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

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.

Simultaneous Measurement Method and Error Analysis of Six Degrees of Freedom Motion Errors of a Rotary Axis Based on Polyhedral Prism

A novel method is proposed for measuring the six degrees-of-freedom (DOF) geometric motion errors of a rotary axis based on a polyhedral prism. An error-sensitive unit which consists of a polyhedral prism and a planar reflector, is designed to carry out measurement of all six DOF errors, including the angular positioning error, the tilt motion error around the Y axis, the tilt motion error around the X axis, the radial motion error along the X and Y axes, and the axial motion error along the Z axis. The mathematical error model, including the six DOF geometric motion errors of the rotary axis, the installation errors between the polyhedral prism and the rotary axis, the manufacturing errors of the polyhedral prism, and the position errors of the sensors, are established. The effectiveness of the proposed method and the compensation model was simulated and experimentally verified.

Thermal Error Modeling of Rotary Axis Based on Convolutional Neural Network

Rotary axes are the key components for five-axis CNC machines, while their motions are dramatically influenced by thermal issues. To precisely model the thermal error of rotary axis, a convolutional neural network (CNN) model is developed. To form data sets for the CNN, a laser interferometer is used to measure the angular positioning error at different temperatures and a thermal imager is taken to obtain thermal images of the rotary axis. The measured thermal error is fitted to a sine curve so that training parameters are reduced. And the thermal pixel values of the initial thermal image are subtracted from all the thermal images to consider the incremental thermal effect, so the influence of the initial temperature is negligible. Finally, a deep CNN model with multiple output classifications is designed to complete the data training, verifying and testing. The experimental results show that the prediction accuracy for the parameters is higher than 90%, and the percentage reduction in error is higher than 80%.