Global route planning for a mobile robot based on graph methods

The problem of global route planning for a mobile robot between two given points in a known area with static obstacles is considered. To solve the problem of constructing a route in an area with a large number of obstacles of complex shape, an integrated approach based on graph theory methods is proposed. It includes the Voronoi diagram, visibility graph and the Dijkstra's algorithm. At the first stage, the study area is represented as a polygonal object, the space outside the object is considered as obstacles. Next, to get a safe distance from obstacles, an internal buffer of the polygonal object is built using the Minkowski difference. Then the vertices of the polygon are compacted, and the Voronoi polygons are constructed from the resulting vertices. The median axis of the polygon is calculated from the Voronoi polygons. Then the Dijkstra's algorithm is applied to calculate the shortest path. The resulting path is used to construct a visibility graph, and the Dijkstra's algorithm is reapplied to the resulting graph. The proposed approach allows to build a route that is optimal in terms of length and distance to obstacles. It significantly reduces the computational complexity of constructing a visibility graph. The approach was implemented in the freely distributed QGIS geographic information system for planning the route of a mobile robot in an aquatic environment. The results of the experiment showed that the Voronoi diagram reduced the number of vertices required to construct the visibility graph by 8.3 times, while the visibility graph improved the path obtained from the Voronoi diagram by 8%. The proposed approach can be used for global planning of routes for mobile robots in various environments.