Locating a robot with angle measurements

Abstract

We consider the problem posed by Sugihara of locating a robot in a planar environment containing n indistinguishable mark points. The robot takes k angular measurements between an unknown subset of mark points. When the robot has a compass, we show that all valid placements of the robot consistent with the measurements may be determined in O ( kn 2 ) time and O ( kn ) space. When the robot does not have a compass, we show how to determine all valid placements in O ( kn 3 ) time and O ( kn ) space. We show that with polynomial-time preprocessing both types of location queries can be answered in O (log n ) time. For both cases we give bounds on the maximum number of valid placements. We also consider the case where there are image processing errors involved in the angle measurements.