Construction of a symbolic gait model for tasks of analysis, prediction, and control synthesis

This paper examines the problem of constructing a predictive and process control model based on telemetry data for a class of bionic prostheses that adapt to the patient’s gait by varying the knee joint torque. The paper presents the results of applying a Markov model of the dynamic process of telemetry data processing, using heuristically introduced indicator functions-states, generally recognized in the analysis of gait biomechanics. The approach describes a complex dynamic process in a compact and easily trainable form, enabling the implementation of patient-adapted prosthesis control systems. The matrix form of the model, derived from a statistically substantiated individual operating history, enables predictive prosthesis control.
EDN: BBLUFO, https://elibrary/bblufo

References

[1] Meshchikhin I.A., Minkov S.S., Lichkunov A.A. The Markov model of a dynamic system based on experimental data for control problems of bionic prostheses. arXiv: 2204.08429, doi: https://doi.org/10.48550/arXiv.2204.08429

[2] Meshchikhin I.A., Gavriushin S.S. The application of elements of information theory to the problem of rational choice of measuring instruments. In: Advances in artificial systems for medicine and education II. Springer, 2018, pp. 705–712, doi: https://doi.org/10.1007/978-3-030-12082-5_64

[3] Kudryavtsev V.B., Aleshin S.V., Podkolzin A.S. Vvedenie v teoriyu avtomatov [Introduction to automata theory.]. Moscow, Nauka Publ., 1985. 320 p. (In Russ.).

[4] Akimov O.E. Diskretnaya matematika: logika, gruppy, grafy [Discrete mathematics: logic, groups, graphs]. Moscow, Laboratoriya bazovykh znaniy Publ., 2001. 376 p. (In Russ.).

[5] Vitenzon A.S., Skvortsov D.V. Diagnosis of mobility pathology using instrumental testing: gait analysis and stabilometry. Vestnik travmatologii i ortopedii im. N.N. Priorova [N.N. Priorov Journal of Traumatology and Orthopedics], 2008, no. 4, pp. 92–93. (In Russ.).

[6] Richey M. The evolution of Markov chain Monte Carlo methods. Amer. Math. Monthly, 2010, vol. 117, no. 5, pp. 383–413, doi: https://doi.org/10.4169/000298910X485923

[7] Pitkin M.R. Biomechanics of lower limb prosthetics. Springer, 2010. 141 p.

[8] Jin Y., Hou L., Zhong S. Extended dynamic mode decomposition with invertible dictionary learning. Neural Netw., 2024, vol. 173, art. 106177, doi: https://doi.org/10.1016/j.neunet.2024.106177

[9] Skvortsov D.V. Concept of pathological gait analysis. Rossiyskiy zhurnal biomekhaniki [Russian Journal of Biomechanics], 1999, vol. 3, no. 2, pp. 104–105. (In Russ.).

[10] Tagawa Y., Yamashita T. Analysis of human abnormal walking using zero moment joint: required compensatory actions. J. Biomech., 2001, vol. 34, no. 6, pp. 783–790, doi: https://doi.org/10.1016/S0021-9290(00)00216-5

[11] Alpin Yu.A., Alpina V.S. The Perron–Frobenius theorem – a proof with the use of Markov chains. Zapiski nauchnykh seminarov POMI, 2008, vol. 359, pp. 5–16. (In Russ.). (Eng. version: J. Math. Sci., 2009, vol. 157, no. 5, pp. 675–680, doi: https://doi.org/10.1007/s10958-009-9347-9)

[12] Suzuki Y., Togame K., Nakamura A. et al. A Markov chain approximation of switched Fokker–Planck equations for a model of on–off intermittency in the postural control during quiet standing. Commun. Nonlinear Sci. Numer. Simul., 2023, vol. 126, art. 107488, doi: https://doi.org/10.1016/j.cnsns.2023.107488

[13] Klus S., Koltai P., Sch?tte C. On the numerical approximation of the Perron-Frobenius and Koopman operator. arXiv:1512.05997, doi: https://doi.org/10.3934/jcd.2016003

[14] Revuz D. Markov processes. Elsevier, 1975. 336 p. (Russ. ed.: Tsepi Markova. Moscow, RFFI Publ., 1997. 431 p.)

[15] Champion K. et al. Data-driven discovery of coordinates and governing equations. PNAS, 2019, vol. 116, no. 45, pp. 22445–22451, doi: https://doi.org/10.1073/pnas.1906995116

[16] Williams M.O., Kevrekidis I.G., Rowley C.W. A data–driven approximation of the Koopman operator: extending dynamic mode decomposition. J. Nonlinear Sci., 2015, vol. 25, no. 6, pp. 1307–1346, doi: https://doi.org/10.1007/s00332-015-9258-5

[17] Ivanova G.E., Skvortsov D.V. An objective clinical gait analysis a survey. Overview. Vestnik vosstanovitelnoy meditsiny [Bulletin of Rehabilitation Medicine], 2015, no. 4, pp. 59–66. (In Russ.).

[18] Osipov G.S., Panov A.I. Relationships and operations in agent’s sign-based model of the world. Iskusstvennyy intellekt i prinyatie resheniy [Artificial Intelligence and Decision Making], 2017, no. 4, pp. 5–22. (In Russ.).

[19] Romeo L. Applied machine learning for health informatics: human motion analysis and affective computing application. PhD Thesis. Universita Politecnica Delle Marche, 2018. 146 p.

[20] Nikulchev E.V. Geometric method of reconstructing systems from experimental data. Pisma v ZhTF, 2007, vol. 33, no. 6, pp. 83–89. (In Russ.). (Tech. Phys. Lett., 2007, vol. 33, no. 3, pp. 267–269, doi: https://doi.org/10.1134/S1063785007030248)