Real-Time Geometric Joint Uncertainty Tracking for Surgical Automation on the dVRK System

Accurate control of surgical robotics under uncertainty is crucial for achieving surgical autonomy. This uncertainty arises from sensor or model inaccuracies in surgical platforms, e.g., dVRK system, where joint bias in positioning and complex transmission effects caused by backlash and cable stretch. Previous approaches usually rely on depth sensors or additional offline calibration steps, making them difficult to deploy in real-world laparoscopy surgeries. In this paper, we propose a real-time geometric approach for calibrating joint errors on-the-fly combined with geometric features. An efficient visual detector is employed to identify the shaft mask and wrist keypoints. Based on the extracted features, we introduce a geometric model to recover the shaft axis pose and determine the first two joints uncertainty. Additionally, we develop a geometric model for wrist joints in projection space, calibrating remaining joint uncertainty through spatial geometry and the analytical structure of dVRK platform. Experimental results in simulation show that our approach significantly reduces joint error from 15° to 0.02°, with end-effector pose accuracy improving from centimeter to sub-millimeter level. This greatly enhances the accuracy and success rate of surgical automation. We also demonstrate robust control performance in diverse surgical tasks, highlighting the effectiveness of our geometric model in achieving accurate control despite joint offsets.