Abstract
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.
Highlights
With the progress of robot-vision-system advanced technology, it is necessary to evaluate the geometric relationships among the robot, sensors, and a reference frame
We present an experimental evaluation of the extended robot–world and hand–eye methods, in which the estimation of rotation, translation, and scale factor can be formulated using the Kronecker product [20], or quaternions [21], or reprojection error [25], and a standard robot–world and hand–eye calibration method [25] with chessboard pattern calibration was used as an approximate truth-value, since no ground truth is available to compare accuracy between different methods
Depending on the different application, the advantages of the proposed extended method may outweigh this drawback. It is especially true for mobile robotics or endoscopy setups that we have in mind, where robot–world and hand–eye calibration has to be performed under specific situations, due to the restrictions in limited onboard weight or the strict sanitary conditions
Summary
With the progress of robot-vision-system advanced technology, it is necessary to evaluate the geometric relationships among the robot, sensors, and a reference frame. The second class of robot–sensor calibration problems is the form AX = ZB, which was first derived by Zhuang et al [18] This equation allowed the simultaneous estimation of the transformations from the robot-base coordinates to the world frame Z, and from the robot-gripper coordinate to the camera coordinate X. The imaging system, based on retroreflective targets (RRTs), is mounted on the robot gripper as an end effector, and non-experts can be allowed to complete the calibration and acquire the three-dimensional (3D) coordinates of the target points attached to the measurement surface from a remote location For these particular situations, an extended robot–world and hand–eye calibration approach without calibrationthe target for a robotic visualbymeasurement system.
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