Shape Reconstruction for Continuum Robot Based on Pythagorean Hodograph–Bézier Curve With IMU and Vision Sensors

The shape information is the key to realize real-time, accurate, and effective control of continuum robots. Traditional image processing method and start-to-end-point fitting method are combined. Inertial measurement unit (IMU) and camera are used to capture the end position and attitude information of continuum robot and do not rely on the acquisition of the global image to solve the problem of limited vision in a traditional image processing method. In addition, a new start-to-end-point fitting method is proposed, which is the Pythagorean hodograph—Bézier (PH-B) fitting method. The new method simplifies the solving steps of control points of fitting curve. The control points can be obtained only through the geometric relationship and do not need to rely on an optimization algorithm for iterative solution. This method has good shape fitting accuracy and applicability in the curvature range from 0° to 90° through the simulation analysis. A variety of experiments are designed to verify the results. The experimental results show that the maximum shape reconstruction error by the proposed method is about 2 mm. This proves the applicability of the PH-B method in the shape reconstruction of continuum robots.