Skip to main content
SpringerLink
Log in

Fast terminal sliding mode control with rapid reaching law for a pediatric gait exoskeleton system

  • Regular Paper
  • Published:
International Journal of Intelligent Robotics and Applications Aims and scope Submit manuscript

Abstract

The parametric variations and external perturbations in the coupled subject-exoskeleton system delay and hinder effective gait tracking in clinical rehabilitation. This problem becomes more challenging in the case of the pediatric exoskeleton system. In this work, to address this benchmark challenge, a fast terminal sliding mode with a rapid reaching law (FTSM-RRL) control scheme is introduced for an uncertain lower-extremity exoskeleton aimed at assisting pediatric gait under different walking speeds. At first, the computer-aided design of the gait exoskeleton system is demonstrated with details of the desired gait trajectories of a male boy aged 12 years (weight: 40 kg, height: 132 cm). A fast terminal sliding mode controller is proposed with a varied exponential approaching rule to guarantee the rapid convergence of system states on the sliding manifold and then towards the origin in a finite period. After that, an upper limit criterion is involved within the reaching control law to compensate for the adverse effects of uncertainties and disturbances as a lumped parameter. Lyapunov’s theory is presented to ensure the expeditious convergence of the tracking error in the reaching and sliding phases. The proposed FTSM-RRL strategy is incorporated to obtain the desired trajectory tracking at slow, self-selected, and fast walking speeds. From numerical experiments, the proposed FTSM-RRL controller is found to be consistently effective (\(> 71\%\) in X-direction and \(> 62\%\) in Y-direction) over the PID controller and (\(> 7\%\) in X-direction and \(> 10\%\) in Y-direction) over the FTSM-ERL controller. In joint space, the proposed FTSM-RRL control consistently surpasses both PID and FTSM-ERL controls in tracking hip movement. While the proposed controller outperforms PID and FTSM-ERL for knee joint tracking, the extent of improvement diminishes at higher speeds. For ankle joint tracking, the proposed control exhibits substantial enhancement at slow speeds but comparatively poorer performance at self-selected and fast speeds when compared to PID control. However, FTSM-RRL consistently outperforms FTSM-ERL across all speeds for ankle joint tracking. Compared to FTSM-ERL control, the proposed FTSM-RRL control accelerates the hip and knee joint sliding surface convergence by 0.52s and 0.24s (slow walking), 0.55s and 0.33s (self-selected walking), and 0.61s and 0.09s (fast walking). The results obtained in this study ensure fast and efficient passive-assist gait training for the pediatric groups using exoskeleton technology.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Availability of data and materials

This is not applicable since no datasets were generated and stored during the study.

References

  • Aljuboury, A.S., Hameed, A.H., Ajel, A.R., Humaidi, A.J., Alkhayyat, A., Mhdawi, A.K.A.: Robust adaptive control of knee exoskeleton-assistant system based on nonlinear disturbance observer. Actuators 11, 78 (2022)

    Article  Google Scholar 

  • Andrade, R.M., Sapienza, S., Bonato, P.: Development of a “transparent operation mode” for a lower-limb exoskeleton designed for children with cerebral palsy. In: 2019 IEEE 16th International Conference on Rehabilitation Robotics (ICORR), pp. 512–517. IEEE (2019)

  • Baud, R., Manzoori, A.R., Ijspeert, A., Bouri, M.: Review of control strategies for lower-limb exoskeletons to assist gait. J. Neuroeng. Rehabil. 18(1), 1–34 (2021)

    Article  Google Scholar 

  • Booth, A.T., Buizer, A.I., Meyns, P., Oude Lansink, I.L., Steenbrink, F., Krogt, M.M.: The efficacy of functional gait training in children and young adults with cerebral palsy: a systematic review and meta-analysis. Dev. Med. Child Neurol. 60(9), 866–883 (2018)

    Article  PubMed  Google Scholar 

  • Borase, R.P., Maghade, D., Sondkar, S., Pawar, S.: A review of pid control, tuning methods and applications. Int. J. Dyn. Control 9, 818–827 (2021)

