Constructing the generalized local Voronoi diagram from laser range scanner data

We consider the problem of building local free space representation by a circular-base robot, operating in an unknown bounded planar environment populated by obstacles of arbitrary shape. In the unknown environment, the robot depends on its sensors; in our case, this is the laser range scanner. A new structure is represented, termed the generalized local Voronoi diagram (GLVD), constructed directly from sensory data, obtained from an observation of the local environment, that is from the visible region, GLVD is obtained by deleting some edges from the ordinary Voronoi diagram, which is generated by the measured scanned points from the visible region. Crucial for the acquisition of the GLVD is the clusterization of the scanned points. Clusterization means grouping of the scanned points into distinct clusters, each having a specific property, e.g., for a particular point in the cluster, the nearest neighboring point should not lie further than a prescribed distance away. The relevant part of GLVD, the portion of GLVD which is in accordance with the generalized Voronoi diagram of the environment, is determined. Eventual differences between these two structures are discussed and experimental results are presented. With the superposition of several GLVDs we show that this structure can be used to construct a global map of the environment, for which the position and the orientation of the robot is needed