Can the Shape of a Planar Pathway Be Estimated Using Proximal Forces of Inserting a Flexible Shaft?

The shape information of flexible endoscopes or other continuum structures, e.g., intro-vascular catheters, is needed for accurate navigation, motion compensation, and haptic feedback in robotic surgical systems. Existing methods rely on optical fiber sensors, electromagnetic sensors, or expensive medical imaging modalities such as X-ray fluoroscopy, magnetic resonance imaging, and ultrasound to obtain the shape information of these flexible medical devices. Here, we propose to estimate the shape/curvature of a continuum structure by measuring the force required to insert a flexible shaft into the internal channel/pathway of the continuum. We found that there is a consistent correlation between the measured insertion force and curvature of the planar continuum pathway. A testbed was built to insert a flexible shaft into a planar continuum pathway with adjustable shapes. The insertion forces, insertion displacement, and the shapes of the pathway were recorded. A neural network model was developed to model this correlation based on the training data collected on the testbed. The trained model, tested on the testing data, can accurately estimate the curvature magnitudes and the accumulated bending angles of the pathway simply based on the measured insertion force at the proximal end of the shaft. The approach may be used to estimate the curvature magnitudes and accumulated bending angles of flexible endoscopic surgical robots or catheters for accurate motion compensation, haptic force feedback, localization, or navigation. The advantage of this approach is that the employed proximal force can be easily obtained outside the pathway or continuum structure without any embedded sensor in the continuum structure. Future work is needed to further investigate the correlation between insertion forces and the pathway and enhance the capability of the model in estimating more complex shapes, e.g., spatial shapes with multiple bends.