The dual quaternion approach to hand-eye calibration

In order to relate measurements made by a sensor mounted on a mechanical link to the robot's coordinate frame we must first estimate the transformation between the sensor and the link frame. In this paper we introduce the use of dual quaternions which are the algebraic counterpart of screws. We prove algebraically that if we consider the camera and motor transformations as screws, then only the line coefficients of the screw axes are relevant regarding the hand-eye calibration. This new parametrization enables us to simultaneously solve for the hand-eye rotation and translation using the singular value decomposition.