In this paper, we propose a new solution for an old problem in robotics related to the calibration of the hand, i.e., the robot’s end-effector, and the eye, i.e., a stereo vision camera. The problem is formulated as a point set matching problem and a nonlinear estimator on manifold SO(3)$\times {\mathbb{R}}^3$ used for obtaining the solution. The main advantage of the proposed approach is that it allows to decouple the error associated with the rotational estimation on Lie group SO(3) from the error of the translational estimation on ${\mathbb{R}}^3$, which subsequently allows to tune the learning rates for the rotation and translation estimation, separately. This will result in significant increase in the convergence speed of the proposed approach. To show the advantages of our approach, we compare the results with those obtained from other conventional hand–eye calibration solutions as well as those based on point set matching. The experimental results will demonstrate that our proposed hand–eye calibration approach outperforms other approaches in terms of accuracy and computational speed.

在本文中，我们提出了一种新的解决方案，用于解决机器人技术中与手（即机器人的末端执行器）和眼睛（即立体摄像头）的校准有关的旧问题。该问题被公式化为点集匹配问题和流形SO（3）上的非线性估计$\times {\mathbb{[R}}^3$用于获得解决方案。所提出方法的主要优点是，它允许将与李群SO（3）上的旋转估计相关的误差与关于李群SO（3）的平移估计的误差解耦。${\mathbb{[R}}^3$，随后可以分别调整旋转和平移估计的学习率。这将大大提高所提出方法的收敛速度。为了展示我们方法的优势，我们将结果与从其他常规手眼校准解决方案以及基于点集匹配的结果进行比较。实验结果将证明，我们提出的手眼校准方法在准确性和计算速度方面优于其他方法。