Optimization of ankle stiffness using genetic algorithm in gait modeling

Document Type : Research Article


School of Mechanical Engineering, Shiraz University, Shiraz, Iran


In the human gait modeling, it is common to employ 2D models that consist of a chain of rigid links joined together by frictionless hinge joints. Although Newton’s method is usually used to obtain equations of motion in the previous studies, in this research, the constrained Lagrange’s method was employed for this purpose. This method has some advantages over the previous one, such as the solution process is independent of the coordinate system and there is no necessity to know the ground reaction force beforehand. In this work, optimization was also performed by genetic algorithm so that the moment of each joint was estimated by tracking the kinematic data. Moreover, by solving the inverse dynamics and by applying Lagrange multipliers, the distribution of ground reaction force under both feet in the double support mode was calculated and compared with the experimental data to verify the effectiveness of the proposed method. Finally, as one of the applications of dynamic modeling of the human gait, the optimal value of passive stiffness in the ankle joint was obtained to provide a better design of the orthoses used for patients with motor impairment. The results show compatibility between the simulations and experiments for normalized joint moments as well as reaction forces. The optimal joint stiffness is also in the range reported by available experimental data. In conclusion, the methodology can be used for modelling human movements and can be considered as an optimal approach in designing assistive devices especially passive exsoskeletons.


Main Subjects

[1] W. Lam, J.C.Y. Leong, Y. Li, Y. Hu, W. Lu, Biomechanical and electromyographic evaluation of ankle foot orthosis and dynamic ankle foot orthosis in spastic cerebral palsy, Gait & posture, 22(3) (2005) 189-197.
[2] A. Roy, H.I. Krebs, C.T. Bever, L.W. Forrester, R.F. Macko, N. Hogan, Measurement of passive ankle stiffness in subjects with chronic hemiparesis using a novel ankle robot, Journal of neurophysiology, 105(5) (2011) 2132-2149.
[3] R.L. Lieber, S. Steinman, I.A. Barash, H. Chambers, Structural and functional changes in spastic skeletal muscle, Muscle & Nerve: Official Journal of the American Association of Electrodiagnostic Medicine, 29(5) (2004) 615-627.
[4] G. Steinwender, V. Saraph, E.-B. Zwick, C. Uitz, W. Linhart, Fixed and dynamic equinus in cerebral palsy: evaluation of ankle function after multilevel surgery, Journal of Pediatric Orthopaedics, 21(1) (2001) 102-107.
[5] M.F. Abel, G.A. Juhl, C.L. Vaughan, D.L. Damiano, Gait assessment of fixed ankle-foot orthoses in children with spastic diplegia, Archives of physical medicine and rehabilitation, 79(2) (1998) 126-133.
[6] S.J. Lawrence, M.J. Botte, Management of the adult, spastic, equinovarus foot deformity, Foot & ankle international, 15(6) (1994) 340-346.
[7] S. Yamamoto, A. Hagiwara, T. Mizobe, O. Yokoyama, T. Yasui, Development of an ankle–foot orthosis with an oil damper, Prosthetics and orthotics international, 29(3) (2005) 209-219.
[8] M. Alam, I.A. Choudhury, A.B. Mamat, Mechanism and design analysis of articulated ankle foot orthoses for drop-foot, The Scientific World Journal, 2014 (2014).
[9] I. Skaaret, H. Steen, A. Huse, I. Holm, Comparison of gait with and without ankle-foot orthoses after lower limb surgery in children with unilateral cerebral palsy, Journal of children's orthopaedics, 13(2) (2019) 180-189.
[10] M. McGrath, D. Howard, R. Baker, The strengths and weaknesses of inverted pendulum models of human walking, Gait & posture, 41(2) (2015) 389-394.
[11] V.T. Inman, H.D. Eberhart, The major determinants in normal and pathological gait, JBJS, 35(3) (1953) 543-558.
[12] H. Elftman, Biomechanics of muscle: with particular application to studies of gait, JBJS, 48(2) (1966) 363-377.
[13] G.A. Cavagna, H. Thys, A. Zamboni, The sources of external work in level walking and running, The Journal of physiology, 262(3) (1976) 639-657.
[14] S. Mochon, T.A. McMahon, Ballistic walking: An improved model, Mathematical Biosciences, 52(3-4) (1980) 241-260.
[15] T. McGeer, Passive dynamic walking, I. J. Robotic Res., 9(2) (1990) 62-82.
[16] T. McGeer, Dynamics and control of bipedal locomotion, Journal of theoretical biology, 163(3) (1993) 277-314.
[17] J.M. Donelan, R. Kram, A.D. Kuo, Mechanical work for step-to-step transitions is a major determinant of the metabolic cost of human walking, Journal of Experimental Biology, 205(23) (2002) 3717-3727.
[18] J.M. Donelan, R. Kram, A.D. Kuo, Simultaneous positive and negative external mechanical work in human walking, Journal of biomechanics, 35(1) (2002) 117-124.
[19] A.D. Kuo, J.M. Donelan, A. Ruina, Energetic consequences of walking like an inverted pendulum: step-to-step transitions, Exercise and sport sciences reviews, 33(2) (2005) 88-97.
[20] M. Srinivasan, Fifteen observations on the structure of energy-minimizing gaits in many simple biped models, Journal of The Royal Society Interface, 8(54) (2011) 74-98.
[21] T. Koolen, T. De Boer, J. Rebula, A. Goswami, J. Pratt, Capturability-based analysis and control of legged locomotion, Part 1: Theory and application to three simple gait models, The international journal of robotics research, 31(9) (2012) 1094-1113.
[22] H. Hong, S. Kim, C. Kim, S. Lee, S. Park, Spring-like gait mechanics observed during walking in both young and older adults, Journal of biomechanics, 46(1) (2013) 77-82.
[23] S. Kim, S. Park, Leg stiffness increases with speed to modulate gait frequency and propulsion energy, Journal of biomechanics, 44(7) (2011) 1253-1258.
[24] M.G. Pandy, N. Berme, A numerical method for simulating the dynamics of human walking, Journal of biomechanics, 21(12) (1988) 1043-1051.
[25] M.G. Pandy, N. Berme, Synthesis of human walking: a planar model for single support, Journal of biomechanics, 21(12) (1988) 1053-1060.
[26] M. McGrath, D. Howard, R. Baker, A lagrange-based generalised formulation for the equations of motion of simple walking models, Journal of biomechanics, 55 (2017) 139-143.
[27] F.C. Anderson, M.G. Pandy, Individual muscle contributions to support in normal walking, Gait & posture, 17(2) (2003) 159-169.
[28] R.L. Haupt, S. Ellen Haupt, Practical genetic algorithms,  (2004).
[29] J.M. Johnson, Y. Rahmat-Samii, Genetic algorithm optimization and its application to antenna design, in:  Proceedings of IEEE Antennas and Propagation Society International Symposium and URSI National Radio Science Meeting, IEEE, 1994, pp. 326-329.
[30] S. Onyshko, D. Winter, A mathematical model for the dynamics of human locomotion, Journal of biomechanics, 13(4) (1980) 361-368.
[31] D. Winter, J. Milsum, Biomechanics of human movement. John Willey & Sons, Influência dos níveis de atividade física no comportamento biomecânico das forças reativas do apoio durante o caminhar em mulheres pós-menopáusicas, 202 (1979).
[32] K. Nomura, T. Yonezawa, H. Mizoguchi, H. Takemura, Measurement of the passive stiffness of ankle joint in 3 DOF using stewart platform type ankle foot device, in:  2016 38th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), IEEE, 2016, pp. 5011-5014.