Freeing the serial mechanism designer from inverse kinematic solvability constraints

Abstract

This paper presents a fast numerical solution for the inverse kinematics of a serial manipulator. The method is implemented on the C-arm, a manipulator designed for use in robotic surgery. The inverse kinematics solution provides all possible solutions for any six degree-of-freedom serial manipulator, assuming that the forward kinematics are known and that it is possible to solve for the remaining joint angles if one joint angle's value is known. With a fast numerical method and the current levels of computing power, designing a manipulator with closed-form inverse kinematics is no longer necessary. When designing the C-arm, we therefore chose to weigh other factors, such as actuator size and patient safety, more heavily than the ability to find a closed-form inverse kinematics solution.

Keywords:

• surgical robotics
• serial manipulator
• inverse kinematics
• numerical inverse kinematics solution

Acknowledgements

The authors would like to acknowledge support from DARPA and US-Army TATRC grant number W81XWH-05-2-0029, which funded development of the C-arms as part of the Trauma Pod Project (Garcia et al. 2009). We also acknowledge technical contributions from Jesse Dosher, Shane Draney, Rainer Leuschke, Mitch Lum, Joel Perry and Tim Ramsey.