Learning the delaunay triangulation of landmarks from a distance ordering sensor

This paper considers a robot that moves in a plane and is only able to sense the distance order of landmarks with respect to its current position. The robot has no access to either metric information about the location of landmarks and its own position, or to odometry or speed controls. We propose several algorithms for the robot that allow it to navigate to certain points in the plane and to learn global information about the landmark locations. We, furthermore, demonstrate example tasks, such as convex hull computation, that can be performed using this information.