Performance and Experimental Analysis of Strain-based Models for Continuum Robots

Although strain-based models have been widely adopted in robotics, no comparison beyond the uniform bending test is commonly recognized to assess their performance. In addition, the increasing effort in prototyping continuum robots highlights the need to assess the applicability of these models and the necessity of comprehensive performance evaluation. To address this gap, this work investigates the shape reconstruction abilities of a third-order strain interpolation method, examining its ability to capture both individual and combined deformation effects. These results are compared and discussed against the Geometric-Variable Strain approach. Subsequently, simulation results are experimentally verified by reshaping a slender rod while recording the resulting configurations using cameras. The rod configuration is imposed using a manipulator displacing one of its tips and extracted through reflective markers, without the aid of any other external sensor -- i.e. strain gauges or wrench sensors placed along the rod. The experiments demonstrate good agreement between the model predictions and observed shapes, with average error of 0.58% of the rod length and average computational time of 0.32s per configuration, outperforming existing models.