Solvability-unconcerned inverse kinematics based on Levenberg-Marquardt method with robust damping

A robust numerical solution to the inverse kinematics is presented based on Levenberg-Marquardt method. The equation solvability in addition to the singularity doesn't concern the method; even in cases where the problem doesn't have solutions or has countless solutions, it converges to the optimum solution in the sense that it minimizes the residual from the target points with the smallest joint deviations. The squared norm of the residual with a small bias is used for the damping factor, while its numerical stability, convergence performance and computation speed are remarkable. It is suitable to large-scale structure-varying kinematic chains, in which the relationship between the number of constraints and the degree-of-freedom frequently changes. It frees robot operators from being careful about the assignment of the target points of effectors. As an application of the proposed method, a stretched-knee walking motion of a humanoid robot is designed.