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LIO-SAM: Tightly-coupled Lidar Inertial Odometry via Smoothing and Mapping

Tixiao ShanBrendan EnglotDrew MeyersWei WangCarlo RattiDaniela Rus

article2020IEEE/RJS International Conference on Intelligent RObots and Systems2,111 citations

Proposes a tightly-coupled lidar-inertial odometry framework built on factor graphs that combines IMU pre-integration with local sub-keyframe scan matching to enable accurate, real-time 3D state estimation and mapping for mobile robots.

Department of Mechanical EngineeringDepartment of Urban Studies and PlanningMassachusetts Institute of TechnologyStevens Institute of Technologyfactor graphsimuinertial measurementslidar-inertial odometrytightly-coupled lidar inertial odometrysmoothing and mapping
arXiv: 2007.00258TixiaoShan/LIO-SAM
  • Paper: SAM 2: Segment Anything in Images and Videos, Nikhila Ravi et al. (2025). Extending beyond 3D point cloud mapping and odometry, this work applies advanced spatio-temporal segmentation transformer architectures to track objects in complex video feeds.
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Abstract

We propose a framework for tightly-coupled lidar inertial odometry via smoothing and mapping, LIO-SAM, that achieves highly accurate, real-time mobile robot trajectory estimation and map-building. LIO-SAM formulates lidar-inertial odometry atop a factor graph, allowing a multitude of relative and absolute measurements, including loop closures, to be incorporated from different sources as factors into the system. The estimated motion from inertial measurement unit (IMU) pre-integration de-skews point clouds and produces an initial guess for lidar odometry optimization. The obtained lidar odometry solution is used to estimate the bias of the IMU. To ensure high performance in real-time, we marginalize old lidar scans for pose optimization, rather than matching lidar scans to a global map. Scan-matching at a local scale instead of a global scale significantly improves the real-time performance of the system, as does the selective introduction of keyframes, and an efficient sliding window approach that registers a new keyframe to a fixed-size set of prior ``sub-keyframes.'' The proposed method is extensively evaluated on datasets gathered from three platforms over various scales and environments.

Topics

factor graphsimuinertial measurementsloop closureodometryoptimizationpoint cloudtightly-coupledsliding windowslidar systems

Keywords

lidar-inertial odometrytightly-coupled lidar inertial odometrysmoothing and mappingrobocentric lidar-inertial state estimatorpoint cloud mapincremental smoothingmulti-sensor fusiontrajectory estimation

Table of Contents

  • I Introduction
  • II Related Work
  • III Lidar Inertial Odometry via Smoothing and Mapping
  • III-A System Overview
  • III-B IMU Preintegration Factor
  • III-C Lidar Odometry Factor
  • III-C1 Sub-keyframes for voxel map
  • III-C2 Scan-matching
  • III-C3 Relative transformation
  • III-D GPS Factor
  • III-E Loop Closure Factor
  • IV Experiments
  • IV-A Rotation Dataset
  • IV-B Walking Dataset
  • IV-C Campus Dataset
  • IV-D Park Dataset
  • IV-E Amsterdam Dataset
  • IV-F Benchmarking Results
  • V Conclusions and Discussion
  • References

Knowls

  1. Knowl 1 — Factor Graph State Estimation Architecture in LIO-SAM

    model/method

    LIO-SAM formulates lidar-inertial state estimation as a maximum a posteriori (MAP) problem solved on a factor graph using incremental smoothing and mapping with the Bayes tree (iSAM2). Assuming Gaussian noise models, MAP inference is equivalent to solving a nonlinear least-squares problem over robot state nodes.

    The robot state variable at time tt associated with a node in the factor graph is defined as:

    x=[RT,pT,vT,bT]Tx = \begin{bmatrix} R^T, p^T, v^T, b^T \end{bmatrix}^T

    where R∈SO(3)R \in SO(3) denotes the orientation rotation matrix transforming the body frame BB to the world frame WW, p∈R3p \in \mathbb{R}^3 denotes the position vector, v∈R3v \in \mathbb{R}^3 is the velocity vector, and b=[(ba)T,(bω)T]T∈R6b = [ (b^a)^T, (b^\omega)^T ]^T \in \mathbb{R}^6 represents the slowly varying accelerometer and gyroscope biases. The rigid body transformation from BB to WW is represented as T=[R∣p]∈SE(3)T = [R \mid p] \in SE(3).

