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Robust Second-order LiDAR Bundle Adjustment Algorithm Using Mean Squared Group Metric

Tingchen Ma, Yongsheng Ou, Sheng Xu

TL;DR

This work addresses robust LiDAR bundle adjustment in SLAM back-ends by introducing the mean square group metric (MSGM), which provides a scale-interpretable, mean-square-based objective for plane landmarks. By embedding a robust kernel, the method reweights measurements to improve robustness, and an explicit second-order estimator (RSO-BA) with analytical Hessian and gradient enables precise optimization. The approach is integrated into a loosely coupled front-end/back-end system with a sliding window and a Hash Adaptive Voxel map, and validated on structured and unstructured public datasets where it outperforms state-of-the-art methods in registration accuracy and map quality, especially in large-scale or complex scenes. The findings highlight the potential for robust LiDAR BA in diverse environments and point toward future multi-sensor fusion to further boost performance.

Abstract

The bundle adjustment (BA) algorithm is a widely used nonlinear optimization technique in the backend of Simultaneous Localization and Mapping (SLAM) systems. By leveraging the co-view relationships of landmarks from multiple perspectives, the BA method constructs a joint estimation model for both poses and landmarks, enabling the system to generate refined maps and reduce front-end localization errors. However, there are unique challenges when applying the BA for LiDAR data, due to the large volume of 3D points. Exploring a robust LiDAR BA estimator and achieving accurate solutions is a very important issue. In this work, firstly we propose a novel mean square group metric (MSGM) to build the optimization objective in the LiDAR BA algorithm. This metric applies mean square transformation to uniformly process the measurement of plane landmarks from one sampling period. The transformed metric ensures scale interpretability, and does not requie a time-consuming point-by-point calculation. Secondly, by integrating a robust kernel function, the metrics involved in the BA algorithm are reweighted, and thus enhancing the robustness of the solution process. Thirdly, based on the proposed robust LiDAR BA model, we derived an explicit second-order estimator (RSO-BA). This estimator employs analytical formulas for Hessian and gradient calculations, ensuring the precision of the BA solution. Finally, we verify the merits of the proposed RSO-BA estimator against existing implicit second-order and explicit approximate second-order estimators using the publicly available datasets. The experimental results demonstrate that the RSO-BA estimator outperforms its counterparts regarding registration accuracy and robustness, particularly in large-scale or complex unstructured environments.

Robust Second-order LiDAR Bundle Adjustment Algorithm Using Mean Squared Group Metric

TL;DR

This work addresses robust LiDAR bundle adjustment in SLAM back-ends by introducing the mean square group metric (MSGM), which provides a scale-interpretable, mean-square-based objective for plane landmarks. By embedding a robust kernel, the method reweights measurements to improve robustness, and an explicit second-order estimator (RSO-BA) with analytical Hessian and gradient enables precise optimization. The approach is integrated into a loosely coupled front-end/back-end system with a sliding window and a Hash Adaptive Voxel map, and validated on structured and unstructured public datasets where it outperforms state-of-the-art methods in registration accuracy and map quality, especially in large-scale or complex scenes. The findings highlight the potential for robust LiDAR BA in diverse environments and point toward future multi-sensor fusion to further boost performance.

Abstract

The bundle adjustment (BA) algorithm is a widely used nonlinear optimization technique in the backend of Simultaneous Localization and Mapping (SLAM) systems. By leveraging the co-view relationships of landmarks from multiple perspectives, the BA method constructs a joint estimation model for both poses and landmarks, enabling the system to generate refined maps and reduce front-end localization errors. However, there are unique challenges when applying the BA for LiDAR data, due to the large volume of 3D points. Exploring a robust LiDAR BA estimator and achieving accurate solutions is a very important issue. In this work, firstly we propose a novel mean square group metric (MSGM) to build the optimization objective in the LiDAR BA algorithm. This metric applies mean square transformation to uniformly process the measurement of plane landmarks from one sampling period. The transformed metric ensures scale interpretability, and does not requie a time-consuming point-by-point calculation. Secondly, by integrating a robust kernel function, the metrics involved in the BA algorithm are reweighted, and thus enhancing the robustness of the solution process. Thirdly, based on the proposed robust LiDAR BA model, we derived an explicit second-order estimator (RSO-BA). This estimator employs analytical formulas for Hessian and gradient calculations, ensuring the precision of the BA solution. Finally, we verify the merits of the proposed RSO-BA estimator against existing implicit second-order and explicit approximate second-order estimators using the publicly available datasets. The experimental results demonstrate that the RSO-BA estimator outperforms its counterparts regarding registration accuracy and robustness, particularly in large-scale or complex unstructured environments.
Paper Structure (16 sections, 30 equations, 3 figures, 4 tables)

This paper contains 16 sections, 30 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Point Cloud Registration
  4. Bundle Adjustment
  5. Method
  6. Problem Formulation
  7. Mean Square Group Metric and Robust LiDAR BA Model
  8. Explicit Second-order Estimator
  9. Integrated System
  10. Front End
  11. Back End
  12. Experiment
  13. Experimental Setup
  14. Structured Scene Experiment
  15. Unstructured Scene Experiment
  16. ...and 1 more sections

Figures (3)

  • Figure 1: System flowchart. The green box represents the proposed explicit second-order BA estimator.
  • Figure 2: The running trajectories of different BA algorithms under UrbanNav Mongkok sequence. The accuracy of PA is much lower than that of RSO-BA and BALM2. BALM2 experienced severe trajectory drift at the location marked by the red star..
  • Figure 3: Single iteration of different BA algorithms.