Development of a Modified Generalized Prandtl–Ishlinskii Modeling and Compensation Method for Complex Hysteresis Behaviors of the Flexible Ureteroscope

The flexible ureteroscope suffers from complex inherent motion hysteresis behaviors due to the lengthy and slender configuration with a typical diameter of less than 3mm, the manual cable-driven approach via tendon-sheath mechanism for force and motion transmission and the associated nonlinear dead zone caused by tendon slackening at around the zero position. The highly constrained intraluminal environment and the lack of sensor integration have further limited the feedback acquisition for closed-loop control. Therefore, the hysteresis compensation for the ureteroscopes has become more essential but remains challenging. To address the associated hand-eye incoordination, limited control accuracy, and increased surgical risks, this work presents an analytical modeling and feedforward compensation method for the ureteroscope based on a modified generalized Prandtl-Ishlinskii (MGPI) model. The designed model cascades a piecewise-linear-envelope-function-based symmetric generalized PI model (SGPI) and a two-sided dead zone model (DZ) to characterize the backlash, asymmetric hysteresis, and nonlinear dead zones. The feedforward compensator has been analytically derived and integrated into a motorized ureteroscope platform. Experimental results indicated that the proposed model has successfully captured the complex hysteresis with a modeling error of only 1.44% within a wide motion range of 440°. The tracking experiments of periodic and non-periodic signals have been performed. The results indicated that the proposed compensator has significantly suppressed the hysteresis by 60%~70% under different circumstances. Comparison simulations and experiments with other compensators have also demonstrated its advantages.