Mass and inertia optimization for natural motion in hands-on robotic surgery

In hands-on robotic surgery, the surgeon controls the motion of a tool mounted on the end effector by applying forces directly to the robot. The mass and inertia properties of the robot at the end effector thus contribute to the ability of the surgeon to move the tool and consequently, the performance of the surgery. As redundant robots have varying mass/inertia properties for different configurations at the same position and orientation of the end effector, we present optimizations which affect the inertial properties to improve the surgeon's movement capabilities. A method for optimizing the overall belted mass/inertia ellipsoids based on the determinant of the inverse pseudo kinetic energy matrices is presented, along with a method for optimizing the effective mass/inertia in a particular direction. Using a gradient based controller operating in the null-space of the end effector position and orientation, the measures are optimized to the local optima without affecting the surgeon's desired tool pose. Through simulation, the efficacy of the method is demonstrated and a comparison with two standard approaches to redundancy resolution is performed. Lastly, a pre-optimized solution is shown to be effective for heavily constrained environments which prevent active optimization.