Planning conditional shortest paths through an unknown environment: a framed-quadtree approach

A conditional shortest path is a collision-free path of shortest distance based on known information on an obstacle-scattered environment at a given time. This paper investigates the problem of finding a conditional L₂ shortest path through an unknown environment in which path planning is implemented “on the fly” as new obstacle information becomes available through external sensors. We propose a novel cell decomposition approach which calculates an L₂ distance transform through the use of a circular path-planning wave. The proposed method is based on a new data structure, called the framed-quadtree, which combines together the accuracy of grid-based path planning techniques with the efficiency of quadtree-based techniques, hence having the advantages of both. The heart of this method is a linear time algorithm for computing dynamic Voronoi diagrams