On Isotropic Sets of Points in the Plane. Application to the Design of Robot Archirectures

TL;DR

This paper explores isotropic point sets in the plane to optimize serial manipulator design, focusing on minimizing Jacobian condition numbers and defining isotropic configurations for revolute joint manipulators.

Contribution

It introduces the concept of isotropic point sets and their application to planar manipulator design, extending the idea of isotropy to optimize robot architectures.

Findings

Isotropic configurations minimize roundoff-error amplification.

Families of isotropic manipulators are defined based on connected isotropic points.

The concepts are currently extended from planar to spatial manipulators.

Abstract

Various performance indices are used for the design of serial manipulators. One method of optimization relies on the condition number of the Jacobian matrix. The minimization of the condition number leads, under certain conditions, to isotropic configurations, for which the roundoff-error amplification is lowest. In this paper, the isotropy conditions, introduced elsewhere, are the motivation behind the introduction of isotropic sets of points. By connecting together these points, we define families of isotropic manipulators. This paper is devoted to planar manipulators, the concepts being currently extended to their spatial counterparts. Furthermore, only manipulators with revolute joints are considered here.