plestan F (2012) A novel adaptive-gain super twisting sliding mode controller: methodology and application. Automatica 48:759–769. https://doi.org/10.1016/j.automatica.2012.02.024

    Article  MathSciNet  MATH  Google Scholar 

  27. Nevil H (1985) Impedance control: an approach to manipulation: Part1, Part2, Part3. J Dyn Syst Meas Contr 107:1–24. https://doi.org/10.1115/1.3140702

    Article  Google Scholar 

  28. Karavas N, Ajoudani A, Tsagarakis N et al (2015) Tele-impedance based assistive control for a compliant knee exoskeleton. Robot Auton Syst 73:78–90. https://doi.org/10.1016/j.robot.2014.09.027

    Article  Google Scholar 

  29. Tran H, Cheng H, Rui H et al (2016) Evaluation of a fuzzy-based impedance control strategy on a powered lower exoskeleton. Int J Soc Robot 8:103–123. https://doi.org/10.1007/s12369-015-0324-9

    Article  Google Scholar 

  30. Chen X, Chen W, Wang J, Zhang J (2017) Impedance control for a lower-limb rehabilitation robot, 2017 12th IEEE conference on industrial electronics and applications (ICIEA), IEEE. 1212–1217. https://doi.org/10.1109/ICIEA.2017.8283024

  31. Pa P, Jou J (2010) Design of a bipedal toy robot with an automatic center of gravity shifting mechanism. Adv Mater Res 120:670–674. https://doi.org/10.4028/www.scientific.net/AMR.118-120.670

    Article  Google Scholar 

  32. Messuri D, Klein C (1985) Automatic body regulation for maintaining stability of a legged vehicle during rough-terrain locomotion. Robot Autom IEEE Robot Automat Soc 1:132–141. https://doi.org/10.1109/JRA.1985.1087012

    Article  Google Scholar 

  33. Moosavian A, Alipour K, Bahramzadeh Y (2007) Dynamics modaling and tip-over stability of suspended wheeled mobile robots with multiple arms. In lntelligent robots and Systems, 2007. IROS 2007. IEEE/International Conference on RSJ. https://doi.org/10.1109/IROS.2007.4398999

  34. Takhmar A, Alghooneh M, Alipour K et al (2007) MHS measure for postural stability monitoring and control of biped robots. In Advanced intelligent Mechatronics, 2008 .AIM 2008. IEEE/ASME lnternational Conference on https://doi.org/10.1109/AIM.2008.4601694

  35. Monje C, Martinez S, Pierro P, Balaguer C (2018) Whole-body balance control of a humanoid robot in real time based on zmp stability regions approach. Cybern Syst 49(7–8):521–537. https://doi.org/10.1080/01969722.2018.1552858

    Article  Google Scholar 

  36. Farzaneh Y, Akbarzadeh A, Akbari A (2014) Online bio-inspired trajectory generation of seven-link biped robot based on T-S fuzzy system. Appl Soft Comput 14:167–180. https://doi.org/10.1016/j.asoc.2013.05.013

    Article  Google Scholar 

  37. Kim J (2016) Harmony search algorithm: a algorithm. Procedia Eng 154:1401–1405. https://doi.org/10.1016/j.proeng.2016.07.510

    Article  Google Scholar 

  38. Kawamoto H, Sankai Y (2005) Power assist method based on phase sequence and muscle force condition for HAL. Adv Robot 19:717–734. https://doi.org/10.1163/1568553054455103

    Article  Google Scholar 

  39. Craig J (2017) Introduction to Robotics: Mechanics and Control. Hall, London, pp 85–310

    Google Scholar 

  40. Moosavian SAA, Takhmar A (2007) Stable gait planning for humanoids motion. ISME, Iran

    Google Scholar 

  41. Moreno JA (2012). Lyapunov function for levant’s second order differentiator. In 2012 IEEE 51st IEEE conference on decision and control (CDC) pp. 6448–6453

  42. Fridman L, Moreno JA, Bandyopadhyay B, Kamal S, Chalanga A (2015) Continuous nested algorithms: the 5th generation of sliding mode controllers. Springer International Publishing, Cham, pp 5–35

    MATH  Google Scholar 

  43. Seraji H, Colbaugh R (1997) Force tracking in impedance control. Int J Robot Res 16:97–117. https://doi.org/10.1177/027836499701600107

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, P.O.B., 1743524155, Tehran, Iran

    Majied Mokhtari, Mostafa Taghizadeh & Mahmood Mazare

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  1. Majied Mokhtari
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  2. Mostafa Taghizadeh
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  3. Mahmood Mazare
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Correspondence to Mostafa Taghizadeh.

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Mokhtari, M., Taghizadeh, M. & Mazare, M. Impedance control based on optimal adaptive high order super twisting sliding mode for a 7-DOF lower limb exoskeleton. Meccanica 56, 535–548 (2021). https://doi.org/10.1007/s11012-021-01308-4

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