DCReg: Decoupled Characterization for Efficient Degenerate LiDAR Registration

arXiv cs.RO / 4/1/2026

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Key Points

DCReg (Decoupled Characterization for Ill-conditioned Registration) proposes a detect–characterize–mitigate framework to stabilize LiDAR point cloud registration in geometrically degenerate settings like corridors where solutions become ill-conditioned.
It detects ill-conditioning reliably by applying Schur complement decomposition to the Hessian, decoupling 6-DoF motion into interpretable 3-DoF rotational and translational subspaces and reducing masking from full-Hessian coupling.
DCReg characterizes the degeneracy by resolving eigen-basis ambiguities through basis alignment, yielding stable mappings from eigenspaces to physical motion directions and quantifying which motions are weakly constrained.
It mitigates instability with a structured preconditioner that uses MAP-inspired eigenvalue clamping only inside the preconditioner, preserving the original least-squares objective and minimizer while enabling faster optimization via Preconditioned Conjugate Gradient.
Experiments report 20–50% better long-duration localization accuracy and large speedups (5–30x, up to 116x) versus degeneracy-aware baselines, and the authors provide code on GitHub.

Abstract

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