A Global Performance Index for the Kinematic Optimization of Robotic Manipulators

TLDR

The condition number of a manipulator’s Jacobian, a known measure of error amplification between joint and Cartesian spaces, motivates a global index that can also apply to other local kinematic or dynamic indices. The paper introduces a global conditioning index (CGI) to evaluate the distribution of the Jacobian condition number across a manipulator’s entire workspace for kinematic optimization. The CGI is applied to various serial and parallel manipulators, including a two‑link serial arm, a spherical wrist, and planar and spherical parallel manipulators, to evaluate workspace conditioning. Optimization results using the CGI show its effectiveness across the tested serial and parallel manipulators.

Abstract

In this paper, a novel performance index for the kinematic optimization of robotic manipulators is presented. The index is based on the condition number of the Jacobian matrix of the manipulator, which is known to be a measure of the amplification of the errors due to the kinematic and static transformations between the joint and Cartesian spaces. Moreover, the index proposed here, termed global conditioning index (CGI), is meant to assess the distribution of the aforementioned condition number over the whole workspace. Furthermore, the concept of a global index is applicable to other local kinematic or dynamic indices. The index introduced here is applied to a simple serial two-link manipulator, to a spherical three-degree-of-freedom serial wrist, and to three-degree-of-freedom parallel planar and spherical manipulators. Results of the optimization of these manipulators, based on the GCI, are included.