    The factor graph incorporates four factor types connected to state nodes:

    1. IMU Preintegration Factors: Model relative body motion and constrain consecutive state nodes while estimating IMU bias.
    2. Lidar Odometry Factors: Provide relative pose constraints between consecutive keyframes via local sliding-window scan-matching.
    3. GPS Factors: Provide global position corrections when pose uncertainty exceeds GPS covariance.
    4. Loop Closure Factors: Link non-consecutive keyframe poses using scan-matching against historical sub-keyframes to eliminate accumulated drift.

  2. Knowl 2 — IMU Preintegration and Motion Estimation Formulation

    equation

    Raw IMU angular velocity ω^t\hat{\omega}_t and linear acceleration a^t\hat{a}_t measurements expressed in the body frame BB are modeled as:

    ω^t=ωt+btω+ntω\hat{\omega}_t = \omega_t + b_t^\omega + n_t^\omega

    a^t=RtBW(at−g)+bta+nta\hat{a}_t = R_t^{BW} (a_t - g) + b_t^a + n_t^a

    where ωt\omega_t and ata_t are the true angular velocity and acceleration, btωb_t^\omega and btab_t^a are time-varying biases, ntωn_t^\omega and ntan_t^a are zero-mean additive Gaussian white noise, RtBW=(RtWB)T=RtTR_t^{BW} = (R_t^{WB})^T = R_t^T is the rotation from world frame WW to body frame BB, and gg is the constant gravity vector in WW.

    Assuming constant acceleration and angular velocity over time interval Δt\Delta t, motion integration yields:

    vt+Δt=vt+gΔt+Rt(a^t−bta−nta)Δtv_{t+\Delta t} = v_t + g\Delta t + R_t(\hat{a}_t - b_t^a - n_t^a)\Delta t

    pt+Δt=pt+vtΔt+12gΔt2+12Rt(a^t−bta−nta)Δt2p_{t+\Delta t} = p_t + v_t\Delta t + \frac{1}{2}g\Delta t^2 + \frac{1}{2}R_t(\hat{a}_t - b_t^a - n_t^a)\Delta t^2

    Rt+Δt=Rtexp⁡((ω^t−btω−ntω)Δt)R_{t+\Delta t} = R_t \exp((\hat{\omega}_t - b_t^\omega - n_t^\omega)\Delta t)

    Preintegrated relative motion measurements Δvij\Delta v_{ij}, Δpij\Delta p_{ij}, and ΔRij\Delta R_{ij} between keyframe timesteps ii and jj (separated by duration Δtij\Delta t_{ij}) are computed in the local frame of state ii:

    Δvij=RiT(vj−vi−gΔtij)\Delta v_{ij} = R_i^T (v_j - v_i - g\Delta t_{ij})

    Δpij=RiT(pj−pi−viΔtij−12gΔtij2)\Delta p_{ij} = R_i^T \left(p_j - p_i - v_i\Delta t_{ij} - \frac{1}{2}g\Delta t_{ij}^2\right)

    ΔRij=RiTRj\Delta R_{ij} = R_i^T R_j

    These preintegrated measurements serve three distinct functions in LIO-SAM:

    1. De-skew raw lidar point clouds by estimating the continuous sensor trajectory during scan acquisition.
    2. Provide an initial transformation guess T~i+1\tilde{T}_{i+1} for lidar scan-matching optimization.
    3. Formulate IMU preintegration factors in the factor graph to jointly optimize robot velocity, position, orientation, and IMU biases.

  3. Knowl 3 — Keyframe Selection and Sliding Window Local Voxel Map Construction

    model/method

    To maintain a sparse factor graph suitable for real-time optimization, LIO-SAM introduces keyframe selection and local sliding-window mapping rather than matching against a dense global map:

    1. Keyframe Selection: A lidar frame Fi+1F_{i+1} (composed of extracted edge features Fi+1eF_{i+1}^e and planar features Fi+1pF_{i+1}^p in body frame BB) is registered as a new keyframe and associated with a new factor graph state node xi+1x_{i+1} only if the estimated pose change relative to the previous state xix_i exceeds user-defined thresholds. The translation threshold is set to 1 m1\,\text{m} and the rotation threshold is set to 10∘10^\circ. Intermediate lidar scans that do not meet these criteria are discarded.

