An accelerated double-step-length iterative method for nonlinear systems of equations with applications to motion control

This article proposes an enhanced accelerated iterative method for solving systems of nonlinear equations based on a double-step-length strategy. To improve computational efficiency, the Jacobian matrix in Newton’s method is approximated using an acceleration mechanism, resulting in a fully derivative-free scheme. Moreover, an inexact line-search technique, inspired by Li and Fukushima [1], is employed to determine the two step lengths adaptively. Under mild assumptions, the global convergence of the proposed method is rigorously established. Numerical experiments confirm the efficiency and robustness of the method, demonstrating superior performance compared with approaches reported in the literature. In addition, the proposed technique is successfully applied to motion control problems involving two-joint planar robotic manipulators, highlighting its practical applicability and effectiveness.