Shortest paths for wheeled robots with limited Field-Of-View: Introducing the vertical constraint

This paper presents the study of shortest paths for a robot with unicycle kinematics equipped with a limited Field-Of-View (FOV) camera, which must keep a given feature in sight. Previous works on this subject have provided the optimal synthesis for the case in which the FOV is limited in the left and right directions (H-FOV). Toward the final goal of obtaining the shortest paths synthesis for a realistic image plane modeled as a rectangle, in this paper we study the complementary case in which only upper and lower image plane direction are limited (V-FOV). A finite alphabet of extremal arcs is obtained. We also show that in some cases there exist no optimal path. However, we are always able to provide a path whose length approximates arbitrarily well any other shorter path.