Kinematic Modeling of Magnetically-Actuated Robotic Catheter in Nonlinearly-Coupled Multi-Field

Magnetically-actuated robotic catheter (MARC) has shown great potential in minimally-invasive surgery because they can be steered remotely and wirelessly. However, when driven by external permanent magnets (EPM), the MARC is subject to nonlinearly-coupled gravitational, magnetic, and elastic forces, simultaneously. Furthermore, the magnetic field force and moment exerted on the IPM are coupled with its pose. These factors make it difficult to calculate the shape of the MARC when controlled by EPM, thus posing a potential threat to the patients. This letter proposes an accurate kinematic model of MARC in nonlinearly-coupled multi-field formed by catheter, EPM and gravity. The proposed approach proceeds from the perspective of energy minimization. The shape of MARC can be obtained by minimizing the total potential energy. Additionally, an initial value algorithm is proposed to handle the two equilibrium states of MARC and enable fast convergence. Comparing to experimental results, we show that the proposed algorithm can effectively estimate the shape of the MARC under complexly coupled forces.