Hierarchical Path Search with Partial Materialization of Costs for a Smart Wheelchair

In this paper, the off-line path planner module of a smart wheelchair aided navigation system is described. Environmental information is structured into a hierarchical graph (H-graph) and used either by the user interface or the path planner module. This information structure facilitates efficient path search and easier information access and retrieval. Special path planning issues like planning between floors of a building (vertical path planning) are also viewed. The H-graph proposed is modelled by a tree. The hierarchy of abstractions contained in the tree has several levels of detail. Each abstraction level is a graph whose nodes can represent other graphs in a deeper level of the hierarchy. Path planning is performed using a path skeleton which is built from the deepest abstraction levels of the hierarchy to the most upper levels and completed in the last step of the algorithm. In order not to lose accuracy in the path skeleton generation and speed up the search, a set of optimal subpaths are previously stored in some nodes of the H-graph (path costs are partially materialized). Finally, some experimental results are showed and compared to traditional heuristic search algorithms used in robot path planning.Comisión Interministerial de Ciencia y Tecnología TER96-2056-C02-0

A Hierarchical Extension of the D ∗ Algorithm

In this paper a contribution to the practice of path planning using a new hierarchical extension of the D ∗ algorithm is introduced. A hierarchical graph is stratified into several abstraction levels and used to model environments for path planning. The hierarchical D∗ algorithm uses a downtop strategy and a set of pre-calculated trajectories in order to improve performance. This allows optimality and specially lower computational time. It is experimentally proved how hierarchical search algorithms and on-line path planning algorithms based on topological abstractions can be combined successfully

Hierarchical D ∗ algorithm with materialization of costs for robot path planning

In this paper a new hierarchical extension of the D ∗ algorithm for robot path planning is introduced. The hierarchical D ∗ algorithm uses a down-top strategy and a set of precalculated paths (materialization of path costs) in order to improve performance. This on-line path planning algorithm allows optimality and specially lower computational time. H-Graphs (hierarchical graphs) are modified and adapted to support on-line path planning with materialization of costs and multiple hierarchical levels. Traditional on-line robot path planning focused in horizontal spaces is also extended to vertical and interbuilding spaces. Some experimental results are showed and compared to other path planning algorithms

Route Planning in Transportation Networks

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle

Hierarchical path-finding for Navigation Meshes (HNA*)

Path-finding can become an important bottleneck as both the size of the virtual environments and the number of agents navigating them increase. It is important to develop techniques that can be efficiently applied to any environment independently of its abstract representation. In this paper we present a hierarchical NavMesh representation to speed up path-finding. Hierarchical path-finding (HPA*) has been successfully applied to regular grids, but there is a need to extend the benefits of this method to polygonal navigation meshes. As opposed to regular grids, navigation meshes offer representations with higher accuracy regarding the underlying geometry, while containing a smaller number of cells. Therefore, we present a bottom-up method to create a hierarchical representation based on a multilevel k-way partitioning algorithm (MLkP), annotated with sub-paths that can be accessed online by our Hierarchical NavMesh Path-finding algorithm (HNA*). The algorithm benefits from searching in graphs with a much smaller number of cells, thus performing up to 7.7 times faster than traditional A¿ over the initial NavMesh. We present results of HNA* over a variety of scenarios and discuss the benefits of the algorithm together with areas for improvement.Peer ReviewedPostprint (author's final draft