Skip to main content
SpringerLink
Log in

Prescribed performance model-free adaptive terminal sliding mode control for the pneumatic artificial muscles elbow exoskeleton

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

This paper focuses on the trajectory tracking issue of the pneumatic artificial muscle (PAM) exoskeleton system. First of all, a new type of the PAM elbow exoskeleton was introduced to assist wearers in elbow flexion/extension movement. Moreover, a model-free adaptive control approach was combined with the prescribed performance control to ensure the tracking errors to be converged to the predefined requirements. Meanwhile, to suffer the influence of the unknown external disturbance on the exoskeleton, a terminal sliding mode control was adopted to reduce the tracking errors. From a theoretical perspective, the stability of the proposed controller can be proved by Lyapunov synthesis. After two sets of experiments, the proposed control method can further improve the tracking accuracy in the PAM elbow exoskeleton, compared with the other three model-free adaptive control methods. Simultaneously, the maximum absolute value of the tracking errors never exceeded the designed boundary.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

PAM:

Pneumatic artificial muscle

SMC:

Sliding mode control

TSMC:

Terminal sliding mode control

MFAC:

Model-free adaptive control

PP:

Prescribed performance

IMU:

Inertial measurement unit

PSA:

Parameter self-adjusting

P:

Prominence coefficient

DOF:

Degree of freedom

VAR:

Variance

References

  1. K. Kiguchi and Y. Hayashi, An EMG-based control for an upper-limb power-assist exoskeleton robot, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 42 (4) (2012) 1064–1071.

    Article  Google Scholar 

  2. E. Swinnen, D. Beckwee, R. Meeusen, J. P. Baeyens and E. Kerckhofs, Does robot-assisted gait rehabilitation improve balance in stroke patients? A systematic review, Topics in Stroke Rehabilitation, 21 (2) (2014) 87–100.

    Article  Google Scholar 

  3. B. Huang, Z. Li, X. Wu, A. Ajoudani, A. Bicchi and J. Liu, Coordination control of a dual-arm exoskeleton robot using human impedance transfer skills, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49 (5) (2019) 954–963.

    Article  Google Scholar 

  4. F. Sado, H. J. Yap, R. A. R. Ghazilla and N. Ahmad, Design and control of a wearable lower-body exoskeleton for squatting and walking assistance in manual handling works, Mechatronics, 63 (2019) 1–20.

    Article  Google Scholar 

  5. J. Garrido, W. Yu and X. Li, Modular design and control of an upper limb exoskeleton, Journal of Mechanical Science and Technology, 30 (5) (2016) 2265–2271.

    Article  Google Scholar 

  6. F. Xiao, Y. Gao, Y. Wang, Y. Zhu and J. Zhao, Design and evaluation of a 7-DOF cable-driven upper limb exoskeleton, Journal of Mechanical Science and Technology, 32 (2) (2018) 855–864.

    Article  Google Scholar 

  7. A. H. A. Stienenw, E. E. G. Hekman, H. Ter Braak, A. M. M. Aalsma, F. C. T. van der Helm and H. van der Kooij, Design of a rotational hydroelastic actuator for a powered exoskeleton for upper limb rehabilitation, IEEE Transactions on Bio-medical Engineering, 57 (3) (2010) 728–735.

    Article  Google Scholar 

  8. A. Otten, C. Voort, A. Stienen, R. Aarts, E. van Assel-donk and H. van der Kooij, LIMPACT: a hydraulically powered self-aligning upper limb exoskeleton, IEEE/ASME Transactions on Mechatronics, 20 (5) (2015) 2285–2298.

    Article  Google Scholar 

  9. A. Gupta, A. Singh, V. Verma, A. K. Mondal and M. K. Gupta, Developments and clinical evaluations of robotic exoskeleton technology for human upper-limb rehabilitation, Advanced Robotics, 34 (15) (2020) 1023–1040.

    Article  Google Scholar 

  10. M. P. De Looze, T. Bosch, F. Krause, K. S. Stadler and L. W. O’Sullivan, Exoskeletons for industrial application and their potential effects on physical work load, Ergonomics, 59 (5) (2016) 671–681.

    Article  Google Scholar 

  11. B. Ugurlu, P. Forni, C. Doppmann, E. Sariyildiz and J. Morimoto, Stable control of force, position, and stiffness for robot joints powered via pneumatic muscles, IEEE Transactions on Industrial Informatics, 15 (12) (2019) 6270–6279.

    Article  Google Scholar 

  12. T. Noda, T. Teramae, B. Ugurlu and J. Morimoto, Development of an upper limb exoskeleton powered via pneumatic electric hybrid actuators with bowden cable, International Conference on Intelligent Robots and Systems (IEEE/RSJ) (2014) 3573–3578.

