Organizations: School of Information Science and Engineering, Yunnan University, Kunming, Yunnan 650500, China. · Yunnan Key Laboratory of Intelligent Systems and Computing, Yunnan University, Kunming, Yunnan 650500, China. · School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China.
LiDAR Odometry and Mapping (LOAM) is a pivotal technique for embodied-AI applications such as autonomous driving and robot navigation. Most existing LOAM frameworks are either contingent on the supervision signal, or lack of the reconstruction fidelity, which are deficient in depicting details of large-scale complex scenes. To overcome these limitations, we propose a multi-scale implicit neural localization and mapping framework using LiDAR sensor, called Hi-LOAM. Hi-LOAM receives LiDAR point cloud as the input data modality, learns and stores hierarchical latent features in multiple levels of hash tables based on an octree structure, then these multi-scale latent features are decoded into signed distance value through shallow Multilayer Perceptrons (MLPs) in the mapping procedure. For pose estimation procedure, we rely on a correspondence-free, scan-to-implicit matching paradigm to estimate optimal pose and register current scan into the submap. The entire training process is conducted in a self-supervised manner, which waives the model pre-training and manifests its generalizability when applied to diverse environments. Extensive experiments on multiple real-world and synthetic datasets demonstrate the superior performance, in terms of the effectiveness and generalization capabilities, of our Hi-LOAM compared to existing state-of-the-art methods.
Figures & tables
Fig. 1 : Reconstructed map and estimated trajectory generated via our implicit Hi-LOAM. The above case is evaluated on the sequence 07 of KITTI dataset, superior mapping quality and accurate poses are obtained via deep utilization of hierarchical neural features.
Fig. 2 : The Overview of Our Hi-LOAM Framework . The main data stream is depicted as following. Sampled points PCt along the ray is used to construct neural signed distance fields (nSDF) based on the octree. For the first two scans, poses P0 and P1 are predefined and nSDF are created. For following scans, original points Pt are firstly matched with octree of sub map to estimate the pose TWCt∗ . Then, Pt is transformed into the global coordinate system via TWCt∗ , PWt is registered to expand the nSDF, this process is repeated in turn. The separate optimization strategies are designed for odometry and mapping, the trainable parameters and frozen parameters are marked correspondingly.
Fig. 3 : The correspondence among the three tables in certain level of octree. The eight corners of a node correspond to eight features stored in table F . The hierarchical nodes and their corresponding corners are stored in Morton code form in tables N and G .
Method
Type
00
01
02
03
04
05
06
07
08
09
10
Avg.
LeGO-LOAM [ 26 ]
feature points
2.17
13.4
2.17
2.34
1.27
1.28
1.06
1.12
1.99
1.97
2.21
2.49
F-LOAM [ 64 ]
feature points
0.78
1.43
0.92
0.86
0.71
0.57
0.65
0.63
1.12
0.77
0.79
0.84
MULLS [ 43 ]
feature points
0.56
0.64
0.55
0.71
0.41
0.30
0.30
0.38
0.78
0.48
0.59
0.52
VG-ICP [ 65 ]
dense points
2.16
2.38
0.99
0.67
0.55
0.45
0.24
0.99
1.74
0.95
0.95
1.10
CT-ICP [ 27 ]
dense points
0.49
0.76
0.52
0.72
0.39
0.25
0.27
0.31
0.81
0.49
0.48
0.50
KISS-ICP [ 19 ]
dense points
0.52
0.63
0.51
0.66
0.36
0.31
0.26
0.33
0.82
0.51
0.56
0.50
TABLE I : Comparison of Average Relative Translational Drifting Error (%) on KITTI Odommetry Benchmark. The best results are highlighted in bold, and the second-best results are underlined. “-” indicates the result is not reported in the related paper, ‘-LO’ in the name of methods indicates that only the odometry component of the method is used for evaluation. And the definition of those symbols are applicable to other tables in the rest of the paper. Consistent with other methods, we use the average relative translational error in % as the metric for evaluating odometry drift.
Method
Type
00
01
02
03
04
05
06
07
08
09
10
Avg.
