Polygon Area Decomposition for Multiple-Robot Workspace Division

Abstract

A new polygon decomposition problem, the anchored area partition problem, which has applications to a multiple-robot terrain-covering problem is presented. This problem concerns dividing a given polygon V into n polygonal pieces, each of a specified area and each containing a certain point (site) on its boundary or in its interior. First the algorithm for the case when V is convex and contains no holes is presented. Then the generalized version that handles nonconvex and nonsimply connected polygons is presented. The algorithm uses sweep-line and divide-and-conquer techniques to construct the polygon partition. The input polygon V is assumed to have been divided into a set of p convex pieces (p = 1 when V is convex), which can be done in 0(vp log log up) time, where vp is the number of vertices of V and p = 0(vp), using algorithms presented elsewhere in the literature. Assuming this convex decomposition, the running time of the algorithm presented here is 0(pn 2 -run), where v is the sum of the number of vertices of the convex pieces.

Area coverage with heterogeneous UAVs using scan patterns

“…The Polygon Area Decomposition algorithm [8] is a stateof-the-art algorithm for partitioning a polygon to a fixed set of regions. Each subpolygon (partition) is anchored to a site, a specific location that corresponds to the starting position of a participating UAV.…”

“…In [8], Hert introduces an algorithm to decompose a polygon into a set of subpolygons. The surface of each subpolygon can be controlled to give larger area to more capable UAVs.…”

New Framework for Decomposing a Polygon with Zero or More Holes

“…In fact, many algorithms perform more efficiently on convex objects than on non-convex objects [5], so convex decomposition, which partitions the model into convex components has applications in many areas including: pattern recognition [6], Minkowski sum computation [7], motion planning [8], computer graphics, and origami folding [9]. Unfortunately, exact convex decomposition can be costly to construct and can result in a representation with an unmanageable number of components.…”

Dynamic decentralized area partitioning for cooperating cleaning robots

“…al. [2,3] deal with the question of how to split an area in parts (for robots), which are equal in size, where each part has to be connected and has to contain a certain point. These points correspond to the robots start positions.…”

“…an airport, the room must be partitioned among the robots. This can be done either statically [2] or dynamically.…”