TABLE I.

Nomenclature, pt. 1

Symbol	Description
gc	3D curve for follow-the-leader extension
t	Time instances during follow-the-leader extension
${\widehat{s}}_c$	Physical location of a robot that follows curve s
$\mathbb{N}$	Set of nonnegative integers
$\mathbb{R}$	Set of real numbers
n	Number of tubes in a robot design
m	Number of sections in a robot design
mn	Number of sections in robot navigation portion
mm	Number of sections in robot manipulation portion
v	Number of robot variable curvature sections
ρ	Total number of arrangements of v variable curvature sections
t	Number of tip task frames for specific procedure
V	Binary m-vector specifying variable curvature sections
Vn	Binary mn-vector specifying variable curvature sections in navigation portion of robot
Vm	Binary mm-vector specifying variable curvature sections in manipulator portion of robot
Vp	Binary vector specifying variable curvature sections extending from straight proximal sections
s	Arc length along centerline of tube or tube set
Li	Total length of tube i
${\widehat{k}}_{\mathit{ix}}\left(s\right)$	Bending pre-curvature of ith tube about x as function of arc length, s
${\widehat{k}}_{\mathit{iy}}(s)$	Bending pre-curvature of ith tube about y as function of arc length, s
${\widehat{u}}_j$	Bending pre-curvature of jth tube or section
$\widehat{u}\in {\mathbb{R}}^m$	Vector of section pre-curvatures
${\widehat{u}}_n\in {\mathbb{R}}^{m_n}$	Vector of navigation section pre-curvatures
${\widehat{u}}_m\in {\mathbb{R}}^{m_m}$	Vector of manipulation section pre-curvatures