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(n²) where n is the total number of obstacle vertices. The focus here is in 1. (a) planning paths faster at the expense of setting for suboptimal path lengths and 2. (b) performance analysis of simple and/or well-known suboptimal methods. 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 paths. Then methods are presented based on the Voronoi diagrams, trapezoidal decomposition and triangulation, which compute (suboptimal) paths in O(n√log n) time with the preprocessing costs of O(n log n), O(n²) and O(n log n), respectively. Using existing navigational algorithms for unknown terrains, algorithms that run in O(n log n) time (after preprocessing) and yield suboptimal paths, are presented. For all these algorithms, upper bounds on the path lengths are estimated in terms of the shortest of the obstacles, etc.