  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.
