SoFFT: Spatial Fourier Transform for Modeling Continuum Soft Robots

TL;DR

This paper introduces a novel Fourier transform-based approach to model continuum soft robots, unifying existing methods and enabling efficient, data-driven deformation analysis validated through simulations and real-world experiments.

Contribution

It proposes viewing the robot's backbone as a signal in space and time, applying Fourier transform for compact deformation modeling within Cosserat Rod Theory.

Findings

Reduces degrees of freedom in deformation modeling

Unifies existing modeling strategies within a Fourier framework

Validated through simulations and real-world experiments

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.