A screw motion approach to uniqueness analysis of head-eye geometry

The screw motion theory is used to solve a class of pose determination problems that can be characterized by a homogeneous transform equation of the form AX=XB, where A and B are known motions and X is an unknown coordinate transformation. Unlike existing methods, this method gives rise to a sound geometric interpretation that takes both rotation and translation into consideration. The author derives a screw congruence theorem and shows that the problem is to find a rigid transformation which will bring one group of lines to overlap another. He also provides a complete analysis of the conditions under which the solution can be uniquely determined