Local Convergence of Multi-Agent Systems Toward Rigid Lattices

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 in spaces of any dimension, 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 rigid lattice configuration. Our theoretical results are complemented by exhaustive numerical simulations confirming their effectiveness and estimating the region of asymptotic stability of the rigid lattice configuration.