Hand-Eye Calibration Using Dual Quaternions
Abstract
To relate measurements made by a sensor mounted on a mechanical link to the robot’s coordinate frame, we must first estimate the transformation between these two frames. Many algorithms have been proposed for this so-called hand-eye calibration, but they do not treat the relative position and orientation in a unified way. In this paper, we introduce the use of dual quaternions, which are the algebraic counterpart of screws. Then we show how a line transformation can be written with the dual-quaternion product. We algebraically prove that if we consider the camera and motor transformations as screws, then only the line coefficients of the screw axes are relevant regarding the hand-eye calibration. The dual-quaternion parameterization facilitates a new simultaneous solution for the hand-eye rotation and translation using the singular value decomposition. Real-world performance is assessed directly in the application of hand-eye information for stereo reconstruction, as well as in the positioning of cameras. Both real and synthetic experiments show the superiority of the approach over two other proposed methods.
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Dual quaternions have proven to be an efficient and useful representation for vision topics such as hand-eye calibration, simultaneous mapping and localisation, and pose estimation and tracking.
“More specifically, they have proven to be an efficient and useful representation for many topics related to vision, such as hand-eye calibration [11], simultaneous mapping and localisation [12] and pose estimation and tracking [13]-[15].”
From Dual Quaternion-Based Visual Servoing for Grasping Moving Objects (2021) · cites this paper as [11]
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A Dual-quaternion Method for Control of Spatial Rigid Body
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Dual Quaternion-Based Visual Servoing for Grasping Moving Objects
De Farias, C., Adjigble, M., Tamadazte, B., Stolkin, R., & Marturi, N. (2021) · 2021 IEEE 17th International Conference on Automation Science and Engineering (CASE) · doi:10.1109/case49439.2021.9551631 · Cited by 1 · see citing works
- Authors
- Daniilidis, K.
- Affiliations
- University of Pennsylvania (US)
- Corresponding author
- Daniilidis, Konstantinos
- Venue
- The International Journal of Robotics Research
- Publisher
- SAGE Publications
- Published
- 1999-03
- Volume
- 18
- Issue
- 3
- Pages
- 286-298
- ISSN
- 0278-3649 (ISSN-L)
- 1741-3176
- OpenAlex
- W2121349631
- Cited by
- 729
- References
- 18
- Citations by year
- 2026: 34 · 2025: 54 · 2024: 52 · 2023: 56 · 2022: 58 · 2021: 49 · 2020: 42 · 2019: 43 · 2018: 40 · 2017: 34 · 2016: 28 · 2015: 21 · 2014: 27 · 2013: 32 · 2012: 19
- FWCI
- 8.04
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- The International Journal of Robotics Research (publishedVersion)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Robotic Mechanisms and Dynamics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Vision and Imaging
- Physical Sciences › Engineering › Control and Systems Engineering › Robot Manipulation and Learning
- Keywords
- hand-eye calibration, dual quaternions, screw theory, singular value decomposition, stereo reconstruction, camera placement
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