An efficient representation of edge shapes in topological maps

There are nodes and edges in a topological map. Node data has been used as a main source of information for the localization of mobile robots. In contrast, edge data is regarded as a minor source of information, and it has been used in an intuitive and heuristic way. However, edge data also can be used as a good source of information and provide a way to use edge data efficiently. For that purpose, we define a data format which describes the shape of an edge. This format is called local generalized Voronoi graph's angle (LGA). However, the LGA is constituted of too many samples; therefore, real time localization cannot be performed. To reduce the number of samples, we propose a compression method which utilizes wavelet transformation. This method abstracts the LGA by key factors using far fewer samples than the LGA. Experiments show that the LGA accurately describes the shape of the edges and that the key factors preserve most information of the LGA while reducing the number of samples.