Estimating search depths in hierarchical path planning

If collision free paths can be found on search graphs with few nodes and coarse resolutions, then traditional A* is fast. However, if such paths exist only on fine resolution graphs or at deeper levels of search hierarchies then A* is usually very slow. The paper studies two questions. First, when it is beneficial to use the plain A* instead of the method resembling an earlier hierarchical planner (Autere and Lehtinen, 1997). Second, which of the following two ways is better? Explore all the, nodes at a resolution i before exploring any nodes at finer resolutions or at deeper levels of the search hierarchy: i+1, i+2, ... . The other way is to explore nodes simultaneously at several finer resolutions (>i). Nine point-to-point path planning tasks in seven test cells are provided for experimental study. The dimensions of the tasks are from three to six. The planning times varied from about one minute to less than an hour