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

Annika Delucchi, Vincenzo Di Paola, Andreas Müller, and Matteo Zoppi

Abstract

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.

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

Abstract

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.
Paper Structure (29 sections, 42 equations, 11 figures, 6 tables)

This paper contains 29 sections, 42 equations, 11 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Rod Model
  3. Kinematics of Rods
  4. Constitutive equations
  5. Equilibrium Equations
  6. Approximated Strain-based Models
  7. Third-order Strain Interpolated Approach
  8. Geometric Variable Strain Model
  9. Evaluation
  10. Accuracy Metric
  11. Computational Time
  12. Simulations
  13. Scenarios
  14. Bending Simulations
  15. Torsion Simulation
  16. ...and 14 more sections

Figures (11)

  • Figure 1: Rod description and parameters: a generic rod undergoing large deformations, where at each $\tau$ corresponds a reference frame $\mathcal{F}_{\tau}$ whose $x$-axis is aligned with the rod centreline.
  • Figure 2: Bending test: rod configurations (a) and evaluation metrics plots (b). The GVS is solved with third degree monomial basis. Although selecting a second degree monomial basis reduces computational time, it remains higher than the interpolated one. On the other hand, accuracy decreases to the same range of the interpolated.
  • Figure 3: Values of $\kappa_1$ (a), $\kappa_2$ (b) and $\kappa_3$ (c) at each $\tau$ for the interpolated model.
  • Figure 4: Two bending test: rod configurations (a) and evaluation metrics plots (b). The GVS model is solved with thirds degree monomial basis.
  • Figure 5: Bending-torsion test: rod configurations for the exact model (a-left), GVS model (a-middle) and interpolated model (a-left), together with evaluation metrics (b). The GVS model is solved with third degree Legendre polynomial basis.
  • ...and 6 more figures

Theorems & Definitions (2)

  • Remark 1
  • Remark 2