GenZ-LIO: Generalizable LiDAR-Inertial Odometry Beyond Confined--Open Boundaries

Daehan Lee; Hyungtae Lim; Seongjun Kim; Soonbin Rho; Changhyeon Lee; Sanghyun Park; Junwoo Hong; Eunseon Choi

Figure 1 : Estimated trajectory and mapping result of our GenZ-LIO on the Handheld-A-01 sequence of our NarrowWide dataset, introduced in this work, where the platform traverses environments with substantially different spatial scales. The trajectory is color-coded by the proposed scale indicator

\bar{m}_{t}

, which reflects the spatial extent of the surrounding scene. By incorporating this indicator, GenZ-LIO adapts to varying spatial scales, enabling consistent odometry estimation while maintaining computational efficiency across both confined and open areas.

Figure 2 : Comparison of adaptive voxelization strategies. (a) LOCUS 2.0 [ 34 ] updates the voxel size for the next scan, denoted by

d_{t+1}

, using the ratio of the current voxelized point count

N_{t}

to the fixed desired point count

N_{\mathrm{desired}}^{\mathrm{fixed}}

. (b) AdaLIO [ 26 ] adaptively selects between the predefined coarse voxel size

d_{\mathrm{coarse}}^{\mathrm{fixed}}

and the fine voxel size

d_{\mathrm{fine}}^{\mathrm{fixed}}

by checking whether the coarse voxelization yields fewer points than a fixed threshold

\tau_{N}^{\mathrm{fixed}}

. (c) LIVOX-CAM [ 9 ] adjusts the voxel size

d_{t}

by first performing a temporary voxelization with a fixed voxel size

d_{\mathrm{temp}}^{\mathrm{fixed}}

and then updating it based on the ratio between the temporary point count

N_{\mathrm{temp},t}

and the desired point count

N_{\mathrm{desired}}^{\mathrm{fixed}}

. This update follows a volume-based scaling strategy rather than the linear scaling used in LOCUS 2.0 [ 34 ] . (d) Our method adaptively computes the desired point count

N_{\mathrm{desired},t}

based on the scale indicator

\bar{m}_{t}

and determines the corresponding voxel size

d_{t}

via proportional-derivative (PD) control with sensitivity-informed gain scheduling. This process corresponds to Fig. 3 (b).

Figure 3 : System overview of GenZ-LIO . (a) In the preprocessing stage, forward propagation uses IMU measurements to propagate the state and covariance, and backward propagation removes motion distortion from the LiDAR scan, yielding the deskewed scan

\mathcal{S}_{t}

. (b) The scan

\mathcal{S}_{t}

is voxelized using the voxel size from the previous timestep to produce the temporary voxelized scan

\mathcal{V}_{\mathrm{temp},t}

. The median range

m_{t}

of points in

\mathcal{V}_{\mathrm{temp},t}

is inserted into a sliding window to compute the spatial-scale indicator

\bar{m}_{t}

. Based on

\bar{m}_{t}

, a target number of voxelized points is set as a scale-informed control setpoint, and the voxel size

d_{t}

is adaptively adjusted via a PD controller with gain scheduling. The updated

d_{t}

is then used for bi-resolution voxelization of

\mathcal{S}_{t}

, yielding

\mathcal{V}_{\mathrm{merge},t}

with

d_{t}/2

for map integration with reduced discretization error and

\mathcal{V}_{t}

with

d_{t}

for state update. (c) The voxelized scan

\mathcal{V}_{t}

is aligned with the voxel map for a voxel-pruned correspondence search, which avoids unnecessary traversal of neighboring voxels. This process produces the point-to-plane correspondence set

\mathcal{C}_{\mathrm{pl}}

and point-to-point correspondence set

\mathcal{C}_{\mathrm{po}}

, which are used in the hybrid-metric state update. Finally, the transformed

\mathcal{V}_{\mathrm{merge},t}

is integrated into the voxel map. For clarity, the control flow of the scale-aware adaptive voxelization is further illustrated in Fig. 2 (d), where the bi-resolution voxelization step is omitted for comparison with other adaptive voxelization strategies.

Figure 4 : Our scale indicator

\bar{m}_{t}

mapped onto the estimated trajectory for the Corridor 02 sequence of the SuperLoc [ 56 ] dataset, demonstrating its variation with the scene’s spatial scale.