    Article  MathSciNet  Google Scholar 

  • Brahmi, B., Driscoll, M., Laraki, M.H., Brahmi, A.: Adaptive high-order sliding mode control based on quasi-time delay estimation for uncertain robot manipulator. Control Theory Technol. 18, 279–292 (2020)

    Article  MathSciNet  Google Scholar 

  • Bumbard, K.B., Herrington, H., Goh, C.-H., Ibrahim, A.: Incorporation of torsion springs in a knee exoskeleton for stance phase correction of crouch gait. Appl. Sci. 12(14), 7034 (2022)

    Article  CAS  Google Scholar 

  • Chen, C.-F., Du, Z.-J., He, L., Wang, J.-Q., Wu, D.-M., Dong, W.: Active disturbance rejection with fast terminal sliding mode control for a lower limb exoskeleton in swing phase. IEEE Access 7, 72343–72357 (2019)

    Article  Google Scholar 

  • Chen, J., Hochstein, J., Kim, C., Tucker, L., Hammel, L.E., Damiano, D.L., Bulea, T.C.: A pediatric knee exoskeleton with real-time adaptive control for overground walking in ambulatory individuals with cerebral palsy. Front. Robot. AI 8, 702137 (2021)

    Article  PubMed  PubMed Central  Google Scholar 

  • Cumplido-Trasmonte, C., Ramos-Rojas, J., Delgado-Castillejo, E., Garcés-Castellote, E., Puyuelo-Quintana, G., Destarac-Eguizabal, M., Barquín-Santos, E., Plaza-Flores, A., Hernández-Melero, M., Gutiérrez-Ayala, A.: Effects of atlas 2030 gait exoskeleton on strength and range of motion in children with spinal muscular atrophy II: a case series. J. Neuroeng. Rehabil. 19(1), 1–10 (2022)

    Article  Google Scholar 

  • Feraru, L.M., Solomon, M.E.: Gradual correction of pediatric equinus deformity. Clin. Podiatr. Med. Surg. 39(1), 143–156 (2022)

    Article  PubMed  Google Scholar 

  • Fricke, S.S., Bayón, C., Kooij, H.V., Asseldonk, E.H.: Automatic versus manual tuning of robot-assisted gait training in people with neurological disorders. J. Neuroeng. Rehabil. 17(1), 1–15 (2020)

    Article  Google Scholar 

  • Hasan, S., Dhingra, A.K.: Development of a sliding mode controller with chattering suppressor for human lower extremity exoskeleton robot. Results Control Optim. 7, 100123 (2022)

    Article  Google Scholar 

  • Hernández, J.H., Cruz, S.S., López-Gutiérrez, R., González-Mendoza, A., Lozano, R.: Robust nonsingular fast terminal sliding-mode control for sit-to-stand task using a mobile lower limb exoskeleton. Control. Eng. Pract. 101, 104496 (2020)

    Article  Google Scholar 

  • Jenhani, S., Gritli, H.: Lmi-based design of an affine pd controller for the robust stabilization of the knee joint of a lower-limb rehabilitation exoskeleton. In: 2023 IEEE International Conference on Advanced Systems and Emergent Technologies (IC_ASET), pp. 1–7. IEEE (2023)

  • Kang, Z., Yu, H., Li, C.: Variable-parameter double-power reaching law sliding mode control method. Automatika 61(3), 345–351 (2020)

    Article  Google Scholar 

  • Khamar, M., Edrisi, M.: Designing a backstepping sliding mode controller for an assistant human knee exoskeleton based on nonlinear disturbance observer. Mechatronics 54, 121–132 (2018)

    Article  Google Scholar 

  • Kupferman, J.C., Zafeiriou, D.I., Lande, M.B., Kirkham, F.J., Pavlakis, S.G.: Stroke and hypertension in children and adolescents. J. Child Neurol. 32(4), 408–417 (2017)

    Article  PubMed  Google Scholar 

  • Lorenzo, T.M., Lara, S.L., Bayón, C., Ramírez, O., Rocon, E.: The cp walker for strength training in children with spastic cerebral palsy: a training program proposal. In: Converging Clinical and Engineering Research on Neurorehabilitation II: Proceedings of the 3rd International Conference on NeuroRehabilitation (ICNR2016), October 18-21, 2016, Segovia, Spain, pp. 1211–1215. Springer (2017)

