Mathematical modeling and optimization of human walking on a below-knee prosthesis

The methodology is proposed for determining kinematic, dynamic and energetic characteristics of human walking on a below-knee prosthesis in the case of experimentally prescribed angles at the leg joints. To human walking the approach is used that is based on the formulation of the optimal control problem for corresponding nonlinear dynamical system with phase restrictions and nonsmooth objective function of is evaluated energy consumption. The algorithm for a numerical solution of the problem is developed via parameterization of system’s generalized coordinates by cubic smoothing splines, utilization of an inverse dynamics approach, as well as methods of external penalty functions and minimization of nonsmooth functions in the orthogonal directions. The efficiency of the proposed methodology and created algorithm are illustrated by computer simulation of human walking on a below-knee prosthesis over a horizontal surface