Table 1.

Mathematical nomenclature used in this paper

Symbol	Definition
$\mathit{\zeta }={\left[{\mathbf{p}}_{\mathcal{B}}{\mathbf{\Omega }}_{\mathcal{B}}\right]}^T\in \mathbb{SE}\left(3\right)$	Quadrotor configuration (pose)
${\mathit{\tau }}_{\mathcal{B}}\in {\mathbb{R}}^4$	Quadrotors control inputs.
${\mathit{\xi }}_j={\left[{\xi }_{i,1}\dots {\xi }_{i,3}\right]}^T\in {\mathbb{R}}^3$	Joint angles of the j-th robotic finger.
${\mathbf{M}}_{j,\mathcal{E}}\left({\mathit{\xi }}_j\right),{\mathbf{C}}_{j,\mathcal{E}}({\mathit{\xi }}_j,{\stackrel{°}{\mathit{\xi }}}_j)\in {\mathbb{R}}^{3\times 3}$	j-th robotic finger’s mass-and Coriolis matrix.
${\mathbf{K}}_{j,\mathcal{E}},{\mathbf{D}}_{j,\mathcal{E}}\in {\mathbb{R}}^{3\times 3}$	j-th robotic finger’s joint stiffness and damping matrices of the robotic finger.
${\mathbf{G}}_{j,\mathcal{E}}\left({\mathit{\xi }}_j{,}^{\mathcal{W}}{\mathbf{\Omega }}_{\mathcal{B}}\right)\in {\mathbb{R}}^{4\times 1}$	Gravity contribution to the j-th finger joint.
${\mathbf{A}}_{j,\mathcal{E}}\in {\mathbb{R}}^{4\times 1}$, ${\tau }_{j,\mathcal{E}}\in \mathbb{R}$	j-th input matrix and tendon tension
$\mathcal{B}{\mathbf{p}}_{\mathcal{E}}\in {\mathbb{R}}^3$	End-Effector (EE) position in $\mathcal{B}$ as computed by the forward kinematics f(ξ).
${\mathbf{J}}_{\mathcal{E}}\left(\mathit{\xi }\right)\in {\mathbb{R}}^{3\times 4}$	ξ-dependent EE Jacobian matrix.
${\mathbf{J}}_{\mathcal{B},\mathcal{E}}\left(\mathit{\xi }\right)\in {\mathbb{R}}^{3\times 6}$	ξ-dependent contact Jacobian matrix for the base.
$\mathcal{C}=\left[{\mathcal{C}}_1\cdots {\mathcal{C}}_i\right]\in {\mathbb{B}}^9$	Vector of all binary contact signals.
${\mathbf{f}}_{\mathcal{E}}\in {\mathbb{R}}^3$	External force at the EE.
${\mathit{\zeta }}_{\mathcal{T}}={\left[{\mathbf{p}}_{\mathcal{T}}{\mathbf{\Omega }}_{\mathcal{T}}\right]}^T\in \mathbb{SE}\left(3\right)$	Perching target pose