Trajectory formation based on the minimum commanded torque change model using the euler-poisson equation

A minimum commanded torque change criterion based on the optimization principle is proposed as a model that accounts for human voluntary motion. It is shown that the trajectory of human arm motion can be well reproduced by the model. In the point-to-point movement, the calculation of the torque based on the minimum commanded torque change criterion requires a highly nonlinear calculation, and it is difficult to determine the optimal trajectory. As solution methods, a Newton-like method and a steepest descent method have been proposed. However, an optimal solution cannot be obtained by these methods, for several reasons. This paper proposes a method in which the trajectory of the joint angle is analytically represented by a system of orthogonal polynomials, and the coefficients of the orthogonal polynomials are estimated by a linear iterative calculation so that the parameters satisfy the EulerPoisson equation, as a necessary condition for the optimal solution. As a result of numerical experiments, it is shown that a solution satisfying the Euler-Poisson equation with high numerical accuracy is obtained in a short time, regardless of the parameters such as those of the boundary conditions.