Sensor-based Planning for Planar Multi-Convex Rigid Bodies

This paper presents a method for a planar rigid body consisting of multiple convex bodies to explore an unknown planar workspace, i.e., an unknown configuration space diffeomorphic to SE(2). This method is based on a roadmap termed concave hierarchical generalized Voronoi graph (concave-HGVG). Just as in our previous work, we decompose the free configuration space into contractible cells in which we define the concave generalized Voronoi graphs (concave-GVG), and then connect these graphs using an additional structure termed one-tangent edges. Since the robot consists of multiple convex bodies, the one-tangent edges are defined using the diameter function of the convex hull of the convex bodies as well as the individual convex bodies. These two structures together form the concave-HGVG, which is a one-dimensional roadmap of the multi-convex bodies in plane. Both components are defined in terms of workspace distance measurement, and thus the concave-HGVG can readily be constructed in a sensor-based way.