A robotic surgical system employs a surgical instrument (20), a robot (40) for navigating the surgical instrument (20) relative to an anatomical region (10) within a coordinate system (42) of the robot (40), and a robot controller (43) for defining a remote center of motion for a spherical rotation of the surgical instrument (20) within the coordinate system (42) of the robot (40) based on a physical location within the coordinate system (42) of the robot (40) of a port (12) into the anatomical region (10). The definition of the remote center of rotation is used by the robot controller (43) to command the robot (40) to align the remote center of motion of the surgical instrument (20) with the port (12) into the anatomical region (10) for spherically rotating the surgical instrument (20) relative to the port (12) into the anatomical region (10).