  13. M. H. Milot, S. J. Spencer, V. Chan, J. P. Allington, J. Klein, C. Chou, J. Ebobrow, S. C. Cramer and D. J. Reinkensmeyer, A crossover pilot study evaluating the functional outcomes of two different types of robotic movement training in chronic stroke survivors using the arm exoskeleton BONES, Journal of Neuroengineering and Rehabilitation, 10 (1) (2013) 112.

    Article  Google Scholar 

  14. L. Peternel, T. Noda, T. Petričl, A. Ude, J. Morimoto and J. Babič, Adaptive control of exoskeleton robots for periodic assistive behaviours based on EMG feedback minimisation, PLoS One, 11 (2) (2016) e0148942.

    Article  Google Scholar 

  15. X. Tu, X. Zhou, J. Li, C. Su, X. Sun, H. Han, X. Jiang and J. He, Iterative learning control applied to a hybrid rehabilitation exoskeleton system powered by PAM and FES, Cluster Comput, 20 (4) (2017) 2855–2868.

    Article  Google Scholar 

  16. D. J. Reinkensmeyer, E. T. Wolbrecht, V. Chan, C. Chou and S. C. Cramer, Comparison of three-dimensional assist-as-needed robotic arm/hand movement training provided with Pneu-WREX to conventional tabletop therapy after chronic stroke, American Journal of Physical Medicine & Rehabilitation, 91 (1103) (2012) 232–241.

    Article  Google Scholar 

  17. G. Spagnuolo, M. Malosio, A. Scano, M. Caimmi, G. Legnani and L. M. Tosatti, Passive and active gravity-compensation of LIGHT arm, an exoskeleton for the upper-limb rehabilitation, IEEE International Conference on Rehabilitation Robotics (ICORR) (2015) 440–445.

  18. Y. Mao and S. K. Agrawal, Design of a cable-driven arm exoskeleton (CAREX) for neural rehabilitation, IEEE Transactions on Robotics, 28 (4) (2012) 922–931.

    Article  Google Scholar 

  19. C. Rosyidi, P. Fitriawati and R. D. Astuti, Optimization model for gas spring of endoskeletal prosthetic leg with maximum energy storage criteria, Asia Pacific Industrial Engineering & Management Systems Conference (2012).

  20. V. A. Dung Cai, P. Bidaud, T. T. Le, A. Ibanez and X. T. Phan, In search of transparency for lower limb exoskeleton devices with a new mechanical design and a robust gait phases detection method, IEEE International Conference on Robotics and Biomimetics (ROBIO) (2015) 1151–1156.

  21. N. Sun, D. Liang, Y. Wu, Y. Chen, Y. Qin and Y. Fang, Adaptive control for pneumatic artificial muscle systems with parametric uncertainties and unidirectional input constraints, IEEE Transactions on Industrial Informatics, 16 (2) (2019) 969–979.

    Article  Google Scholar 

  22. K. C. Wickramatunge and T. Leephakpreeda, Study on mechanical behaviors of pneumatic artificial muscle, International Journal of Engineering Science, 48 (2) (2010) 188–198.

    Article  Google Scholar 

  23. T. Hassan, M. Cianchetti, M. Moatamedi, B. Mazzolai, C. Laschi and P. Dario, Finite-element modeling and design of a pneumatic braided muscle actuator with multifunctional capabilities, IEEE/ASME Transactions on Mechatronics, 24 (1) (2019) 109–119.

    Article  Google Scholar 

  24. M. Tóthová and J. Pitel, Reference model for hybrid adaptive control of pneumatic muscle actuator, IEEE 9th IEEE International Symposium on Applied Computational Intelligence and Informatics (SACI) (2014) 105–109.

  25. M. E. Giannaccini, C. Xiang, A. Atyabi, T. Theodoridis, S. Nefti-Meziani and S. Davis, Novel design of a soft lightweight pneumatic continuum robot arm with decoupled variable stiffness and positioning, Soft Robot, 5 (1) (2018) 54–70.

    Article  Google Scholar 

  26. K. C. Wickramatunge and T. Leephakpreeda, Study on mechanical behaviors of pneumatic artificial muscle, International Journal of Engineering Science, 48 (2) (2010) 188–198.

    Article  Google Scholar 

  27. D. Zhang, X. Zhao and J. Han, Active model-based control for pneumatic artificial muscle, IEEE Transactions on Industrial Electronics, 64 (2) (2017) 1686–1695.

