A Quasi-Static Model Accounting for Friction-Induced Hysteresis in Tendon-Actuated Superelastic Notched Tube Instruments

Superelastic notched tube instruments are being increasingly employed in surgical robotics. Due to their superelastic material properties, they can achieve small bending radii even for large bending angles, which makes them very interesting for minimally invasive interventions, typically dealing with confined spaces. Several works have aimed to model the behavior of such tubes in regard to the actuation force. The most extensive considers the superelastic material properties as well as the friction between the instrument and the tendon. However, no model is able to capture both the hysteresis behavior of the superelastic material as well as the hysteresis behavior induced by the friction. This text proposed a quasi-static method for modeling the behavior of nitinol notched tube instruments accounting for both material- and friction-induced hysteresis. The model is validated on four samples and compared to state of the art models. Results show an average notch position root mean square error of 1.06 mm (5.5%) and 0.46 mm (2.4%) for the method with measured parameters and optimized parameters, respectively.