LeGO-LOAM [ 26 ]
feature points
2.3
19.7
5.3
1.6
0.4
1.2
1.0
1.5
5.9
2.0
1.7
5.3
F-LOAM [ 64 ]
feature points
5.0
3.2
8.6
0.7
0.3
3.4
0.5
0.6
3.1
1.6
1.2
2.6
KISS-ICP [ 19 ]
dense points
5.7
30.7
17.8
3.4
1.1
1.9
0.9
0.8
4.8
3.7
2.3
6.6
SuMa [ 30 ]
surfels
2.9
13.8
8.4
0.9
0.4
1.2
0.4
0.5
2.8
2.9
1.3
3.2
Litamin [ 66 ]
normal distribution
5.8
15.9
10.7
0.8
0.7
2.4
0.9
0.6
2.5
2.1
1.0
3.9
Puma [ 44 ]
mesh
6.6
32.6
18.5
2.2
0.9
3.3
2.4
0.9
6.3
3.9
4.4
7.5
TABLE II : Comparison of Absolute Trajectory Error (m) on KITTI Odometry Benchmark.
Method
KA1
KA2
KA3
DC1
DC2
DC3
RS1
RS2
RS3
Avg.
F-LOAM [ 64 ]
49.16
35.93
38.36
36.89
26.72
31.97
91.85
104.25
119.79
59.44
KISS-ICP [ 19 ]
20.81
13.52
14.85
20.26
12.79
13.17
14.35
32.74
75.14
24.18
SuMa [ 30 ]
10.45
9.33
10.33
13.00
86.04
12.03
114.89
818.74
367.41
160.25
MULLS [ 43 ]
19.72
15.26
6.93
14.95
11.31
6.00
41.25
45.05
44.18
22.74
PIN-LO [ 17 ]
29.07
24.74
23.05
22.07
12.94
23.42
45.81
54.41
44.41
31.10
Hi-LOAM
18.73
20.80
25.98
20.20
16.38
15.42
42.36
52.14
38.95
27.88
TABLE III : Localization Performance Comparison (ATE RMSE [m]) on MulRAN LiDAR Dataset.
Fig. 4 : The Qualitative Results of Odometry Comparison on Sequence 00 of KITTI Dataset. The left side displays trajectories comparison of different methods. The right side compares errors along the X, Y, and Z axes among our method and other methods. The black dashed line represents the ground truth trajectory. ( Best viewed with zoom-in. )
Method
00
01
02
03
04
05
Avg.
SLAMesh [ 59 ]
0.28
0.56
0.28
0.29
0.38
0.33
0.35
MULLS [ 43 ]
0.38
0.55
0.26
0.35
0.38
0.43
0.39
PIN-SLAM [ 17 ]
0.25
0.39
0.19
0.26
0.24
0.27
0.27
Hi-LOAM
0.27
0.29
0.22
0.25
0.23
0.23
0.25
TABLE IV : Localization Performance Comparison (ATE RMSE [m]) on SemanticPOSS LiDAR Dataset.
Fig. 5 : The Qualitative Results of Our Odometry on MulRAN Dataset. The black dashed line represents the ground truth, while the blue solid line represents our trajectory. ( Best viewed with zoom-in. )
Method
rpg
lab
base1
base4
cons2
camp2
Avg.
F-LOAM [ 64 ]
2.78
0.18
0.91
0.29
11.52
8.95
4.10
KISS-ICP [ 19 ]
0.22
0.07
0.32
0.11
0.84
1.98
0.58
HDLGraph-SLAM [ 75 ]
0.35
0.05
0.28
0.37
0.74
0.35
0.36
SLAMesh [ 59 ]
0.17
0.05
0.18
0.33
0.34
0.65
0.29
SuMa [ 30 ]
0.26
0.05
2.24
0.29
1.64
-
0.90
PIN-SLAM [ 17 ]
0.21
0.04
0.30
0.08
0.41
0.11
0.19
TABLE V : Localization Performance Comparison (ATE RMSE [m]) on Hilti-21 LiDAR Dataset.
Method
01
02
quad_e
math_e
ug_e
cloister
stairs
Avg.
F-LOAM [ 64 ]
6.74
✗
0.40
0.26
0.09
7.69
✗
3.04
KISS-ICP [ 19 ]
0.62
1.88
0.10
0.07
0.33
0.30
✗
0.55
SuMa [ 30 ]
2.03
3.65
0.28
0.16
0.09
0.20
1.85
1.18
MULLS [ 43 ]
2.51
8.39
0.12
0.35
0.86
0.41
✗
2.11
MD-SLAM [ 76 ]
-
1.74
0.25
-
-
0.36
0.34
-
SC-LeGO-LOAM [ 26 ]
-
1.30
0.09
-
-
0.20
3.20
-
TABLE VI : Localization Performance Comparison (ATE RMSE [m]) on Newer College LiDAR Dataset. ✗ denotes the execution failure.
