This paper studies the distributed formation control of multiple differential-drive robots. To solve such problem, we propose a novel class of distributed population dynamics, formulated in discrete-time, and we obtain sufficient conditions to guarantee asymptotic stability in practical implementations where computations are necessarily discrete. Moreover, we apply the proposed dynamics to a real multi-robot platform where robots achieve geometric formations under partial information and limited communication capabilities. Our proposed method achieves comparable and even better performance than other distributed methods, and displays some invariance properties that make it attractive for several other engineering applications.