Forthcoming

Adaptive control of a robotic exoskeleton for enhanced knee rehabilitation

Author affiliations

Authors

  • Duc Toan Luu \(^1\) College of Engineering and Computer Science, VinUniversity, Hanoi, Vietnam
    \(^2\) VinUni-Illinois Smart Health Center, VinUniversity, Hanoi, Vietnam
    https://orcid.org/0009-0007-8720-8005
  • Vu Linh Nguyen \(^1\) College of Engineering and Computer Science, VinUniversity, Hanoi, Vietnam
    \(^2\) VinUni-Illinois Smart Health Center, VinUniversity, Hanoi, Vietnam
    \(^3\) Center for AI Research, VinUniversity, Hanoi, Vietnam
    https://orcid.org/0000-0002-2959-4127

DOI:

https://doi.org/10.15625/0866-7136/23798

Keywords:

rehabilitation, machine learning, variable stiffness actuator, spring design

Abstract

Variable stiffness actuators (VSAs) offer significant potential for diverse applications due to their ability to adjust stiffness in response to operational requirements. The proposed VSA comprises 12 pairs of outer pulleys and six pairs of inner pulleys, uniformly arranged around a central axis and connected in series to a spring via a cable. Rotation of the inner pulleys around the center extends the spring, generating an elastic force that is transmitted through the cable to the output link, producing output torque and stiffness. The output stiffness varies with the angle of rotation, posing challenges for control system design. This study proposes machine learning-based approaches to achieve accurate and low-latency control. Specifically, neural network models are developed to estimate the spring preload at various actuator positions, enabling precise control of the desired stiffness. The results show that the Feedforward Neural Network enables the actuator to achieve a stiffness with a root-mean-square error of 0.0073 Ncm/degree.

Downloads

Download data is not yet available.

References

Ajaev, V. S., & Davis, S. H. (2004). The effect of tri-junction conditions in droplet solidification. Journal of Crystal Growth, 264(1–3), 452–462. https://doi.org/10.1016/j.jcrysgro.2003.11.119

Allen, J. T., Giammanco, I. M., Kumjian, M. R., Jurgen Punge, H., Zhang, Q., Groenemeijer, P., Kunz, M., & Ortega, K. (2020). Understanding hail in the Earth system. Reviews of Geophysics, 58(1), e2019RG000665. https://doi.org/10.1029/2019rg000665

Bhagat, K. D., Vu, T. V., Wells, J. C., Takakura, H., Kawano, Y., & Ogawa, F. (2019). Production of hollow germanium alloy quasi-spheres through a coaxial nozzle. Japanese Journal of Applied Physics, 58(6), 068001. https://doi.org/10.7567/1347-4065/ab1b59

Biancardo, M., Taira, K., Kogo, N., Kikuchi, H., Kumagai, N., Kuratani, N., Inagawa, I., Imoto, S., & Nakata, J. (2007). Characterization of microspherical semi-transparent solar cells and modules. Solar Energy, 81(6), 711–716. https://doi.org/10.1016/j.solener.2006.10.009

Chu, F., Gao, S., Zhang, X., Wu, X., & Wen, D. (2019). Droplet re-icing characteristics on a superhydrophobic surface. Applied Physics Letters, 115(7), 073703. https://doi.org/10.1063/1.5109283

Dalili, N., Edrisy, A., & Carriveau, R. (2009). A review of surface engineering issues critical to wind turbine performance. Renewable and Sustainable Energy Reviews, 13(2), 428–438. https://doi.org/10.1016/j.rser.2007.11.009

Dang, Q., Song, M., Dang, C., Zhan, T., & Zhang, L. (2022). Experimental study on solidification characteristics of sessile urine droplets on a horizontal cold plate surface under natural convection. Langmuir, 38(25), 7846–7857. https://doi.org/10.1021/acs.langmuir.2c01154

Enríquez, O. R., Marín, Á. G., Winkels, K. G., & Snoeijer, J. H. (2012). Freezing singularities in water drops. Physics of Fluids, 24(9), 091102. https://doi.org/10.1063/1.4747185