    Article  Google Scholar 

  28. X. Gao, X. Li, Y. Sun, L. Hao, H. Yang and C. Xiang, Modelfree tracking control of continuum manipulators with global stability and assigned accuracy, IEEE Transactions on Systems, Man, and Cybernetics: System (2020) 1–11.

  29. Z. Hou and Z. Wang, From model-based control to data-driven control: survey, classification and perspective, Information Sciences, 235 (2013) 3–35.

    Article  MathSciNet  MATH  Google Scholar 

  30. H. P. Huy Anh, N. N. Son and C. Van Kien, Adaptive neural compliant force-position control of serial PAM robot, J. Intell. Robot. Syst., 89 (2018) 351–369.

    Article  Google Scholar 

  31. T. Leephakpreeda, Fuzzy logic based PWM control and neural controlled-variable estimation of pneumatic artificial muscle actuators, Expert Systems with Applications, 38 (6) (2011) 7837–7850.

    Article  Google Scholar 

  32. D. Zhang, X. Zhao, J. Han, X. Li and B. Zhang, Active modeling and control for shape memory alloy actuators, IEEE Access, 7 (2019) 162549–162558.

    Article  Google Scholar 

  33. H. Yang, C. Xiang, L. Hao, L. Zhao and B. Xue, Research on PSA-MFAC for a novel bionic elbow joint system actuated by pneumatic artificial muscles, Journal of Mechanical Science and Technology, 31 (7) (2017) 3519–3529.

    Article  Google Scholar 

  34. D. Liu and G. H. Yang, Data-driven adaptive sliding mode control of nonlinear discrete-time systems with prescribed performance, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49 (12) (2019) 2598–2604.

    Article  Google Scholar 

  35. X. Wang, X. Li, J. Wang, X. Fang and X. Zhu, Data-driven model-free adaptive sliding mode control for the multi degree-of-freedom robotic exoskeleton, Information Sciences, 327 (2016) 246–257.

    Article  MathSciNet  MATH  Google Scholar 

  36. A. Riani, T. Madani, A. Benallegue and K. Djouani, Adaptive integral terminal sliding mode control for upper-limb rehabilitation exoskeleton, Control Engineering Practice, 75 (2018) 108–117.

    Article  Google Scholar 

  37. Y. Wang and M. Hou, Model-free adaptive integral terminal sliding mode predictive control for a class of discrete-time nonlinear systems, ISA Transactions, 93 (2019) 209–217.

    Article  Google Scholar 

  38. C. P. Bechlioulis and G. A. Rovithakis, Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems, Automatica, 45 (2) (2009) 532–538.

    Article  MathSciNet  MATH  Google Scholar 

  39. J. X. Zhang and G. H. Yang, Adaptive prescribed performance control of nonlinear output — feedback systems with unknown control direction, International Journal of Robust and Nonlinear Control, 28 (16) (2018) 4696–4712.

    Article  MathSciNet  MATH  Google Scholar 

  40. J. Zhang and G. Yang, Fuzzy adaptive output feed-back control of uncertain nonlinear systems with prescribed performance, IEEE Transactions on Cybernetics, 48 (5) (2018) 1342–1354.

    Article  Google Scholar 

  41. D. Liu and G. Yang, Data-driven adaptive sliding mode control of nonlinear discrete-time systems with prescribed performance, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49 (12) (2017) 2598–2604.

    Article  Google Scholar 

  42. D. Liu and G. Yang, Prescribed performance model-free adaptive integral sliding mode control for discrete-time nonlinear systems, IEEE Transactions on Neural Networks and Learning Systems, 30 (7) (2018) 2222–2230.

    Article  MathSciNet  Google Scholar 

  43. S. I. Han, H. Ha and J. Lee, Barrier lyapunov function-based model-free constraint position control for mechanical systems, Journal of Mechanical Science and Technology, 30 (7) (2016) 3331–3338.

    Article  Google Scholar 

  44. A. Mauri, J. Lettori, G. Fusi, D. Fausti, M. Mor, F. Braghin and L. Roveda, Mechanical and control design of an industrial exoskeleton for advanced human empowering in heavy parts manipulation tasks, Robotics, 8 (3) (2019) 65.

    Article  Google Scholar 

  45. H. Kobayashi, A. Uchimura and T. Shiiba, Development of muscle suit for upper body, International Conference on Intelligent Robots and Systems (IROS) (2003) 3624–3629.

  46. L. Tiseni, M. Xiloyannis, D. Chiaradia, N. Lotti, M. Solazzi, H. Van der Kooij and L. Masia, On the edge between soft and rigid: an assistive shoulder exoskeleton with hyper-redundant kinematics, International Conference on Rehabilitation Robotics (ICORR) (2019) 618–624.

