Calibration of wrist-mounted robotic sensors by solving homogeneous transform equations of the form AX=XB

To use a wrist-mounted sensor (such as a camera) for a robot task, the position and orientation of the sensor with respect to the robot wrist frame must be known. The sensor mounting position can be found by moving the robot and observing the resulting motion of the sensor. This yields a homogeneous transform equation of the form AX=XB , where A is the change in the robot wrist position, B is the resulting sensor displacement, and X is the sensor position relative to the robot wrist. The solution to an equation of this form has one degree of rotational freedom and one degree of translation freedom if the angle of rotation of A is neither 0 nor π radians. To solve for X uniquely, it is necessary to make two arm movements and form a system of two equations of the form: A₁X=XB₁ and A ₂X=XB₂. A closed-form solution to this system of equations is developed and the necessary conditions for uniqueness are stated