Abstract
A new formulation of the problem of designing a femoral prosthesis is proposed. This formulation reduces to solving the problem of the energy-optimal control with parameters for a nonlinear multidimensional mechanical system that models the human locomotor system with a femoral prosthesis. The results of numerical solution of the optimal control problem for two types of prostheses with pneumatic and hydraulic knee mechanisms are described.
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References
V. V. Beletsy, Bipedal Walk: Model Problems of Dynamics and Control [in Russian], Nauka, Moscow (1984).
V. Ye. Berbyuk, Dynamics and Optimization of Automatic Devices [in Russian], Naukova Dumka, Kyiv (1989).
V. Ye. Berbyuk and N. I. Nishchenko, “Energetically optimal control of the movement of man in the phase of stepping on a prosthetic leg, ” Probl. Upravl. Inf., 2, 75–86 (1997).
V. Ye. Berbyuk, G. V. Krasyuk, and I. N. Nishchenko, “Mathematical modeling of the dynamics of walking of man in the saggital plane, ” Mat. Met. Fyz.-Mekh. Polya, 40, No. 4, 127–138 (1997).
B. A. Bordyug, V. B. Larin, and A. G. Timoshenko, Problems of Control of Walking Devices [in Russian], Naukova Dumka, Kyiv (1985).
V. V. Smyslov, Hydraulics and Aerodynamics [in Russian], Vyshcha Skola, Kyiv (1979).
D. M. Himmelblau, Applied Nonlinear Programming, McGraw-Hill, New York (1972).
V. E. Berbyuk, “Multibody system modeling and optimization problems of lower limb prostheses, ” in: IUTAM Symposium on Optimization of Mechanical Systems (D. Bestle and W. Schiehlen, eds.), Proceedings, Kluwer Academic Publishers, The Netherlands (1996), pp. 25–32.
C. K. Chrow and D. H. Jacobson, “Studies of human locomotion via optimal programming, ” Math. Biosci., 10, No. 3/4, 239–306 (1971).
S. Johansson, B. Christiansson, and D. Karlsson, “Gait analysis when comparing two polycentric prosthetic kneejoint amputees, ” Biomech. Sem., 7, 152–156 (1993).
D. Winter, The Biomechanics and Motor Control of Human Gait, Univ. of Waterloo Press, Canada (1991).
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Berbyuk, V.E., Nishchenko, N.I. Mathematical Design of Energy-Optimal Femoral Prostheses. Journal of Mathematical Sciences 107, 3647–3654 (2001). https://doi.org/10.1023/A:1011966912564
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DOI: https://doi.org/10.1023/A:1011966912564