Counting Targets with Mobile Sensors in an Unknown Environment

We consider the problem of counting the number of indistinguishable targets using a simple binary sensing model. Our setting includes an unknown number of point targets in a (simplyor multiply-connected) polygonal workspace, and a moving point-robot whose sensory input at any location is a binary vector representing the cyclic order of the polygon vertices and targets visible to the robot and the presence of walls between consecutive vertices. In particular, the sensing model provides no coordinates, distance or angle measurements. We investigate this problem under two natural models of environment, friendly and hostile, which differ only in whether the robot can visit the targets or not, and under three different models of motion capability. In the friendly scenario we show that the robots can count the targets, whereas in the hostile scenario we prove that no (2 − ε)-approximation is possible, for any ε > 0 and we show a 2-approximation algorithm. Further we present a class of polygons recognizable by our robots where the problem can be exactly solved. Next we consider two, slightly more powerful robots ans show that they can count the targets exactly in any