High-Precision Tip Shape Estimation for Flexible Endoscope based on Multiple Magnet Positioning and NURBS Curve Approximation

Flexible endoscopes can reach the lesion through a small incision or the patient’s natural orifices, exhibiting minimally invasive or non-invasive diagnosis and surgery capabilities. The soft tip of the flexible endoscope can be easily bent to position the endoscope towards the lesion. The positioning and shape estimation of the soft tip is key to high-precision endoscopic operations. Different from the conventional radiation-based measurements, this study proposes a tip-shape estimation method for the flexible endoscope based on permanent magnet positioning. The tip shape of the flexible endoscope is estimated using the nonuniform rational B-spline (NURBS) curve approximation by the reverse seeking of the control points via the magnetic rings. Simulation results demonstrate that the average contour error is within the range of 0.21-0.78 mm with different bending angles. The proposed method achieves a good estimation performance, thus showing great potential for non-radiation measurement and navigation in flexible endoscopic surgeries.