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

We present an algorithm that enables a convex shaped robot to explore an unknown planar workspace, i.e., an unknown configuration space diffeomorphic to SE(2). This algorithm is based on a roadmap called the convex hierarchical generalized Voronoi graph (convex-HGVG), which is the central contribution of the paper. Since this roadmap is defined in terms of workspace distance information which is within line of sight of the convex body, we can use this roadmap to direct the robot to explore the unknown space. The challenge in defining the roadmap is that SE(2), with holes removed from it, does not have, in general, a one-dimensional 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 R-edges. The convex-GVG edges and the R-edges together form the convex-HGVG. We show that the convex-HGVG is indeed a roadmap and then we demonstrate the control laws that a robot can invoke that incrementally constructs the roadmap.