Connectivity Preserving Formation Stabilization in an obstacle-cluttered environment in the presence of time-varying communication delays

This technical note addresses the formation stabilization problem for Multi-Agent Systems composed of dynamical agents moving within an obstacle-cluttered environment and sharing information via non ideal wireless communication networks. A novel distributed cooperative Navigation Functions-based control strategy is proposed, that drives the MAS to a desired formation without any collision, while counteracting the presence of unavoidable communication impairments originated by the wireless network. By recasting the formation stabilization problem into a consensus one and by combining the Lyapunov stability theory with Halanay's Lemma, Uniformly Ultimately Bounded stability of the whole delayed closed-loop system is proved. In the special case of an obstacle-free environment, our approach guarantees exponential stability of the closed-loop networked system. The stability analysis also provides an estimation of the delay-upper bound and allows to evaluate the stability margins with respect to the latencies that can be observed in practical application scenarios. Theoretical derivations are verified through non-trivial simulations.