Self-triggered rendezvous of gossiping second-order agents

A recent paper by some of the authors introduced several self-triggered coordination algorithms for first-order continuous-time systems. The extension of these algorithms to second-order agents is relevant in many practical applications but presents some challenges that are tackled in this contribution and that require to depart from the analysis that was carried out before. We design a self-triggered gossiping coordination algorithm that induces a time-varying communication graph, which is enough connected to guarantee useful convergence properties, and allows us to achieve the desired coordination task in a formation of double-integrator agents that (i) establish pair-wise communication at suitably designed times and (ii) exchange relative measurements while reducing the sensing and communication effort.