A Modern Solution for an Old Calibration Problem

Abstract

Cameras endow a robot with a sense of vision to see the world. The data acquired from a camera is originally expressed in the camera coordinate system. However, a robot manipulator only accepts the data represented in the robot coordinate system. Under such circumstances, robotic applications that employ cameras necessitate the requirement of converting the camera-acquired data into the robot coordinate system. Since the robot coordinate system is often attached to the base of the robot, the relationship between the camera's and the robot's frames (commonly described by a homogeneous transformation matrix) is composed of two parts: the transformation matrix between the base frame and the end-effector frame of the robot manipulator; and the transformation matrix between the end-effector frame and the camera frame. As the first transformation matrix can be attained from robot kinematics, the problem of representing the camera-acquired data in the robot coordinate system boils down to the estimation of the transformation matrix between the robot's end-effector frame and the camera frame. This estimation problem is widely known as the hand-eye calibration problem since the end-effector and the camera are commonly regarded as the hand and the eye of a robot, respectively. The hand-eye calibration problem plays an important role in robotic applications as it enables the use of cameras in such applications. This problem also emerges in other applications such as visual servoing, 3D scanning systems, and other sensor calibrations.