Construction of Minimized Topological Graphs on Occupancy Grid Maps Based on GVD and Sensor Coverage Information

One of the tasks to be carried out during the robot exploration of an unknown environment, is the construction of a complete map of the environment at bounded time interval. In order for the exploration to be efficient, a smart planning method must be implemented so that the robot can cover the space as fast as possible. One of the most important information that an intelligent agent can have, is a representation of the environment, not necessarily in the form of a map, but of a topological graph of the plane, which can be used to perform efficient planning. This work proposes a method to produce a topological graph of an Occupancy Grid Map (OGM) by using a Manhattan distance function to create the Approximate Generalized Voronoi Diagram (AGVD). Several improvements in the AGVD are made, in order to produce a crisp representation of the spaces skeleton, but in the same time to avoid the complex results of other methods. To smooth the final AGVD, morphological operations are performed. A topological graph is constructed from the AGVD, which is minimized by using sensor coverage information, aiming at planning complexity reduction.