    2. Sliding Window Sub-Keyframes: Instead of matching against a global map, LIO-SAM builds a local voxel map Mi={Mie,Mip}M_i = \{M_i^e, M_i^p\} from a sliding window containing the n=25n = 25 most recent sub-keyframes {Fi−n,…,Fi}\{F_{i-n}, \dots, F_i\}. Each sub-keyframe is transformed into the world frame WW using its estimated transformation Tk∈{Ti−n,…,Ti}T_k \in \{T_{i-n}, \dots, T_i\}:

    Mie=WFie∪WFi−1e∪⋯∪WFi−neM_i^e = {^W F_i^e} \cup {^W F_{i-1}^e} \cup \dots \cup {^W F_{i-n}^e}

    Mip=WFip∪WFi−1p∪⋯∪WFi−npM_i^p = {^W F_i^p} \cup {^W F_{i-1}^p} \cup \dots \cup {^W F_{i-n}^p}

    1. Voxel Downsampling: MieM_i^e and MipM_i^p are downsampled using voxel grids to remove duplicate features in overlapping cells. The downsampling leaf size is 0.2 m0.2\,\text{m} for the edge voxel map MieM_i^e and 0.4 m0.4\,\text{m} for the planar voxel map MipM_i^p.

  4. Knowl 4 — Lidar Odometry Point-to-Line and Point-to-Plane Optimization Factor

    equation

    Lidar odometry factors in LIO-SAM are obtained by matching the features of a new keyframe Fi+1={Fi+1e,Fi+1p}F_{i+1} = \{F_{i+1}^e, F_{i+1}^p\} against the local edge voxel map MieM_i^e and planar voxel map MipM_i^p. Features are initialized in world coordinates WW as WFi+1e{^W F_{i+1}^e} and WFi+1p{^W F_{i+1}^p} using the IMU motion prior T~i+1\tilde{T}_{i+1}.

    For each transformed edge feature point pi+1,ke∈WFi+1ep_{i+1,k}^e \in {^W F_{i+1}^e}, the distance to its corresponding edge line in MieM_i^e (defined by points pi,uep_{i,u}^e and pi,vep_{i,v}^e) is:

    dek=∥(pi+1,ke−pi,ue)×(pi+1,ke−pi,ve)∥∥pi,ue−pi,ve∥d_{ek} = \frac{\|(p_{i+1,k}^e - p_{i,u}^e) \times (p_{i+1,k}^e - p_{i,v}^e)\|}{\|p_{i,u}^e - p_{i,v}^e\|}

    For each transformed planar feature point pi+1,kp∈WFi+1pp_{i+1,k}^p \in {^W F_{i+1}^p}, the distance to its corresponding planar patch in MipM_i^p (defined by points pi,upp_{i,u}^p, pi,vpp_{i,v}^p, and pi,wpp_{i,w}^p) is:

    dpk=∣(pi+1,kp−pi,up)⋅((pi,up−pi,vp)×(pi,up−pi,wp))∣∥(pi,up−pi,vp)×(pi,up−pi,wp)∥d_{pk} = \frac{|(p_{i+1,k}^p - p_{i,u}^p) \cdot ((p_{i,u}^p - p_{i,v}^p) \times (p_{i,u}^p - p_{i,w}^p))|}{\|(p_{i,u}^p - p_{i,v}^p) \times (p_{i,u}^p - p_{i,w}^p)\|}

    The optimal pose Ti+1T_{i+1} is computed via Gauss-Newton minimization:

    min⁡Ti+1{∑pi+1,ke∈WFi+1edek+∑pi+1,kp∈WFi+1pdpk}\min_{T_{i+1}} \left\{ \sum_{p_{i+1,k}^e \in {^W F_{i+1}^e}} d_{ek} + \sum_{p_{i+1,k}^p \in {^W F_{i+1}^p}} d_{pk} \right\}

    The relative transformation factor ΔTi,i+1\Delta T_{i, i+1} linking state xix_i and xi+1x_{i+1} is then formulated as:

