Curved cannula surgical system control

A surgical system comprising:

• a master manipulator;
• a slave manipulator controllable in response to input at the master manipulator;
• a curved cannula coupled to the slave manipulator, and movable about a center of motion of the curved cannula;
• an instrument comprising:
• a passively flexible shaft,
• a wrist mechanism disposed at a distal end of the passively flexible shaft, and
• a surgical end effector coupled to the wrist mechanism,
• wherein the passively flexible shaft is advanceable past a distal end of the curved cannula,
• wherein a straight line instrument insertion and withdrawal axis is defined by a straight line that extends from a longitudinal axis of the curved cannula at the distal end of the curved cannula;
• and
• a control system in communication with the master manipulator and the slave manipulator,
• wherein the control system is configured to determine a motion for the curved cannula based on kinematic control parameters that define the passively flexible shaft as being positioned along the straight line insertion and withdrawal axis, and
• wherein the control system is configured to command the slave manipulator to move the distal end of the curved cannula around the cannula center of motion based on the determined motion of the curved cannula.