Hysteresis Modeling and Compensation for Tendon-Sheath Mechanisms in Robot-Assisted Endoscopic Surgery Based on the Modified Bouc-Wen Model With Decoupled Model Parameters

The tendon-sheath mechanism (TSM) has been widely applied in flexible endoscopy (FE) and natural orifice transluminal endoscopic surgery (NOTES) owing to its advantages of remote force and displacement transmission, size reduction, compactness, and convenient implementation. However, the positioning accuracy of TSMs is highly restrained by the motion hysteresis due to the complex friction condition between the tendon and sheath. The hysteresis phenomenon has posed significant challenges for modeling and controlling TSMs. This paper proposes a modified Bouc-Wen-based mathematical model to characterize the asymmetric hysteresis loop with distinct inflection points. The model parameters are decoupled, facilitating identification and reducing computational costs. Moreover, the model has retained the Bouc-Wen model structure, allowing for efficient derivation of the feedforward compensator based on the inverse multiplicative structure. The compensator was derived and cascaded with the TSM system to suppress the hysteresis phenomenon. Totally 120 trials of experiments were conducted to validate the proposed model and the feedforward control scheme on the two TSMs with different accumulated curvatures of 180° and 360°. The results indicated that the proposed method achieved a 25.5% and 43.9% lower estimation and compensation error than the classical Bouc-Wen model. Further, it is worth noting that the model parameter identification time consumption has been significantly reduced to 5.8ms. The proposed model and the feedforward compensator can effectively linearize the TSM system and further facilitate delicate operations in robot-assisted surgical procedures.