    ΔTi,i+1=TiTTi+1\Delta T_{i,i+1} = T_i^T T_{i+1}

  5. Knowl 5 — Covariance-Gated GPS Factor Insertion

    model/method

    To constrain long-term drift without over-constraining the graph when lidar-inertial odometry is locally accurate, LIO-SAM integrates GPS measurements using a covariance-gating mechanism:

    1. Coordinate Transformation and Synchronization: Received raw GPS measurements are converted into local Cartesian coordinates. When GPS signals are not hardware-synchronized with lidar scans, GPS positions are linearly interpolated based on the timestamps of the lidar keyframes.
    2. Covariance-Based Gating: LIO-SAM estimates position covariance at each state node. A GPS factor is inserted into the factor graph at a new state node only when the estimated position covariance of the lidar-inertial odometry exceeds the received GPS measurement covariance.

    This selective insertion prevents unnecessary graph densification during periods when lidar-inertial odometry drift is negligible.

  6. Knowl 6 — Euclidean Distance-Based Loop Closure Detection and Factor Formulation

    model/method

    Loop closures in LIO-SAM are detected and incorporated as follows:

    1. Candidate Retrieval: When a new state node xi+1x_{i+1} is added, the factor graph is queried for past state nodes within a Euclidean search radius of 15 m15\,\text{m}.
    2. Local Loop Map Construction: For an identified candidate node xkx_k (where k≪i+1k \ll i+1), a local sub-keyframe window {Fk−m,…,Fk,…,Fk+m}\{F_{k-m}, \dots, F_k, \dots, F_{k+m}\} is extracted with index radius m=12m = 12. These sub-keyframes are transformed into the world frame WW and merged into a local target feature map.
    3. Scan-Matching and Factor Addition: The current keyframe Fi+1F_{i+1} is transformed into WW and aligned with the candidate local map via point-to-line and point-to-plane scan-matching. The resulting relative transformation ΔTk,i+1\Delta T_{k, i+1} is inserted into the factor graph as a loop closure factor.

    This loop closure mechanism eliminates accumulated horizontal drift and is crucial for correcting altitude drift in setups where GPS elevation measurements exhibit high noise.

  7. Knowl 7 — End-to-End Translation Error Across Sensor and Factor Ablations

    data/table

    The end-to-end translational drift (in meters) upon returning to the starting position was evaluated across three real-world datasets: Campus (1437 m handheld trajectory), Park (2898 m UGV trajectory), and Amsterdam (19065 m boat trajectory). The benchmark compares LOAM, LIOM, and three ablation variants of the proposed method: LIO-odom (IMU preintegration + lidar odometry only), LIO-GPS (IMU preintegration + lidar odometry + GPS), and full LIO-SAM (all factors including loop closures).

    Dataset LOAM LIOM LIO-odom LIO-GPS LIO-SAM
    Campus 192.43 Fail 9.44 6.87 0.12
    Park 121.74 34.60 36.36 2.93 0.04
    Amsterdam Fail Fail Fail 1.21 0.17

    LOAM and LIOM suffer substantial drift or initialization failure under rapid rotation or sparse features. LIO-odom limits drift compared to LOAM but drifts over extended trajectories. LIO-GPS mitigates horizontal drift but fails to close loops completely due to altitude errors in GPS elevation. Full LIO-SAM achieves near-zero end-to-end drift (0.04 m0.04\,\text{m} to 0.17 m0.17\,\text{m}) by resolving altitude and horizontal drift through loop closure factors.

  8. Knowl 8 — Trajectory Accuracy Relative to GPS Ground Truth

    data/table

    Root mean square error (RMSE) of horizontal trajectory translation (in meters) evaluated against full GPS measurement history on the Park dataset (2898 m trajectory on an unmanned ground vehicle):

    Dataset LOAM LIOM LIO-odom LIO-GPS LIO-SAM
    Park 47.31 28.96 23.96 1.09 0.96

    Methods relying solely on scan-matching and inertial odometry without absolute positioning (LOAM: 47.31 m47.31\,\text{m}, LIOM: 28.96 m28.96\,\text{m}, LIO-odom: 23.96 m23.96\,\text{m}) accumulate large drift over long trajectories. In contrast, incorporating intermittent GPS measurements in open areas (green segments) enables LIO-GPS (1.09 m1.09\,\text{m}) and LIO-SAM (0.96 m0.96\,\text{m}) to achieve sub-meter global accuracy.

