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Direct LiDAR-Inertial Odometry: Lightweight LIO with Continuous-Time Motion Correction

Kenny Chen, Ryan Nemiroff, Brett T. Lopez

arXiv:2203.03749v4cs.RO

TL;DR

Aggressive motion distorts LiDAR scans, and existing remedies can be too simplistic or costly for resource-constrained robots. DLIO builds continuous-time trajectories for parallelizable deskewing, integrates motion correction with prior generation and scan-to-map registration, and reports improved accuracy with lower computational overhead. Its observer supplies convergent state estimates needed to initialize IMU integration and the condensed pipeline.

  • Problem

    Aggressive flights and traversal of irregular terrain distort LiDAR scans, while existing mitigation methods may be too simplistic or computationally costly for resource-constrained robots.

  • Method

    DLIO uses coarse-to-fine continuous-time trajectory construction, analytical point-wise motion correction, condensed scan-to-map registration, and a nonlinear geometric observer.

  • Results

    DLIO achieves superior localization accuracy, map quality, and computational overhead across public benchmark and self-collected datasets, including the lowest trajectory RMSE and per-scan time in Newer College.

  • Takeaways & Limitations

    DLIO provides accurate real-time state estimates and detailed maps for resource-constrained mobile robots.

Abstract

from arXiv · show

Aggressive motions from agile flights or traversing irregular terrain induce motion distortion in LiDAR scans that can degrade state estimation and mapping. Some methods exist to mitigate this effect, but they are still too simplistic or computationally costly for resource-constrained mobile robots. To this end, this paper presents Direct LiDAR-Inertial Odometry (DLIO), a lightweight LiDAR-inertial odometry algorithm with a new coarse-to-fine approach in constructing continuous-time trajectories for precise motion correction. The key to our method lies in the construction of a set of analytical equations which are parameterized solely by time, enabling fast and parallelizable point-wise deskewing. This method is feasible only because of the strong convergence properties in our nonlinear geometric observer, which provides provably correct state estimates for initializing the sensitive IMU integration step. Moreover, by simultaneously performing motion correction and prior generation, and by directly registering each scan to the map and bypassing scan-to-scan, DLIO's condensed architecture is nearly 20% more computationally efficient than the current state-of-the-art with a 12% increase in accuracy. We demonstrate DLIO's superior localization accuracy, map quality, and lower computational overhead as compared to four state-of-the-art algorithms through extensive tests using multiple public benchmark and self-collected datasets.

I. INTRODUCTION

Aggressive robot motion distorts LiDAR scans, while existing correction methods can lose precision or efficiency outside structured, predictable settings. DLIO addresses these challenges with continuous-time motion correction, a condensed scan-to-map architecture, and a nonlinear geometric observer.

  • Aggressive maneuvers and uneven terrain can induce significant LiDAR distortion that challenges reliable localization and mapping.
  • Existing methods may degrade under irregular conditions because of simplistic motion models, discretization losses, or computational inefficiency.
  • DLIO constructs continuous-time trajectories using analytical constant-jerk and angular-acceleration equations for fast, parallelizable point-wise motion correction.
  • DLIO combines motion correction with prior construction, removes scan-to-scan processing, and directly registers scans to the map to reduce computational overhead.
  • The nonlinear geometric observer provides strong convergence properties for accurate full-state estimation and initialization of the motion-correction pipeline.

III. METHOD

DLIO represents each LiDAR sweep and robot state in shared coordinate frames, then uses synchronized IMU measurements to estimate the robot state and map. Its formulation explicitly models pose, velocity, sensor biases, and measurement noise.

  • A LiDAR sweep P_k contains points indexed by n, while W, R, B, and L denote world, robot, IMU, and LiDAR frames.
  • The robot state includes position, quaternion orientation, velocity, accelerometer bias, and gyroscope bias.
  • IMU acceleration and angular-velocity measurements are modeled with sensor biases and white noise, with gravity represented by a rotated vector.
  • The estimation problem is to recover the robot state and geometric map from accumulated LiDAR points and IMU measurements between scans.

C. Preprocessing

DLIO accepts dense LiDAR point clouds and high-rate, time-synchronized six-axis IMU data, then processes each scan through initialization, motion correction, registration, state update, and map update steps. Preprocessing applies calibration and limited filtering before downstream estimation.

  • DLIO uses dense 3D point clouds from modern 360° mechanical LiDARs and time-synchronized acceleration and angular-velocity measurements from six-axis IMUs.
  • The algorithm initializes each scan from the previous estimated state and transforms incoming points into the robot frame.
  • Continuous-time motion correction is applied point-wise before scan-to-map registration.
  • The geometric observer updates the state, after which the keyframe map is updated for the next iteration.
  • Extrinsic calibration transforms sensor data to the robot center of gravity, and a 1m^3 box filter removes points near the robot.

D. Continuous-Time Motion Correction with Joint Prior

DLIO corrects LiDAR motion distortion with a coarse-to-fine continuous-time trajectory that combines discrete IMU integration with analytical point-wise transforms. The corrected cloud also incorporates a GICP prior, but reliable correction depends on accurate initial velocity, IMU biases, and orientation.

