Developing an Energy-Based Three-Dimensional Pseudo-Rigid-Body Model Founded on Kirchhoff Rod Theory for Magnetic Continuum Robots

During the last few years, magnetic continuum robots have been employed in a variety of medical applications. The necessity to precisely control and actuate the tip of such robots requires the appropriate kinematic modeling. Pseudo rigid body (PRB) model is a type of kinematic modeling in which the continuum robot is replaced with rigid links connected by revolute joints having torsional springs; the benefit of utilizing PRB modeling is the reduced computation time in comparison with other existing models like Cosserat rod theory. In the present work, a 3D PRB model founded on Kirchhoff rod theory and with the aid of minimization of the potential energy is developed, and the corresponding parameters were optimized for a three-joint PRB model. The proposed model's error is less than 0.6% in evaluating the location and direction of the robot's end-effector, and the computation time is two orders of magnitude faster with respect to Kirchhoff rod theory for each set of applied external loading.