Empirical modeling of hysteresis in a tendon–sheath mechanism on multi-segmented curves

Flexible surgical robots can move with increased flexibility compared with conventional laparoscopic surgical robots, enabling surgeries along arbitrary curved paths. Because of these characteristics, flexible surgical robots are used for performing minimally invasive surgeries. The tendon–sheath mechanism (TSM) plays a pivotal role as a core component of flexible surgical robots. The TSM can transmit displacement through small-diameter pathways along arbitrary trajectories; however, it exhibits nonlinear hysteresis depending on the shape of the curved paths encountered. In this study, the hysteresis changes occurring in the TSM when handling multiple-curved paths were investigated using different variable combinations. A hysteresis model for a single-curved path proposed in a previous study was extended to estimate the magnitude of hysteresis in a multiple-curved path. Results showed that the position of the curved path has a significant influence on hysteresis; therefore, the hysteresis model was modified using an exponential function of the position. By superimposing the model for the hysteresis magnitude in single-curved paths with a nonlinear superposition method, we extended the model to include the hysteresis phenomena in multiple-curved paths. To validate this model, the experimental hysteresis results for a triple-curve path were compared with the model predicted values. The results show that the model proposed in this study can predict the hysteresis in a TSM on an arbitrary multiple-curved path and can serve as a basis for designing algorithms to compensate for the hysteresis in real time.