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Simultaneous Robot–World and Hand–Eye Calibration without a Calibration Object

Institute of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China
Key Laboratory of the Ministry of Education for Optoelectronic Measurement Technology and Instrument, Beijing Information Science and Technology University, Beijing 100192, China
Author to whom correspondence should be addressed.
Sensors 2018, 18(11), 3949;
Received: 9 August 2018 / Revised: 29 October 2018 / Accepted: 5 November 2018 / Published: 15 November 2018
(This article belongs to the Section Physical Sensors)
PDF [2931 KB, uploaded 15 November 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. This approach could be performed for mobile or medical robotics applications, where precise, expensive, or unsterile calibration objects, or enough movement space, cannot be made available at the work site. Firstly, a mathematical model is established to formulate the robot-gripper-to-camera rigid transformation and robot-base-to-world rigid transformation using the Kronecker product. Subsequently, a sparse bundle adjustment is introduced for the optimization of robot–world and hand–eye calibration, as well as reconstruction results. Finally, a validation experiment including two kinds of real data sets is designed to demonstrate the effectiveness and accuracy of the proposed approach. The translation relative error of rigid transformation is less than 8/10,000 by a Denso robot in a movement range of 1.3 m × 1.3 m × 1.2 m. The distance measurement mean error after three-dimensional reconstruction is 0.13 mm. View Full-Text
Keywords: robot–world calibration; hand–eye calibration; calibration object; Kronecker product; sparse bundle adjustment robot–world calibration; hand–eye calibration; calibration object; Kronecker product; sparse bundle adjustment

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Li, W.; Dong, M.; Lu, N.; Lou, X.; Sun, P. Simultaneous Robot–World and Hand–Eye Calibration without a Calibration Object. Sensors 2018, 18, 3949.

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