Analytical Computation of the Contact Force Jacobian for MRI-Actuated Robotic Catheter

Contact force Jacobian relates the changes in the contact force to the changes in the actuation of a robotic catheter in contact with a surface. In this paper, we present an analytical method for calculating the contact force Jacobian for the Cosserat rod model of an MRI-actuated robotic catheter. First, the Cosserat rod model of the MRI-actuated robotic catheter under tip contact position constraint is introduced. For the analytical derivation of contact force Jacobian, the initial value problem parameter derivatives are defined and calculated analytically. Finally, simulation results show that the presented analytical method calculates the contact force Jacobian in significantly shorter computation time with comparable accuracy, compared to direct numerical computation.