Optimal Paths for Landmark-Based Navigation by Differential-Drive Vehicles With Field-of-View Constraints

In this paper, we consider the problem of planning optimal paths for a differential-drive robot with limited sensing, that must maintain visibility of a fixed landmark as it navigates in its environment. In particular, we assume that the robot´s vision sensor has a limited field of view (FOV), and that the fixed landmark must remain within the FOV throughout the robot´s motion. We first investigate the nature of extremal paths that satisfy the FOV constraint. These extremal paths saturate the camera pan angle. We then show that optimal paths are composed of straight-line segments and sections of these these extremal paths. We provide the complete characterization of the shortest paths for the system by partitioning the plane into a set of disjoint regions, such that the structure of the optimal path is invariant over the individual regions