Application of the fast marching method for outdoor motion planning in robotics

In this paper, a new path planning method for robots used in outdoors environments is presented. The proposed method applies Fast Marching to a 3D surface represented with a triangular mesh to calculate a smooth trajectory from one point to another. The method uses a triangular mesh instead of a square mesh since this kind of grid adapts better to 3D surfaces. The novelty of this approach is that, before running the algorithm, the method calculates a weight matrix W based on the information extracted from the 3D surface characteristics. In the presented experiments those features are the height, the spherical variance, and the gradient of the surface. This matrix can be viewed as a difficulty map situated over the 3D surface, and it is used to limit the speed propagation of the Fast Marching wave in order to find the best path depending on the task requirements, e.g., the less energy consumption path, the fastest path, the most plain terrain. The algorithm also gives the velocity for the robot which is based on the wave front propagation speed. The results presented in this paper show how varying this W matrix, the paths obtained are different.