Abstract
In this paper we obtain a mathematical model for the flexion–extension (flex-ext) motion of the human lower limb joints in the sagittal plane. This model is composed of a system of differential equations based on quadratic polinoms, obtained from the experimental data collected during walking. Numerical integrations of the mathematical model and the construction of the state space by utilizing numerical solutions and the comparison with the state space obtained from experimental data are obtained. The trajectories of the solution of the phenomenological model are very close to the result of the measurements of the flex-ext angles of the Subject’s joints before the pre-processing stage, but they are narrower, more similar with those obtained after pre-processing.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Hilborn, R., Mangel, M.: The ecological detective: confronting models with data 28 (1997)
Brunton, S., et al.: Discovering governing equations from data: sparse identification of nonlinear dynamical systems. Proc. Natl. Acad. Sci. 113, 3932–3937 (2015)
Breeden, J., Hübler, A.: Reconstructing equations of motion from experimental data with unobserved variables. Phys. Rev. A 42, 5817–5826 (1990)
Baker, G., Gollub, J., Blackburn, J.: Inverting chaos: extracting system parameters from experimental data. Chaos 6, 528–533 (1997)
Tarnita, D., et al.: Applications of nonlinear dynamics to human knee movement on plane &inclined treadmill. In: New Trends in Medical & Service Robots, vol. 39. Springer, pp. 59–73 (2016)
Tarnita, D., Geonea, I.: Numerical Simulations and Experimental Human Gait Analysis Using Wearable Sensors, pp. 289–304. New Trends in Medical and Service Robots, Springer (2018)
Major, Z.Z. et al.: The impact of robotic rehabilitation on the motor system in neurological diseases. A multimodal neurophysiological approach. Int. J. Environ. Res. Public Health 17, 6557 (2020)
Pisla, D., et al.: A parallel robot with torque monitoring for brachial monoparesis rehabilitation tasks. Appl. Sci. 11, 9932 (2021)
Pisla, D., et al.: Development of a control system and functional validation of a parallel robot for lower limb rehabilitation. Actuators 10, 277 (2021)
Tarnita, D. et al.: Experimental characterization of human walking on stairs applied to humanoid dynamics. In: Advances in Robot Design and Intelligent Control, RAAD16, pp. 293–301. Springer (2017)
Takens, F.: Detecting strange attractors in turbulence. In: Dynamical Systems and Turbulence, 1981, pp. 366–381. Warwick (1980)
Broomhead, D.S., King, G.P.: Extracting qualitative dynamics from experimental data. Phys. D Nonlinear Phenom. 20(2–3), 217–236 (1986)
Fraser, A.M., Swinney, H.L.: Independent coordinates for strange attractors from mutual information. Phys. Rev. A 33(2), 1134–1140 (1986)
Kennel, M.B., et al.: Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A 45(6), 3403–3411 (1992)
Tarnita, D., Marghitu, D.-B.: Nonlinear dynamics of normal and osteoarthritic human knee. In: Proceedings of the Romanian Academy, pp. 353–360 (2017)
Golyandina, N. et al.: Singular Spectrum Analysis with R (2018)
Golyandina, N., Korobeynikov, A.: Basic singular spectrum analysis and forecasting with R. Comput. Stat. Data Anal. 71, 934–954 (2014)
Georgescu, M.: Contributions on the human gait stability. Ph.D. thesis, Craiova (2021)
Hershey, D.: Finite Difference Calculus Transport Analysis, pp. 299–326. Springer, Boston (1973)
Kahle, D.: Mpoly: multivariate polynomials in R. R J. 5, 181–187 (2013)
Mourrain, B., Pan, V.Y.: Multivariate polynomials, duality, and structured matrices. J. Complex. 16(1), 110–180 (2000)
Wei-Dong, L., et al.: Global vector-field reconstruction of nonlin dynamical systems from a time series with SVD method validation with Lyap exp. Chinese Phys. 12, 1366 (2003)
Huffaker, R., Bittelli, M., Rosa, R.: Nonlinear time series analysis with R (2018)
Zhang, T., Yang, B.: An exact approach to ridge regression for big data. Comput. Stat. 32(3), 909–928 (2017)
Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B. R. Stat. Soc. Ser. B 58, 267–288 (1996)
Gauraha, N.: Introduction to the LASSO. Resonance 23(4), 439–464 (2018)
Yazdi, M., Golilarz, N.A., Nedjati, A., Adesina, K.A.: An improved lasso regression model for evaluating the efficiency of intervention actions in a system reliability analysis. Neural Comput. Appl. 33(13), 7913–7928 (2021)
Ekstrøm, C.T.: MESS: miscellaneous esoteric statistical scripts (2020). https://cran.r-project.org/web/packages/MESS/index.html. Accessed 10 Jan 2020
Hastie, T., Qian, J., Tay, K.: An Introduction to glmnet (2020). https://glmnet.stanford.edu, https://glmnet.stanford.edu/articles/glmnet.html. Accessed 12 Jan 2020
Soetaert, K., Petzoldt, T., Setzer, R.: Package deSolve: solving initial value differential equations in R. R J. 2, 5–15 (2010)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Georgescu, M., Tarniță, D., Berceanu, C., Geonea, I., Tarniță, DN. (2024). Phenomenological Modelling of the Nonlinear Flexion–Extension Movement of Human Lower Limb Joints. In: Pisla, D., Carbone, G., Condurache, D., Vaida, C. (eds) Advances in Service and Industrial Robotics. RAAD 2024. Mechanisms and Machine Science, vol 157. Springer, Cham. https://doi.org/10.1007/978-3-031-59257-7_18
Download citation
DOI: https://doi.org/10.1007/978-3-031-59257-7_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-59256-0
Online ISBN: 978-3-031-59257-7
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)