Hand-eye calibration

This paper deals with the hand-eye calibration problem. The guestion is to find the relative position and orientation between a camera rigidly mounted on the robot last joint and the gripper. Hand-eye calibration is useful in many cases as for example, grasping objects Or reconstructing 3D scenes. Almost all existing solutions lead to solve for homogeneous transformation equations of the form AX = XB. We propose a new formulation. Our method determines simultaneously the hand-eye transformation and the location of a calibration object with respect to the robot world coordinate system. The main advantage is that the number of unknows remains constant and the solution is constrainted to be consistent with the whole set of calibration data. Results of simulation experiments and comparisons with classical techniques are reported and analysed. Real experiments with a Cartesian robot are described and the results accuracy discussed.