A cable-pulley system modeling based position compensation control for a laparoscope surgical robot

Due to nonlinear friction and backlash characteristics of cable-driven mechanism (CDM) in laparoscope surgical robot end-effector, it is difficult to predict force and control position precisely during the surgical procedure. Current studies of transmission characteristics of CDM mainly focus on the tendon-sheath system (TSS) with the classical Capstan equation which neglects the effect of bending rigidity of the cable. However, analysis for transmission characteristics of a cable-pulley system (CPS) is rare. This paper presents a tension and displacement transmission model of a CPS in the end-effector of laparoscope surgical robot. The model considers the bending rigidity of the cable and spatial location of the pulleys. Experiments validate the proposed model. Based on the model, a position compensation algorithm of feedforward control is presented to reduce the tracking position errors. The experimental validations show substantial improvements on performance of position tracking errors for the use of the proposed algorithm.