Modeling of natural terrain based on fractal geometry

Abstract

Abstract This paper proposes a method of modeling a natural terrain based on fractal geometry which can be applied to problems such as route planning for outdoor exploration by autonomous mobile robots. The method uses elevation data of a terrain which are derived from range data obtained by a scanning‐laser range‐finder at irregular positions. The method handles a problem of reconstruction of 3‐dimensional data with an arbitrary resolution and uncertainty. Assuming that the terrain is fractal shape, the method solves the following modeling problems: (a) estimation of terrain roughness based on fractal Brownian function model; (b) reconstruction of the terrain surface adaptive to the roughness (using interpolation of elevation data with Maximum A Posteriori (MAP) estimation); and (c) estimation of uncertainty distribution of the elevation map of terrain using the Monte Carlo method. The solution of each problem is given. The usefulness of the method is confirmed by simulations and experiments using observational data.