L2Calib: $SE(3)$-Manifold Reinforcement Learning for Robust Extrinsic Calibration with Degenerate Motion Resilience

-- Extrinsic calibration is essential for multi-sensor fusion, existing methods rely on structured targets or fully-excited data, limiting real-world applicability. Online calibration further suffers from weak excitation, leading to unreliable estimates. T o address these limitations, we propose a reinforcement learning (RL)-based extrinsic calibration framework that formulates extrinsic calibration as a decision-making problem, directly optimizes SE (3) extrinsics to enhance odometry accuracy. Our approach leverages a probabilistic Bingham distribution to model 3D rotations, ensuring stable optimization while inherently retaining quaternion symmetry. A trajectory alignment reward mechanism enables robust calibration without structured targets by quantitatively evaluating estimated tightly-coupled trajectory against a reference trajectory. Additionally, an automated data selection module filters uninformative samples, significantly improving efficiency and scalability for large-scale datasets. Extensive experiments on UA Vs, UGVs, and handheld platforms demonstrate that our method outperforms traditional optimization-based approaches, achieving high-precision calibration even under weak excitation conditions. The code is available at https://github.com/