Towards Accurate Shape Prediction for Compact Spring Backbone Tendon-Driven Continuum Robots

Continuum robots deliver exceptional dexterity and adaptability in confined environments, making them highly suitable for tasks such as minimally invasive surgery and inspection. Among various configurations, tendon-driven designs represent a common approach that relies on an elastic backbone and one or more drive tendons. Utilising springs for the backbone element offers specific design advantages, including wide availability, tuneable mechanical properties, and an open central channel. However, this approach increases axial compliance, leading to reduced actuation efficiency, increased tendon friction, and a reduction in the validity of common model assumptions. This paper considers the applicability of two modelling approaches to a compact spring backbone tendon-driven continuum robot design. Specific comparison is made between a geometric model based on the constant curvature assumption and a force-based analytical elastic model that considers axial compression and tendon friction under actuation loading. Experimental validation via a single-tendon prototype indicates that, while the geometric model offers simplicity and can be optimised for predicting tip position (mean error of 2.4 mm), large discrepancies exist when predicting the full shape of the robot (RMSE of 9.3 mm). Conversely, the analytic model achieves substantially improved accuracy for both tip (mean error of 1.4 mm) and shape (RMSE of 5.3 mm), and may offer an improved model for informing design and control of this class of continuum robot.