The motion planning problem requires that a collision-free path be determined for a robot moving amidst a fixed set of obstacles. Most neural network approaches to this problem are for the situation in which only local knowledge about the configuration space is available. The main goal of the paper is to show that neural networks are also suitable tools in situations with complete knowledge of the configuration space. In this paper we present an approach that combines a neural network and deterministic techniques. We define a colored version of Kohonen's self-organizing map that consists of two different classes of nodes. The network is presented with random configurations of the robot and, from this information, it constructs a road map of possible motions in the work space. The map is a growing network, and different nodes are used to approximate boundaries of obstacles and the Voronoi diagram of the obstacles, respectively. In a second phase, the positions of the two kinds of nodes are combined to obtain the road map. In this way a number of typical problems with small obstacles and passages are avoided, and the required number of nodes for a given accuracy is within reasonable limits. This road map is searched to find a motion connecting the given source and goal configurations of the robot. The algorithm is simple and general; the only specific computation that is required is a check for intersection of two polygons. We implemented the algorithm for planar robots allowing both translation and rotation and experiments show that compared to conventional techniques it performs well, even for difficult motion planning scenes.