Orientation of user-input devices for controlling surgical arms

A surgical system for use with a surgical end effector, the system comprising:

• a. an array of one or more input devices;
• and
• b. an articulated mechanical arm having a surgical end effector at a distal end thereof, the arm comprising a plurality of arm segments connected by a plurality of arm joints configured to flex and rotate in response to a control signal generated by an input device,
• wherein the surgical system is configured to:
• i. retroflect the distal end of the arm, in response to an electronic control-output from a first user-input device, so as to deliver the end effector to a retroflex operating position, employing a first coordinate translation matrix defining a first X-y-z space to translate the user inputs to respective flexions and rotations of an arm joint,
• ii. transition to a second coordinate translation matrix that is based on a current orientation of the end effector, in response to and contingent upon a detection that said current orientation of the end effector corresponds to a current orientation of a second user-input device, and
• iii. perform a surgical activity using the end effector after the transitioning and in response to an electronic control-output from the second user-input device, employing the second coordinate translation matrix defining a second x-y-z space to translate the user-inputs to respective flexions and rotation of an arm joint.