Real-Time Dynamics of Concentric Tube Robots With Reduced-Order Kinematics Based on Shape Interpolation

Concentric tube robots (CTRs) are catheter-like robots that can navigate anatomical lumen to reach surgical targets that are deep inside the body. While CTRs have been extensively studied in quasi-static conditions, unique robot behaviours such as hysteresis and snapping, i.e. the sudden release of elastic energy accumulated due to robot tubes’ twisting, are relatively underexplored. For the first time, we present a real-time dynamic model that captures both snapping and hysteresis for CTRs with arbitrary number of tubes and precurved shape. We pursue Reduced-Order Modelling (ROM) with shape interpolation-based kinematics to reach a system of minimal states appropriate for ultimate real-time non-linear control. We implement and incorporate our theoretical contributions within the open-source modelling software package
TMTDyn
and make them available to the robotics community. Our method is experimentally verified using a highly curved CTR that undertakes complex 3D dynamic motions, for the first time predicting similar pathways during highly nonlinear snapping motions, which is when classical models fail, while preserving the state-of-the-art modeling accuracy of
$\approx$
6% mean error.