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This paper investigates and compares the shape reconstruction accuracy of a third-order strain interpolation method and the Geometric-Variable Strain approach for continuum robots, considering both individual and combined deformation effects. It addresses the lack of comprehensive performance evaluations for strain-based models beyond uniform bending tests. Experimental validation, achieved by reshaping a slender rod and tracking its configuration with cameras and reflective markers, demonstrates that the third-order strain interpolation method achieves good agreement with observed shapes, with an average error of 0.58% of the rod length and average computational time of 0.32s per configuration.
A third-order strain interpolation method for continuum robots achieves 0.58% shape reconstruction error and 0.32s computation time, surpassing existing models in accuracy and speed.
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.
