Understanding friction and superelasticity in tendon-driven continuum robots

Tendon-driven continuum robots are conventionally modeled with either discrete or differential representations of their shapes, which neglect the physical design of the robot itself. As each segment of these robotic systems is usually realized by alternating compliant elements and rigid disks for tendon routing, these discontinuities cause non-negligible position and orientation errors. Although the factors that cause these curvature errors have often been identified in the mechanical behavior of the compliant element (usually made of superelastic alloys), tendon routing, and friction, no study available in the open literature gives a satisfactory explanation of these phenomena. In this article, a Finite Element (FE) model is proposed in conjunction with a bottom-up approach to study the physical behavior of this class of robots and ultimately to quantify the impact of these factors on the shape of a tendon-driven continuum robot. The model proved capable of approximating the experimental data with good accuracy, showing an average percentage error of 0.80% and a peak percentage error at the maximum curvature of the continuum robot of 1.30%, significantly smaller than the average error of 4.1% and peak error of 13.86% obtained with a conventional model.