  Geometric pattern formation is an important emergent behavior in many
applications involving large-scale multi-agent systems, such as sensor networks
deployment and collective transportation. Attraction/repulsion virtual forces
are the most common control approach to achieve such behavior in a distributed
and scalable manner. Nevertheless, for most existing solutions only numerical
and/or experimental evidence of their convergence is available. Here, we
revisit the problem of achieving pattern formation giving sufficient conditions
to prove analytically that under the influence of appropriate virtual forces, a
large-scale multi-agent swarming system locally converges towards a stable and
robust triangular lattice configuration. Specifically, the proof is carried out
using LaSalle's invariance principle and geometry-based arguments. Our
theoretical results are complemented by exhaustive numerical simulations
confirming their effectiveness and estimating the region of asymptotic
stability of the triangular configuration.
