Hand-eye calibration algorithms are mature and provide accurate transformation estimations for an effective camera-robot link but rely on a sufficiently wide range of calibration data to avoid errors and degenerate configurations. To solve the hand-eye problem in robotic-assisted minimally invasive surgery and also simplify the calibration procedure by using neural network method cooporating with the new objective function. We present a neural network-based solution that estimates the transformation from a sequence of images and kinematic data which significantly simplifies the calibration procedure. The network utilises the long short-term memory architecture to extract temporal information from the data and solve the hand-eye problem. The objective function is derived from the linear combination of remote centre of motion constraint, the re-projection error and its derivative to induce a small change in the hand-eye transformation. The method is validated with the data from da Vinci Si and the result shows that the estimated hand-eye matrix is able to re-project the end-effector from the robot coordinate to the camera coordinate within 10 to 20 pixels of accuracy in both testing dataset. The calibration performance is also superior to the previous neural network-based hand-eye method. The proposed algorithm shows that the calibration procedure can be simplified by using deep learning techniques and the performance is improved by the assumption of non-static hand-eye transformations.

翻译：手眼标定算法已趋于成熟，能够为有效的相机-机器人连接提供精确的变换估计，但这类方法依赖于足够广泛的标定数据以避免误差和退化构型。为解决机器人辅助微创手术中的手眼问题，并简化标定流程，本研究提出一种结合新型目标函数的神经网络方法。我们提出一种基于神经网络的解决方案，通过图像序列和运动学数据估计变换关系，显著简化了标定流程。该网络利用长短期记忆架构提取数据中的时序信息，并求解手眼问题。目标函数由远程运动中心约束、重投影误差及其导数的线性组合推导而来，以诱导手眼变换的微小变化。该方法通过达芬奇Si系统数据进行验证，结果显示，在两个测试数据集中，估计得到的手眼矩阵能够将机器人坐标系中的末端执行器重投影至相机坐标系，精度达10至20像素。该标定性能亦优于此前基于神经网络的手眼方法。本算法表明，利用深度学习技术可简化标定流程，且通过非静态手眼变换的假设提升了性能。