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 comput ation of the transformations from robot world to robot base and from r obot tool to robot flange coordinate frames. The flange frame is defin ed 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 r obot 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 equa tions of the form A(i)X = YB(i), i, = 1. 2, ..., m. Quaternion algebra is applied to derive explicit linear solutions for X and Y provided t hat three robot pose measurements are available. Necessary and suffici ent conditions for the uniqueness of the solution are stated. Computat ionally, the resulting solution algorithm is noniterative, fast and ro bust.