Approach
Sensor
MaiCity 01
SuMa [ 30 ]
Velodyne HDL-64
6.1
F-LOAM [ 64 ]
6.2
KISS-ICP [ 19 ]
✗
Puma [ 44 ]
5.8
SLAMesh [ 59 ]
1.7
Mesh-LOAM [ 60 ]
1.6
TABLE VII : Localization Performance Comparison (ATE RMSE [cm]) on the Sequence 01 of MaiCity Dataset. ✗ denotes the execution failure.
Method
Pose
Quad from Newer College
Mai City
Map. Acc. ↓
Map. Comp. ↓
C-l1. ↓
F-score (20cm) ↑
Map. Acc. ↓
Map. Comp. ↓
C-l1. ↓
F-score (10cm) ↑
VDB-Fusion [ 12 ]
KISS-ICP [ 19 ]
14.03
25.46
19.75
69.50
15.21
28.66
21.94
63.35
SHINE [ 24 ]
14.87
20.02
17.45
68.85
14.46
34.03
24.24
64.38
Puma [ 44 ]
Own Odometry
15.30
71.91
43.60
57.27
7.89
9.14
8.51
68.04
SLAMesh [ 59 ]
19.21
48.83
34.02
45.24
5.67
12.99
9.33
75.10
NeRF-LOAM [ 16 ]
12.89
22.21
17.55
74.37
5.69
11.23
8.46
77.23
TABLE VIII : The 3D Reconstruction Accuracy of Different Methods on Newer College and Mai City Datasets.
Fig. 6 : The Visualization of Our 3D Reconstruction Results on Mai City Dataset via Comparing with Other Related Methods. The mapping results in first row are original reconstruction result, and the second row presents the error maps with ground truth mesh as a reference, where the red points stand for large error above 25cm. ( Best viewed with zoom in. )
Fig. 7 : The Visualization of Our 3D Reconstruction Results on Newer College Dataset via Comparing with Other Related Methods. The mapping results in first row are original reconstruction result, and the second row presents the error maps with using ground truth mesh as a reference, where the red points mean larger error up to 50 cm. ( Best viewed with zoom in.)
Fig. 8 : The Reconstructed Mesh of Our Hi-LOAM on Newer College Dataset. We show the estimated trajectory by overlapping it on the map for the sequence of the underground, and we show the inner structure for the sequence of stairs. ( Best viewed with zoom in. )
Fig. 9 : The Qualitative Results of Our Reconstructed Mesh on KITTI Dataset. Our reconstructed mesh on sequence 00, 04, 06, and 08 demonstrate the construction capacity of Hi-LOAM in large-scale environment.
Fig. 10 : The Reconstructed Mesh of our Hi-LOAM on Hilti-21 and Hilti-23 Datasets. The mapping environment of Hilti-23 is made up by construction sites, which are full with highly-repetitive or feature-less walls. The mapping ability for this extreme condition is shown in the above sub-figures. The estimated trajectory is also overlapped in the map to visualize the localization result. ( Best viewed with zoomin. )
LOF
KITTI
SemanticPOSS
00
02
04
06
08
10
Avg.
00
01
02
03
04
05
Avg.
1
5.96
10.42
0.45
0.76
2.93
0.88
3.57
0.28
0.43
0.21
0.29
0.25
0.29
0.29
2
5.00
11.35
0.17
0.66
2.93
0.88
3.50
0.27
0.41
0.20
0.28
0.22
0.24
0.27
3
5.00
8.60
0.14
0.63
2.80
0.81
3.00
0.27
0.29
0.22
0.25
0.23
0.23
0.25
TABLE IX : The Ablation Study of the Level of Feature (LOF) on KITTI and SemanticPOSS LiDAR Benchmark. Localization Performance (ATE RMSE [m]) are reported for system evaluation.
Fig. 11 : Ablation Study of Different Optimizer Setting. The blue line represents the results obtained by replacing the Levenberg-Marquardt (LM) method with the Adam optimizer in our approach. The black dashed line represents the ground truth trajectory. It is evaluated by first 380 scans in KITTI 06 , which is a typical case for optimizer selection.
