  In this paper, we develop a consensus algorithm for distributed computation
of the Riemannian center of mass (RCM) on Lie Groups. The algorithm is built
upon a distributed optimization reformulation that allows developing an
intrinsic, distributed (without relying on a consensus subroutine), and a
computationally efficient protocol for the RCM computation. The novel idea for
developing this fast distributed algorithm is to utilize a Riemannian version
of distributed gradient flow combined with a gradient tracking technique. We
first guarantee that, under certain conditions, the limit point of our
algorithm is the RCM point of interest. We then provide a proof of global
convergence in the Euclidean setting, that can be viewed as a "geometric"
dynamic consensus that converges to the average from arbitrary initial points.
Finally, we proceed to showcase the superior convergence properties of the
proposed approach as compared with other classes of consensus
optimization-based algorithms for the RCM computation.
