Multiscale Terrain Characterization Using Fourier and Wavelet Transforms for Unmanned Ground Vehicles

This paper investigates the use of the Fourier transform and Wavelet transform as methods to supplement the more common root mean squared elevation and power spectral density methods of terrain characterization. Two dimensional terrain profiles were generated using the Weierstrass-Mandelbrot fractal equation. The Fourier and Wavelet transforms were used to decompose these terrains into a parameter set. A two degree of freedom quarter car model was used to evaluate the vehicle response before and after the terrain characterization. It was determined that the Fourier transform can be used to reduce the profile into the key frequency components. The Wavelet transform can effectively detect discontinuities of the profile and changes in the roughness of the profile. These two techniques can be added to current methods to yield a more robust terrain characterization.