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

arXiv: https://arxiv.org/abs/2508.06330 · HTML: https://mlsanity.com/paper/2508.06330/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for robot navigation and UAV control, one of 15 directions in Deep reinforcement learning methods.
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 8 Aug 2025.

## Placed in

- Deep reinforcement learning methods / [RL for robot navigation and UAV control](https://mlsanity.com/deeprl/rl-for-robot-navigation-and-uav-control/)

## Builds on (most cited first, 13 of 13)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [FAST-LIO2: Fast Direct LiDAR-inertial Odometry](https://mlsanity.com/paper/2107.06829/) (2021)
- [NTU VIRAL: A Visual-Inertial-Ranging-Lidar Dataset, From an Aerial Vehicle Viewpoint](https://mlsanity.com/paper/2202.00379/) (2022)
- [MCD: Diverse Large-Scale Multi-Campus Dataset for Robot Perception](https://mlsanity.com/paper/2403.11496/) (2024)
- [Reinforcement Learning Meets Visual Odometry](https://mlsanity.com/paper/2407.15626/) (2024)
- [Bingham Policy Parameterization for 3D Rotations in Reinforcement Learning](https://mlsanity.com/paper/2202.03957/) (2022)
- [Targetless Calibration of LiDAR-IMU System Based on Continuous-time Batch Estimation](https://mlsanity.com/paper/2007.14759/) (2020)
- [Robust Real-time LiDAR-inertial Initialization](https://mlsanity.com/paper/2202.11006/) (2022)
- [Observability-Aware Intrinsic and Extrinsic Calibration of LiDAR-IMU Systems](https://mlsanity.com/paper/2205.03276/) (2022)
- [iKalibr: Unified Targetless Spatiotemporal Calibration for Resilient Integrated Inertial Systems](https://mlsanity.com/paper/2407.11420/) (2024)
- [Traj-LO: In Defense of LiDAR-Only Odometry Using an Effective Continuous-Time Trajectory](https://mlsanity.com/paper/2309.13842/) (2023)
- [LiDAR-Camera Calibration under Arbitrary Configurations: Observability and Methods](https://mlsanity.com/paper/1903.06141/) (2019)
- [GRIL-Calib: Targetless Ground Robot IMU-LiDAR Extrinsic Calibration Method using Ground Plane Motion Constraints](https://mlsanity.com/paper/2312.14035/) (2023)

## Abstract (arXiv)

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. To 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 UAVs, UGVs, and handheld platforms demonstrate that our method outperforms traditional optimization-based approaches, achieving high-precision calibration even under weak excitation conditions. Our framework simplifies deployment on diverse robotic platforms by eliminating the need for high-quality initial extrinsics and enabling calibration from routine operating data. The code is available at https://github.com/APRIL-ZJU/learn-to-calibrate.