Using a Robot to Learn Geometric Information from Permutations of Landmarks

This paper considers a robot that moves in the plane and is only able to sense the cyclic order of landmarks with respect to its current position. No metric information is available regarding the robot or landmark positions; moreover, the robot does not have a compass or odometers (e.g., coordinates). We carefully study the information space of the robot, and establish its capabilities in terms of mapping the environment and accomplishing tasks, such as navigation and patrolling. The information space can be nicely characterized using the notion of order type, which provides information powerful enough to determine which points lie inside the convex hulls of subsets of landmarks. An extension to this work using braid groups is briefly discussed at the end of the paper.