Dynamic Friction Model for Tendon-Sheath Actuated Surgical Robots: Modelling and Stability Analysis

Abstract

This paper presents a novel dynamic friction model for flexible tendon-sheath mechanism in surgical robots. It allows for accurate modelling of both sliding and presliding regimes. Unlike existing approaches in the literature, the novel model employs not only velocity information but also acceleration information and it is able to capture nonlinear hysteresis characteristics using a unique equation. In addition, transition between two regimes is guaranteed to be smooth without using any switching functions and it permits an arbitrary configuration of sheath, i.e. helical and spatial shape. The model incorporates a set of velocity and acceleration dependent equations with a differential function and it is independent configuration of the tendon-sheath mechanism. Moreover, characterization of different dynamic properties for the novel model has been shown in terms of existence and uniqueness for the solution, bounded input-bounded output (BIBO) stability, and dissipative property. The proposed model has been experimentally reported with arbitrary input signals. It assures an accurate prediction of nonlinear hysteresis behavior between the tendon and the sheath. It also represents a significant application in haptic feedback in surgical systems and higher fidelity for control purposes.