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arXiv 1706.03498cs.RO
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关于X在AX = XB中的协方差

On the covariance of X in AX = XB

Nanyang Technological University(南洋理工大学)

Huy Nguyen, Quang-Cuong Pham

摘要:

手眼标定是机器人视觉中的一个基本问题,它涉及到机器人末端执行器上安装的摄像机与机器人末端执行器之间的刚体变换。在数学上,这个问题可以表述为:在AX = XB中求解X。本文给出了当A和B是随机扰动矩阵时解X的协方差的严格推导。这种细粒度的信息对于需要高度感知精度的应用程序至关重要。我们的方法包括在SE(3)中应用协方差传播方法。实验涉及合成和真实的校准数据证实,我们的方法可以预测的手-眼变换的协方差具有良好的精度。

英文摘要:

Hand-eye calibration, which consists in identifying the rigid- body transformation between a camera mounted on the robot end-effector and the end-effector itself, is a fundamental problem in robot vision. Mathematically, this problem can be formulated as: solve for X in AX = XB. In this paper, we provide a rigorous derivation of the covariance of the solution X, when A and B are randomly perturbed matrices. This fine-grained information is critical for applications that require a high degree of perception precision. Our approach consists in applying covariance propagation methods in SE(3). Experiments involving synthetic and real calibration data confirm that our approach can predict the covariance of the hand-eye transformation with excellent precision.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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