Unified tracking and shape estimation for concentric tube robots

Tracking and shape estimation of flexible robots that navigate through the human anatomy are prerequisites to safe intracorporeal control. Despite extensive research in kinematic and dynamic modelling, inaccuracies and shape deformation of the robot due to unknown loads and collisions with the anatomy make shape sensing important for intra-operative navigation. To address this issue, vision-based solutions have been explored. The task of 2 D tracking and 3 D shape reconstruction of flexible robots as they reach deep-seated anatomical locations is challenging, since the image acquisition techniques usually suffer from low signal-to-noise ratio (SNR) or slow temporal responses. Moreover, tracking and shape estimation are thus far treated independently despite their coupled relationship. This paper aims to address tracking and shape estimation in a unified framework based on Markov Random Fields (MRF). By using concentric tube robots as an example, the proposed algorithm fuses information extracted from standard monoplane X-ray fluoroscopy with the kinematics model to achieve joint 2 D tracking and 3 D shape estimation in realistic clinical scenarios. Detailed performance analyses of the results demonstrate the accuracy of the method for both tracking and shape reconstruction