Robot sensor calibration: solving AX=XB on the Euclidean group

Abstract

The equation AX=XB on the Euclidean group arises in the problem of calibrating wrist-mounted robotic sensors. In this article the authors derive, using methods of Lie theory, a closed-form exact solution that can be visualized geometrically, and a closed-form least squares solution when A and B are measured in the presence of noise.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>