Machine Vision and Applications

, Volume 28, Issue 5–6, pp 569–590 | Cite as

Solving the robot-world hand-eye(s) calibration problem with iterative methods

  • Amy Tabb
  • Khalil M. Ahmad Yousef
Original Paper


Robot-world, hand-eye calibration is the problem of determining the transformation between the robot end-effector and a camera, as well as the transformation between the robot base and the world coordinate system. This relationship has been modeled as \({\mathbf {AX}}={\mathbf {ZB}}\), where \({\mathbf {X}}\) and \({\mathbf {Z}}\) are unknown homogeneous transformation matrices. The successful execution of many robot manipulation tasks depends on determining these matrices accurately, and we are particularly interested in the use of calibration for use in vision tasks. In this work, we describe a collection of methods consisting of two cost function classes, three different parameterizations of rotation components, and separable versus simultaneous formulations. We explore the behavior of this collection of methods on real datasets and simulated datasets and compare to seven other state-of-the-art methods. Our collection of methods returns greater accuracy on many metrics as compared to the state-of-the-art. The collection of methods is extended to the problem of robot-world hand-multiple-eye calibration, and results are shown with two and three cameras mounted on the same robot.


Robot Hand-eye Calibration Reconstruction 



We also would like to thank anonymous reviewers of our previous paper [15] and this paper for their helpful comments.

Compliance with ethical standards

Conflict of interest

A. Tabb received a grant from the US National Science Foundation, grant number IOS-1339211.


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Copyright information

© Springer-Verlag Berlin Heidelberg (outside the USA) 2017

Authors and Affiliations

  1. 1.United States Department of Agriculture, Agricultural Research ServiceAppalachian Fruit Research LaboratoryKearneysvilleUSA
  2. 2.Computer Engineering DepartmentThe Hashemite UniversityZarqaJordan

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