Gathering Multiple Robotic A(ge)nts with Limited Sensing Capabilities

We consider a swarm of simple ant-robots (or a(ge)nts) on the plane, which are anonymous, homogeneous, memoryless and lack communication capabilities. Their sensors are range-limited and they are unable to measure distances. Rather, they can only acquire the directions to their neighbors. We propose a simple algorithm, which makes them gather in a small region or a point. We discuss three variants of the problem: A continuous-space discrete-time problem, a continuous-time limit of that problem, and a discrete-space discrete-time analog. Using both analysis and simulations, we show that, interestingly, the system’s global behavior in the continuous-time limit is fundamentally different from that of the discrete-time case, due to hidden “Zenoness” in it.