  Consensus algorithms are popular distributed algorithms for computing
aggregate quantities, such as averages, in ad-hoc wireless networks. However,
existing algorithms mostly address the case where the measurements lie in a
Euclidean space. In this work we propose Riemannian consensus, a natural
extension of the existing averaging consensus algorithm to the case of
Riemannian manifolds. Unlike previous generalizations, our algorithm is
intrinsic and, in principle, can be applied to any complete Riemannian
manifold. We characterize our algorithm by giving sufficient convergence
conditions on Riemannian manifolds with bounded curvature and we analyze the
differences that rise with respect to the classical Euclidean case. We test the
proposed algorithms on synthetic data sampled from manifolds such as the space
of rotations, the sphere and the Grassmann manifold.