Figure 5 : Candidate voxel selection based on the region occupied by a query point within its corresponding root voxel. The root voxel is divided into 27 regions, and the occupied region falls into one of four cases: (a) center case, selecting no neighboring voxel; (b) surface case, selecting one surface-sharing neighboring voxel; (c) edge case, selecting three edge-sharing neighboring voxels; and (d) corner case, selecting seven corner-sharing neighboring voxels. The selected neighboring voxels, together with the root voxel, are considered candidate voxels for correspondence search. In Algorithm 2 , the function GetCandidateVoxels selects the candidate voxels based on these sharing relations.

Notation	Explanation
$\boxplus$ / $\boxminus$	The encapsulated “boxplus” and “boxminus” operations on the state manifold
${{}^{W}(\cdot)}$	A vector ${(\cdot)}$ in the world frame
${{}^{L}(\cdot)}$	A vector ${(\cdot)}$ in the LiDAR frame
${}^{I}\mathbf{T}_{L}$	The extrinsic of the LiDAR frame w.r.t. the IMU frame
${}^{W}\mathbf{T}_{I}$	The pose of the IMU frame w.r.t. the world frame
$\mathbf{x},\widehat{\mathbf{x}}$ , $\bar{\mathbf{x}}$	The true state, propagated estimate, and updated estimate

Table 1 : Some important notations in an error-state iterated Kalman filter.

Figure 6 : Definition of the distance

d_{\mathrm{nbr}}

between a query point and selected neighboring voxels. In Fig. 5 , the distance from the query point to a selected neighboring voxel falls into one of three categories: (a) point-to-surface distance (surface-sharing relation); (b) point-to-edge distance (edge-sharing relation); and (c) point-to-corner distance (corner-sharing relation). In Algorithm 2 , the function ComputeDistanceToVoxel determines the distance type based on these sharing relations between the query point’s occupied region and the selected neighboring voxel.

Figure 7 : Overview of the NarrowWide dataset. (a) Data acquisition environment designed to evaluate robotic systems for disaster-response scenarios. (b) Platforms used for data collection: a tracked robot and two handheld devices. These platforms employ different LiDAR sensors to cover diverse sensing configurations, as detailed in Table 2 . (c) Field experiments across different spatial scales using a tracked robot and handheld sensor platforms. The handheld platforms complement the tracked robot experiments by covering confined spaces that are difficult for the tracked robot to access due to its physical size. Details and traversal routes of the individual sequences are provided in Table 3 and Fig. 8 , respectively.

Figure 8 : Mapping results and estimated trajectories of GenZ-LIO on the six sequences of the NarrowWide dataset.

Platform	Tracked robot	Handheld A	Handheld B
LiDAR	Livox MID-70	Velodyne VLP-16	Livox AVIA
FoV (H $\times$ V)	$70.4^{\circ}$ circular	$360^{\circ}\times 30^{\circ}$	$70.4^{\circ}\times 77.2^{\circ}$
Max. range [m]	260	100	450
Frequency [Hz]	10	10	10
IMU	VectorNav VN-100	VectorNav VN-100	Bosch BMI088
Frequency [Hz]	200	200	200

Table 2 : Sensor configurations of the three platforms used to collect the NarrowWide dataset. The platforms correspond to those shown in Fig. 7 (b).

Sequence	Platform	Dist. [m]	Duration [s]	Min. width [m]	# of confined– open transitions
Tracked-01	Tracked robot	265.7	621.0	1.0	8
Tracked-02	Tracked robot	269.2	578.2	1.0	8
Handheld-A-01	Handheld A	263.0	521.9	0.3	6
Handheld-A-02	Handheld A	244.9	402.4	0.3	6
Handheld-B-01	Handheld B	408.7	636.0	0.5	10
Handheld-B-02	Handheld B	415.9	529.1	0.5	8

Table 3 : Characteristics of each sequence in the NarrowWide dataset. The minimum width denotes the width of the narrowest space traversed in each sequence, whereas the widest open areas traversed exceed

100\,\mathrm{m}

in all sequences. Note that every sequence returns to its starting position, forming a loop.

