On second order consensus protocols allowing joint-agent interactions

In this note, we propose a second order consensus protocol allowing joint-agent interactions. Our analysis is addressed to networks where agents are grouped in interaction triplets. A triplet is a set of three distinct agents, where the interaction dynamics is such that one member is sensitive to the influence brought by the other two only when it receives simultaneous and consistent opinions from them. This allows the network to reach a second order consensus configuration more robustly, even in the presence of exogenous disturbances on the dynamics of one or more agents. The piecewise linear function used to model the robust interaction within a triplet leads to the energy of the interaction being conserved along certain directions, as if some agents were connected by virtual springs. In conclusion, a convergence analysis is performed by means of the recursive detection of such conservation laws.