  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 large curvature, such as aortas or industrial pipes.
Accurate kinematic modeling of CTRs is required for the development of advanced
control and sensing algorithms. To this end, we extended the conventional CTR
kinematics model to a more general case with large tube-to-tube clearance and
large 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 4.36 mm in 3D case,
outperforming the state-of-the-art model by 71% and 66%, respectively.
