Comments on "Calibration of wrist-mounted robotic sensors by solving homogeneous transform equations of the form AX=XB" [with reply]

The commenters point out that the derivation of the closed-form solution to the homogeneous transform equation AX=XB by Y.C. Shiu and S. Ahmad (see ibid., vol.5, no.1, p.16-27, Feb.1989), although containing many useful ideas, is somewhat lengthy. It can be presented much more compactly using quaternion algebra. Direct benefits of such an approach are presented. In their reply, Shiu and Ahmad admit that the commenters' method has significant advantages over the original solution for the rotational part. However, it does not provide the geometric insight that the solution for AX=XB has a rotational degree of freedom about k/sub A/ (the axes of rotation of A). The solution to the translational part of X discussed in the original paper is not affected by this discussion since its computation is not dependent on how the rotational part is computed.>