Learning to Calibrate - Estimating the Hand-eye Transformation Without Calibration Objects

Hand-eye calibration is a method to determine the transformation linking between the robot and camera coordinate systems. Conventional calibration algorithms use a calibration grid to determine camera poses, corresponding to the robot poses, both of which are used in the main calibration procedure. Although such methods yield good calibration accuracy and are suitable for offline applications, they are not applicable in a dynamic environment such as robotic-assisted minimally invasive surgery (RMIS) because changes in the setup can be disruptive and time-consuming to the workflow as it requires yet another calibration procedure. In this paper, we propose a neural network-based hand-eye calibration method that does not require camera poses from a calibration grid but only uses the motion from surgical instruments in a camera frame and their corresponding robot poses as input to recover the hand-eye matrix. The advantages of using neural network are that the method is not limited by a single rigid transformation alignment and can learn dynamic changes correlated with kinematics and tool motion/interactions. Its loss function is derived from the original hand-eye transformation, the re-projection error and also the pose error in comparison to the remote centre of motion. The proposed method is validated with data from da Vinci Si and the results indicate that the designed network architecture can extract the relevant information and estimate the hand-eye matrix. Unlike the conventional hand-eye approaches, it does not require camera pose estimations which significantly simplifies the hand-eye problem in RMIS context as updating the hand-eye relationship can be done with a trained network and sequence of images. This introduces a potential of creating a hand-eye calibration approach that is capable of accurately updating the hand-eye matrix according to the changes in RMIS setup.