Convergence Analysis of an Iterative Targeting Method for Keyhole Robotic Surgery

In surgical procedures, robots can accurately position and orient surgical instruments. Intraoperatively, external sensors can localize the instrument and compute the targeting movement of the robot, based on the transformation between the coordinate frame of the robot and the sensor. This paper addresses the assessment of the robustness of an iterative targeting algorithm in perturbed conditions. Numerical simulations and experiments (with a robot with seven degrees of freedom and an optical tracking system) were performed for computing the maximum error of the rotational part of the calibration matrix, which allows for convergence, as well as the number of required iterations. The algorithm converges up to 50 degrees of error within a large working space. The study confirms the clinical relevance of the method because it can be applied on commercially available robots without modifying the internal controller, thus improving the targeting accuracy and meeting surgical accuracy requirements.