  47. Y. Zhang, H. Liu, T. Ma, L. Hao and Z. Li, A comprehensive dynamic model for pneumatic artificial muscles considering different input frequencies and mechanical loads, Mechanical Systems and Signal Processing, 148 (2021) 1–18.

    Article  Google Scholar 

  48. X. Gao, X. Li, C. Zhao, L. Hao and C. Xiang, Variable stiffness structural design of a dual-segment continuum manipulator with independent stiffness and angular position, Robotics and Computer-Integrated Manufacturing, 67 (2021) 1–13.

    Article  Google Scholar 

  49. A. M. Khan, D. W. Yun, M. A. Ali, K. M. Zuhaib, C. Yuan, J. Iqbal and C. Han, Passivity based adaptive control for upper extremity assist exoskeleton, International Journal of Control, Automation and Systems, 14 (2016) 291–300.

    Article  Google Scholar 

  50. C. P. Bechlioulis, G. A. Rovithakis and A. George, Robust adaptive fuzzy control of nonaffine systems guaranteeing transient and steady state error bounds, International Journal of Adaptive Control and Signal Processing, 26 (7) (2012) 576–591.

    Article  MathSciNet  MATH  Google Scholar 

  51. S. Pezeshki, M. A. Badamchizadeh, A. R. Ghiasi and S. Ghaemi, Control of overhead crane system using adaptive model-free and adaptive fuzzy sliding mode controllers, Journal of Control, Automation and Electrical Systems, 26 (1) (2015) 1–15.

    Article  Google Scholar 

  52. A. Levant, Principles of 2-sliding mode design, Automatica, 43 (4) (2007) 576–586.

    Article  MathSciNet  MATH  Google Scholar 

  53. A. Levant, Sliding order and sliding accuracy in sliding mode control, International Journal of Control, 58 (6) (1993) 1247–1263.

    Article  MathSciNet  MATH  Google Scholar 

  54. D. B. Reynolds, D. W. Repperger, C. A. Phillips and G. Bandry, Modeling the dynamic characteristics of pneumatic muscle, Annals of Biomedical Engineering, 31 (3) (2003) 310–317.

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by Research Program supported by the National Natural Science Foundation, China (61503070). Fundamental Research Funds for the Central Universities, China (N18240007-2).

Author information

Authors and Affiliations

  1. School of Mechanical and Engineering, Northeastern University, Liaoning, 110319, China

    Zhirui Zhao, Lina Hao, Mingfang Liu & Haoze Gao

  2. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Liaoning, 110319, China

    Xing Li

Authors
  1. Zhirui Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lina Hao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mingfang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Haoze Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xing Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xing Li.

Additional information

Zhirui Zhao was born in Liaoning, China, in 1991. He received the M.S. degree in Mechanical Design, Manufacturing and Automation from Shenyang Aerospace University of Technology, Shenyang, China, in 2017. He is currently working toward a Ph.D. degree majoring in Mechatronics Engineering at Northeastern University, Shenyang, China. His current research interests include the upper-limb exoskeleton structure design and nonlinear system control.

Lina Hao was born in Liaoning, China, in 1968. She received Ph.D. degree in Control Theory and Control Engineering from Northeastern University, Shenyang, China in 2001. Currently, she is a Professor in Department of Mechanical Engineering and Automation in Northeastern University, China. Her research interests include robot system and intelligent control, intelligent structure and precision motion control system, pattern recognition and condition monitoring.

Mingfang Liu was born in Liaoning, China, in 1990. He received the B.E. degree in Mechanical Engineering and Automation from Dalian Polytechnic University in 2013 and the M.E. degree in Chemical Process Equipment from Northeastern University in 2017. He is currently pursuing the Ph.D. degree in Northeastern University. His recent research interest includes smart materials, model free control and prescribed performance control.

Haze Gao is a master student of the School of Mechanical Engineering and Automation, Northeastern University, Shenyang, China. He received the B.E. degree in Mechanical Engineering and Automation from Inner Mongolia University of Technology in 2019. His research interests include intelligent materials and exoskeleton structure.

Xing Li is an Associate Professor at the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. She received her Ph.D. degree in Power Electronics and Power Transmission from Northeastern University in 2012. Her research interest covers model-free adaptive control, intelligent robot system and exoskeleton system. She is the corresponding author of this paper.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, Z., Hao, L., Liu, M. et al. Prescribed performance model-free adaptive terminal sliding mode control for the pneumatic artificial muscles elbow exoskeleton. J Mech Sci Technol 35, 3183–3197 (2021). https://doi.org/10.1007/s12206-021-0639-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-021-0639-4

Keywords

Search

Navigation