Inverse kinematics of a surgical robot for teleoperation with hardware constraints
Various approaches to solve for inverse kinematics may be used for teleoperation of a surgical robotic system. In one approach, an iterative solver solves for the linear component of motion independently from solving for the angular component of motion. One solver may be used to solve for both together. In another approach, all limits (e.g., position, velocity, and acceleration) are handled in one solution. Where a limit is reached, the limit is used as a bound in the intermediate solution, allowing solution even where a bound is reached. In another approach, a ratio of limits of position are used to create a slow-down region near the bounds to more naturally control motion. In yet another approach, the medical-based teleoperation uses a bounded Gauss-Siedel solver, such as with successive-over-relaxation.
1 . A surgical robotic system for teleoperation, the surgical robotic system comprising:
a robotic arm;
a surgical instrument coupled to a distal end of the robotic arm; and
a controller configured to:
(1) receive a user command to move the surgical tool,
(2) solve iteratively for linear motion of the move, providing a solution for the linear motion without solving for angular motion,
(3) solve iteratively for the angular motion of the move, providing a solution for the angular motion without solving for the linear motion, the solution for the angular motion being decoupled as a separate solution than the solution for the linear motion such that any limit violation affects the linear motion and angular motion independently due to the decoupling, and
(4) control the robotic arm based on the solution for the angular motion and the solution for the linear motion.
2 . The surgical robotic system of claim 1 wherein, when the user command is received, the robotic arm has one or more joints locked in place with a fixed remote center of motion at a patient entry point.
3 . The surgical robotic system of claim 1 ,
wherein the user command is for teleoperation for fewer than six degrees of freedom, and
wherein an optimization for the solution for the linear motion and/or an optimization for the solution for the angular motion includes use of a Jacobian matrix for six degrees of freedom with zero terms for the linear and/or angular motion not in the fewer than six degrees of freedom.
4 . The surgical robotic system of claim 1 ,
wherein an optimization for the solution for the linear motion is performed with all limitations on a linear component of the move of the robotic arm being in the solution for the linear motion, and
wherein an optimization for the solution for the angular motion is performed with all limitations on an angular component of the move of the robotic arm being in the solution for the angular motion.
5 . The surgical robotic system of claim 4 ,
wherein a first term in the optimization for the solution for the linear motion includes positive and negative position, velocity, and acceleration bounds as all the limitations, and
wherein a second term in the optimization for the solution for angular motion includes positive and negative position, velocity, and acceleration bounds as all the limitations.
6 . The surgical robotic system of claim 1 wherein a limit violation effects the linear motion and the angular motion independently due to the decoupling.
7 . The surgical robotic system of claim 1 wherein a position, velocity, or acceleration limit is used as a result in the solution for the linear motion and/or the solution for the angular motion.
8 . The surgical robotic system of claim 1 ,
wherein an optimization for the solution for the linear motion and an optimization for the solution for the angular motion each comprises a first control loop nested in a second control loop,
wherein the first control loop includes a bound generator operating with a solver and a termination check for iterative solving by the solver,
wherein the second control loop includes a forward kinematic determination of a position of the surgical tool, a command generation of the move from the user command and the position of the surgical tool, the move provided to the second control loop, and a second termination check receiving termination from the first control loop.
9 . The surgical robotic system of claim 1 wherein the controller is configured to define a region of slow down to approach a position limitation of a joint of the robotic arm with a position limit ratio.
10 . The surgical robotic system of claim 1 wherein an optimization for the solution for the linear motion and/or for the solution for the angular motion comprises application of a bounded solver.
11 . The surgical robotic system of claim 10 wherein the bounded solver comprises a bounded Gauss-Seidel solver with successive-over-relaxation.
12 . The surgical robotic system of claim 10 wherein the bounded solver clamps an intermediate solution to a bound in position, velocity, or acceleration of the robotic arm.