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We present a consensus-based distributed pose graph optimization algorithm for obtaining an estimate of the 3D translation and rotation of each pose in a pose graph, given noisy relative measurements between poses. The algorithm, called GeoD, implements a continuous time distributed consensus protocol to minimize the geodesic pose graph error. GeoD is distributed over the pose graph itself, with a separate computation thread for each node in the graph, and messages are passed only between neighboring nodes in the graph. We leverage tools from Lyapunov theory and multi-agent consensus to prove the convergence of the algorithm. We identify two new consistency conditions sufficient for convergence: pairwise consistency of relative rotation measurements, and minimal consistency of relative translation measurements. GeoD incorporates a simple one step distributed initialization to satisfy both conditions. We demonstrate GeoD on simulated and real world SLAM datasets. We compare to a centralized pose graph optimizer with an optimality certificate (SE-Sync) and a Distributed Gauss-Seidel (DGS) method. On average, GeoD converges 20 times more quickly than DGS to a value with 3.4 times less error when compared to the global minimum provided by SE-Sync. GeoD scales more favorably with graph size than DGS, converging over 100 times faster on graphs larger than 1000 poses. Lastly, we test GeoD on a multi-UAV vision-based SLAM scenario, where the UAVs estimate their pose trajectories in a distributed manner using the relative poses extracted from their on board camera images. We show qualitative performance that is better than either the centralized SE-Sync or the distributed DGS methods.