Evaluation of fractal terrain model for vehicle dynamic simulations

Fractals are a popular method for modeling terrains that include various scales. This paper investigates the effectiveness of using fractals for generating artificial terrains which can be used for vehicle simulations. The 3-D Weierstrass–Mandelbrot function was used to generate surfaces based on experimentally measured terrains. There is an exponential relationship between the root means squared elevation of the surfaces and the fractal scaling parameter. This relationship was used to determine the required fractal parameters to generate a surface with a desired roughness. A light detection and ranging (LiDAR) sensor coupled with a global positioning system (GPS) and inertial navigation system (INS) was used to measure two off road surfaces. The experimental terrain was then compared to the simulated terrain. Based on the comparison, the fractal model can capture the general roughness of the experimentally measured terrains as determined by the dynamic response of a suspension model. However, the fractal model fails to capture some of the nuances and non-periodic events observed in experimental terrains.