An Hierarchical Terrain Representation for Approximately Shortest Paths

Optimistic shortest paths on uncertain terrains

Shortest path problems are a well-studied class of problems in theoretical computer science. One particularly applicable type of shortest path problem is to find the geodesic shortest path on a terrain. This type of algorithm finds the shortest path between two points that stays on the surface of a terrain. The most popular methods for finding such a shortest path involve a variant of Dijkstra’...

Design and Implementation of an Efficient Hierarchical Speed-up Technique for Computation of Exact Shortest Paths in Graphs

Any-Angle Path Planning

In robotics and video games, one often discretizes continuous terrain into a grid with blocked and unblocked grid cells and then uses path-planning algorithms to find a shortest path on the resulting grid graph. This path, however, is typically not a shortest path in the continuous terrain. In this overview article, we discuss a path-planning methodology for quickly finding paths in continuous ...

Shortest Anisotropic Paths on Terrains

We discuss the problem of computing shortest an-isotropic paths on terrains. Anisotropic path costs take into account the length of the path traveled, possibly weighted, and the direction of travel along the faces of the terrain. Considering faces to be weighted has added realism to the study of (pure) Euclidean shortest paths. Parameters such as the varied nature of the terrain, friction, or s...

A Graph-Search Based Navigation Algorithm for Traversing A Potentially Hazardous Area with Disambiguation

The authors consider the problem of navigating an agent to safely and swiftly traverse a two dimensional terrain populated with possible hazards. Each potential hazard is marked with a probabilistic estimate of whether it is indeed true. In proximity to any of these potential hazards, the agent is able to disambiguate, at a cost, its true-false status. The method presented in this paper is to d...