Abstract: A hierarchial calibration arrangement is used to provide ever-increasing levels of accuracy in positioning a robot arm end effectuator. A first level of positional calibration is the use of a home position to provide an approximate position of the robot arm end effectuator. Subsequent calibration operations provide a finer degree of positional accuracy of the robot arm end effectuator with a vision system being used to provide the most precise positioning of this apparatus. The final step in the calibration process occurs with each tape cartridge retrieval or replacement operation that is completed in the automated tape cartridge library system. Every tape cartridge storage cell in the library system contains a visual target for the final fine positioning of the robot arm end effectuator by the use of the vision element. The use of this hierarchial calibration process enables the robot arm to operate in a non-linear, non-uniform workspace.