Model-Based Position Control of a Tendon-driven Variable-Length Continuum Robot for Minimally Invasive Mitral Valve Repair

Minimally invasive mitral valve repair offers significant advantages over traditional open-heart surgery, yet it remains a complex procedure that exposes both patients and medical staff to radiation. To address these challenges, a significant research interest is growing in automating these manual procedures. Continuum robots represent a promising approach, thanks to their ability to navigate confined spaces. However, their nonlinear behavior presents challenges in modeling and control. In this study, we developed a robust position control method for a variable-length tendon-driven continuum robot. We designed a control system that effectively tracks the desired target positions by employing a constant curvature model and a Jacobian-based control algorithm with real-time position feedback. We assessed the stability of our system through Lyapunov analysis, demonstrating reliable convergence to these target positions. Experimental validation conducted in a cardiovascular phantom demonstrated significant improvements with respect to the state of the art. Our method achieved a trajectory following error of approximately 2.43 mm [1.63, 3.23] and a target position error of about 1.92 mm [1.73, 3.13]. Moreover, the computation time per trajectory point was reduced to approximately 0.04 seconds, highlighting enhanced computational efficiency. These results showcase improved accuracy and efficiency in minimally invasive mitral valve repair procedures.