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

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.

Methods for Simultaneous Robot-World Hand-Eye Calibration: A Comparative Study

“…However, the number of poses and camera resolution remain almost same. It can be observed that the method by Shah [8] provides a better distribution of the rotational error and hence has the lowest relative rotation error ( ) values, while the method by Li et al [9] yields a comparable result. The lowest relative translation error ( ) varies for both datasets and is yielded by the proposed method Xc2 and Park and Martin [31].…”

“…Many researchers favor this approach since the calibration pattern is easy to acquire and its use yields good results. In contrast, some studies [22,23] prefer Structure from Motion (SFM) to acquire the relative camera transformation when the camera is moved from one point to another. The approach is independent of the calibration pattern and can acquire the correspondences from the feature-rich environment.…”

“…This process continues until the system reaches the condition to terminate the iterative estimation. In a recent study, Shah [8] proposed a separable approach that forms its bases on the methods presented by Li et al [9]. Shah suggests using the Kronecker product to solve the hand-eye calibration problem.…”

“…To compensate for this issue, the best approximations for orthonormal rotational matrices are obtained using Singular Value Decomposition (SVD). The primary difference between the work of [8] and [9] is that Li et al do not update the positions that were only optimal for the rotational transformation before the orthonormal approximation. This augments to any errors that might already be present in the solution.…”

Methods for Simultaneous Robot-World-Hand–Eye Calibration: A Comparative Study

“…Many researchers favor this approach since the calibration pattern is easy to acquire and its use yields good results. In contrast, some studies [23,24] prefer Structure from Motion (SFM) to acquire the relative camera transformation when the camera is moved from one point to another. The approach is independent of the calibration pattern and can acquire the correspondences from the feature-rich environment.…”