Mobile robot networks emerged in the past few years as a promising distributed computing model, where simple limited entities perform complex collaborative tasks. Existing works in the literature verify mobile robot protocols by writing \emph{ad hoc} proofs, which, in the case of more complex asynchronous environments, reveals both cumbersome and error-prone. In this paper, we propose the first formal modeling and verification methodology for mobile robots protocols operating in a discrete space. We use a known protocol for exclusive perpetual exploration with three robots as a case study. Our technique shows that in the synchronous and semi-synchronous environments, this protocol is correct, yet safety properties can be violated in the completely asynchronous environment. Finally, we present a protocol fix for the safety problem and verify the correctness of our change.