In this paper we present an example of incremental build up of a topological map to be used by a mobile robot which is programmed for navigation tasks. For this purpose we will use the concept of virtual expansion of the receptive field and invariant properties of the centre of areas in a region of open space around the robot. Then we propose, as basic elements in the building of this map, polygons of open space detected around the robot and referred to centres of area. The data structure that underlies our map is a graph where each node contains an open space polygon and where each arc represents the connectivity between these polygons.
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