HAND-EYE CALIBRATION
HAND-EYE CALIBRATION
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DOI：
10.1177/027836499501400301
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发表时间：
1995-06-01
影响因子：
9.2
通讯作者：
DORNAIKA, F
中科院分区：
文献类型：
--
作者：
HORAUD, R;DORNAIKA, F
当传感器安装在机器人手上时，了解传感器和手之间的关系是很重要的。确定这种关系的问题被称为手眼校准问题。手眼校准在至少两种类型的任务中是重要的：（1）将传感器中心的测量映射到机器人工作空间框架中，以及（2）允许机器人精确地移动传感器的任务。过去提出了一些解决方案，特别是在传感器是电视摄像机的情况下。几乎没有例外，所有现有的解决方案都试图解决形式AX = XB的齐次矩阵方程。本文的主要贡献如下。首先，我们表明，有al-e手眼校准问题的两种可能的配方。一种提法是刚才提到的经典提法。第二个公式采用以下齐次矩阵方程的形式：MY = M ′ YB后一个公式的优点是不需要使摄像机的外部和内部参数显式化。实际上，该公式直接使用与骆驼a相对于校准框架的两个位置相关联的3x 4透视矩阵（M和M '）。此外，这个配方与经典的一个涵盖了更广泛的基于相机的传感器进行校准相对于机器人的手：单扫描线相机，立体头，测距仪等第二，我们开发了一个共同的数学框架来解决的手眼校准问题，使用这两种配方。我们用一个单位四元数表示旋转，并提出了两种方法：（1）一个封闭形式的解决方案，解决旋转使用单位四元数，然后解决平移和（2）同时解决旋转和平移的非线性技术。第三，我们对我们的两种方法和Tsai和Lent（1989）开发的线性方法进行了稳定性分析。这种分析可以比较这三种方法。根据这种比较，同时解决旋转和平移的非线性优化方法似乎是相对于噪声和测量误差最鲁棒的方法。
Whenever a sensor is mounted on a robot hand, it is important to know the relationship between the sensor and the hand. The problem of determining this relationship is referred to as the hand-eye calibration problem, Hand-eye calibration is important in at least two types of tasks: (1) map sensor centered measurements into the robot workspace frame and (2) tasks allowing the robot to precisely move the sensor In the past some solutions were proposed, particularly in the case of the sensor being a television camera. With almost no exception, all existing solutions attempt to solve a homogeneous matrix equation of the form AX = XB. This article has the following main contributions. First we show that there al-e two possible formulations of the hand-eye calibration problem. One formulation is the classic one just mentioned. A second formulation takes the form of the following homogeneous matrix equation: MY = M'YB The advantage of the latter formulation is that the extrinsic and intrinsic parameters of the camera need not be made explicit. Indeed, this formulation directly uses the 3x4 perspective matrices (M and M') associated with two positions of the camel-a with respect to the calibration frame. Moreover this formulation together with the classic one covers a wider range of camera-based sensors to be calibrated with respect to the robot hand: single scan-line cameras, stereo heads, range finders, etc. Second, we develop a common mathematical framework to solve for the hand-eye calibration problem using either of the two formulations. We represent rotation by a unit quaternion and present two methods: (1) a closed-form solution for solving for rotation using unit quaternions and then solving for translation and (2) a nonlinear technique for simultaneously solving for rotation and translation. Third, we perform a stability analysis both for our two methods and for the linear method developed by Tsai and Lent (1989). This analysis allows the comparison of the three methods. In light of this comparison, the nonlinear optimization method, which solves for rotation and translation simultaneously, seems to be the most robust one with respect to noise and measurement errors.