Abstract
In order to create an autonomous mobile robot it is necessary to develop powerful methods for path planning, avoiding collisions with low computational costs. In this paper, a mathematical formalism for the general evaluation of the representation in the configuration space of any set of obstacles is presented. The use of such representation reduces drastically the complexity of the problem. As it is shown in the paper, with the proposed method, the obstacle representation can be seen as a convolution of two functions that describe the robot and the obstacles respectively. Additionally, the computational load is independent of the shape and number of obstacles and of the robot shape. In the final implementation the Fast Fourier Transform is used to take advantage of the intrinsic parallelable nature of this tool. The resulting algorithm can also be very easily implemented in a parallel way. All the considerations above allow to reduce drastically the computational time making the algorithm suitable for real applications. The method has been applied to robots moving on a plane in a 2D and a 3D dimensional workspace
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