Uninterrupted Coverage of a Planar Region with Rotating Directional Antennae

Assume that n directional antennae located at distinct points in the plane are rotating at constant identical speeds. They all have identical range and sensor angle (or field of view). We propose and study the Rotating Antennae Coverage Problem, a new problem concerning rotating sensors for the uninterrupted coverage of a region in the plane. More specifically, what is the initial orientation of the sensors, minimum angle, and range required so that a given (infinite or finite) line or planar domain is covered by the rotating sensors at all times? We give algorithms for determining the initial orientation of the sensors and analyze the resulting angle/range tradeoffs for ensuring continuous coverage of a given region or line in the plane with identical rotating sensors of given transmission angle and range. We also investigate other variants of the problem whereby for a given parameter T (representing time) there is no point in the domain that is left unattended by some sensor for a period of time longer than T . Despite the apparent simplicity of the problem several of the algorithms proposed are intricate and elegant. We have also implemented our algorithms in C++ and the code can be downloaded on the web.