Cornered Quadtrees/Octrees and Multiple Gateways Between Each Two Nodes; A Structure for Path Planning in 2D and 3D Environments

In this paper, modified versions of quadtree/octree, as structures used in path planning, are proposed which we call them cornered quadtree/octree. Also a new method of creating paths in quadtrees/octrees, once quadrants/octants to be passed are determined, is proposed both to improve traveled distance and path smoothness. In proposed modified versions of quadtree/octree, four corner cells of quadrants and eight corner voxels of octants are also considered as nodes of the graph to be searched for finding the shortest path. This causes better quadrant/octant selection during graph search relative to simple quadtrees and octrees. On the other hand, after that all quadrants/octants are determined, multiple gateways are nominated between each two selected nodes and path is constructed by passing through the gateway which its selection leads in shorter and smoother path. Proposed structures in this paper alongside the utilized path construction approach, creates better paths in terms of path length than those created if simple trees are used, somehow equal to the quality of the achieved paths by framed trees, meanwhile interestingly, consumed time and memory in our proposed method are closer to the used time and memory if simple trees are used.