Applying Optimal Control Algorithm to Estimate Muscle Activation during the Gait Cycle

Document Type : Research Paper

Authors

Department of Mechanical Engineering, Shiraz University, Mulla Sadra St., Shiraz, 71936-16548, Iran

Abstract

The effective procedure for activating muscles and improving movements in individuals who have a central nervous system injury is Functional electrical stimulation (FES). To have accurate movements of the limbs, appropriate stimulation patterns should be generated and exerted on the muscles. The challenging problem is the redundancy in the musculoskeletal system that makes it necessary to use optimal control to derive muscle activations. For doing this, the redundant musculoskeletal model of the ankle joint is derived in this paper, then an optimal control method for estimating muscle activation during the gait cycle is designed. The aim of optimal control theory is to minimize the cost function, including muscle activation as the control input and joint angle tracking error as the output of the model. Two optimal control algorithms are implemented in this research. These approaches present direct and indirect control methods to solve the optimization problem of ankle movement achieved by experimental research on two healthy males during the gait cycle. Based on the results, the direct method is smoother for nonlinear systems and estimates desired muscle activation more precisely and the cost function coefficients are chosen with logical and less values in comparison to the indirect method.

Keywords

Main Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Stewart, J.D., Foot drop: where, why and what to do?, Practical Neurology, 8, 2008, 158–169.
[2] Aout, T., Begon, M., Jegou, B., Peyrot, N., Caderby, T., Effects of Functional Electrical Stimulation on Gait Characteristics in Healthy Individuals: A Systematic Review, Sensors, 23, 2023, 8684.
[3] Mijic, M., Schoser, B., Young, P., Efficacy of functional electrical stimulation in rehabilitating patients with foot drop symptoms after stroke and its correlation with somatosensory evoked potentials—a crossover randomised controlled trial, Neurological Sciences, 44, 2023, 1301–1310.
[4] Arsianti, R.W., Arifin, A., Rehabilitation for Gait Restoration Using Functional Electrical Stimulation, Fidelity: Jurnal Teknik Elektro, 5, 2023, 61–68.
[5] Bean, N.F., Lombardo, L.M., Triolo, R.J., Audu, M.L., Facilitation of dependent transfers with functional neuromuscular stimulation: a computer simulation study, Medical & Biological Engineering & Computing, 2022, 1–11.
[6] Benoussaad, M., Rotella, F., Chaibi, I., Flatness of musculoskeletal systems under functional electrical stimulation, Medical & Biological Engineering & Computing, 58, 2020, 1113–1126.
[7] Odle, B., Reinbolt, J., Forrest, G., Dyson-Hudson, T., Construction and evaluation of a model for wheelchair propulsion in an individual with tetraplegia, Medical & Biological Engineering & Computing, 57, 2019, 519–532.
[8] Tu, X., Huang, J., He, J., Leg hybrid rehabilitation based on hip-knee exoskeleton and ankle motion induced by FES, in 2016 international conference on advanced robotics and mechatronics (ICARM), IEEE, 2016.
[9] Doll, B.D., Kirsch, N.A., Bao, X., Dicianno, B.E., Sharma, N., Dynamic optimization of stimulation frequency to reduce isometric muscle fatigue using a modified Hill‐Huxley model, Muscle & Nerve, 57, 2018, 634–641.
[10] Arash Haghpanah, S., Farrokhnia, M., Taghvaei, S., Eghtesad, M., Ghavanloo, E., Tracking ankle joint movements during gait cycle via control of functional electrical stimulation, Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, 236, 2022, 239–247.
[11] Ezati, M., Ghannadi, B., McPhee, J., A review of simulation methods for human movement dynamics with emphasis on gait, Multibody System Dynamics, 47, 2019, 265–292.
[12] He, L., et al., Control strategy for vibration suppression of a vehicle multibody system on a bumpy road, Mechanism and Machine Theory, 174, 2022, 104891.
[13] Dorschky, E., et al., Optimal control simulation predicts effects of midsole materials on energy cost of running, Computer Methods in Biomechanics and Biomedical Engineering, 22, 2019, 869–879.
[14] Dorschky, E., Nitschke, M., Seifer, A.-K., van den Bogert, A.J., Eskofier, B.M., Estimation of gait kinematics and kinetics from inertial sensor data using optimal control of musculoskeletal models, Journal of Biomechanics, 95, 2019, 109278.
