A Motion Transmission Model for a Class of Tendon-Based Mechanisms With Application to Position Tracking of the da Vinci Instrument

Tendon-based motion/force transmission is a conventional approach in the design of surgical robots. However, due to compliance in the tendons and significant frictions between the tendons, the pulleys, and the sheath, tendon-based systems exhibit highly nonlinear behavior that, in particular, includes hysteresis. In this paper, based on the concepts of creep theory in belt drive mechanics, a novel motion transmission model is developed for tendon-pulley mechanisms. The developed model is of pseudokinematic type; specifically, it relates the output displacement to both the input displacement and the input force. The model parameters are identified for a da Vinci instrument, and the model performance is experimentally evaluated. The experimental results demonstrate greater than 50% improvement in terms of root-mean-square position error as compared to a more conventional friction/compliance-free kinematic model. The model is subsequently used for position control of the tip of the instrument, resulting in elimination of the hysteresis and in accurate trajectory tracking.