  9. Knowl 9 — Mapping Scan Runtime and Stress-Test Playback Scalability

    data/table

    Average mapping runtime (in milliseconds) required to register one lidar frame across five datasets on an Intel i7-10710U CPU (single-threaded, no GPU/parallel computation), alongside the maximum playback speed multiplier achieved in stress tests without tracking failure:

    Dataset LOAM LIOM LIO-SAM Stress test
    Rotation 83.6 Fail 41.9 13×
    Walking 253.6 339.8 58.4 13×
    Campus 244.9 Fail 97.8 10×
    Park 266.4 245.2 100.5 9×
    Amsterdam Fail Fail 79.3 11×

    LOAM and LIOM frequently exceed the real-time threshold (100 ms100\,\text{ms} for 10 Hz10\,\text{Hz} lidar) or fail. LIO-SAM processes each frame in 41.9 ms41.9\,\text{ms} to 100.5 ms100.5\,\text{ms}, executing up to 13×13\times faster than real time. Runtime is governed by local feature density (e.g., dense vegetation in Park took 100.5 ms100.5\,\text{ms} for 4,573 nodes and 9,365 factors) rather than the global factor graph scale (Amsterdam took 79.3 ms79.3\,\text{ms} despite having 23,304 nodes and 49,617 factors).

  10. Knowl 10 — Operational Failure Modes in Feature-Degenerate and GPS-Degraded Regimes

    limitation

    LIO-SAM exhibits specific failure modes and sensitivities across challenging operating environments:

    1. Degenerate Geometric Features and Optical Noise: In environments devoid of vertical planar features (such as under canal bridges or in featureless corridors), lidar scan-matching becomes under-constrained. Furthermore, direct sunlight into the lidar receiver causes optical noise and false returns (observed during approximately 20% of data acquisition in open canal environments), leading to scan-matching failure for odometry-only pipelines.
    2. GPS Vertical Inaccuracy: Elevation data from GPS is highly inaccurate in practice, introducing vertical altitude errors approaching 100 m100\,\text{m} if GPS elevation is directly trusted without altimeters or loop closure factors.
    3. Loop Closure Dependency for Altitude Correction: In GPS-only configurations (LIO-GPS) lacking loop closures or external altitude sensors (such as barometric altimeters), unconstrained vertical drift prevents complete loop convergence upon returning to the origin.

Coverage note — None was omitted; all contributed models, factor graph formulations, scan-matching equations, empirical benchmarks, runtime tests, and failure mode analyses are fully represented.

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Citation

MLA
Shan, T., et al. “LIO-SAM: Tightly-coupled Lidar Inertial Odometry via Smoothing and Mapping”. arXiv, 2020, http://arxiv.org/abs/2007.00258v3.
APA
Shan, T., Englot, B., Meyers, D., Wang, W., Ratti, C., & Rus, D. (2020). LIO-SAM: Tightly-coupled Lidar Inertial Odometry via Smoothing and Mapping. arXiv. http://arxiv.org/abs/2007.00258v3
Chicago
Shan, T., B. Englot, D. Meyers, W. Wang, C. Ratti, and D. Rus. 2020. “LIO-SAM: Tightly-coupled Lidar Inertial Odometry via Smoothing and Mapping”. arXiv. http://arxiv.org/abs/2007.00258v3.
Harvard
Shan, T. et al. (2020) “LIO-SAM: Tightly-coupled Lidar Inertial Odometry via Smoothing and Mapping”, arXiv [Preprint]. Available at: http://arxiv.org/abs/2007.00258v3.
Vancouver
1. Shan T, Englot B, Meyers D, Wang W, Ratti C, Rus D (2020) LIO-SAM: Tightly-coupled Lidar Inertial Odometry via Smoothing and Mapping. arXiv

BibTeX

@article{shan2020lio,
  title = {LIO-SAM: Tightly-coupled Lidar Inertial Odometry via Smoothing and Mapping},
  author = {Shan, Tixiao and Englot, Brendan and Meyers, Drew and Wang, Wei and Ratti, Carlo and Rus, Daniela},
  year = {2020},
  journal = {arXiv},
  url = {http://arxiv.org/abs/2007.00258v3},
  eprint = {2007.00258}
}
Metadata:arXiv

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