用空间傅里叶变换压缩软体机器人建模自由度，提升效率与精度。
SoFFT: Spatial Fourier Transform for Modeling Continuum Soft Robots
- 将机器人的主曲线视为时空信号，用傅里叶变换紧凑描述变形。
- 实验与仿真验证：自由度显著降低，仍保持高变形精度。
- 适合做软体机器人建模、数据驱动控制的研究者参考。
连续体软体机器人由柔性材料构成，理论上具有无限自由度，能在非结构化环境中表现出优异适应性。柯塞拉杆理论已成为高效建模的主流框架，将连续体软体机器人表示为随时间变化的曲线，即主曲线。本文提出将机器人的主曲线视为时空信号，应用傅里叶变换以紧凑方式描述其变形。该方法统一了柯塞拉杆理论框架下的现有建模策略，揭示了常用启发式方法的内在机理。此外，傅里叶变换支持数据驱动方法，可实验捕获机器人变形。所提方法在数值模拟与真实原型实验中均得到验证，显著降低自由度的同时保持变形表征精度。
原文摘要 · Abstract (English)
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.
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