Constraint reformulation in a hierarchical path planner

Robot path planning consists of approximating the set of free configurations of the robot by a collection of rectangloid cells at successive levels of approximation and, at each level, searching the graph representing the adjacency relation among these cells. A set of algorithms which specifically address the main two computational issues underlying this approach, cell decomposition and graph searching, has been developed. The authors have implemented a planner which incorporates these algorithms and have experimented with it on examples. The experiments show that the planner is significantly faster than previous planners based on the same general approach. The authors focus on the planner´s cell-decomposition algorithms. They use a constraint reformulation technique that consists of approximating the obstacles intersecting the cell to be decomposed by a collection of rectangloids and computing their complements in the cell. Two types of approximations are used, bounding and bounded approximations. This technique produces much less cells than previously proposed techniques, resulting in smaller search graphs. Experimental results are presented