Base invariance of the manipulability index

Abstract

The manipulability index suggested by Yoshikava is an important tool for the design of mechanisms and their control. It represents a quantitative measure of the functionality and the ability for realizing some tasks or groups of tasks. This index is some kind of performance measure and should be taken into consideration in the design phase of a mechanism and also in the design of control algorithms.In this paper two important properties of the manipulability index are investigated. The first part of the present work demonstrates that manipulability of a mechanism is independent of task space coordinates. In the second part, a proof of the independency of the manipulability index on the first DOF is given.This invariance is important for simplification of the mechanism's Jacobian matrix and gives excellent insight into the dependences of configuration space coordinates on this index. Moreover, it proves that the manipulability index is determined only by relative positions of the mechanism itself and by the mechanism's geometry.Finally, the properties of the manipulability index are illustrated by some examples for fundamental open kinematical chain structures.

Efficient Closed-Form Task Space Manipulability for a 7-DOF Serial Robot

“…Further, derivatives can be calculated analytically. As outlined by Staffetti et al [37], it is not a true metric for distance to a singularity but nonetheless serves as a relative comparison of manipulability qualities between joint configurations [38].…”

Manipulator Performance Measures - A Comprehensive Literature Survey

“…In [64] the authors have showed that the manipulability index is base invariant, that is, it is independent of the manipulator's first DoF and depends solely on the relative positioning of the links and geometry of the manipulator structure. It is also independent of the location of the operation point ( [13], [64]), where the operation point is defined as the point on the end-effector up which the Jacobian is based [13].…”

“…It is also independent of the location of the operation point ( [13], [64]), where the operation point is defined as the point on the end-effector up which the Jacobian is based [13]. This is another drawback of the manipubility index as it fails to distinguish between a long end-effector and a short one.…”

“…This is another drawback of the manipubility index as it fails to distinguish between a long end-effector and a short one. The manipulability index is independent of the task-space coordinates [64].…”

A Method for the Approximation of the Multiple IK Solutions of Regular Manipulators Based on the Uniqueness Domains and Using MLP

“…In addition, the Jacobian's determinant is h 1 invariant [3] the uniqueness domains depend only on h 2 ; h 3 . In manipulators with low degrees of freedom, detðJÞ ¼ 0 is easily solved, however, for 6 DoF the solution is much more complicated.…”