TRACE: Privacy-Preserving Next-Best-View Selection over Distributed 3D Gaussian-Splat Maps

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Share the light, not the map. We study next-best-view selection for a team of robots, each of which builds its own 3D Gaussian Splatting map and keeps it private. A robot picks the view with the largest expected information gain (EIG) about the splats along its own path. This gain depends on the other maps. Their splats occlude its own and shine behind them, so the gain has to be evaluated against the pooled map. No robot has this map. We show that the coupling passes through only two ray quantities, the transmittance in front of a splat and the radiance behind it, and that both are sums over the hits of the ray. Hence, they decompose across the robots, and each robot sums them over depth bins in its own map, along the rays of a candidate view, and sends the sums with their pose derivatives. The robot planning the view turns them into its EIG and gradient on SO(3). Transmittance and Radiance Aggregates, communicated for the EIG, give the protocol its name: TRACE. No robot shares its splats, and the message size does not grow with a map. We prove that the reconstruction is exact unless a depth bin behind a splat mixes hits of two robots, and we bound the error otherwise. Over 100 next-best-view decisions in Habitat-Sim, TRACE picks a heading within 15 degrees of the centralized one in 83.3% of the cases, and its views reach 97.9% of the centralized EIG.