Technical Paper:

# Kinematic Modeling of Six-Axis Industrial Robot and its Parameter Identification: A Tutorial

## Md. Moktadir Alam, Soichi Ibaraki^{†}, and Koki Fukuda

Graduate School of Advanced Science and Engineering, Hiroshima University

1-4-1 Kagamiyama, Higashi-hiroshima, Hiroshima 739-8511, Japan

^{†}Corresponding author

In advanced industrial applications, like machining, the absolute positioning accuracy of a six-axis robot is indispensable. To improve the absolute positioning accuracy of an industrial robot, numerical compensation based on positioning error prediction by the Denavit and Hartenberg (D-H) model has been investigated extensively. The main objective of this study is to review the kinematic modeling theory for a six-axis industrial robot. In the form of a tutorial, this paper defines a local coordinate system based on the position and orientation of the rotary axis average lines, as well as the derivation of the kinematic model based on the coordinate transformation theory. Although the present model is equivalent to the classical D-H model, this study shows that a different kinematic model can be derived using a different definition of the local coordinate systems. Subsequently, an algorithm is presented to identify the error sources included in the kinematic model based on a set of measured end-effector positions. The identification of the classical D-H parameters indicates a practical engineering application of the kinematic model for improving a robot’s positioning accuracy. Furthermore, this paper presents an extension of the present model, including the angular positioning deviation of each rotary axis. The angular positioning deviation of each rotary axis is formed as a function of the axis’ command angles and the direction of its rotation to model the effect of the rotary axis backlash. The identification of the angular positioning deviation of each rotary axis and its numerical compensation are presented, along with their experimental demonstration. This paper provides an essential theoretical basis for the error source diagnosis and error compensation of a six-axis robot.

*Int. J. Automation Technol.*, Vol.15, No.5, pp. 599-610, 2021.

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