This paper presents the application of the Anisotropic Fast Marching Method to the path planning problem of mobile robots moving in 3D environments. The slope of a terrain can be considered as a tensor filed because at any point on a 3D surface there are two main slopes: the maximum, which is the slope of the gradient, and the minimum, which is the slope perpendicular direction to the gradient. The resulting trajectory of the path planning should take both into account so that the slopes in the trajectory are minimized, just as the Romans used flocks of cows to make Roman roads and so that the descent of the road was small as possible. In this work, this is achieved by the use of the Anisotropic Fast Marching Method. Numerical simulations are presented to show the advantage of this method over its isotropic version. Besides, the influence of the anisotropic index and the traversability of the resultant paths are analyzeded.
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