A computationally efficient method for hand–eye calibration

Purpose: Surgical robots with cooperative control and semiautonomous features have shown increasing clinical potential, particularly for repetitive tasks under imaging and vision guidance. Effective performance of an autonomous task requires accurate hand–eye calibration so that the transformation between the robot coordinate frame and the camera coordinates is well defined. In practice, due to changes in surgical instruments, online hand–eye calibration must be performed regularly. In order to ensure seamless execution of the surgical procedure without affecting the normal surgical workflow, it is important to derive fast and efficient hand–eye calibration methods. Methods: We present a computationally efficient iterative method for hand–eye calibration. In this method, dual quaternion is introduced to represent the rigid transformation, and a two-step iterative method is proposed to recover the real and dual parts of the dual quaternion simultaneously, and thus the estimation of rotation and translation of the transformation. Results: The proposed method was applied to determine the rigid transformation between the stereo laparoscope and the robot manipulator. Promising experimental and simulation results have shown significant convergence speed improvement to 3 iterations from larger than 30 with regard to standard optimization method, which illustrates the effectiveness and efficiency of the proposed method

A Graph-based Optimization Framework for Hand-Eye Calibration for Multi-Camera Setups

Hand-eye calibration is the problem of estimating the spatial transformation between a reference frame, usually the base of a robot arm or its gripper, and the reference frame of one or multiple cameras. Generally, this calibration is solved as a non-linear optimization problem, what instead is rarely done is to exploit the underlying graph structure of the problem itself. Actually, the problem of hand-eye calibration can be seen as an instance of the Simultaneous Localization and Mapping (SLAM) problem. Inspired by this fact, in this work we present a pose-graph approach to the hand-eye calibration problem that extends a recent state-of-the-art solution in two different ways: i) by formulating the solution to eye-on-base setups with one camera; ii) by covering multi-camera robotic setups. The proposed approach has been validated in simulation against standard hand-eye calibration methods. Moreover, a real application is shown. In both scenarios, the proposed approach overcomes all alternative methods. We release with this paper an open-source implementation of our graph-based optimization framework for multi-camera setups.Comment: This paper has been accepted for publication at the 2023 IEEE International Conference on Robotics and Automation (ICRA