  • D. Continuous-Time Motion Correction with Joint Prior: DLIO uses a constant jerk and angular acceleration model to compute a unique transform for each point through coarse-to-fine propagation.The approach avoids assuming constant velocity during a sweep.
  • D. Continuous-Time Motion Correction with Joint Prior: Each point receives a unique deskewing transform obtained from closed-form motion equations initialized at the closest preceding IMU measurement.The equations are parameterized only by time, allowing transforms to be queried at arbitrary timestamps.
  • D. Continuous-Time Motion Correction with Joint Prior: The trajectory is first constructed by numerical IMU integration, then refined with analytical continuous-time equations for each point.The analytical solution begins from the nearest preceding IMU transformation.
  • D. Continuous-Time Motion Correction with Joint Prior: The two-step procedure produces a motion-corrected cloud approximately aligned with the map and inherently incorporates the GICP optimization prior.This combines motion correction and prior generation before registration.
  • D. Continuous-Time Motion Correction with Joint Prior: Reliable motion correction depends on accurate initial velocity, estimated IMU biases, and initial body orientation, supplied through the observer's guaranteed global convergence.Accurate scan matching is also required for this reliability guarantee.

E. Scan-to-Map Registration

DLIO registers motion-corrected scans directly to an extracted submap using GICP, optimizing a correction transform over corresponding points and planes. This scan-to-map design uses the prior-transformed cloud and bypasses scan-to-scan registration.

  • E. Scan-to-Map Registration: DLIO directly registers the corrected cloud to an extracted keyframe-based submap by optimizing a transformation that improves alignment.The optimized transform is used for global pose refinement, map construction, and observer updating.
  • E. Scan-to-Map Registration: By combining motion correction with GICP prior generation, DLIO bypasses the scan-to-scan procedure used in previous methods.The architecture therefore performs direct scan-to-map registration.
  • E. Scan-to-Map Registration: The scan-to-map objective minimizes GICP residual error across corresponding points and planes.The formulation uses covariance matrices for corresponding points and the submap.
  • E. Scan-to-Map Registration: The resulting correction transform globally aligns the prior-transformed scan to the submap.The prior is incorporated before the final scan-to-map correction.

F. Geometric Observer

DLIO uses a hierarchical nonlinear geometric observer to fuse scan-to-map alignment with IMU measurements and produce full state estimates. Its convergence properties support direct scan-to-map registration without scan-to-scan alignment.

  • The observer fuses scan-to-map alignment W k with IMU measurements to generate the full state estimate ˆXk.
  • The observer’s quaternion estimate converges exponentially near the true orientation, after which a contracting observer estimates translation states.
  • The hierarchical nonlinear update decouples attitude correction from translation correction and enables scan-to-map registration using only an IMU prior.

IV. RESULTS

DLIO was evaluated on Newer College and self-collected UCLA Campus data against four state-of-the-art odometry algorithms. The experiments compare localization accuracy and computational efficiency under differing motion-compensation strategies.

  • DLIO was evaluated on the Newer College benchmark and self-collected UCLA Campus datasets.
  • Accuracy and efficiency were compared against DLO, CT-ICP, LIO-SAM, and FAST-LIO2.
  • The comparison covers algorithms using different degrees and methods of motion compensation.

A. Ablation Study and Comparison of Motion Correction

An ablation study shows that increasingly complete deskewing improves DLIO’s tracking accuracy, especially during aggressive motion. Continuous-time correction produces more representative point clouds and preserves fine map detail.

  • On the Dynamic dataset, with rotational speeds up to 3.5 rad/s, no correction produced 0.1959 RMSE, while continuous correction reduced error to 0.0612 RMSE.
  • The ablation compares None, Discrete nearest-IMU integration, and Continuous correction using both equations (4) and (5).
  • More accurate motion correction improves scan-matching inputs by creating more authentic point clouds, which improves trajectory accuracy.
  • DLIO captures minute environmental detail that simple or absent motion correction loses during aggressive maneuvers.

1) Newer College Dataset:

On the original Newer College benchmark, DLIO achieved the lowest trajectory RMSE and lowest average per-scan computational time across five datasets. Its low trajectory error persisted over more than three kilometers in the Long Experiment.

  • DLIO produced the lowest trajectory RMSE across the five Newer College datasets.
  • DLIO also achieved the lowest overall average per-scan computational time among the compared state-of-the-art algorithms.
  • In the Long Experiment, DLIO maintained low trajectory error relative to ground truth after more than three kilometers of travel.

2) UCLA Campus Dataset:

The UCLA evaluation used four large-scale hand-carried aerial-platform datasets totaling 2261.37 m, with an Ouster OS1 LiDAR and an approximately $10 IMU. Without ground truth, end-to-end translational error served as a proxy, and DLIO outperformed the alternatives in both error and per-scan efficiency while producing detailed maps.

  • Dataset and evaluation: Four UCLA datasets covered 2261.37 m of hand-carried aerial-platform trajectories for additional comparison.The datasets used an Ouster OS1 LiDAR and a 6-axis InvenSense MPU-6050 IMU.
  • Dataset and evaluation: Absolute trajectory error was unavailable because the datasets lacked ground truth, so end-to-end translational error was used as a proxy metric.
  • Results: DLIO outperformed all compared methods in both end-to-end translational error and per-scan efficiency.
  • Results: DLIO produced maps that captured fine environmental detail and provided more intricate information cues for terrain traversability.
  • Results: The results support DLIO as a real-time LIO algorithm for resource-constrained mobile robots, with accurate state estimates and detailed maps.
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