Path Planning in Topologically Evolving Planar Environments

Abstract

The task of planning a path between two spatial configurations of an artifact moving among obstacles is an important problem in many geometrically-intensive applications. Despite the ubiquity of the problem, the existing approaches make specific limiting assumptions about the geometry and mobility of the obstacles, or those of the environment in which the motion of the artifact takes place. In this paper we propose a powerful approach for 2D path planning in a dynamic environment that can undergo drastic topological changes. Our algorithm is based on a potent paradigm for medial axis computation that relies on constructive representations of shapes with R-functions that operate on real-valued half-spaces as logic operations. Our approach can handle problems in which the environment is not fully known a priori, intrinsically supports local and parallel skeleton computations for domains with rigid or evolving boundaries, and appears to extend naturally to 3D domains. Furthermore, our path planning algorithm can be implemented in any commercial geometric kernel, and has attractive computational properties. The capability of the proposed technique are explored through several examples designed to resemble highly dynamic environments.