On the Correlation between Positive Definiteness of Inertia Matrix by Base-parameter Values in the Equation of Motion for Manipulators and Manipulability

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  • マニピュレータの運動方程式における基底パラメータ値による慣性行列の正定値性と可操作性との相関関係について

Abstract

<p>An inertia matrix in the equations of motion for a manipulator is positive definite. The positive definiteness of the inertia matrix depends on set of base-parameter values. Once all the base-parameter values are given, each element of the inertia matrix becomes a function of the joint variables. The base parameters, which consist of the inertia parameters, in the manipulator's motion equations, need to be estimated using parameter identification. Therefore, the inertia matrix can reveal non-positive-definite postures depending on the combination of base parameter values, and these combinations are referred to as physically impossible. The positive definiteness of the inertia matrix based on base-parameter values pertains to dynamics. On the other hand, there is the concept of manipulability in kinematics. While positive definiteness and manipulability may seem like separate concepts, it was found that for a three-degree-of-freedom manipulator, there is a correlation between the postures where the inertia matrix becomes non-positive-definite due to physically impossible base-parameter values and the postures with low manipulability.</p>

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