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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 438576, 11 pages
Research Article

Dynamic Detection of Topological Information from Grid-Based Generalized Voronoi Diagrams

College of Information System and Management, National University of Defense Technology, Hunan, Changsha, 410073, China

Received 11 July 2013; Revised 3 October 2013; Accepted 3 October 2013

Academic Editor: Piermarco Cannarsa

Copyright © 2013 Long Qin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the context of robotics, the grid-based Generalized Voronoi Diagrams (GVDs) are widely used by mobile robots to represent their surrounding area. Current approaches for incrementally constructing GVDs mainly focus on providing metric skeletons of underlying grids, while the connectivity among GVD vertices and edges remains implicit, which makes high-level spatial reasoning tasks impractical. In this paper, we present an algorithm named Dynamic Topology Detector (DTD) for extracting a GVD with topological information from a grid map. Beyond the construction and reconstruction of a GVD on grids, DTD further extracts connectivity among the GVD edges and vertices. DTD also provides efficient repair mechanism to treat with local changes, making it work well in dynamic environments. Simulation tests in representative scenarios demonstrate that (1) compared with the static algorithms, DTD generally makes an order of magnitude improvement regarding computation times when working in dynamic environments; (2) with negligible extra computation, DTD detects topologies not computed by existing incremental algorithms. We also demonstrate the usefulness of the resulting topological information for high-level path planning tasks.