$$\begin{aligned}
\mathcal{L}_{\text{hand pose}}
&= \left\lVert \mathbf{p}^{\,h}_{\text{thumb}} - \mathbf{p}^{\,r}_{\text{thumb}} \right\rVert_2^2 \\
&\quad + \beta_{\text{rot}}\,
\mathrm{angle}\!\left(\mathbf{q}^{\,h}_{\text{wrist}},\, \mathbf{q}^{\,r}_{\text{wrist}}\right)
\end{aligned}\tag{1}$$
$$\mathcal{L}_{\text{fingertip pos}}
= \sum_{i=1}^{N} \left\lVert \mathbf{v}^{\,h}_{i} - \mathbf{v}^{\,r}_{i} \right\rVert_2^2\tag{2}$$
$$\mathcal{L}_{\text{pinch}}
= \sum_{i=1}^{N-1} s(d_i)\,
\left\lVert \boldsymbol{\gamma}^{\,r}_{i} - l(d_i)\,\hat{\boldsymbol{\gamma}}^{\,h}_{i} \right\rVert_2^2\tag{3}$$
$$\mathcal{L}_{\text{fingertip rot}}
= \sum_{i=1}^{N} \left\lVert \mathbf{r}^{\,h}_{i} - \mathbf{r}^{\,r}_{i} \right\rVert_2^2\tag{5}$$
$$\begin{aligned}
\mathcal{L}_{\text{total}}
&= \lambda_1 \mathcal{L}_{\text{thumb pos}}
+ \lambda_2 \mathcal{L}_{\text{wrist rot}} \\
&\quad + \lambda_3 \mathcal{L}_{\text{fingertip pos}}
+ \lambda_4 \mathcal{L}_{\text{fingertip rot}} \\
&\quad + \lambda_5 \mathcal{L}_{\text{pinch}}
+ \mathcal{L}_{\text{joint}}
+ \mathcal{L}_{\text{vel}}
\end{aligned}\tag{6}$$