Leaf Node Size
KITTI 03
KITTI 05
KITTI 06
KITTI 04
quad_e
ug_e
stairs
MaiCity 01
Avg.
25m × 400m
10m × 400m
8m × 15m
5m × 8m
40m × 30m
30m × 20m
10m × 2m
100m × 5m
0.1
✗
2.097552
0.728338
0.155302
0.111781
4.796704
0.112531
0.016174
1.145483
0.2
✗
1.636037
0.529766
0.134920
0.093267
0.052786
0.077359
0.006776
0.360590
0.25
0.477824
1.460346
0.391477
0.154256
0.097045
0.076913
0.265139
0.014541
0.367193
0.3
0.544378
1.547646
0.521631
0.170558
0.099131
✗
0.261116
0.013292
0.451107
TABLE X : Sensitivity Analysis of Leaf Node Sizes on KITTI , Newer College , and Mai City Benchmark. Localization Performance (ATE RMSE [m]) are reported for system evaluation. ✗ denotes the execution failure.
Tree Levels
KITTI 03
KITTI 05
KITTI 06
KITTI 04
quad_e
ug_e
stairs
MaiCity 01
25m × 400m
10m × 400m
8m × 15m
5m × 8m
40m × 30m
30m × 20m
10m × 2m
100m × 5m
9
✗
✗
✗
✗
0.100113
0.052786
0.169223
0.012432
10
✗
✗
✗
✗
0.097937
0.081195
0.079966
0.006776
11
82.758527
✗
0.761584
44.536743
0.099720
0.230535
0.112515
0.009499
12
0.477824
1.621471
0.488580
0.142222
0.104466
0.214824
0.138130
0.010439
13
0.572033
1.653113
0.391477
0.134920
0.100589
0.464130
0.194548
0.016236
TABLE XI : Sensitivity Analysis of Tree Level Numbers on KITTI , Newer College , and Mai City Benchmark. Localization Performance (ATE RMSE [m]) are reported for system evaluation. ✗ denotes the execution failure.
Submap Numbers
KITTI 03
KITTI 05
KITTI 06
KITTI 04
quad_e
ug_e
stairs
MaiCity 01
25m × 400m
10m × 400m
8m × 15m
5m × 8m
40m × 30m
30m × 20m
10m × 2m
100m × 5m
50
✗
✗
✗
✗
0.093394
0.052786
0.077359
0.006267
60
✗
✗
✗
✗
0.093809
0.068807
0.089445
0.012224
100
0.538114
1.564616
0.513978
0.150586
0.093267
0.081796
0.079966
0.012838
150
0.582111
1.717656
0.486967
0.145847
0.094171
0.069654
0.106437
✗
200
0.581955
1.460346
0.391477
0.134920
0.099720
0.134966
0.143389
✗
TABLE XII : Sensitivity Analysis of Submap Numbers on KITTI , Newer College , and Mai City Benchmark. Localization Performance (ATE RMSE [m]) are reported for system evaluation. ✗ denotes the execution failure.
Method
KITTI 00
KITTI 05
KITTI 08
NCD 02
Raw point cloud
13624.2
8284.7
12214.1
26559.0
SuMa [ 30 ]
887.7
512.6
835.7
79.0
Puma [ 44 ]
2032.9
1317.4
1894.1
1503.7
VDB Fusion [ 12 ]
748.1
434.6
958.6
462.5
PIN-SLAM [ 17 ]
102.1
66.3
138.8
76.8
Hi-LOAM
242.1
169.5
284.3
176.6
TABLE XIII : Memory consumption comparison with different method in MB. NCD means Newer College dataset.
Method
Time per frame [s] ↓
FPS [Hz] ↑
ARTE [%] ↓
PIN-SLAM [ 17 ]
0.034
29.4
0.51
NeRF-LOAM [ 16 ]
4.53
0.2
1.69
Hi-LOAM
0.6
1.7
0.48
TABLE XIV : Comparison of the average running time and the localization error of different method on KITTI sequence 00-10. ARTE represents the average relative translational error.