  • Narayan, J., Dwivedy, S.K.: Biomechanical study and prediction of lower extremity joint movements using Bayesian regularization-based backpropagation neural network. J. Comput. Inf. Sci. Eng. 22(1), 014503 (2022)

    Article  Google Scholar 

  • Narayan, J., Kumar Dwivedy, S.: Preliminary design and development of a low-cost lower-limb exoskeleton system for paediatric rehabilitation. Proc. Inst. Mech. Eng. 235(5), 530–545 (2021)

    Article  Google Scholar 

  • Narayan, J., Bhoir, A.A., Borgohain, A., Dwivedy, S.K.: Design and analysis of a stand-aided lower-limb exoskeleton system for pediatric rehabilitation. In: 2021 International Conference on Computational Performance Evaluation (ComPE), pp. 950–955. IEEE (2021)

  • Narayan, J., Abbas, M., Dwivedy, S.K.: Robust adaptive backstepping control for a lower-limb exoskeleton system with model uncertainties and external disturbances. Automatika 64(1), 145–161 (2023)

    Article  Google Scholar 

  • Narayan, J., Auepanwiriyakul, C., Jhunjhunwala, S., Abbas, M., Dwivedy, S.K.: Hierarchical classification of subject-cooperative control strategies for lower limb exoskeletons in gait rehabilitation: a systematic review. Machines 11(7), 764 (2023)

    Article  Google Scholar 

  • Orekhov, G., Fang, Y., Luque, J., Lerner, Z.F.: Ankle exoskeleton assistance can improve over-ground walking economy in individuals with cerebral palsy. IEEE Trans. Neural Syst. Rehabil. Eng. 28(2), 461–467 (2020)

    Article  PubMed  PubMed Central  Google Scholar 

  • Sancho-Pérez, J., Pérez, M., García, E., Sanz-Merodio, D., Plaza, A., Cestari, M.: Mechanical description of atlas 2020, a 10-dof paediatric exoskeleton. In: Advances in cooperative robotics, pp. 814–822. World Scientific, Cham (2017)

    Google Scholar 

  • Sarajchi, M., Al-Hares, M.K., Sirlantzis, K.: Wearable lower-limb exoskeleton for children with cerebral palsy: a systematic review of mechanical design, actuation type, control strategy, and clinical evaluation. IEEE Trans. Neural Syst. Rehabil. Eng. 29, 2695–2720 (2021)

    Article  PubMed  Google Scholar 

  • Shi, D., Zhang, W., Zhang, W., Ding, X.: A review on lower limb rehabilitation exoskeleton robots. Chin. J. Mech. Eng. 32(1), 1–11 (2019)

    Article  CAS  Google Scholar 

  • Smania, N., Bonetti, P., Gandolfi, M., Cosentino, A., Waldner, A., Hesse, S., Werner, C., Bisoffi, G., Geroin, C., Munari, D.: Improved gait after repetitive locomotor training in children with cerebral palsy. Am. J. Phys. Med. Rehabil. 90(2), 137–149 (2011)

    Article  PubMed  Google Scholar 

  • Sousa, D.G., Harvey, L.A., Dorsch, S., Glinsky, J.V.: Interventions involving repetitive practice improve strength after stroke: a systematic review. J. Physiother. 64(4), 210–221 (2018)

    Article  PubMed  Google Scholar 

  • Sun, Y., Tang, Y., Zheng, J., Dong, D., Chen, X., Bai, L.: From sensing to control of lower limb exoskeleton: a systematic review. Annu. Rev. Control. 53, 83–96 (2022)

    Article  MathSciNet  Google Scholar 

  • Tole, G., Raymond, M.J., Williams, G., Clark, R.A., Holland, A.E.: Strength training to improve walking after stroke: how physiotherapist, patient and workplace factors influence exercise prescription. Physiother. Theory Pract. 38(9), 1198–1206 (2022)

    Article  PubMed  Google Scholar 

  • Torabi, M., Sharifi, M., Vossoughi, G.: Robust adaptive sliding mode admittance control of exoskeleton rehabilitation robots. Scientia Iranica 25(5), 2628–2642 (2018)

