A consistent null-space based approach to inverse kinematics of redundant robots

Abstract

A unified formulation is presented for the inverse kinematics of redundant arms based on a special formulation of the null space of the Jacobian. By extending (appropriately rescaling) previously used null space parameterizations, the manipulability measure, the null space projector, and particular solutions for the joint velocities are obtained in a unified fashion. The minimum norm pseudo-inverse solution is obtained as a projection from any particular solution, and the method provides an intuitive visualization of the self-motion. The approach is applied to the case of the extended Jacobian (extra subtask constraints) to yield the measure of manipulability of the extended Jacobian, and also to find the joint velocities (including subtask) as a projection of any particular solution of the joint velocities. It is argued that relationships among the optimal joint velocities for arbitrary different tasks can be easily visualized via the null space of the Jacobian by using the authors' approach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>