DUAG-C: Decentralized uncertainty-aware Gaussian consensus for multi-robot dense mapping

Dense multi-robot Simultaneous Localization and Mapping (SLAM) has, to date, been realized exclusively through centralized architectures, precluding deployment in infrastructure-free or adversarial environments. The obstacle is representational, not bandwidth-related: 3D Gaussian primitives are constrained heterogeneously by each agent’s local observations, and naive peer-to-peer averaging allows poorly-determined Gaussians from one agent to corrupt the well-constrained map of another. Resolving this requires a per-primitive epistemic uncertainty measure that is data-driven, manifold-compatible, and amenable to distributed optimization with provable guarantees. We present DUAG-C, a fully peer-to-peer dense SLAM system built on volumetric 3D Gaussian Splatting (3DGS). The central contribution is a per-Gaussian diagonal Fisher Information Matrix (FIM), derived via the Laplace approximation to the photometric loss and accumulated from gradients already produced during standard 3DGS optimization. These weights drive a Riemannian Alternating Direction Method of Multipliers (ADMM) consensus on the joint product manifold SE⁢(3)|𝒱|×(𝕊3 ++×ℝ7)𝑁𝐺, with closed-form updates under the Log-Euclidean metric. We prove convergence to an 𝒪⁡(ɛ) neighborhood of the global optimum, establish for a scalar-weight surrogate that higher FIM contrast strictly accelerates convergence, and prove a dimension-wise contraction bound that governs the implemented per-dimension algorithm directly—to our knowledge the first convergence guarantees for decentralized dense mapping, where existing certifiable results address sparse pose-graph optimization alone. Communication priority emerges naturally: transmitting high-FIM Gaussians first maximizes information delivered per byte without an explicit rate-control layer. Across four benchmarks spanning synthetic indoor, real-sensor, and outdoor Unmanned Ground Vehicle (UGV) settings with 2–8 robots, DUAG-C attains 0.066 cm Absolute Trajectory Error (ATE) averaged over all four ReplicaMultiagent scenes—surpassing MAC-Ego3D by 2.1× and GRAND-SLAM by 3.8× without any central infrastructure—and achieves the best reported geometric fidelity (Learned Perceptual Image Patch Similarity, LPIPS, 0.043; Depth L1 0.36 cm). An Expected Calibration Error (ECE) of 0.032 confirms the FIM weights encode genuine per-Gaussian reliability. The code is available at https://github.com/HZAI-ZJNU/DUAG-SLAM