Continuum robots have emerged as a promising technology in the medical field due to their potential of accessing deep sited locations of the human body with low surgical trauma. When deriving physics-based models for these robots, evaluating the models poses a significant challenge due to the difficulty in accurately measuring their intricate shapes. In this work, we present an optimization based 3D shape registration algorithm for estimation of the backbone shape of slender continuum robots as part of a pho togrammetric measurement. Our approach to estimating the backbones optimally matches a parametric three-dimensional curve to images of the robot. Since we incorporate an iterative closest point algorithm into our method, we do not need prior knowledge of the robots position within the respective images. In our experiments with artificial and real images of a concentric tube continuum robot, we found an average maximum deviation of the reconstruction from simulation data of 0.665 mm and 0.939 mm from manual measurements. These results show that our algorithm is well capable of producing high accuracy positional data from images of continuum robots.

翻译：连续体机器人因其能以较低手术创伤进入人体深部位置而成为医疗领域一项前景广阔的技术。在建立这类机器人的物理模型时，由于难以精确测量其复杂形态，模型评估面临重大挑战。本研究提出一种基于优化的三维形状配准算法，作为摄影测量系统的一部分，用于估计细长连续体机器人的中轴线形状。我们的中轴线估计方法通过将参数化三维曲线与机器人图像进行最优匹配来实现。由于在方法中融入了迭代最近点算法，我们无需预先获知机器人在各图像中的位置。在使用同心管连续体机器人的仿真图像和真实图像进行的实验中，重建结果与仿真数据的平均最大偏差为0.665毫米，与人工测量数据的平均最大偏差为0.939毫米。这些结果表明，本算法能够从连续体机器人图像中生成高精度的位置数据。