Sensor based planning. I. The generalized Voronoi graph

This paper introduces a 1-dimensional network of curves termed the generalized Voronoi graph (GVG) and its extension, the hierarchical generalized Voronoi graph (HGVG), which can be used as a basis for a roadmap or retract-like structure. The GVG and HGVG provide a basis for sensor based path planning in an unknown static environment. In this paper, the GVG and HGVG are defined and some of their properties are exploited to show their utility for motion planning. A companion paper describes how to use the GVG and HGVG for the purposes of sensor based planning.