Fig. 3
From: Landing control of a magnetically actuated robotic catheter on beating heart surface

The touchdown angle \(\alpha _d\) is defined as the angle between the catheter tip normal \(n_c\) and the surface normal \(-n_s\) for a given surface configuration. \(\Psi\) denotes the instantaneous heart surface frame. \(\beta _d\) is the rotation angle with respect to the z axis of the surface frame. 90 sampled catheter configurations are used for touchdown motion analysis with touchdown angles \(\alpha _d\) from \(0^ \circ \sim 30 ^\circ\) and tangential angles \(\beta _d\) from \(0^ \circ \sim 360 ^\circ .\).