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Fractional-order Modeling for Nonlinear Soft Actuators via Particle Swarm Optimization

Wu-Te Yang, Masayoshi Tomizuka

TL;DR

The paper tackles the challenge of accurately modeling soft pneumatic actuators by introducing a fractional-order differential equation framework. Parameters are identified via particle swarm optimization directly from experimental data, removing the need for material databases or tensile tests. The approach yields high-accuracy, data-efficient models that outperform a nonlinear second-order baseline across two soft materials, while also analyzing PSO limitations and data requirements. This work advances soft-robot modeling by incorporating memory effects and providing practical, database-free tools for design and control. Overall, it demonstrates that fractional-order models can robustly capture viscoelastic actuator dynamics with relatively low data demands.

Abstract

Modeling soft pneumatic actuators with high precision remains a fundamental challenge due to their highly nonlinear and compliant characteristics. This paper proposes an innovative modeling framework based on fractional-order differential equations (FODEs) to accurately capture the dynamic behavior of soft materials. The unknown parameters within the fractional-order model are identified using particle swarm optimization (PSO), enabling parameter estimation directly from experimental data without reliance on pre-established material databases or empirical constitutive laws. The proposed approach effectively represents the complex deformation phenomena inherent in soft actuators. Experimental results validate the accuracy and robustness of the developed model, demonstrating improvement in predictive performance compared to conventional modeling techniques. The presented framework provides a data-efficient and database-independent solution for soft actuator modeling, advancing the precision and adaptability of soft robotic system design.

Fractional-order Modeling for Nonlinear Soft Actuators via Particle Swarm Optimization

TL;DR

The paper tackles the challenge of accurately modeling soft pneumatic actuators by introducing a fractional-order differential equation framework. Parameters are identified via particle swarm optimization directly from experimental data, removing the need for material databases or tensile tests. The approach yields high-accuracy, data-efficient models that outperform a nonlinear second-order baseline across two soft materials, while also analyzing PSO limitations and data requirements. This work advances soft-robot modeling by incorporating memory effects and providing practical, database-free tools for design and control. Overall, it demonstrates that fractional-order models can robustly capture viscoelastic actuator dynamics with relatively low data demands.

Abstract

Modeling soft pneumatic actuators with high precision remains a fundamental challenge due to their highly nonlinear and compliant characteristics. This paper proposes an innovative modeling framework based on fractional-order differential equations (FODEs) to accurately capture the dynamic behavior of soft materials. The unknown parameters within the fractional-order model are identified using particle swarm optimization (PSO), enabling parameter estimation directly from experimental data without reliance on pre-established material databases or empirical constitutive laws. The proposed approach effectively represents the complex deformation phenomena inherent in soft actuators. Experimental results validate the accuracy and robustness of the developed model, demonstrating improvement in predictive performance compared to conventional modeling techniques. The presented framework provides a data-efficient and database-independent solution for soft actuator modeling, advancing the precision and adaptability of soft robotic system design.

Paper Structure

This paper contains 19 sections, 19 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Fractional-Order Dynamic Model
  3. Soft Pneumatic Actuator
  4. Fractional Differential Equation
  5. Definition of Fractional Differential Equations
  6. Fractional-order Dynamic Systems
  7. Analytical Solution of Fractional-order Equations
  8. Particle Swarm Optimization
  9. Experimental Evaluation
  10. Fractional-order Models Setup
  11. Experimental Setup
  12. System Response Test
  13. Design 1 Test
  14. Design 2 Test
  15. Discussion and Conclusion
  16. ...and 4 more sections

Figures (4)

  • Figure 1: The soft pneumatic actuator is undergoing bending $\theta$ with equivalent force $F(P)$ when it is pressurized by an air pump.
  • Figure 2: The schematic of experimental setup.
  • Figure 3: Comparisons between seven experimental data, nonlinear dynamical equation, and fractional-order equation for the soft actuator made of Dragon Skin 20.
  • Figure 4: Comparisons between seven experimental data, nonlinear dynamical equation, and fractional-order equation of the soft actuator made of Dragon Skin FX-Pro.