BarySLAM: Barycentric Consensus Geometry for Collaborative 3D Gaussian SLAM

Collaborative 3D Gaussian SLAM must reconcile independently reconstructed submaps whose overlap is often partial and whose Gaussian decompositions may differ across agents. Pairwise registration and sequential fusion can make the global estimate sensitive to uncertain intermediate geometry and fusion order. We present BarySLAM, which organizes cross-agent information around Barycentric Consensus Geometry, a partially supported latent geometric representation shared by agents observing the same scene structure. BarySLAM derives structural observations from local Gaussian fields, establishes partial cross-agent support through unbalanced optimal transport, and jointly refines submap poses and consensus geometry with held-out validation to suppress inconsistent cross-agent evidence. The validated consensus is then transferred to the original Gaussian primitives for global map construction, maintaining a common geometric basis from collaborative estimation to reconstruction. Experiments on synthetic and real multi-agent benchmarks show SOTA overall performance in trajectory estimation and Gaussian reconstruction, with improved robustness under limited overlap and corrupted cross-agent registration and reduced sensitivity to fusion order. https://gaoxin09.github.io/BarySLAM/.