Global converegence properties of a consensus protocol on the n-sphere

This paper provides a novel analysis of the global convergence properties of a well-known consensus protocol for multi-agent systems that evolve in continuous time on the n-sphere. The feedback is intrinsic to the n-sphere, i.e., it does not rely on the use of local coordinates obtained through a parametrization. It is shown that, for any connected undirected graph topology and all n ∈ N\{1}, the consensus protocol yields convergence that is akin to almost global consensus in a weak sense. Simulation results suggest that actual almost global consensus holds. This result is of interest in the context of consensus on Riemannian manifolds since it differs from what is known with regard to the 1-sphere and SO(3) where more advanced intrinsic consensus protocols are required in order to generate equivalent results.