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MULLS: Versatile LiDAR SLAM via Multi-metric Linear Least Square

Yue Pan, Pengchuan Xiao, Yujie He, Zhenlei Shao, Zesong Li

arXiv:2102.03771v3cs.ROcs.CV

TL;DR

MULLS targets LiDAR SLAM systems that must work across different sensor specifications and complex scenes, where sensor-dependent representations limit versatility. It combines multi-class feature extraction, multi-metric linear least square ICP, and submap pose-graph optimization with loop closures. Experiments across more than 100,000 frames from seven LiDAR types report real-time performance, low drift, and high map quality across varied outdoor and indoor scenarios.

  • Problem

    LiDAR SLAM methods often rely on sensor-dependent point-cloud representations and ad-hoc scene-specific frameworks, limiting versatility across LiDAR specifications and challenging environments.

  • Method

    MULLS extracts roughly classified geometric features, jointly optimizes plane and line error metrics with linear least square ICP, and applies submap-based pose graph optimization with map-to-map loop closures.

  • Results

    More than 100,000 frames from seven LiDARs show real-time performance, low drift, and high map quality across challenging outdoor and indoor scenarios.

  • Takeaways & Limitations

    MULLS provides a scan-line-independent LiDAR-only SLAM solution reported to operate in real time across varied scenarios and rank among the top LiDAR-only systems on KITTI.

Abstract

from arXiv · show

The rapid development of autonomous driving and mobile mapping calls for off-the-shelf LiDAR SLAM solutions that are adaptive to LiDARs of different specifications on various complex scenarios. To this end, we propose MULLS, an efficient, low-drift, and versatile 3D LiDAR SLAM system. For the front-end, roughly classified feature points (ground, facade, pillar, beam, etc.) are extracted from each frame using dual-threshold ground filtering and principal components analysis. Then the registration between the current frame and the local submap is accomplished efficiently by the proposed multi-metric linear least square iterative closest point algorithm. Point-to-point (plane, line) error metrics within each point class are jointly optimized with a linear approximation to estimate the ego-motion. Static feature points of the registered frame are appended into the local map to keep it updated. For the back-end, hierarchical pose graph optimization is conducted among regularly stored history submaps to reduce the drift resulting from dead reckoning. Extensive experiments are carried out on three datasets with more than 100,000 frames collected by seven types of LiDAR on various outdoor and indoor scenarios. On the KITTI benchmark, MULLS ranks among the top LiDAR-only SLAM systems with real-time performance.

I. INTRODUCTION

MULLS addresses the limited versatility of LiDAR SLAM systems by using scan-line-independent representations and multi-class geometric features. Its MULLS-ICP front end and submap-based back end target adaptable, low-drift, real-time operation across varied scenarios.

  • Motivation: Existing LiDAR SLAM methods often depend on ring or range-image representations requiring detailed sensor parameters, limiting adaptation to newer LiDAR configurations.These approaches are difficult to transfer directly to mechanical LiDARs with unique beam configurations and solid-state LiDARs with limited fields of view.
  • Motivation: Ad-hoc LiDAR SLAM frameworks for specific environments can become stuck in degenerate cases or during rapid scene changes.
  • Proposed system: MULLS processes 3D coordinates without converting them into rings or range images, making the system independent of LiDAR specifications while preserving 3D structure.
  • Proposed system: MULLS extracts geometric feature categories including ground, facade, pillar, beam, and roof, then estimates ego-motion with multi-metric linear least square ICP.
  • Proposed system: Submap-based pose graph optimization uses map-to-map global registration to construct loop-closure constraints for reducing accumulated drift.
  • Reported positioning: MULLS is presented as a scan-line-independent LiDAR-only SLAM solution with low drift, real-time performance, and a top-10 KITTI benchmark ranking.

III. METHODOLOGY

The method uses point timestamps to compute each point’s relative acquisition time and transform points to a common frame-end time. Without an IMU, this deskewing relies on uniform-motion interpolation.

  • Motion compensation: For point p_i with timestamp τ_i, the time ratio s_i is computed relative to the frame start and end timestamps τ_b and τ_e.
  • Motion compensation: When no IMU is available, the point transformation to the frame-end pose is computed under a uniform-motion assumption.
  • Motion compensation: Spherical linear interpolation and estimated rotation and translation across the frame are used to obtain each transformed point.
  • Motion compensation: The undistorted point cloud is formed by collecting all transformed points at the end of the frame.

