SoFFT: Spatial Fourier Transform for Modeling Continuum Soft Robots

TL;DR

This work reframes continuum soft robot modeling by treating the backbone as a spatial-temporal signal and applying Spatial and Space-Time Fourier Transforms, unifying Cosserat Rod Theory with spectral reconstruction methods. A data-driven spectrum extraction pipeline, including Basis Pursuit Denoising, selects compact basis sets (polynomial, trig, Gaussian) to accurately fit strains while reducing degrees of freedom. The approach is validated through numerical simulations and real-world experiments, demonstrating accurate deformation representation with substantially fewer DoFs and revealing resonance phenomena through STFT analyses. The spectral perspective provides a principled basis for model reduction and basis selection, offering a pathway to efficient, data-informed control of soft robots.

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.

Figures (17)

• Figure 1: Representative scheme for applying the Fourier transform to CSR. (a) The strain field can be extracted from the backbone and analyzed in the spatial frequency domain. (b) The spatial spectrum of a sampled strain field. Due to the unbounded nature of the strain field spectrum, aliasing is inevitable.
• Figure 2: Impact of the phase in a planar rod with a sinusoidal curvature function. Varying the phase, the deformation is distributed differently along the rod.
• Figure 3: Comparison of the different spatial discretization methodologies. By treating the strain field as a signal, existing modeling approaches can be interpreted as reconstructors.
• Figure 4: Illustration of the proposed data-driven methodology. The robot is subjected to the standard signals and the samples of the strain field are measured by the sensors. Through FFT, the space-time spectrum can be computed.
• Figure 5: Sketch of the H-Support robot, a cylindrical CSR with 3 longitudinal and 4 helicoidal actuators. The geometrical and physical parameters are listed in Tab. \ref{['tab:sim_parameters']}.