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Using Neural Networks to Model Hysteretic Kinematics in Tendon-Actuated Continuum Robots

Yuan Wang, Max McCandless, Abdulhamit Donder, Giovanni Pittiglio, Behnam Moradkhani, Yash Chitalia, Pierre E. Dupont

TL;DR

This work addresses how to model hysteretic kinematics in tendon-actuated continuum robots using neural networks. It systematically compares three architectures—FNN, FNN with a history input buffer, and LSTM—for both forward and inverse mappings, demonstrating that history-inclusive models capture history dependence and rate effects effectively. Across two robot designs, FNN-HIB and LSTM achieve comparable performance in modeling rate-dependent hysteresis, while the standard FNN fails to capture hysteresis. The findings highlight design-dependent hysteresis and suggest NN-based approaches can enable real-time, data-driven control where traditional physics-based models struggle.

Abstract

The ability to accurately model mechanical hysteretic behavior in tendon-actuated continuum robots using deep learning approaches is a growing area of interest. In this paper, we investigate the hysteretic response of two types of tendon-actuated continuum robots and, ultimately, compare three types of neural network modeling approaches with both forward and inverse kinematic mappings: feedforward neural network (FNN), FNN with a history input buffer, and long short-term memory (LSTM) network. We seek to determine which model best captures temporal dependent behavior. We find that, depending on the robot's design, choosing different kinematic inputs can alter whether hysteresis is exhibited by the system. Furthermore, we present the results of the model fittings, revealing that, in contrast to the standard FNN, both FNN with a history input buffer and the LSTM model exhibit the capacity to model historical dependence with comparable performance in capturing rate-dependent hysteresis.

Using Neural Networks to Model Hysteretic Kinematics in Tendon-Actuated Continuum Robots

TL;DR

This work addresses how to model hysteretic kinematics in tendon-actuated continuum robots using neural networks. It systematically compares three architectures—FNN, FNN with a history input buffer, and LSTM—for both forward and inverse mappings, demonstrating that history-inclusive models capture history dependence and rate effects effectively. Across two robot designs, FNN-HIB and LSTM achieve comparable performance in modeling rate-dependent hysteresis, while the standard FNN fails to capture hysteresis. The findings highlight design-dependent hysteresis and suggest NN-based approaches can enable real-time, data-driven control where traditional physics-based models struggle.

Abstract

The ability to accurately model mechanical hysteretic behavior in tendon-actuated continuum robots using deep learning approaches is a growing area of interest. In this paper, we investigate the hysteretic response of two types of tendon-actuated continuum robots and, ultimately, compare three types of neural network modeling approaches with both forward and inverse kinematic mappings: feedforward neural network (FNN), FNN with a history input buffer, and long short-term memory (LSTM) network. We seek to determine which model best captures temporal dependent behavior. We find that, depending on the robot's design, choosing different kinematic inputs can alter whether hysteresis is exhibited by the system. Furthermore, we present the results of the model fittings, revealing that, in contrast to the standard FNN, both FNN with a history input buffer and the LSTM model exhibit the capacity to model historical dependence with comparable performance in capturing rate-dependent hysteresis.
Paper Structure (18 sections, 9 equations, 8 figures, 1 table)

This paper contains 18 sections, 9 equations, 8 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. Hysteretic Kinematic Modeling
  3. Training Data
  4. Neural Network Models
  5. FNN
  6. FNN with a history input buffer
  7. LSTM
  8. Forward and inverse kinematic modeling
  9. EXPERIMENTAL MODELING
  10. Robot with Superelastic Central Backbone and Spacer Disks
  11. Clinical Cardiac Catheter Robot
  12. Tendon Pre-tension
  13. Hysteretic Rate Dependence
  14. Comparison of Neural Network Models
  15. Data collection
  16. ...and 3 more sections

Figures (8)

  • Figure 1: Tendon-actuated continuum robots. (a) Superelastic central backbone with spacer disks. (b) Clinical cardiac catheter.
  • Figure 2: History-dependent kinematic mappings. (a) Forward kinematic map. (b) Inverse kinematic map.
  • Figure 3: Neural network model structures. (a) FNN. (b) FNN with a history input buffer. (c) LSTM.
  • Figure 4: Training dataset tendon displacement sinusoidal function types conducted on the robot in Fig.\ref{['fig:robots']}(b) following (\ref{['eq:training']}) (each with $\tau$ = $f_h \cdot \log(\frac{7}{6})$). (a) 0 baseline: $q_\text{max}$ = 3mm, $c$ = 1, $q_\text{offset}$ = 0. (b) Mid baseline: $q_\text{max}$ = 3mm, $c$ = 0, $q_\text{offset}$ = 3mm. (c) End baseline: $q_\text{max}$ = 3mm, $c$ = -1, $q_\text{offset}$ = 6mm.
  • Figure 5: Alternative forward kinematic maps of robot shown in Fig. \ref{['fig:robots']}(a). (a) Tip tangent angle as a function of tendon tension. (b) Tip tangent angle as a function of tendon displacement.
  • ...and 3 more figures