A Newton-like algorithm to compute the inverse of a nonlinear map that converges in finite time

Abstract

This paper deals with the problem of inverting a nonlinear map. The proposed solution consists in a nonlinear state observer, which mimics a Newton-like algorithm, that allows to determine the inverse of a given diffeomorphism in finite time. The results are illustrated by application to the inverse kinematics of a three DOF planar manipulator.