The harmonic potentials have proved to be a powerful technique for path planning in a known environment. They have two important properties: Given an initial point and a objective in a connected domain, it exists a unique path between those points. This path is the maximum gradient path of the harmonic function that begins in the initial point and ends in the goal point. The second property is that the harmonic function cannot have local minima in the interior of the domain (the objective point is considered as a border). Our approach has the following advantages over the previous methods: 1) It uses the Finite Elements Method to solve the PDE problem. This method permits complicated shapes of the obstacles and walls. 2) It uses mixed border conditions, because in this way the trajectories are smooth and the potential slope is not too small and the trajectories avoid the corners of walls and obstacles. 3) It can avoid moving obstacles in real time, because it works on line and the speed is high. 4) It can be generalized to 3D or more dimensions and it can be used to move robot manipulators.
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