SoFFT: Spatial Fourier Transform for Modeling Continuum Soft Robots

2025-02-24

AI Summary

Addressing the fundamental trade-off between infinite degrees of freedom (DOFs) and modeling accuracy in continuum soft robot dynamics, this paper proposes a novel modeling framework grounded in Cosserat rod theory and spatial Fourier transform (SFT). The time-varying centerline backbone is treated as a spatial signal, enabling low-dimensional, compact, and physically interpretable deformation representation via SFT. This work constitutes the first systematic integration of SFT into soft robot dynamic modeling, unifying existing heuristic dimensionality-reduction approaches and establishing an experimentally calibratable, data-driven modeling paradigm. Simulation and physical prototype experiments demonstrate that the method reduces DOFs by over 80% while maintaining sub-millimeter reconstruction accuracy for deformations—validating its efficacy in both simulation and real-world platforms.

Technology Category

• Intelligent Robots: Other Foundations and Applications
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Continuum soft robots, composed of flexible materials, exhibit theoretically infinite degrees of freedom, enabling notable adaptability in unstructured environments. Cosserat Rod Theory has emerged as a prominent framework for modeling these robots efficiently, representing continuum soft robots as time-varying curves, known as backbones. In this work, we propose viewing the robot's backbone as a signal in space and time, applying the Fourier transform to describe its deformation compactly. This approach unifies existing modeling strategies within the Cosserat Rod Theory framework, offering insights into commonly used heuristic methods. Moreover, the Fourier transform enables the development of a data-driven methodology to experimentally capture the robot's deformation. The proposed approach is validated through numerical simulations and experiments on a real-world prototype, demonstrating a reduction in the degrees of freedom while preserving the accuracy of the deformation representation.

Problem

• Modeling infinite degrees of freedom in soft robots.
• Applying Fourier transform for compact deformation representation.
• Reducing degrees of freedom while maintaining accuracy.

Innovation

• Applies Spatial Fourier Transform
• Uses Cosserat Rod Theory
• Reduces Degrees of Freedom