ON FAST PLANNING OF SUBOPTIMAL PATHS AMIDST POLYGONAL OBSTACLES IN PLANE

The problem of planning a path for a point robot from a source point s to a destination point d so as to avoid a set of polygonal obstacles in plane is considered. Using well-known methods, a shortest path from s to d can be computed with a time complexity of O(n(2)) where n is t he total number of obstacle vertices. The focus here is in (a) plannin g paths faster at the expense of setting for suboptimal path lengths a nd (b) performance analysis of simple and/or well-known suboptimal met hods. A method that enables a hierarchical implementation of any path planning algorithm with no increase in the worst-case time complexity, is presented; this implementation enables fast planning of simple pat hs. Then methods are presented based on the Voronoi diagrams, trapezoi dal decomposition and triangulation, which compute (suboptimal) paths in O(n root log n) time with the preprocessing costs of O(n log n), O( n(2)) and O(n log n), respectively. Using existing navigational algori thms for unknown terrains, algorithms that run in O(n log n) time (aft er preprocessing) and yield suboptimal paths, are presented. For all t hese algorithms, upper bounds on the path lengths are estimated in ter ms of the shortest of the obstacles, etc.