Modeling Cable Driven Robot with Hysteresis and Cable-Pulley Network Friction

In this article, a method of modeling robotic systems with closed-circuit cable–pulley transmissions using the independently developed hysteretic cable stretch model and cable–pulley network friction model is presented. The hysteretic cable stretch model captures the responses of the cable including elasticity, internal friction, material damping, and hysteresis. The cable–pulley network friction is a function of cable tension, average individual wrap angle of cable around pulley, and number of pulleys. For the verification of the method, these two models are integrated into the dynamic model of the first three joints of the RAVEN II robotic surgery platform. The parameters of the developed model are specifically tuned for the RAVEN II and the performance of the model is compared against the kinematic model and a previous, simplified dynamic model (a model with exponential cable stretch and linear damping model). The result showed that even though significant improvements were not observed for the first two joints, the average error and the maximum error of the third joint, which uses smaller diameter and longer cable and more guide pulleys, could be reduced by 10–20% and 5–10%, respectively, over the previous, simplified dynamic model. Also, analysis with various input trajectories indicated that cable-driven systems with very low speed, frequent change in the loading condition, and high cable tension benefit from the proposed method.