Organizations: State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, China. · Hangzhou Guixing Intelligent Technology Co., Ltd., Hangzhou, China.
We present NeuRIO, a streaming neural estimator for anchor-free 6-DoF relative inertial odometry using only identified inter-robot bearings, ranges, and IMU measurements. NeuRIO canonicalizes measurements into gravity-aligned coordinates, represents robots as nodes and mutual observations as factors, and uses attention for spatial reasoning and GRUs for temporal modeling. As a graph network, NeuRIO applies shared node-wise and factor-wise operators throughout the network, enabling it to handle different team sizes and time-varying observation graphs. NeuRIO is trained on a simulator that couples various motion patterns, device-level sensor characteristics, and diverse, realistic modeled, and temporally persistent sensor corruptions. In this way, NeuRIO achieves zero-shot sim-to-real transfer. Across 24 real-world sequences, NeuRIO achieves 14.1cm position RMSE and 3.9∘ rotation RMSE. More importantly, NeuRIO demonstrates strong computational scalability, maintaining an update cost below 20ms with up to 400 robots in simulation, while optimization-based methods exceed 20ms at only 24 robots. Moreover, even trained on limited team sizes, NeuRIO transfers directly to unseen larger teams without architectural or parameter changes.
Figures & tables
Fig. 1: (a) Relative localization estimates neighboring robots’ 6-DoF poses in a moving reference robot’s frame from bearings, ranges, and inertial measurements. (b) Overall position RMSE versus the number of robots within 20ms ( 50Hz camera frames). See detailed configurations in Sec. VI-A (AnyAmber [ 5 ] excludes its MatchNet, and uses ground-truth as priors).
Fig. 2: Architecture of NeuRIO, which directly predicts relative poses from bearings, ranges, and IMU measurements.
Bearing
Base
Noise
Rotate about an isotropically sampled axis by a angle with σ0∼U(0.1,4.0)∘ , multiplied by a device-specific scale U(0.5,2.2) .
Field-of-view
Assign omnidirectional cameras with probability 0.25 , otherwise a half-angle U(60.0,115.0)∘ . Outside bearings are removed.
Occlusion
Remove bearings whose connecting segment intersects an obstacle.
Dropout
Missed
Independently miss up to 20% of candidates.
Flicker
Eligible links switch off with probability min(1,(1−p)/κ) and on with min(1,p/κ) , where κ∼U(0.5,2.0) frames and p∼U(0.30,0.95) .
Short blackout
Short outages have λ≤0.15s−1 and τ from 0.5 to 3.0s .
Long blackout
Long outages have λ≤0.01s−1 and τ from 8 to 60s .
TABLE I: Sensor configurations and failure processes.
Fig. 3: Visualization of LOS_1 , NLOS_1 , SDM_1 , HDM_1 , MRP_1 , and TEN_1 . The top row shows the ground-truth trajectories of the reference robot (red) and other robots (blue). The bottom row shows the error of NeuRIO’s predicted pose of device 1 with respect to the ground-truth (blue) and the predicted uncertainty (orange). The uncertainty is visualized as the predicted position RMS scale 3exp(sp) , where sp is the predicted position log variance.
Seq.
CREPES
CREPES-X
CT-RIO
AnyAmber
NeuRIO
Pretrained
Fine-tuned
Pretrained (GT prior)
Fine-tuned (GT prior)
LOS_1
6.4 / 2.1
6.3 / 1.9
5.7 / 1.9
failed
12.8 / 4.1
9.3 / 2.6
9.5 / 2.8
7.1 / 2.0
LOS_2
8.6 / 2.4
7.8 / 2.1
6.7 / 2.0
failed
10.6 / 3.0
9.6 / 2.6
9.0 / 2.2
8.6 / 2.3
LOS_3
8.5 / 2.8
6.9 / 2.1
6.1 / 2.1
failed
8.7 / 3.0
9.6 / 2.7
7.3 / 2.0
7.8 / 2.2
LOS_4
7.2 / 2.1
8.0 / 2.5
7.0 / 2.5
failed
13.8 / 4.4
9.9 / 2.9
10.6 / 2.9
8.5 / 2.8
NLOS_1
6.5 / 2.2
5.0 / 1.8
4.6 / 1.8
failed
13.9 / 69.7
9.7 / 2.3
7.0 / 1.8
6.7 / 2.5
TABLE II: Comparison over 24 real-world sequences (RMSE in cm / deg).
Fig. 4: Computational scalability and accuracy in simulation as the number of robots increases. (a) Mean computation time, with a 20ms reference corresponding to 50Hz sensing. AnyAmber uses published timings with MatchNet excluded (which is used for anonymous bearing association) [ 5 ] . (b) Position and rotation RMSE of the frozen network in simulation. Complete denotes a fully connected observation graph; otherwise, each target robot has min(d,n−1) observed neighbors.
