Motion planning for a rod-shaped robot in R3: connecting the rod-HGVG using the point-HGVG

This work considers the motion planning for a rod-shaped robot in a three-dimensional space. Our approach is to construct a roadmap in the configuration space of the rod and use it to navigate and map unknown spaces. Previously, we defined the rod-HGVG, which is a roadmap for a rod-shaped robot operating in a three-dimensional space. However, the rod-HGVG is only guaranteed to be connected if the point-GVG is connected. This work extends the rod-HGVG into more general environments where the point-GVG may not be connected but the point-HGVG is connected. For this, we define new components, termed the higher-order edges for the rod-HGVG and linking strategies which are based on the point-HGVG. Just as there is a close relationship between the components of the point-GVG and the rod-HGVG, there is a close relationship between the components of the point-HGVG and the higher-order edges of the rod-HGVG. We provide the construction procedures for the higher-order edges, which, like the components of the rod-HGVG, can be constructed using only sensor-provided information.