    Google Scholar 

  • Wang, J., Liu, J., Zhang, G., Guo, S.: Periodic event-triggered sliding mode control for lower limb exoskeleton based on human–robot cooperation. ISA Trans. 123, 87–97 (2022)

    Article  PubMed  Google Scholar 

  • WHO: World report on disability 2011. World Health Organization (2011)

  • Wu, J., Gao, J., Song, R., Li, R., Li, Y., Jiang, L.: The design and control of a 3dof lower limb rehabilitation robot. Mechatronics 33, 13–22 (2016)

    Article  CAS  Google Scholar 

  • Yamada, T., Kadone, H., Shimizu, Y., Suzuki, K.: An exoskeleton brake unit for children with crouch gait supporting the knee joint during stance. In: 2018 International Symposium on Micro-nanomechatronics and Human Science (MHS), pp. 1–7. IEEE (2018)

  • Yang, X., She, H., Lu, H., Fukuda, T., Shen, Y.: State of the art: bipedal robots for lower limb rehabilitation. Appl. Sci. 7(11), 1182 (2017)

    Article  Google Scholar 

  • Yang, S., Han, J., Xia, L., Chen, Y.-H.: An optimal fuzzy-theoretic setting of adaptive robust control design for a lower limb exoskeleton robot system. Mech. Syst. Signal Process. 141, 106706 (2020)

    Article  Google Scholar 

  • Yu, S., Yu, X., Shirinzadeh, B., Man, Z.: Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica 41(11), 1957–1964 (2005)

    Article  MathSciNet  Google Scholar 

  • Yu, X., Feng, Y., Man, Z.: Terminal sliding mode control—an overview. IEEE Open J. Ind. Electron. Soc. 2, 36–52 (2020)

    Article  Google Scholar 

  • Zhang, X., Wang, H., Tian, Y., Peyrodie, L., Wang, X.: Model-free based neural network control with time-delay estimation for lower extremity exoskeleton. Neurocomputing 272, 178–188 (2018)

    Article  Google Scholar 

  • Zhihong, M., Yu, X.H.: Terminal sliding mode control of mimo linear systems. IEEE Trans. Circ. Syst. I: Fundam. Theory Appl. 44(11), 1065–1070 (1997)

    Article  MathSciNet  Google Scholar 

  • Zhou, Z., Tang, G., Huang, H., Han, L., Xu, R.: Adaptive nonsingular fast terminal sliding mode control for underwater manipulator robotics with asymmetric saturation actuators. Control Theory Technol. 18, 81–91 (2020)

    Article  MathSciNet  Google Scholar 

  • Znegui, W., Gritli, H., Belghith, S.: Stabilization of the passive walking dynamics of the compass-gait biped robot by developing the analytical expression of the controlled poincaré map. Nonlinear Dyn. 101, 1061–1091 (2020)

    Article  Google Scholar 

Download references

Acknowledgements

The authors are thankful to DSIR-PRISM, India, for sponsoring the project (DSIR/PRISM/78/2016) under which this study was carried out. Moreover, the authors express their gratitude to the Mechatronics and Robotics Lab at the IIT Guwahati for its research support.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039, India

    Jyotindra Narayan & Santosha K. Dwivedy

  2. National Engineering School of Tunis, University of Tunis El Manar, Tunis, 1002, Tunisia

    Hassène Gritli

  3. Higher Institute of Information and Communication Technologies, University of Carthage, Borj-Cedria, Tunis, 1164, Tunisia

    Hassène Gritli

Authors
  1. Jyotindra Narayan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hassène Gritli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Santosha K. Dwivedy
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Conceptualization: JN; Methodology: JN, HG; Formal analysis and investigation: JN, HG; Writing - original draft preparation: JN, HG; Writing - review and editing: JN, HG, SKD; Resources: SKD; Supervision: SKD.

Corresponding author

Correspondence to Jyotindra Narayan.

Ethics declarations

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Narayan, J., Gritli, H. & Dwivedy, S.K. Fast terminal sliding mode control with rapid reaching law for a pediatric gait exoskeleton system. Int J Intell Robot Appl 8, 76–95 (2024). https://doi.org/10.1007/s41315-023-00314-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41315-023-00314-x

Keywords

Search

Navigation