On the Parameterization and the Geometry of the Configuration Space of a Single Planar Robot

Abstract

Translating and rotating planar polygonal robots are studied in the literature for decades. An integral part of this study is the configuration space which corresponds to the work space. In the context of motion planning problems, the boundary between the free and forbidden parts of the configuration space plays a major role. In this paper we find an explicit parameterization of the boundary of the forbidden space. Using this parameterization we detail several geometrical properties of the various elements which constitute this boundary. In addition, this parameterization enables us to visualize these elements.