Improving Kinematic Accuracy of Laparoscopic Surgical Robots Through Sub-Millimeter-Scale Kinematics^*

As automation in robotic surgery develops, the kinematics and kinematic accuracy of laparoscopic robots have become important prerequisites for development in the field. However, the kinematics of these robots remain inaccessible to purely analytic solutions, and manufacturing imprecision causes the kinematic parameters to vary from robot to robot, requiring calibration. In this paper, we present a novel iterative numerical kinematic algorithm which exploits the tool-and-arm structure of a typical surgical robot to provide arbitrarily precise inverse kinematic solutions with the use of an arbitrary number of calibration parameters. To our knowledge, this is the first inverse kinematic algorithm to be presented in the literature, which specifically exploits the properties of laparoscopic surgical robots. We also present an improved calibration methodology to rapidly and reliably determine these parameters. Both components are evaluated on a da Vinci Surgical Unit in a direct accuracy measurement test involving precise contact with locations on a physical target. With a root-mean-squared accuracy of 2.54mm, and a maximum positioning error of 3.78mm, our methods meet or exceed the state of the art in improving the accuracy of computer-controlled surgical robots.