Scale	Dataset / Sequence		FAST-LIO2 [ 48 ]	Faster-LIO [ 1 ]	AdaLIO [ 26 ]	Point-LIO [ 13 ]	LIO-EKF [ 47 ]	DLIO [ 5 ]	iG-LIO [ 7 ]	PV-LIO [ 32 ] (Baseline)	Baseline w/ adap. vox.	Baseline w/ hybrid-metric	Ours
Confined	SM	Long Corridor	1.77	9.76	1.74	29.10	26.52	2.29	1.55	2.01	1.90	1.90	1.90
	SM	Laurel Cavern	3.64	4.22	4.63	5.91	$\times$	0.58	0.36	0.42	0.37	0.39	0.34
	SL	Cave 01	$\times$	1.10	$\times$	0.18	$\times$	0.28	0.12	0.15	0.25	0.13	0.12
		Cave 02	4.49	0.81	3.98	6.57	$\times$	0.57	0.43	0.43	0.44	0.42	0.44
		Cave 04	1.59	$\times$	2.89	0.52	$\times$	6.11	0.17	0.26	0.21	0.22	0.21
	H’21	Basement 04	0.63	0.27	0.47	0.50	–	$\times$	0.27	0.13	0.05	0.06	0.05

Table 4 : Absolute translational errors (ATE), reported as RMSE in meters, for each sequence. Due to space limitations, dataset names are abbreviated as follows: SubT-MRS [ 55 ] ( SM ), SuperLoc [ 56 ] ( SL ), 2021 HILTI [ 15 ] ( H’21 ), 2022 HILTI [ 54 ] ( H’22 ), GEODE [ 6 ] ( GD ), M3DGR [ 51 ] ( M3D ), NTU-VIRAL [ 27 ] ( NV ), ENWIDE [ 29 ] ( EW ), and Oxford Spires [ 42 ] ( OS ). The best result is shown in bold . Note that “

\times

” denotes a divergent run, defined as an ATE RMSE exceeding

200\,\mathrm{m}

, whereas “–” indicates that the method cannot process the LiDAR sensor used in the sequence. The divergence rate is computed as the percentage of divergent runs among the sequences that the method can process. For each sequence, the method with the lowest ATE is ranked first, and the resulting ranks are averaged across sequences. Divergent cases receive the worst rank, and cases marked with “–” are excluded.

Figure 9 : Qualitative comparison on the Exp 16 sequence of the 2022 HILTI [ 54 ] dataset. (a) Onboard views captured in a confined staircase. (b) Divergence of the baseline [ 32 ] in the confined staircase shown in (a). (c) Stable odometry estimation by the baseline with adaptive voxelization in the same staircase. Note that the coordinate frame corresponds to the body frame of the mobile platform. The accumulated map is shown in gray, while the current voxelized scan is shown in blue.

Figure 10 : Qualitative comparison on the Waterways-Short sequence of the GEODE [ 6 ] dataset. (a) Onboard view captured in an open waterway. (b) Pose drift of the baseline [ 32 ] in the open area shown in (a). (c) Stable odometry estimation by the baseline with the hybrid-metric state update in the same open area. Note that the coordinate frame corresponds to the body frame of the mobile platform. The accumulated map is shown in gray, while the point-to-plane constraints are shown in blue and the point-to-point constraints in red.

Figure 11 : Qualitative comparison on the Handheld-A-01 sequence of the NarrowWide dataset. (a) Data acquisition using a handheld device in an extremely confined corner less than

0.5\,\mathrm{m}

wide. (b) Divergence of the baseline [ 32 ] in the confined corner shown in (a). (c) Stable odometry estimation by GenZ-LIO in the same corner. This scene corresponds to region C in Fig. 12 . Note that the coordinate frame corresponds to the body frame of the handheld device. The accumulated map is shown in gray, while the point-to-plane constraints are shown in blue and the point-to-point constraints in red.

Figure 12 : Comparison of adaptive voxelization strategies [ 34 , 26 , 9 ] applied to a baseline system [ 32 ] on the Handheld-A-01 sequence of the NarrowWide dataset. (a) Temporal evolution of the proposed scale indicator

\bar{m}_{t}

. The markers A–F correspond to the regions A–F in Fig. 1 , respectively. (b) Voxel sizes adjusted by each adaptive strategy. (c) Number of points in the voxelized scan obtained using the adjusted voxel size. (d) Relative translational error of the estimated poses. (e) CPU usage, visualized using a sliding-window temporal average with a shaded band indicating one standard deviation to reduce short-term fluctuations. (f) Computation time per frame, visualized using the same smoothing scheme for clarity. The baseline system diverged during the sequence and is therefore plotted only up to the divergence point, which is indicated by a

\times

marker. These results are further summarized in Table 5 .