B. Geometric feature points extraction and encoding

MULLS extracts and encodes geometric feature points through dual-threshold ground filtering, PCA-based nonground classification, refinement, and neighborhood context encoding. The resulting multi-class features support registration and global localization.

  • Pipeline overview: Raw frame point clouds are processed into six feature-point types with associated primary and normal vectors.
  • Ground filtering: Dual-threshold ground filtering uses grid-wise minimum heights and neighboring-grid heights to separate roughly determined ground and nonground points.
  • Ground filtering: RANSAC refines ground points by fitting a plane in each grid, retaining inliers and assigning them the fitted plane’s surface normal.
  • Nonground classification: PCA classifies downsampled nonground neighborhoods using covariance eigenvalues and eigenvectors to derive linearity, planarity, and curvature.
  • Nonground classification: Feature points are assigned to facade, roof, pillar, beam, or vertex categories, then refined with category-specific non-maximum suppression and isotropic downsampling.
  • Context encoding: Neighborhood category context encodes neighborhood category proportions, normalized intensity, and height above ground for vertex keypoints used in back-end global registration.

C. Multi-metric linear least square ICP

MULLS-ICP registers multi-class feature points by jointly optimizing point-to-point, point-to-plane, and point-to-line errors in a weighted linear least-squares framework. A tiny-angle approximation converts transformation estimation into a six-parameter Gauss–Markov problem, with robust and adaptive correspondence weighting.

  • Multi-class closest point association: MULLS-ICP associates nearest neighbors within each feature category while checking distance and direction consistency for planar and linear features.The categories are ground, facade, roof, pillar, beam, and vertex points; the distance threshold decreases across iterations.
  • Multi-metric transformation estimation: The transformation jointly minimizes point-to-point, point-to-plane, and point-to-line distances for vertex, planar, and linear correspondences.The three metrics are applied to vertex V, planar G/F/R, and linear P/B feature classes.
  • Multi-metric transformation estimation: Under the tiny-angle assumption, the unknown vector ξ = [t_x t_y t_z α β γ]^T yields a weighted linear least-square problem solved by Gauss–Markov estimation.α, β, and γ denote roll, pitch, and yaw under the stated Euler-angle convention.
  • Multi-metric transformation estimation: The design matrix A and observation vector b collect correspondence-wise components, while ATPA and ATPb can be accumulated in parallel.The estimated vector is used to reconstruct the transformation matrix.
  • Multi-strategy weighting function: A multi-strategy weighting function combines residual robustness, balanced directional contribution, and intensity consistency.The residual component fixes κ = 1, producing a pseudo-Huber kernel with normalized residuals and an inlier noise threshold.
  • Multi-index registration quality evaluation: After ICP convergence, posterior standard deviation, an information matrix, and nonground overlap evaluate registration quality.The final transformation estimate and its accuracy indexes are produced by the iterative procedure.

D. MULLS front-end

The MULLS front-end combines feature extraction, MULLS-ICP registration, and local-map management. It first performs scan-to-scan alignment for initialization, then refines scan-to-map alignment against a maintained map of historical static features.

  • Front-end: The front-end extracts and downsamples roughly classified feature points while maintaining a local map of static features from historical frames.The front-end combines feature processing, registration, and map management.
  • Front-end: Scan-to-scan MULLS-ICP uses the previous frame’s ego-motion as an initial guess and runs for only a few iterations.It operates between sparser current-frame features and denser features from the last frame.
  • Front-end: The scan-to-scan estimate initializes scan-to-map MULLS-ICP, which iterates against local-map features until convergence.The local map is the target point cloud for the refinement stage.

E. MULLS back-end

MULLS organizes periodically saved submaps into a hierarchical pose graph, using global registration and refined MULLS-ICP edges to support loop-closure correction. The KITTI visualizations show urban loop-closure areas and highway trajectory behavior, including lane-level final drift in a challenging sequence.

