Hand to sensor calibration: a geometrical interpretation of the matrix equation ax=xb

In this paper, the matrix equation AX=XB used for hand to sensor calibration of robot-mounted sensors is analyzed using a geometrical approach. The analysis leads to an original way to describe the properties of the equation and to find all of its solutions. It will also be highlighted why, when multiple instances A(i)X=XBi (i=1,2,...) of the equation are to be solved simultaneously, the system is overconstrained. Finally, singular cases are also discussed.