A Frequency-Domain Path-Following Method for Discrete Data-Based Paths

TL;DR

This paper introduces a frequency-domain method using FFT for path following with discrete data, creating a non-singular guiding vector field that improves computational efficiency and noise robustness.

Contribution

It proposes a novel FFT-based frequency-domain algorithm for path following that handles discrete data and reduces computational complexity.

Findings

Effective noise suppression demonstrated in simulations

Provides an upper bound for mean-square path-following error

Reduces computational complexity compared to time-domain methods

Abstract

This paper presents a novel frequency-domain approach for path following problem, specifically designed to handle paths described by discrete data. The proposed algorithm utilizes the fast Fourier Transform (FFT) to process the discrete path data, enabling the construction of a non-singular guiding vector field. This vector field serves as a reference direction for the controlled robot, offering the ability to adapt to different levels of precision. Additionally, the frequency-domain nature of the vector field allows for the reduction of computational complexity and effective noise suppression. The efficacy of the proposed approach is demonstrated through a numerical simulation, and theoretical analysis provides an upper bound for the ultimate mean-square path-following error.