  • E. MULLS back-end: Periodically saved submaps serve as processing units for constructing adjacent and loop-closure pose-graph edges.
  • E. MULLS back-end: TEASER initializes inter-submap correspondences, while map-to-map MULLS-ICP refines transformations and information matrices before edge verification.
  • E. MULLS back-end: Hierarchical pose-graph optimization corrects free submap poses after loop closure and adjusts frame poses within each submap.
  • E. MULLS back-end: KITTI seq.00 visualizes the urban map, detailed loop-closure areas, and trajectory comparison.
  • E. MULLS back-end: KITTI seq.01 includes a challenging high-similarity, few-feature scene and shows only lane-level final drift on the highway sequence.

IV. EXPERIMENTS

The experiments evaluate MULLS qualitatively and quantitatively across three datasets, varied indoor and outdoor scenes, and seven LiDAR types using a common PC platform.

  • IV. EXPERIMENTS: MULLS is evaluated on KITTI, MIMAP, and HESAI across various outdoor and indoor scenes using seven different types of LiDAR.
  • IV. EXPERIMENTS: All experiments use a PC equipped with an Intel Core i7-7700HQ@2.80GHz CPU for fair comparison.

A. Quantitative experiment

Quantitative evaluations report KITTI localization accuracy, indoor mapping error, qualitative HESAI map consistency, and registration-variant trade-offs. MULLS achieves strong KITTI odometry and angular accuracy while allowing fewer iterations for faster operation.

  • A. Quantitative experiment: 0.49% ATE is achieved by MULLS-LO on KITTI seq. 00-10, the best result among the reported methods.
  • A. Quantitative experiment: 0.13°/100m ARE is achieved by MULLS-SLAM with loop closure and pose-graph optimization, although its ATE is worse.
  • A. Quantitative experiment: 6.7cm mean mapping error is obtained on MIMAP by comparing the MULLS map with TLS point clouds.
  • A. Quantitative experiment: HESAI results cover consistent maps from four mechanical LiDARs across indoor and outdoor scenes without provided ground-truth pose or map.
  • A. Quantitative experiment: Five scan-to-map iterations yield about 0.6% ATE, close to converged MULLS performance, enabling a small accuracy sacrifice for faster operation.

B. Qualitative experiments

The experiments combine quantitative KITTI evaluation with qualitative indoor and cross-LiDAR mapping assessments. Results include indoor TLS agreement, geometric-feature and weighting ablations, and adaptation across diverse LiDAR beam configurations.

  • B. Qualitative experiments: 6.7cm mean mapping error measures agreement between the MULLS indoor map and TLS point clouds on the five-floor MIMAP building.
  • B. Qualitative experiments: Table II reports KITTI quantitative evaluation and comparison using ATE and ARE, with smaller errors preferred.
  • B. Qualitative experiments: Table III presents an ablation study of MULLS geometric feature points.
  • B. Qualitative experiments: Weighting-function ablations on KITTI sequences 00 and 01 report ATE and ARE for balanced, residual, and intensity weighting components.
  • B. Qualitative experiments: HESAI qualitative maps assess adaptation to four mechanical LiDARs with different beam numbers and distributions in indoor and outdoor scenes.

C. Ablation studies

The ablations show that geometric feature categories and weighting functions materially affect MULLS performance across scene types. They also identify a boundary condition: tunnels offer too few structured features.

  • Vertex correspondences reduce LO accuracy because regular structures are more reliable than high-curvature vegetation points.Consequently, vertex points are reserved for keypoints in back-end global registration.
  • Linear points from pillars, beams, guardrails, and curbs are necessary for the best performance on highway scenes.These features impose cross-direction constraints.
  • MULLS may encounter problems in tunnels, where structured features are rare.
  • All three weighting functions improve performance on both evaluated sequences, including translation estimation on featureless highways when intensity consistency is considered.

D. Runtime analysis

MULLS maintains real-time operation across LiDAR datasets and point-count conditions, while loop-heavy sequences can temporarily increase processing time. Running loop closure on another thread preserves real-time performance on a moderate PC.

  • MULLS operates faster than 10Hz on average across four typical KITTI and HESAI sequences with different points per frame.
  • 0.2 ms per ICP iteration is required for transformation estimation with approximately 2k source and 20k target feature points.
  • Loop-heavy sequences can exceed 100 ms, but loop closure can run on another thread to preserve real-time performance on a moderate PC.
  • Experiments covering more than 100,000 frames from seven LiDAR types report real-time performance with low drift and high map quality across challenging outdoor and indoor scenarios.
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