Polynomial Curvature Model for IMU-Based Proprioception in Soft Robotic Manipulators Under External Forces

Due to its structural flexibility and compliance in motion, the soft manipulator shows significant potential and application prospects in robot-human and environment interaction fields. However, its theoretically infinite degrees of freedom in deformation pose challenges for modeling and sensing under external forces. Traditional piecewise constant curvature models, while effective for configuration modeling of soft manipulators, can deviate from actual deformations under complex external forces in unstructured environments. This study generalizes and extends the piecewise polynomial curvature model to 3D and proposes a soft manipulator configuration reconstruction method based on IMU sensing and the polynomial curvature model. Compared to traditional piecewise constant curvature-based methods, this approach not only achieves higher reconstruction accuracy but also effectively captures continuous curvature variations of the soft robot. This provides an excellent solution for deformation sensing of soft robots under complex external forces.