A Unified Monocular Camera-Based and Pattern-Free Hand-to-Eye Calibration Algorithm for Surgical Robots With RCM Constraints

With progressive advancements in modern technologies, image-guided automation, which plans and manipulates particular tasks by utilizing visual cues, is becoming an emerging sector in medical robotics. Its prevalence nowadays requires a reliable hand-to-eye calibration owing to various configurations of surgical robots, especially for those with remote center of motion (RCM) constraints, e.g., da Vinci Research Kit (dVRK). In this article, we proposed a novel unified calibration method, which leverages the structure characteristics and establishes an explicit geometric model to solve the hand-to-eye relationship only with a monocular camera's feedback. By freely moving the patient side manipulator in dVRK, our method can first recover the 3-D poses of its shaft at various configurations using Plucker coordinates. To obtain the hand-to-eye translation relationship, these recovered poses are further converged by softly intersecting them within a minimal spatial sphere while preserving their coordinates using an aggregating sphere loss. Meanwhile, the orientation mapping can be recovered by leveraging the corresponding longitudinal-axis information. To improve the calibration accuracy, a local optimization strategy that utilizes the bundle adjustment to refine the transformation using the previous outcomes is also introduced. With such a hierarchical calibration scheme, the hand-to-eye relationship of any RCM constrained robot can be successfully achieved. Extensive simulations and experiments are conducted based on dVRK platform. By comparing with the traditional method, the validation results prove the feasibility and superiority of our unified algorithm in calibration accuracy and robustness.