Submodule
KITTI 03
MaiCity 01
Quad_e
KA1
Lab
POSS 00
Odometry
0.3
0.14
0.34
0.38
0.2
0.49
Map Optimization
3.6
2.87
3.0
5.5
4.7
4.5
TABLE XV : Breakdown of Average Running Time per Frame (s) for Each Module on Different Datasets. Quad_e from the Newer College dataset, KAI from the MulRAN dataset, Lab from the Hilti-21 dataset, POSS 00 from the SemanticPOSS dataset.
Geometric light detection and ranging (LiDAR)--inertial simultaneous localization and mapping (SLAM) provides efficient state estimation but lacks the continuous map representation and global refinement capabilities of neural implicit SLAM, while neural implicit methods remain computationally expensive. We propose Lightweight LiDAR--Inertial Neural SLAM (LIN-SLAM), a hybrid method that couples high-rate geometric LiDAR--inertial estimation with neural implicit tracking, continual mapping, and global refinement for accurate real-time onboard SLAM. Experiments on twelve representative sequences from three datasets spanning 32-, 64-, and 128-channel LiDAR configurations show that LIN-SLAM achieves the lowest overall mean absolute trajectory error (ATE) among the evaluated state-of-the-art geometric and neural implicit methods, while substantially reducing runtime compared with existing neural implicit SLAM methods. On a Unitree Go2 equipped with an NVIDIA Jetson Orin NX and a 16-channel LiDAR, LIN-SLAM sustains real-time localization and neural mapping over a 1.47-km indoor trajectory through challenging repetitive corridor environments, with an endpoint closure error of only 0.141~m. To the best of our knowledge, LIN-SLAM is the first LiDAR--inertial SLAM system with a neural implicit backend to achieve real-time online operation on a mobile robotic platform while maintaining state-of-the-art localization accuracy. The code will be released upon acceptance.
Shiqi Che, Yijie Liu, Shuo Wang +1
School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China
This paper introduces 2Fast-2Lamaa, a lidar-inertial state estimation framework for odometry, mapping, and localization. Its first key component is the optimization-based undistortion of lidar scans, which uses continuous IMU preintegration to model the system's pose at every lidar point timestamp. The continuous trajectory over 100-200ms is parameterized only by the initial scan conditions (linear velocity and gravity orientation) and IMU biases, yielding eleven state variables. These are estimated by minimizing point-to-line and point-to-plane distances between lidar-extracted features without relying on previous estimates, resulting in a prior-less motion-distortion correction strategy. Because the method performs local state estimation, it directly provides scan-to-scan odometry. To maintain geometric consistency over longer periods, undistorted scans are used for scan-to-map registration. The map representation employs Gaussian Processes to form a continuous distance field, enabling point-to-surface distance queries anywhere in space. Poses of the undistorted scans are refined by minimizing these distances through non-linear least-squares optimization. For odometry and mapping, the map is built incrementally in real time; for pure localization, existing maps are reused. The incremental map construction also includes mechanisms for removing dynamic objects. We benchmark 2Fast-2Lamaa on over 750km of public and self-collected datasets from both automotive and handheld systems. The framework achieves state-of-the-art performance across diverse and challenging scenarios, reaching odometry and localization errors as low as 0.22% and 0.06 m, respectively. The real-time implementation is publicly available at https://github.com/clegenti/2fast2lamaa.
Cedric Le Gentil, Raphael Falque, Daniil Lisus +1
Robotics Institute, University of Toronto Institute for Aerospace Studies, Canada · Robotics Institute, University of Technology Sydney, Australia
Neural implicit representations provide memory-efficient signed distance field (SDF) parameterizations for large-scale LiDAR scenes, but the geometry recovered from sparse and often noisy inputs carries jitter and artifacts. Classical geometric optimization techniques resolve such artifacts with surface energy functionals, whose minimizers correspond to smooth surfaces. Motivated by this principle, we formulate neural LiDAR mapping as the optimization of energy functionals over the parameter space of neural implicit representations. Specifically, we regularize the signed distance field with an energy functional defined on the shape operator of its level set, which represents the curvature of the surface, thus encouraging smoothness along the surface. This adapts classical geometric priors to the scale of million-point LiDAR maps. Experiments on large-scale datasets show reconstructions with improved smoothness at preserved geometric fidelity, and no additional inference-time cost. The code is publicly available at https://github.com/HrishikeshVish/nieo
Hrishikesh Viswanath, Md Ashiqur Rahman, Chi Lin +2
Purdue University, USA · DEVCOM, Army Research Laboratory, USA