Koopman-Operator-Based Data-Driven Hysteresis Compensation for Tendon-Sheath-Driven Surgical Continuum Robots

Precision control of tendon-sheath-driven continuum robots (TSCRs) in surgical applications is impeded by nonlinear hysteresis from tendon-sheath interactions and material viscoelasticity. This paper introduces a novel data-driven framework for hysteresis modeling and compensation in teleoperated TSCRs using Koopman operator theory. The method approximates both dynamic and static hysteresis using extended dynamic mode decomposition (EDMD), deriving a globally linearized representation of nonlinear hysteresis without relying on physical analytical models. A feedforward-feedback control strategy is designed to eliminate hysteresis-induced positioning errors. The feedforward component utilizes the identified static model for proactive compensation, while a Linear Quadratic Regulator (LQR) feedback controller based on the dynamic model corrects residual errors. Experimental validation on a continuum robotic platform demonstrates an 85.96% reduction in mean tracking error compared to baseline methods, with enhanced closed-loop stability. The model-free framework enhances teleoperated surgical interventions by adapting to complex hysteresis phenomena.