解决激光雷达在狭窄环境下的定位不稳问题，提升精度与速度。
DCReg: Decoupled Characterization for Efficient Degenerate LiDAR Registration
- 通过分解海森矩阵分离旋转与平移子空间，精准识别退化状态。
- 实现物理可解释的运动方向约束分析，定位弱约束方向。
- 仅用一个参数优化预条件器，显著提速且不破坏原始目标函数。
激光雷达点云配准是机器人感知与导航的基础。在几何退化环境（如走廊）中，配准变得病态：某些运动方向约束不足，导致解不稳定、精度下降。现有检测-缓解方法难以可靠检测、物理解释并稳定此类病态问题，且易破坏优化过程。本文提出DCReg（解耦表征用于病态配准），建立检测-表征-缓解范式，包含三项创新：首先，通过海森矩阵的舒尔补分解，将6自由度配准解耦为3自由度纯净的旋转与平移子空间，消除全海森分析中的耦合干扰，实现可靠退化检测；其次，在子空间内设计可解释的表征方法，通过基对齐解决特征基歧义，建立特征空间与物理运动方向的稳定映射，明确哪些运动缺乏约束及其程度；第三，基于该谱信息，设计针对性缓解策略：采用结构化预条件器，通过最大后验（MAP）正则化在预条件器中施加特征值钳制，而非修改原问题。该方法保留最小二乘目标函数与最优解，支持使用预条件共轭梯度法进行高效优化，仅需一个可解释参数。实验表明，DCReg在多样环境中相比退化感知基线，长期定位精度提升20%-50%，速度提升5-30倍（最高达116倍）。代码已开源。
原文摘要 · Abstract (English)
LiDAR point cloud registration is fundamental to robotic perception and navigation. In geometrically degenerate environments (e.g., corridors), registration becomes ill-conditioned: certain motion directions are weakly constrained, causing unstable solutions and degraded accuracy. Existing detect-then-mitigate methods fail to reliably detect, physically interpret, and stabilize this ill-conditioning without corrupting the optimization. We introduce DCReg (Decoupled Characterization for Ill-conditioned Registration), establishing a detect-characterize-mitigate paradigm that systematically addresses ill-conditioned registration via three innovations. First, DCReg achieves reliable ill-conditioning detection by employing Schur complement decomposition on the Hessian matrix. This decouples the 6-DoF registration into 3-DoF clean rotational and translational subspaces, eliminating coupling effects that mask degeneracy in full-Hessian analyses. Second, within these subspaces, we develop interpretable characterization techniques resolving eigen-basis ambiguities via basis alignment. This establishes stable mappings between eigenspaces and physical motion directions, providing actionable insights on which motions lack constraints and to what extent. Third, leveraging this spectral information, we design a targeted mitigation via a structured preconditioner. Guided by MAP regularization, we implement eigenvalue clamping exclusively within the preconditioner rather than modifying the original problem. This preserves the least-squares objective and minimizer, enabling efficient optimization via Preconditioned Conjugate Gradient with a single interpretable parameter. Experiments demonstrate DCReg achieves 20-50% higher long-duration localization accuracy and 5-30x speedups (up to 116x) over degeneracy-aware baselines across diverse environments. Code: https://github.com/JokerJohn/DCReg
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