Method	CPU [%]		Comp. time [ms]		RTE [cm]	ATE [m]
	Mean	p95	Mean	p95	RMSE	RMSE
Baseline [ 32 ]	270.12	485.02	16.83	36.70	$\times$	$\times$
+ LOCUS 2.0 [ 34 ]	273.92	477.59	20.98	42.65	1.49	0.29
+ AdaLIO [ 26 ]	294.57	467.87	24.14	50.35	1.56	0.34
+ LIVOX-CAM [ 9 ]	245.93	372.98	19.60	34.59	1.60	0.30
+ Ours	212.23	314.16	16.64	26.24	1.42	0.16

Table 5 : Comparison of computational efficiency and odometry accuracy for different adaptive voxelization strategies evaluated on the Handheld-A-01 sequence of the NarrowWide dataset. CPU usage and computation time are reported using the mean and the 95th percentile (p95). RTE and ATE denote the relative and absolute translational errors, respectively, both reported as RMSE. All adaptive voxelization methods [ 34 , 26 , 9 ] are evaluated within the same baseline framework [ 32 ] . The baseline values shown in gray report CPU usage and computation time only up to the divergence point and are therefore excluded from direct comparison. The symbol “

\times

” indicates divergence, and the best performance is highlighted in bold . The temporal behavior of each method over the sequence is further illustrated in Fig. 12 .

Figure 13 : Setpoint tracking performance comparison on the Exp 16 sequence of the 2022 HILTI [ 54 ] dataset. The plots show the temporal evolution of the scale-informed setpoint

N_{\mathrm{desired},t}

and the corresponding voxelized point count

N_{t}

for the following ablations: (a) PD controller with fixed gains, (b) ours without scale indicator

\bar{m}_{t}

, (c) ours without the error terms

|e_{t}|

and

|\Delta e_{t}|

in gain scheduling, and (d) ours with sensitivity-informed gain scheduling. Region A in (b) and region B in (c) correspond to the zoomed regions in (d), highlighting differences in local tracking behavior.

Method	IAE [ $\times 10^{3}$ ] $\downarrow$	Overshoot $\downarrow$	ATE [m] $\downarrow$
Linear scaling [ 34 ]	14.03	0.24	0.21
Volume-based scaling [ 9 ]	270.71	0.87	0.34
Fixed gains	53.74	1.63	0.24
Ours w/o scale indicator	13.32	0.16	0.19
Ours w/o error terms	7.95	0.15	0.21
Ours	6.04	0.09	0.13

Table 6 : Ablation study results on voxel size control strategies for tracking a scale-informed setpoint

N_{\mathrm{desired},t}

, evaluated on the Exp 16 sequence of the 2022 HILTI [ 54 ] dataset. IAE denotes the integral of absolute error; see Sec. 6-D . All control methods are evaluated within the same baseline odometry framework. The best performance is highlighted in bold .

Figure 14 : Box plots of the condition number on (a) the Waterways-Short sequence of the GEODE [ 6 ] dataset and (b) the Handheld-B-02 sequence of the NarrowWide dataset, evaluated by applying the proposed modules to the baseline system [ 32 ] . A lower condition number indicates improved numerical stability of the system [ 8 ] . The **** annotations indicate paired

t

-test results with

p<10^{-4}

.

Figure 15 : Mapping result of GenZ-LIO on the Waterways-Short sequence of the GEODE [ 6 ] dataset. Translational and rotational directions that are weakly constrained due to insufficient geometric constraints, and are therefore susceptible to LiDAR degeneracy, are indicated by orange arrows. The visualized coordinate frame corresponds to the robot body frame, and the camera image is included solely for improved scene understanding.

Figure 16 : Average computation time and ATE (RMSE) on the Offroad-04 sequence of the GEODE [ 6 ] dataset under different correspondence search strategies for the following systems: (a) GenZ-LIO and (b) LIO-EKF [ 47 ] .

Stage	Method	Adaptation criterion	Control strategy
Adaptive voxelization	LOCUS 2.0 [ 34 ]	Fixed target number of voxelized points $N_{\mathrm{desired}}^{\mathrm{fixed}}$	Linear scaling
	AdaLIO [ 26 ]	Fixed threshold for the number of voxelized points $\tau_{N}^{\mathrm{fixed}}$	Threshold-based switching between two predefined voxel sizes
	LIVOX-CAM [ 9 ]	Fixed target number of voxelized points $N_{\mathrm{desired}}^{\mathrm{fixed}}$	Volume-based scaling
	GenZ-LIO	Scale-informed target number of voxelized points $N_{\mathrm{desired},t}$	PD control with gain scheduling
Stage	Method	Residual type	Residual weighting
State update	PV-LIO [ 32 ]	Point-to-plane [ 36 ] residual	LiDAR measurement noise model [ 50 ]

Table 7 : Comparison between GenZ-LIO and related methods.

