• Corpus ID: 7446157

# Simultaneous robot-world and hand-eye calibration using dual-quaternions and Kronecker product

@article{Li2010SimultaneousRA,
title={Simultaneous robot-world and hand-eye calibration using dual-quaternions and Kronecker product},
author={Ai Guo Li and Lin Wang and Defeng Wu},
journal={International Journal of Physical Sciences},
year={2010},
volume={5},
pages={1530-1536}
}
• Published 4 September 2010
• Engineering
• International Journal of Physical Sciences
Two solutions of the homogeneous matrix equation AX=ZB, that allows a simultaneous computation of the transformations from robot world to robot base and from robot tool to robot wrist coordinate frames, are proposed. The presented methods introduce the Kronecker product and dual quaternions to solve the rotations and translations problem, simultaneously, with no propagation error. The experimental results in a simulated and a real environment are reported and analyzed.   Key words: Hand…

## Figures and Tables from this paper

Solving the Robot-World/Hand-Eye Calibration Problem Using the Kronecker Product
This paper constructs a separable closed-form solution to the robot-world/hand-eye calibration problem AX1⁄4YB. Qualifications and properties that determine the uniqueness of X and Y as well as error
Optimal robot-world and hand-eye calibration with rotation and translation coupling
• Physics
Robotica
• 2022
A classic hand-eye system involves hand-eye calibration and robot-world and hand-eye calibration. Insofar as hand-eye calibration can solve only hand-eye transformation, this study aims to
Simultaneous Robot–World and Hand–Eye Calibration without a Calibration Object
• Computer Science
Sensors
• 2018
An extended robot–world and hand–eye calibration method is proposed in this paper to evaluate the transformation relationship between the camera and robot device and to demonstrate the effectiveness and accuracy of this approach.
Hand-eye and robot-world calibration by global polynomial optimization
• Computer Science
2014 IEEE International Conference on Robotics and Automation (ICRA)
• 2014
This paper shows that the method of convex linear matrix inequality (LMI) relaxations can be used to effectively solve these problems and to obtain globally optimal solutions to hand-eye calibration problems.
Simultaneous Calibration of Hand-Eye Relationship, Robot-World Relationship and Robot Geometric Parameters with Stereo Vision
• Materials Science
ICCSIP
• 2016
A novel calibration method is proposed which can calibrate hand-eye relationship, robot-world relationship and robot geometric parameters simultaneously simultaneously, and least square method is introduced to solve calibration equations.
Simultaneous Hand–Eye, Tool–Flange, and Robot–Robot Calibration for Comanipulation by Solving the $\mathbf{AXB=YCZ}$ Problem
• Materials Science
IEEE Transactions on Robotics
• 2016
This work formulated the problem of hand-eye, tool-flange, and robot-robot calibration to a matrix equation AXB=YCZ and introduced a closed-form solution based on quaternions to give an initial value.
Parameterizations for reducing camera reprojection error for robot-world hand-eye calibration
• Computer Science
2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
• 2015
This paper parameterizes the rotation components using Euler angles and finds a solution using Levenberg-Marquadt iterative approach and offers a method to determine A, X, and Z, by formulating the robot-world, hand-eye calibration problem in terms of camera reprojection error.
Calibration-Free Robot-Sensor Calibration approach based on Second-Order Cone Programming
• Computer Science
• 2018
A calibration-free approach that solve the robot-sensor calibration problem of the form AX = YB based on Second-Order Cone Programming based on Structure-From-Motion approach and dual quaternion theory can effectively improve the calibration accuracy of the Robot-world and hand-eye relation, and extend the application field of robot-Sensor calibration method.
Hand-eye calibration method with a three-dimensional-vision sensor considering the rotation parameters of the robot pose
• Engineering
International Journal of Advanced Robotic Systems
• 2020
A new calibration method considering the rotation parameters of the robot pose whose slight errors cause large disturbance to the solution are selected by analyzing the coefficient matrices of the error items.

## References

SHOWING 1-10 OF 16 REFERENCES
Simultaneous robot-world and hand-eye calibration
• Mathematics
IEEE Trans. Robotics Autom.
• 1998
Two new solutions that attempt to solve the homogeneous matrix equation of the for, AX=ZB are presented: a closed-form method which uses quaternion algebra and a positive quadratic error function associated with this representation; and a method based on nonlinear constrained minimization and which simultaneously solves for rotations and translations.
Hand-Eye Calibration Using Dual Quaternions
This paper algebraically prove that if the authors consider the camera and motor transformations as screws, then only the line coefficients of the screw axes are relevant regarding the hand-eye calibration, and shows how a line transformation can be written with the dual-quaternion product.
Simultaneous robot/world and tool/flange calibration by solving homogeneous transformation equations of the form AX=YB
• Materials Science
IEEE Trans. Robotics Autom.
• 1994
A linear solution that allows a simultaneous computation of the transformations from robot world to robot base and from robot tool to robot flange coordinate frames and is noniterative, fast and robust.
Hand-eye calibration
• Computer Science
Proceedings of the 1997 IEEE/RSJ International Conference on Intelligent Robot and Systems. Innovative Robotics for Real-World Applications. IROS '97
• 1997
This work determines simultaneously the hand-eye transformation and the location of a calibration object with respect to the robot world coordinate system and proposes a new formulation that is constrained to be consistent with the whole set of calibration data.
A new technique for fully autonomous and efficient 3D robotics hand/eye calibration
• Computer Science
IEEE Trans. Robotics Autom.
• 1989
A novel technique for computing position and orientation of a camera relative to the last joint of a robot manipulator in an eye-on-hand configuration aimed at simplicity, efficiency, and accuracy while giving ample geometric and algebraic insights is described.
Hand/eye calibration for electronic assembly robots
• Hanqi Zhang
• Computer Science
IEEE Trans. Robotics Autom.
• 1998
A new linear solution method for the problem of hand/eye calibration is given and an iterative method is also proposed that improves the accuracy of calibration.
Robot sensor calibration: solving AX=XB on the Euclidean group
• Mathematics
IEEE Trans. Robotics Autom.
• 1994
The authors derive, using methods of Lie theory, a closed-form exact solution that can be visualized geometrically, and aclosed-form least squares solution when A and B are measured in the presence of noise.
Hand-Eye Calibration
• Mathematics
Int. J. Robotics Res.
• 1995
A common mathematical framework is developed to solve for the hand-eye calibration problem using either of the two formulations and the nonlinear optimization method, which solves for rotation and translation simultaneously, seems to be the most robust one with respect to noise and measurement errors.
Simultaneous sensor and hand-sensor calibration of a robot-based measurement system
• Materials Science
• 2009
.This paper presents a system for object digitalization by use of a laser stripe triangulation displacement sensor and an industrial MOTOMAN robot. In order to ensure the precision of the scanning
Calibration of wrist-mounted robotic sensors by solving homogeneous transform equations of the form AX=XB
• Mathematics, Engineering
IEEE Trans. Robotics Autom.
• 1989
Etalonnage d'un capteur monte sur le poignet d'un robot par resolutions des equations des transformations homogenes de la forme AX=XB