A motion transmission model for multi-DOF tendon-driven mechanisms with hysteresis and coupling: Application to a da Vinci® instrument

Tendon-driven mechanisms used in robotic surgery exhibit strong nonlinearities, particularly a static backlash-like hysteresis, in their motion transmission behavior. In this paper, an extension of a previously developed model is proposed that allows for estimation of angular displacements in multi-DOF tendon-driven devices where special attention is given to the coupling effect between DOFs. The proposed model consists of the conventional coupling matrix and a novel elongation matrix which compensates for the coupled hysteretic effect. The model is applied to the problem of position estimation in three DOFs (one pitch and two grasping DOFs) of a da Vinci® surgical instrument. As a further extension, a preliminary dynamic model is also suggested to deal with high-frequency inputs. According to the experimental results obtained, the proposed quasi-static model can describe the transmission behavior with goodness-of-fit of 76–92 per cent, and the estimates are improved by 35–72 per cent in terms of the RMSE for the proposed dynamic model as compared to the conventional rigid model.