Iterative Kinematic Inversion of General Five-Axis Robot Manipulators

Abstract

A kinematic model is derived that allows the computation of the joint coordinates and their time rates, given the Cartesian coordinates, velocities, and accelerations of five-axis manipu lators of arbitrary architecture. The model leads to a for mally overdetermined nonlinear algebraic system of six equations in five unknowns. Its least-squares approximation produces the desired joint coordinates. Joint rates are com puted as the least-squares approximation of a formally over determined linear algebraic system of six equations in five unknowns, relating the desired rates with the Cartesian ve locities. The time derivatives of the joint rates are computed similarly, but from Cartesian accelerations. The procedure is illustrated with two fully solved examples.