Pseudo-Rigid-Body Model and Kinematic Analysis of MRI-Actuated Catheters

This paper presents a kinematic study of a pseudorigid-body model (PRBM) of MRI-compatible, magnetically actuated, steerable catheters. It includes a derivation of a mathematical model of the PRBM of the catheter, singularity studies of the model, and a new manipulability measure. While the forward kinematics of the model presented here is applicable to PRBMs for other applications, actuation method is unique to the particular design. Hence, a careful study of singularities and manipulability of the model is required. The singularities are studied from the underlying equations of motion with intuitive interpretations. The proposed manipulability measure is a generalization of the inverse condition number manipulability measure of robotic manipulators. While the PRBM is an approximation of the flexible catheter, kinematic studies of the PRBM still provide some insight into feasibility and limitations of the catheter, which is beneficial to the design and motion planning of the catheter.