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.
Figures & tables
Fig. 1: Overview of TRACE: robots maintain private local 3DGS maps, construct trajectory-conditioned masks, exchange factorized ray context, and optimize masked information gain for distributed NBV selection.
Method
Agents N=3 (Cantwell)
Agents N=7 (Frankton)
Agents N=10 (Frankton)
Navigation
Exploration
Navigation
Exploration
Exploration
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
PSNR ↑
SSIM ↑
LPIPS ↓
Decentralized
20.40
.647
.468
19.00
.601
.402
20.66
.659
.502
18.53
.501
.475
18.50
.553
.478
Centralized Map-Sharing
21.19
.697
.459
18.93
.599
.410
22.63
.762
.347
18.69
.565
.471
20.35
.699
.433
Centralized Oracle
24.55
.877
.290
21.22
.785
.368
24.13
.832
.252
21.86
.776
.371
21.11
.708
.343
TRACE (ours)
21.07
.653
.467
19.64
.603
.393
21.74
.705
.370
18.84
.569
.440
20.01
.621
.45
TABLE I: Reconstruction quality across five Methods on two tasks, and team sizes N∈{3,7,10} . All metrics are evaluated at the poses each run actually executed and therefore describe the map along the trajectory each planner produced.
Method
Comm. (MB/step)
NBV time (s)
Map size ( 103 )
N=3
N=7
N=10
N=3
N=7
N=10
N=3
N=7
N=10
Map Sharing
18.73
67.24
89.05
4.97
5.37
6.79
138.2
213.3
188.3
Oracle
0.27
0.87
1.14
3.82
5.82
6.34
175.5
248.0
248.0
TRACE
1004.48
1547.89
2055.25
2.91
3.04
3.51
135.4
138.0
218.4
TRACE-Sparse
1.45
4.91
8.42
1.21
1.46
2.01
126.4
209.2
203.2
TABLE II: Communication, NBV time, and mean map size during multi-robot exploration.
Fig. 2: Four robots navigating toward a goal in the Lakeville scene. Each color represents a robot’s private local 3DGS map and trajectory.
Fig. 3: Representative NBV selections along two agents’ trajectories: centralized, TRACE, and decentralized headings at each waypoint.
Map Reconstruction
Agents
Method
Comm./Step (MB) ↓
Avg. NBV Time (s) ↓
PSNR ↑
SSIM ↑
LPIPS ↓
2
TRACE-Sparse
0.35
0.59
17.99
0.635
0.423
TRACE-Discrete
0.09
9.46
18.64
0.679
0.386
5
TRACE-Sparse
3.86
1.69
17.33
0.642
0.415
TRACE-Discrete
0.80
22.34
18.15
0.661
0.399
TABLE III: Comparison of sparse gradient based and discrete NBV selection methods.
Method
NBV match ↑
EIG retained ↑
Overlap ↓
Exact
Within 15∘
Centralized
100.0
100.0
100.0
18.0
TRACE (ours)
77.8
83.3
97.9
15.9
Decentralized
25.9
38.9
69.2
25.7
Random
4.2
12.5
46.3
–
TABLE IV: Agreement with the centralized NBV, retained EIG, and inter-robot map overlap. All entries are percentages.
Multi-agent Next-Best-View (NBV) selection for safe path planning in uncertain and unknown environments requires informative, safety-aware, and efficient coordination. Centralized approaches rely on sharing raw sensor data or significant communication overhead, resulting in limited scalability. We propose a distributed, risk-aware multi-agent NBV framework in which each robot maintains a private local 3D Gaussian Splatting map and the team jointly maximizes expected information gain (EIG) restricted to masked zones along planned trajectories. The resulting distributed objective is solved by Consensus ADMM (C-ADMM) over a communication graph, with each robot exchanging only candidate viewpoints, planned trajectory descriptors, and scalar EIG contributions. Collision risk along each trajectory is modeled via Average Value-at-Risk (AV@R) over the local 3DGS map and used both to shape the masking radius and to score planned paths. Experiments in Gibson environments at multiple team sizes show that the distributed formulation approaches the centralized baseline in mapping quality and trajectory safety while reducing communication by orders of magnitude.
Amirhossein Mollaei Khass, Vivek Pandey, Guangyi Liu +3
Department of Mechanical Engineering and Mechanics, Lehigh University · Amazon Robotics
Radiance fields need hundreds of views, and their placement matters as much as their number. Next-best-view (NBV) selection for 3D Gaussian Splatting (3DGS) usually scores every candidate in the pool and keeps one. Searching for information and choosing a camera, however, are separable problems. We present AGILE-GS, an anchor-guided NBV method that separates the two. A virtual anchor pose is optimized on SE(3) by Riemannian gradient ascent on expected information gain. It need not be reachable or in the pool; it marks where the model is most uncertain. Candidates are scored against the anchor's viewing geometry, and a greedy ridge-leverage step distills the pool into a small, non-redundant shortlist without rendering any candidate. The shortlist can be used in two ways. AGILE-GS takes the first view on it as the next view, so no Fisher information is computed for any candidate. AGILE-GS+ computes the Fisher information gain of each shortlisted view and picks the best, so the expensive evaluation runs on a handful of views rather than the whole pool. On standard benchmarks and in closed-loop embodied acquisition, both match or exceed existing baselines while cutting selection latency by one to two orders of magnitude.
Amirhossein Mollaei Khass, Nader Motee
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, 18015, USA
Existing active reconstruction systems with Gaussian-splatting maps select observations greedily, optimizing a single next-best-view (NBV) at each step and connecting the chosen views by short-horizon path planning. This greedy decoupling disregards the global structure of scene information, producing inefficient trajectories that waste sensing capacity in transit between selected views. In this work, we study active reconstruction as an ergodic coverage problem: the time-averaged spatial statistics of the sensor trajectory should match a target information distribution induced by the current map. Our approach derives this target distribution online from uncertainty and visibility, and calculates ergodic trajectories via a kernel-ergodic horizon planner with gradient flow and footprint depletion, closing the loop between mapping and trajectory optimization. We thoroughly evaluate TRACE on the Replica dataset against the Next-Best-View (NBV) baselines, improving PSNR by 1.5 dB. Code: https://github.com/spikelab-jhu/trace-active-reconstruction.
Ziyue Zheng, Linli Shi, Bingkun He +2
1Johns Hopkins University, USA · University of Pennsylvania, USA