Modeling and Compensation of Stiffness-Dependent Hysteresis for Stiffness-Tunable Tendon-Sheath Mechanism in Flexible Endoscopic Robots

Robot-assisted gastrointestinal endoscopic surgery requires flexible manipulators to possess a compact dimension and stiffness tuning capability. Current stiffness-tunable miniature manipulators (STMM) using tendon-sheath mechanism (TSM) experience the problem of stiffness-influenced hysteresis. To address this, we propose the first stiffness-dependent Modified Generalized Prandtl-Ishlinski (PI) model and a specific compensation strategy. First, we analyzed the stiffness tuning mechanism and extracted the stiffness parameter. Based on this, the analytical hysteresis model and its inverse function were built and verified in simulations and experiments, which increases the fitting accuracy of the hysteresis. Then, with the assistance of the compensation strategy, the real-time input-output relationship of the STMM's stiffness-tunable joints can be approximately linear. The average errors of trajectory tracking achieve a significant improvement of over 85%. This work provides a new method to model and compensate for the dynamic hysteresis in flexible endoscopic robots with the stiffness-tunable TSM.