TABLE 1.

Nomenclature.

Symbol	Definition
$e_i$	Position error of the end-effector along the $i$ -axis in the task-space
$\mathit{e}$	Position error vector of the end-effector in the task-space
${\dot{e}}_i$	Velocity error of the end-effector along the $i$ -axis in the task-space
$\dot{\mathit{e}}$	Velocity error vector of the end-effector in the task-space
$e_{{\max }_{\mathrm{i}}}$	Sensitivity threshold of the position error of the end-effector along the $i$ -axis in the task-space for the MTJ controller
${\dot{e}}_{{\max }_{\mathrm{i}}}$	Sensitivity threshold of the velocity error of the end-effector along the $i$ -axis in the task-space for the MTJ controller
$\mathit{h}$	Vector of feedback linearization estimator term in the MTJ controller
$\mathit{I}$	Identity matrix
$\mathit{J}$	Linear Jacobian matrix
$\mathit{K}$	Coefficient matrix of the feedback linearization estimator in the MTJ controller
${\mathit{K}}_D$	Derivative coefficient matrix of the MTJ controller
${\mathit{K}}_I$	Integral coefficient matrix of the MTJ controller
${\mathit{K}}_P$	Proportional coefficient matrix of the MTJ controller
$l_i$	Length of tendon $i$ in the continuum robotic arm
$\mathit{L}$	Vector of tendon lengths in the continuum robotic arm
$\dot{\mathit{L}}$	Vector of tendon length change rates in the continuum robotic arm
$\mathit{p}$	Position vector of a point on the backbone of the continuum robotic arm
$s$	Backbone reference length parameter
$T$	Transpose of the vector or matrix
$T_i$	Tension of tendon $i$
$\mathit{T}$	Vector of generalized forces in joint space (tendon tensions)
${\mathit{T}}^{+}$	Vector of generalized forces in joint space (tendon tensions) after passing the null-space projection operator
$t$	Time
$\mathit{X}$	Task-space variables vector (end-effector position vector)
$\dot{\mathit{X}}$	Task-space velocities vector (end-effector velocity vector)
$\mathit{\eta }$	Non-trivial solution to the linear algebraic system
$\mathit{\zeta }$	Null-space adjustment vector ( $\mathit{\zeta }\in {\mathbb{R}}^6$ )
$\mathcal{F}$	Vector of generalized forces in the task-space
$†$	Pseudo-inverse of a non-square matrix