Figure 17 : Fixed point-count setpoint analysis under different spatial scales. (a) Distribution of the scale indicator

\bar{m}_{t}

for each evaluated sequence, where the white diamond and black line indicate the mean and median, respectively. (b) ATE and average computation time obtained by fixing the target point count to

N_{\mathrm{desired},t}\in\{1,\!000,2,\!000,3,\!000,4,\!000\}

. The filled markers identify the setpoints with the lowest ATE. (c) Sequence-wise ACE score

S_{N}^{\mathrm{ACE}}

, which jointly summarizes ATE and computation time; higher values indicate a better accuracy–efficiency trade-off within the same sequence.

Figure 18 : Comparison of the frame-wise medians of the point-to-plane covariance

R_{\mathrm{pl}}^{\ell}

and the normalized point-to-point covariance

R_{\mathrm{po}}^{\mathrm{norm},\ell}

over time on the Tracked-01 sequence of our NarrowWide dataset. The two covariance terms show a persistent numerical scale gap throughout the sequence.

$\lambda_{\mathrm{po}}$	Stairs	Waterways-Short	Tracked-01	Average rank
0.01	0.25	1.73	0.31	4.00
0.05	0.24	0.69	0.16	1.00
0.1	0.36	0.91	0.17	2.67
0.2	0.31	0.95	0.18	3.00
0.5	0.39	2.42	0.22	5.00
1	0.38	4.10	0.28	5.33

Table 8 : Sensitivity analysis of the point-to-point covariance scaling factor

\lambda_{\mathrm{po}}

on the Stairs and Waterways-Short sequences of GEODE [ 6 ] and the Tracked-01 sequence of our NarrowWide dataset. ATE is reported as RMSE in meters. The lowest ATE and the lowest average rank are shown in bold .

Figure 19 : Temporal evolution of the frame-wise minimum combined point-to-point covariance

R_{\mathrm{po}}^{\mathrm{comb},\ell}

with and without the discretization-error variance

R_{\mathrm{disc}}

. The minimum in each frame is computed over all point-to-point correspondences generated in that frame. Stairs and Waterways-Short are sequences of the GEODE [ 6 ] dataset, and Tracked-01 is a sequence of our NarrowWide dataset.

Method	Stairs	Waterways-Short	Tracked-01
Full $R_{\mathrm{po}}^{\mathrm{comb},\ell}$ (Proposed)	0.24	0.69	0.16
$R_{\mathrm{po}}^{\mathrm{comb},\ell}$ w/o $R_{\mathrm{disc}}$	0.76	1.09	3.35

Table 9 : Ablation study on the combined point-to-point covariance with and without the discretization-error variance

R_{\mathrm{disc}}

. Stairs and Waterways-Short are sequences of the GEODE [ 6 ] dataset, and Tracked-01 is a sequence of our NarrowWide dataset. ATE RMSE is reported in meters and the best result on each sequence is shown in bold .

Parameter / Value		Exp 16	Offroad-02	Handheld-A-01
$\tau_{m}$	20.0	0.307	0.305	0.221
	30.0 ∗	0.196	0.298	0.192
	40.0	0.151	0.304	0.205
	50.0	0.367	0.301	0.217
$p$	0.5	0.242	0.300	0.198
	1.0	0.224	0.302	0.235

Table 10 : One-at-a-time parameter sensitivity analysis under different spatial-scale conditions. ATE is reported as RMSE in meters. Except for the parameter group indicated in the first column, all parameters are fixed at their default values. “

\ast

” indicates the default value of each parameter group, and the best result is shown in bold .

Method	NTU-VIRAL [ 27 ]			GrandTour [ 12 ]			Avg. rank
	eee_01	sbs_01	tnp_01	KÄB-2	HÖB-2	ALB-2
FAST-LIO2 [ 48 ]	0.89	0.35	0.30	0.07	0.03	0.07	6.00
Faster-LIO [ 1 ]	0.86	0.36	0.24	0.06	0.03	0.06	4.83
AdaLIO [ 26 ]	0.91	0.29	0.20	0.07	0.03	0.07	4.67
Point-LIO [ 13 ]	0.25	0.26	0.24	0.08	0.06	0.09	6.67
LIO-EKF [ 47 ]	0.56	0.28	0.25	0.07	0.68	0.07	6.17

Table 11 : Absolute translational errors on additional structured and unstructured sequences without pronounced spatial-scale variations, reported as RMSE in meters. The best results are shown in bold . Note that “

\times

” denotes divergence and receives the worst rank.

GenZ-LIO: Generalizable LiDAR-Inertial Odometry Beyond Confined--Open Boundaries

Abstract

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