Simple Robots in Polygonal Environments: A Hierarchy

With the current progress in robot technology and related areas, sophisticated moving and sensing capabilities are at hand to design robots capable of solving seemingly complex tasks. With the aim of understanding the limitations of such capabilities, swarms of simple and cheap robots play an increasingly important role. Their advantages are, among others, the cost, reusability, and fault-tolerance. While it can be expected that for a variety of problems a wealth of robot models are proposed, it is rather unfortunate that almost all proposals fail to point out their assumptions explicitly and clearly. This is problematic because seemingly small changes in the models can lead to significant differences in the capabilities of the robots. Hence, a clean assessment of the “power of robot models” is dearly needed, not only in absolute terms, but also relative to each other. We make a step in this direction by explaining for a set of elementary sensing devices which of these devices (alone and in combination) enable a robot to solve which problems. This not only leads to a natural relation (and hierarchy) of power between robot models that supports a more systematic design, but also exhibits surprising connections and equivalences. For example, one of the derived relations between the robot models implies that a very simple robot (that cannot measure distances) moving inside a simple polygon can find a shortest path between two vertices by means of a sensor that detects for an angle at a vertex of the polygon whether it is convex. We give an explicit algorithm which allows the robot to find a shortest path.