Sensor-based exploration for convex bodies: a new roadmap for a convex-shaped robot

We present a new roadmap that can be used to guide a convex body to explore an unknown planar workspace, i.e., to map an unknown configuration space diffeomorphic to SE(2). This new roadmap is called the convex hierarchical generalized Voronoi graph (convex-HGVG). Since this roadmap is defined in terms of workspace distance information that is within line of sight of the convex body, we can use it to direct the robot to explore an unknown configuration space diffeomorphic to SE(2). The challenge in defining the roadmap is that SE(2), with holes removed from it, generally does not have a one-dimensional deformation retract. Therefore, we decompose the punctured SE (2) into contractible regions, in which we define convex generalized Voronoi graphs (convex-GVG), and then connect these graphs with additional structures called convex-R edges. We formally show that the convex-HGVG, which is the union of the convex-GVG edges and the convex-R edges, is indeed a roadmap.