[15] Eom, G.-M., Lee, J.-K., Kim, K.-S., Watanabe, T., Futami, R., Nonlinear fes control of knee joint by inversely compensated feedback system, International Journal of Control, Automation, and Systems, 4, 2006, 302–307.
[16] Pappalardo, C.M., Guida, D., Dynamic Analysis and Control Design of Kinematically-Driven Multibody Mechanical Systems, Engineering Letters, 28, 2020, 1125.
[17] van den Bogert, A.J., Blana, D., Heinrich, D., Implicit methods for efficient musculoskeletal simulation and optimal control, Procedia Iutam, 2, 2011, 297–316.
[18] Ruggiero, A., Sicilia, A., A Novel Explicit Analytical Multibody Approach for the Analysis of Upper Limb Dynamics and Joint Reactions Calculation Considering Muscle Wrapping, Applied Sciences, 10, 2020, 7760.
[19] Tang, G., Hauser, K., A data-driven indirect method for nonlinear optimal control, Astrodynamics, 3, 2019, 345–359.
[20] Passenberg, B., Theory and algorithms for indirect methods in optimal control of hybrid systems, Doctoral dissertation, Technische Universität München, Germany, 2012.
[21] Pikuliński, M., Malczyk, P., Adjoint method for optimal control of multibody systems in the Hamiltonian setting, Mechanism and Machine Theory, 166, 2021, 104473.
[22] De Groote, F., Kinney, A.L., Rao, A.V., Fregly, B.J., Evaluation of direct collocation optimal control problem formulations for solving the muscle redundancy problem, Annals of Biomedical Engineering, 44, 2016, 2922–2936.
[23] Porsa, S., Lin, Y.-C., Pandy, M.G., Direct methods for predicting movement biomechanics based upon optimal control theory with implementation in OpenSim, Annals of Biomedical Engineering, 44, 2016, 2542–2557.
[24] Lin, Y.-C., Walter, J.P., Pandy, M.G., Predictive simulations of neuromuscular coordination and joint-contact loading in human gait, Annals of Biomedical Engineering, 46, 2018, 1216–1227.
[25] Kim, J., Moon, J.H., Kim, J., Impedance Control of Human Ankle Joint With Electrically Stimulated Antagonistic Muscle Co-Contraction, IEEE Transactions on Neural Systems and Rehabilitation Engineering, 29, 2021, 1593–1603.
[26] Ferrarin, M., Palazzo, F., Riener, R., Quintern, J. Model-based control of FES-induced single joint movements, IEEE Transactions on Neural Systems and Rehabilitation Engineering, 9, 2001, 245–257.
[27] Winter, D.A., Biomechanics and Motor Control of Human Movement, John Wiley & Sons, 2009.
[28] Hoy, M.G., Zajac, F.E., Gordon, M.E., A musculoskeletal model of the human lower extremity: the effect of muscle, tendon, and moment arm on the moment-angle relationship of musculotendon actuators at the hip, knee, and ankle, Journal of Biomechanics, 23, 1990, 157–169.
[29] Han, J., Ding, Q., Xiong, A., Zhao, X., A state-space EMG model for the estimation of continuous joint movements, IEEE Transactions on Industrial Electronics, 62, 2015, 4267–4275.
[30] Ding, Q.C., Xiong, A.B., Zhao, X.G., Han, J.D., A novel EMG-driven state space model for the estimation of continuous joint movements, in 2011 IEEE International Conference on Systems, Man, and Cybernetics, IEEE, 2011.
[31] Koelewijn, A.D., Predictive Simulations of Gait and Their Application in Prosthesis Design, Doctoral dissertation, Cleveland State University, Ohio, USA, 2018.
[32] Pardo, D., Möller, L., Neunert, M., Winkler, A.W., Buchli, J., Evaluating direct transcription and nonlinear optimization methods for robot motion planning, IEEE Robotics and Automation Letters, 1, 2016, 946–953.
[33] Wu, G., et al., ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion—part I: ankle, hip, and spine, Journal of Biomechanics, 35, 2002, 543–548.
[34] Haghpanah, S.A., Farahmand, F., Zohoor, H., Razeghi, M., Generating the Activation Patterns of the Leg Muscles During Human Locomotion Using the Central Pattern Generators as a Control Structure, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 40, 2016, 87–94.
[35] Hermens, H.J., et al., European recommendations for surface electromyography, Roessingh Research and Development, 8, 1999, 13–54.
[36] Winter, D.A., Biomechanics and Motor Control of Human Movement, John Wiley & Sons, 2009.
[37] Azocar, A.F., Rouse, E.J., Stiffness perception during active ankle and knee movement, IEEE Transactions on Biomedical Engineering, 64, 2017, 2949–2956.