Simultaneous robot/world and tool/flange calibration by solving homogeneous transformation equations of the form AX=YB

The paper presents a linear solution that allows a simultaneous computation of the transformations from robot world to robot base and from robot tool to robot flange coordinate frames. The flange frame is defined on the mounting surface of the end-effector. It is assumed that the robot geometry, i.e., the transformation from the robot base frame to the robot flange frame, is known with sufficient accuracy, and that robot end-effector poses are measured. The solution has applications to accurately locating a robot with respect to a reference frame, and a robot sensor with respect to a robot end-effector. The identification problem is cast as solving a system of homogeneous transformation equations of the form A_iX=YB_i,i=1, 2, ..., m. Quaternion algebra is applied to derive explicit linear solutions for X and Y provided that three robot pose measurements are available. Necessary and sufficient conditions for the uniqueness of the solution are stated. Computationally, the resulting solution algorithm is noniterative, fast and robust