Robotic cops: the intruder problem

In this paper we present a self-stabilizing algorithm for the intruder problem. The problem can be formulated as follows: an enemy unit, or intruder, is trying to sneak through a field patrolled by an arbitrary number of friendly autonomous (i.e. robotic) units. These units must reach the intruder and block it by surrounding it. Our solution to this problem, provided as an algorithm for the autonomous patrolling units, makes minimal assumptions on their capabilities. In particular, we assume they are completely asynchronous, and moreover that they have no observable identities, no memory, and no means to explicitly communicate with each other. Each unit needs only to be capable of observing the current position of its fellows and of the intruder. All these features, while making the task harder, give to the algorithm the nice property of self-stabilization, thus improving its robustness. For example, if any unit is knocked out, all the others automatically adjust their behavior, in order to still complete the task. By concentrating on extremely simple units, we are also able to investigate which capabilities are really needed to solve this problem, with obvious cost benefits (especially if the units are deployed in a hostile environment). In the paper, we first present a computational model for our robotic "cops", followed by the description of the algorithm we propose. We also show results of computer simulations, providing quantitative measures on the efficiency of the algorithm.