Active Data-Driven Model and Robust Control Scheme for Twisted Tendon-Sheath Hysteresis System Using Koopman Operator

Hysteresis is a typical nonlinear characteristic that exists in mechanical systems, which brings significant challenges to the robust tracking control of twisted tendon-sheath systems. In this paper, an active data-driven model is proposed to describe the hysteresis phenomenon of a twisted tendon-sheath system based on the Koopman operator, and a robust controller is designed to cancel the effect of the model error and deal with the physical constraints in practical applications. First, by utilizing the Koopman theory, an active data-driven model is built to describe the twisted tendon-sheath hysteresis system in a straightforward linear form. Then, an active model is proposed based on a modified set-membership filter to estimate the finite-dimensional approximation error. Furthermore, a robust controller is developed by taking advantage of both the magnitude and bound of the model error (obtained by the active model) to enhance the control performance while considering security constraints. To the best of our knowledge, the rule-based constraint term is first considered in the data-driven model-based control scheme to prevent potential instabilities for the twisted tendon-sheath system. The theoretical stability of the closed-loop system is proven by using the barrier Lyapunov theory to ensure the security boundary. Extensive experiments are also carried out on a self-built robotic ureteroscopy prototype to demonstrate the superior tracking performance and robustness of the proposed method. Note to Practitioners-This paper is motivated by the accurate transmission problems of twisted tendon-sheath hysteresis systems, which aims to provide a precise active modeling method and a robust controller for the robotic-assisted instrument (e.g., endoscope, catheter, etc.) twisting in the sheath/orifice. Most existing studies on tendon-sheath hysteresis systems realize trajectory tracking controllers by using parametric-model-based compensation, which still lacks a practical data-driven modeling approach to characterize the hysteresis phenomenon in the linear form, and ignore the security constraints of tendon outputs. Based on the set-membership filter, this paper builds an active Koopman-based model, which is a practical method to follow for systems characterized by complex dynamics. Subsequently, by employing the constructed active model and a rule-based term to handle output constraints, a robust controller is elaborately designed to realize accurate tracking control for twisted tendon-sheath hysteresis systems. In particular, no priori knowledge of the complex dynamics is required in the implementation and gains selection of the proposed controller, which holds theoretically and practically significance for various tendon-sheath hysteresis systems. A series of comparative hardware experiments further validate the effectiveness and robustness of the suggested control scheme. In future work, we will aim to extend the applicability of the proposed active modeling and control scheme to interventional procedures of endoscopic operation robots for complex steerings with varying sheath configurations.