Fig. 9.

Representative experimental model-predictive control results of the articulating tip of the robotically actuated delivery sheath during tracking of (a) circular reference path (${\mathbf{r}}_d$) and (${\mathbf{r}}_{\mathrm{AHV}}=$ 0), (b) constrained circular reference path (${\mathbf{r}}_d$) and (${\mathbf{r}}_{\mathrm{AHV}}=$0) and (c) and (d) aortic heart valve (AHV) motion trajectories according to ${\mathbf{r}}_{\mathrm{AHV}}=[f_x{f}_{y}0{]}^T$ and ${\mathbf{r}}_d=$0. The red line trajectory represents the reference path ( r) described in (25), while the blue line represents the actual path ( y$=[p_x{p}_{y}0{]}^T$) followed by the articulating tip.