Felton, R. (2009). Hollow metal spheres put Fraunhofer on a roll. Metal Powder Report. http://www.sciencedirect.com/science/article/pii/S0026065710700187

Frisby, E. M., & Sansom, H. W. (1967). Hail incidence in the tropics. Journal of Applied Meteorology, 6(2), 339–354. https://doi.org/10.1175/1520-0450(1967)006%253C0339:hiitt%253E2.0.co;2

Gao, W., Smith, D. W., & Sego, D. C. (2000). Freezing behavior of freely suspended industrial wastewater droplets. Cold Regions Science and Technology, 31(1), 13–26. https://doi.org/10.1016/s0165-232x(99)00036-1

Ho, N. X., Pham, B. D., & Vu, T. V. (2024). Containerless solidification of a hollow droplet with forced convection. Microgravity Science and Technology, 36(3), 30. https://doi.org/10.1007/s12217-024-10112-0

Ho, N. X., Vu, T. V., & Pham, B. D. (2021). A numerical study of a liquid compound drop solidifying on a horizontal surface. International Journal of Heat and Mass Transfer, 165, 120713. https://doi.org/10.1016/j.ijheatmasstransfer.2020.120713

Hu, L., Zhu, X., Hu, C., Chen, J., & Du, Z. (2017). Wind turbines ice distribution and load response under icing conditions. Renewable Energy, 113, 608–619. https://doi.org/10.1016/j.renene.2017.05.059

Huang, L., Liu, Z., Liu, Y., Gou, Y., & Wang, L. (2012). Effect of contact angle on water droplet freezing process on a cold flat surface. Experimental Thermal and Fluid Science, 40, 74–80. https://doi.org/10.1016/j.expthermflusci.2012.02.002

Ilyasoglu Buyukkestelli, H., & El, S. N. (2021). Enhancing sweetness using double emulsion technology to reduce sugar content in food formulations. Innovative Food Science & Emerging Technologies, 74, 102809. https://doi.org/10.1016/j.ifset.2021.102809

Kendall, J. M., Lee, M. C., & Wang, T. G. (1982). Metal shell technology based upon hollow jet instability. Journal of Vacuum Science and Technology, 20(4), 1091–1093. https://doi.org/10.1116/1.571574

Lian, W., & Xuan, Y. (2017). Experimental investigation on a novel aero-engine nose cone anti-icing system. Applied Thermal Engineering, 121, 1011–1021. https://doi.org/10.1016/j.applthermaleng.2017.04.160

Maan, A. A., Schroën, K., & Boom, R. (2011). Spontaneous droplet formation techniques for monodisperse emulsions preparation – Perspectives for food applications. Journal of Food Engineering, 107(3–4), 334–346. https://doi.org/10.1016/j.jfoodeng.2011.07.008

Marín, A. G., Enríquez, O. R., Brunet, P., Colinet, P., & Snoeijer, J. H. (2014). Universality of tip singularity formation in freezing water drops. Physical Review Letters, 113(5), 054301. https://doi.org/10.1103/physrevlett.113.054301

McClements, D. J. (2012). Advances in fabrication of emulsions with enhanced functionality using structural design principles. Current Opinion in Colloid & Interface Science, 17(5), 235–245. https://doi.org/10.1016/j.cocis.2012.06.002

Nadler, J. H., Sanders, Jr., Thomas H., & Cochran, J. K. (2000). Aluminum hollow sphere processing. Materials Science Forum, 331–337, 495–500. https://doi.org/10.4028/www.scientific.net/msf.331-337.495

Pan, Y., Shi, K., Duan, X., & Naterer, G. F. (2019). Experimental investigation of water droplet impact and freezing on micropatterned stainless steel surfaces with varying wettabilities. International Journal of Heat and Mass Transfer, 129, 953–964. https://doi.org/10.1016/j.ijheatmasstransfer.2018.10.032

Pham, B. D., & Vu, T. V. (2022). A numerical study of a suspended compound droplet solidifying under forced convection. International Journal of Heat and Mass Transfer, 196, 123296. https://doi.org/10.1016/j.ijheatmasstransfer.2022.123296

