An iterative closest point algorithm for marker-free 3D shape registration of continuum robots

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.