Robot Localization without Depth Perception

Consider the problem of placing reflectors in a 2-D environment in such a way that a robot equipped with a basic laser can always determine its current location. The robot is allowed to swivel at its current location, using the laser to detect at what angles some reflectors are visible, but no distance information is obtained. A polygonal map of the environment and reflectors is available to the robot. We show that there is always a placement of reflectors that allows the robot to localize itself from any point in the environment, and that such a reflector placement can be computed in polynomial time on a real RAM. This result improves over previous techniques which have up to a quadratic number of ambiguous points at which the robot cannot determine its location [1, 9]. Further, we show that the problem of optimal reflector placement is equivalent to an art-gallery problem within a constant factor.