Fig. 3.

Overview of the geometric relations used to estimate an initial value for the arc curvature ($\hat{\kappa }$) of the robotically actuated delivery sheath (RADS). The arc length ($\ell$) and rigid link length ($l_t$) combined with the RADS tip position (${\mathbf{|}\mathbf{r}}_t^0|$) are used to estimate the bend angle ($\hat{\theta }$). The estimated bend angle ($\hat{\theta }$) and the approximated length ($\frac{1}{2}(\ell +l_t)$) are used to evaluate an initial estimate of the arc curvature ($\hat{\kappa }$) of the RADS.