Robotics researchers have studied robots that can follow trails laid by other robots. We, on the other hand, study robots that leave trails in the terrain to cover closed terrain repeatedly. How to design such ant robots has so far been studied only theoretically for gross robot simplifications. In this article, we describe for the first time how to build physical ant robots that cover terrain and test their design both in realistic simulation environments and on a Pebbles III robot. We show that the coverage behavior of our ant robots can be modeled with a modified version of node counting, a real-time search method. We then report on first experiments that we performed to understand their efficiency and robustness in situations where some ant robots fail, they are moved without realizing this, the trails are of uneven quality, and some trails are destroyed. Finally, we report the results of a large-scale simulation experiment where ten ant robots covered a factory floor of 25 by 25 m...