Hand-Eye Calibration of Surgical Instrument for Robotic Surgery Using Interactive Manipulation

Conventional robot hand-eye calibration methods are impractical for localizing robotic instruments in minimally-invasive surgeries under intra-corporeal workspace after preoperative set-up. In this letter, we present a new approach to autonomously calibrate a robotic instrument relative to a monocular camera without recognizing calibration objects or salient features. The algorithm leverages interactive manipulation (IM) of the instrument for tracking its rigid-body motion behavior subject to the remote center-of-motion constraint. An adaptive controller is proposed to regulate the IM-induced instrument trajectory, using visual feedback, within a 3D plane which is observable from both the robot base and the camera. The eye-to-hand orientation and position are then computed via a dual-stage process allowing parameter estimation in low-dimensional spaces. The method does not require the exact knowledge of instrument model or large-scale data collection. Results from simulations and experiments on the da Vinci Research Kit are demonstrated via a laparoscopy resembled set-up using the proposed framework.