Max number
LOS
NLOS
SDM
HDM
MRP
TEN
Overall
3 robots
16.6 / 3.6
26.4 / 6.2
10.5 / 4.7
45.9 / 7.0
57.6 / 17.5
58.4 / 10.0
35.9 / 8.2
5 robots
9.5 / 2.4
8.9 / 2.6
6.5 / 6.3
28.1 / 4.1
26.9 / 6.4
18.1 / 4.7
16.3 / 4.4
7 robots
8.6 / 2.4
7.8 / 2.4
6.1 / 5.3
25.1 / 4.1
22.0 / 5.5
14.6 / 3.9
14.0 / 3.9
10 robots
8.0 / 2.3
7.5 / 2.3
7.0 / 5.0
24.9 / 4.0
22.6 / 5.8
14.6 / 3.7
14.1 / 3.9
TABLE III: Generalization across training numbers (RMSE in cm / deg).
Spatial block
LOS
NLOS
SDM
HDM
MRP
TEN
Overall
GATv2
21.3 / 4.4
24.9 / 5.0
23.3 / 5.6
67.0 / 9.1
failed
87.4 / 8.3
56.3 / 8.3
GINE
12.4 / 2.9
13.4 / 3.3
13.5 / 6.5
47.7 / 7.2
44.9 / 8.9
50.1 / 6.5
30.3 / 5.9
GENConv
12.3 / 2.9
12.1 / 3.0
14.2 / 7.0
48.9 / 7.6
42.2 / 9.1
45.2 / 6.0
29.1 / 5.9
TransformerConv
10.9 / 2.6
10.8 / 2.8
12.2 / 5.9
41.2 / 5.9
39.6 / 8.1
39.5 / 5.4
25.7 / 5.1
ResGated
10.7 / 2.7
9.8 / 2.7
10.9 / 7.4
41.3 / 6.0
37.0 / 7.8
38.7 / 5.3
24.7 / 5.3
TokenGT
11.6 / 2.4
12.0 / 3.0
7.9 / 7.6
38.3 / 5.7
37.3 / 12.5
42.3 / 6.9
24.9 / 6.3
TABLE IV: Comparison of spatial blocks (RMSE in cm / deg).
Variant
LOS
NLOS
SDM
HDM
MRP
TEN
Overall
NeuRIO
8.0 / 2.3
7.5 / 2.3
7.0 / 5.0
24.9 / 4.0
22.6 / 5.8
14.6 / 3.7
14.1 / 3.9
w/o GC
9.6 / 3.4
9.3 / 3.1
6.9 / 3.6
33.5 / 5.0
30.3 / 12.4
19.0 / 4.1
18.1 / 5.3
w/o IE
9.0 / 2.4
8.5 / 2.6
6.2 / 3.3
24.5 / 4.3
27.2 / 7.7
22.8 / 4.9
16.4 / 4.2
w/o FNM
7.6 / 2.3
7.1 / 2.4
5.6 / 7.2
27.2 / 4.0
22.6 / 5.3
14.0 / 3.6
14.0 / 4.1
w/o FFM
8.6 / 2.4
7.7 / 2.4
6.1 / 4.7
24.8 / 4.0
22.2 / 5.4
15.6 / 4.2
14.2 / 3.9
w/o LNM
9.0 / 3.2
8.1 / 3.0
7.0 / 4.9
27.3 / 5.4
29.4 / 9.6
21.6 / 5.7
17.1 / 5.3
TABLE V: Backbone ablation results (RMSE in cm / deg).
Simulator
LOS
NLOS
SDM
HDM
MRP
TEN
Overall
Default
8.0 / 2.3
7.5 / 2.3
7.0 / 5.0
24.9 / 4.0
22.6 / 5.8
14.6 / 3.7
14.1 / 3.9
w/o Temp.
8.7 / 2.7
9.6 / 3.1
7.1 / 7.1
41.9 / 6.5
40.5 / 11.8
34.4 / 6.5
23.7 / 6.3
w/o CamD
8.9 / 2.4
10.1 / 3.0
10.2 / 8.3
44.4 / 6.3
30.5 / 7.3
18.3 / 4.7
20.4 / 5.3
w/o CamC
9.2 / 3.0
8.1 / 3.3
6.1 / 4.0
35.4 / 5.7
41.1 / 20.0
14.9 / 3.8
19.1 / 6.6
w/o UWBD
8.3 / 2.3
7.7 / 2.5
5.8 / 6.1
26.3 / 4.2
29.5 / 5.6
43.7 / 4.0
20.2 / 4.1
w/o UWBC
8.5 / 2.4
7.4 / 2.4
7.0 / 5.6
24.8 / 4.0
22.7 / 6.4
17.0 / 3.8
14.6 / 4.1
TABLE VI: Simulator ablation results (RMSE in cm / deg).