Projection operator for inverse kinematics of a surgical robot for low degree of freedom tools

A method for accounting for a limited degree of freedom of a tool in a surgical robotic system, the method comprising:

• minimizing a difference between a change in joint position of the surgical robotic system and a change in pose of an end effector of the tool;
• weighting the difference in the minimizing with a matrix distinguishing feasible and infeasible poses of the end effector of the tool based on the limited degrees of freedom;
• and
• controlling the surgical robotic system based on the change in the joint position.

A surgical robotic system for medical teleoperation, the surgical robotic system comprising:

• a robotic arm;
• a first surgical instrument connected to the robotic arm, where an end effector of the first surgical instrument as connected to the robotic arm cannot rotate about at least one axis;
• and
• a controller configured to solve for motion of the first surgical instrument in response to user input of a move command, the solution being with inverse kinematics, the inverse kinematics including a projection of the user input from a higher dimensional space to a lower dimensional space that accounts for the lack of rotation about the at least one axis.