DCReg：解耦表徵法實現高效退化LiDAR點雲配准

摘要

LiDAR点云配准是机器人感知与导航的基础。然而，在几何退化或狭窄的环境中，配准问题会变得病态，导致解的不稳定和精度下降。尽管现有方法尝试处理这些问题，但未能解决核心挑战：准确检测、解释并解决这种病态性，从而导致漏检或解的质量受损。在本研究中，我们提出了DCReg，一个通过三项集成创新系统性地解决病态配准问题的原则性框架。首先，DCReg通过采用Schur补分解对Hessian矩阵进行处理，实现了可靠的病态性检测。该技术将配准问题解耦为干净的旋转和平移子空间，消除了传统分析中掩盖退化模式的耦合效应。其次，在这些干净的子空间内，我们开发了定量表征技术，建立了数学特征空间与物理运动方向之间的明确映射，为哪些具体运动缺乏约束提供了可操作的见解。最后，利用这一干净的子空间，我们设计了一种有针对性的缓解策略：一种新颖的预处理器，它选择性地仅稳定已识别的病态方向，同时保留可观测空间中所有良好约束的信息。这使得通过具有单一物理可解释参数的预条件共轭梯度法实现高效且鲁棒的优化成为可能。大量实验表明，DCReg在多种环境下的定位精度比现有最先进方法提高了至少20%至50%，速度提升了5至100倍。我们的实现将发布于https://github.com/JokerJohn/DCReg。

English

LiDAR point cloud registration is fundamental to robotic perception and navigation. However, in geometrically degenerate or narrow environments, registration problems become ill-conditioned, leading to unstable solutions and degraded accuracy. While existing approaches attempt to handle these issues, they fail to address the core challenge: accurately detection, interpret, and resolve this ill-conditioning, leading to missed detections or corrupted solutions. In this study, we introduce DCReg, a principled framework that systematically addresses the ill-conditioned registration problems through three integrated innovations. First, DCReg achieves reliable ill-conditioning detection by employing a Schur complement decomposition to the hessian matrix. This technique decouples the registration problem into clean rotational and translational subspaces, eliminating coupling effects that mask degeneracy patterns in conventional analyses. Second, within these cleanly subspaces, we develop quantitative characterization techniques that establish explicit mappings between mathematical eigenspaces and physical motion directions, providing actionable insights about which specific motions lack constraints. Finally, leveraging this clean subspace, we design a targeted mitigation strategy: a novel preconditioner that selectively stabilizes only the identified ill-conditioned directions while preserving all well-constrained information in observable space. This enables efficient and robust optimization via the Preconditioned Conjugate Gradient method with a single physical interpretable parameter. Extensive experiments demonstrate DCReg achieves at least 20% - 50% improvement in localization accuracy and 5-100 times speedup over state-of-the-art methods across diverse environments. Our implementation will be available at https://github.com/JokerJohn/DCReg.

DCReg：解耦表徵法實現高效退化LiDAR點雲配准

DCReg: Decoupled Characterization for Efficient Degenerate LiDAR Registration

摘要

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