Toward Extending Concentric Tube Robot Kinematics for Large Clearance and Impulse Curvature

Concentric Tube Robots (CTRs) have been proposed to operate within the unstructured environment for minimally invasive surgeries. In this letter, we consider the operation scenario where the tubes travel inside the channels with a large clearance or impulse curvature, such as aortas or industrial pipes. Accurate kinematic modeling of CTRs is required for the development of motion planning and control within these operation scenarios. To this end, we extended the conventional CTR kinematics model to a more general case with large tube-to-tube clearance and impulse centerline curvature. Numerical simulations and experimental validations are conducted to compare our model with respect to the conventional CTR kinematic model. In the physical experiments, our proposed model achieved a tip position error of 1.53 mm in the 2D planer case and 3.86 mm in 3D case, outperforming the state-of-the-art model by 71% and 61%, respectively.