Pham, B. D., Vu, T. V., Nguyen, L. V. T., Ho, N. X., Nguyen, C. T., Nguyen, H. D., Nguyen, V. T., & Vu, H. V. (2021). A numerical study of geometrical effects on solidification of a compound droplet on a cold flat surface. Acta Mechanica, 232(10), 3767–3779. https://doi.org/10.1007/s00707-021-03024-2

Schultz, W. W., Worster, M. G., & Anderson, D. M. (2001). Solidifying sessile water droplets. In P. Ehrhard, D. S. Riley, & P. H. Steen (Eds.), Interactive Dynamics of Convection and Solidification (pp. 209–226). Springer Netherlands. https://doi.org/10.1007/978-94-015-9807-1_24

Shetabivash, H., Dolatabadi, A., & Paraschivoiu, M. (2020). A multiple level-set approach for modelling containerless freezing process. Journal of Computational Physics, 415, 109527. https://doi.org/10.1016/j.jcp.2020.109527

Starostin, A., Strelnikov, V., Dombrovsky, L. A., Shoval, S., Gendelman, O., & Bormashenko, E. (2022). Effect of asymmetric cooling of sessile droplets on orientation of the freezing tip. Journal of Colloid and Interface Science, 620, 179–186. https://doi.org/10.1016/j.jcis.2022.04.019

Teh, S.-Y., Lin, R., Hung, L.-H., & Lee, A. P. (2008). Droplet microfluidics. Lab on a Chip, 8(2), 198–220. https://doi.org/10.1039/b715524g

Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S., & Jan, Y.-J. (2001). A front-tracking method for the computations of multiphase flow. Journal of Computational Physics, 169(2), 708–759. https://doi.org/10.1006/jcph.2001.6726

Virozub, A., Rasin, I. G., & Brandon, S. (2008). Revisiting the constant growth angle: Estimation and verification via rigorous thermal modeling. Journal of Crystal Growth, 310(24), 5416–5422. https://doi.org/10.1016/j.jcrysgro.2008.09.004

Vu, T. V., & Luu, Q. H. (2019). Containerless solidification of a droplet under forced convection. International Journal of Heat and Mass Transfer, 143, 118498. https://doi.org/10.1016/j.ijheatmasstransfer.2019.118498

Vu, T. V., Pham, B. D., Pham, P. H., Vu, H. V., & Tran, B. X. (2021). A numerical study of hollow water drop breakup during freezing. Physics of Fluids, 33(11), 112110. https://doi.org/10.1063/5.0071795

Vu, T. V., Takakura, H., Wells, J. C., & Minemoto, T. (2010). Production of hollow spheres of eutectic tin–lead solder through a coaxial nozzle. Journal of Solid Mechanics and Materials Engineering, 4(10), 1530–1538. https://doi.org/10.1299/jmmp.4.1530

Vu, T. V., Tryggvason, G., Homma, S., & Wells, J. C. (2015). Numerical investigations of drop solidification on a cold plate in the presence of volume change. International Journal of Multiphase Flow, 76, 73–85. https://doi.org/10.1016/j.ijmultiphaseflow.2015.07.005

Vu, T. V., & Wells, J. C. (2017). Numerical simulations of solidification around two tandemly-arranged circular cylinders under forced convection. International Journal of Multiphase Flow, 89, 331–344. https://doi.org/10.1016/j.ijmultiphaseflow.2016.11.007

Wu, G., Li, R., Yuan, Y., Jiang, L., & Sun, D. (2014). Sound absorption properties of ceramic hollow sphere structures with micro-sized open cell. Materials Letters, 134, 268–271. https://doi.org/10.1016/j.matlet.2014.07.082

Zhang, X., Wu, X., & Min, J. (2017). Freezing and melting of a sessile water droplet on a horizontal cold plate. Experimental Thermal and Fluid Science, 88, 1–7. https://doi.org/10.1016/j.expthermflusci.2017.05.009

Downloads

Published

03-07-2026

How to Cite

Luu, D. T., & Nguyen, V. L. (2026). Adaptive control of a robotic exoskeleton for enhanced knee rehabilitation. Vietnam Journal of Mechanics. https://doi.org/10.15625/0866-7136/23798

Funding data

Most read articles by the same author(s)