Hexagon-Based Generalized Voronoi Diagrams Generation for Path Planning of Intelligent Agents

Grid-based Generalized Voronoi Diagrams (GVDs) are widely used to represent the surrounding environment of intelligent agents in the fields of robotics, computer games, and military simulations, which improve the efficiency of path planning of intelligent agents. Current studies mainly focus on square-grid-based GVD construction approaches, and little attention has been paid to constructing GVDs from hexagonal grids. In this paper, an algorithm named hexagon-based crystal growth (HCG) is presented to extract GVDs from hexagonal grids. In addition, two thinning patterns for obtaining one-cell-wide GVDs from rough hexagon-based GVDs are proposed. On the basis of the principles of a leading square-grid-based algorithm named Brushfire, a hexagon-based Brushfire algorithm is realized. A comparison of the HCG and the hexagon-based Brushfire algorithm shows that HCG is much more efficient. Further, the usefulness of hexagon-based GVDs for the path planning tasks of intelligent agents is demonstrated using several representative simulation experiments.