Sensor based planning for a planar rod robot: incremental construction of the planar rod-HGVG

This work considers sensor based motion planning for rod-shaped robots in unknown environments. The motion planning scheme is based on the rod hierarchical generalized Voronoi graph (rod-HGVG). The rod-HGVG is a roadmap for rod-like robots, and is an extension of a prior roadmap for point-like robots. We give an incremental method to construct the rod-HGVG thereby enabling exploration of unknown environments. An important practical feature of the algorithm is its sole reliance upon the use of work space distance measurements to objects that are within line of sight. Such measurements can be readily provided by conventional range sensors. Moreover, motion planning in a configuration space is achieved without explicitly constructing each configuration space obstacle. A key result derived in this paper is the distance gradient between two convex sets.