HAND-EYE CALIBRATION

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 deter mining this relationship is referred to as the hand-eye calibration pr oblem, Hand-eye calibration is important in at least two types of task s: (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 sen sor being a television camera. With almost no exception, all existing solutions attempt to solve a homogeneous matrix equation of the form A X = XB. This article has the following main contributions. First we sh ow that there al-e two possible formulations of the hand-eye calibrati on problem. One formulation is the classic one just mentioned. A secon d formulation takes the form of the following homogeneous matrix equat ion: MY = M'YB The advantage of the latter formulation is that the ext rinsic and intrinsic parameters of the camera need not be made explici t. 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 calibra ted with respect to the robot hand: single scan-line cameras, stereo h eads, range finders, etc. Second, we develop a common mathematical fra mework to solve for the hand-eye calibration problem using either of t he two formulations. We represent rotation by a unit quaternion and pr esent two methods: (1) a closed-form solution for solving for rotation using unit quaternions and then solving for translation and (2) a non linear technique for simultaneously solving for rotation and translati on. Third, we perform a stability analysis both for our two methods an d for the linear method developed by Tsai and Lent (1989). This analys is allows the comparison of the three methods. In light of this compar ison, the nonlinear optimization method, which solves for rotation and translation simultaneously, seems to be the most robust one with resp ect to noise and measurement errors.