A controller stores the orientations of a master tool grip and a slave surgical instrument tip upon completion of a master-slave alignment process, and enters following. During following each commanded movement of the slave surgical instrument tip from the master tool grip is processed by the controller to compensate for any alignment error between the master tool grip and the slave surgical instrument tip before following was entered. The result of this processing is that the motion of the slave surgical instrument tip intuitively corresponds to the motion of the master tool grip despite an initial swooping orientation misalignment between the master tool grip and the slave surgical instrument tip.
