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DualQuat-LOAM: LiDAR Odometry and Mapping parametrized on Dual Quaternions

Edison P. Velasco-Sánchez, Luis F. Recalde, Guanrui Li, Francisco A. Candelas-Herias, Santiago T. Puente-Mendez, Fernando Torres-Medina

TL;DR

This work targets LiDAR odometry with minimal drift by parameterizing both motion and descriptors in dual quaternions, providing a compact and singularity-free $SE(3)$ representation. It integrates edge, surface, and STD descriptors within a unified dual-quaternion optimization framework, leveraging Plücker lines, planes, and unit dual quaternions to form three residuals solved in Ceres on a custom manifold. Empirical validation on KITTI shows competitive translation and rotation accuracy with real-time performance (~$53$ ms per pose), and additional evaluations on a robotics platform and public benchmarks illustrate robustness and limitations across diverse environments. The approach advances LiDAR-only odometry by enabling tight fusion of pose and local geometry through dual-quaternion algebra and STD-based descriptors, with clear pathways for extending to IMU integration and Jacobian-efficient optimization.

Abstract

This paper reports on a novel method for LiDAR odometry estimation, which completely parameterizes the system with dual quaternions. To accomplish this, the features derived from the point cloud, including edges, surfaces, and Stable Triangle Descriptor (STD), along with the optimization problem, are expressed in the dual quaternion set. This approach enables the direct combination of translation and orientation errors via dual quaternion operations, greatly enhancing pose estimation, as demonstrated in comparative experiments against other state-of-the-art methods. Our approach reduced drift error compared to other LiDAR-only-odometry methods, especially in scenarios with sharp curves and aggressive movements with large angular displacement. DualQuat-LOAM is benchmarked against several public datasets. In the KITTI dataset it has a translation and rotation error of 0.79% and 0.0039°/m, with an average run time of 53 ms.

DualQuat-LOAM: LiDAR Odometry and Mapping parametrized on Dual Quaternions

TL;DR

This work targets LiDAR odometry with minimal drift by parameterizing both motion and descriptors in dual quaternions, providing a compact and singularity-free representation. It integrates edge, surface, and STD descriptors within a unified dual-quaternion optimization framework, leveraging Plücker lines, planes, and unit dual quaternions to form three residuals solved in Ceres on a custom manifold. Empirical validation on KITTI shows competitive translation and rotation accuracy with real-time performance (~ ms per pose), and additional evaluations on a robotics platform and public benchmarks illustrate robustness and limitations across diverse environments. The approach advances LiDAR-only odometry by enabling tight fusion of pose and local geometry through dual-quaternion algebra and STD-based descriptors, with clear pathways for extending to IMU integration and Jacobian-efficient optimization.

Abstract

This paper reports on a novel method for LiDAR odometry estimation, which completely parameterizes the system with dual quaternions. To accomplish this, the features derived from the point cloud, including edges, surfaces, and Stable Triangle Descriptor (STD), along with the optimization problem, are expressed in the dual quaternion set. This approach enables the direct combination of translation and orientation errors via dual quaternion operations, greatly enhancing pose estimation, as demonstrated in comparative experiments against other state-of-the-art methods. Our approach reduced drift error compared to other LiDAR-only-odometry methods, especially in scenarios with sharp curves and aggressive movements with large angular displacement. DualQuat-LOAM is benchmarked against several public datasets. In the KITTI dataset it has a translation and rotation error of 0.79% and 0.0039°/m, with an average run time of 53 ms.

Paper Structure

This paper contains 27 sections, 14 equations, 15 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Mathematical Preliminaries
  3. Quaternions
  4. Dual Quaternions
  5. Point Cloud Feature Extraction
  6. Edges and Surfaces
  7. STD: Stable Triangle Descriptor
  8. Pose Estimation
  9. Dual-Quaternions Parametrization
  10. Plücker Lines
  11. Planes represented by dual quaternion
  12. STD descriptors represented by unit dual quaternions
  13. Residuals Computation
  14. Point-to-edge Cost Function
  15. Point-to-Plane Cost Function
  16. ...and 12 more sections

Figures (15)

  • Figure 1: Results of the proposed DualQuat-LOAM method on Sequence 01 of the KITTI dataset. In the lower left and upper right corner are shown the beginning and end of the sequence respectively, with their corresponding STD map.
  • Figure 2: System overview of our DualQuat-LOAM approach.
  • Figure 3: (a) The components of STD descriptor. (b) Reference frame of four STD descriptors detected in a point cloud. Each triangle has a unique reference system that does not vary with rigid transformations.
  • Figure 4: Elements extracted from the input point cloud parameterized as dual quaternions.
  • Figure 5: Illustrative representation of the dual quaternion Manifold$\mathcal{M}$ and its tangent plane $\mathcal{T}_{I}\mathcal{M}$
  • ...and 10 more figures