Model-Based Shape Estimation and Closed-Loop Control of Magnetic Continuum Robot Based on Monocular Vision

Magnetic continuum robots (MCRs) show promising potential for applications in narrow lumens, such as vascular interventions. Accurate shape sensing of these robots is crucial for the success of interventional surgeries. However, the submillimeter dimensions of MCRs poses significant challenges for integrating additional sensors. An alternative approach is shape estimation from images, yet the lack of precise MCR kinematics can make this process time-consuming. In this work, we propose a novel MCR design featuring a rectangular tip capable of specific planar bending, along with a corresponding kinematic model and a mechanical model. Additionally, we introduce a model-based shape estimation method that enables the estimation of the MCR's shape from a single-view image without the need for external markers. Experimental results demonstrate that our method can estimate an MCR's shape with a mean absolute error (MAE) of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{0.58}\pm \mathbf{0.41}\mathbf{mm}$</tex> within 85ms, facilitating real-time application. Furthermore, closed-loop control based on this method has achieved an end position error below 11% of the tip's total length, highlighting the accuracy and practicality of our approach for surgical interventions.