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. 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.

Monocular Event-Inertial Odometry with Adaptive decay-based Time Surface and Polarity-aware Tracking

Event cameras have garnered considerable attention due to their advantages over traditional cameras in low power consumption, high dynamic range, and no motion blur. This paper proposes a monocular event-inertial odometry incorporating an adaptive decay kernel-based time surface with polarity-aware tracking. We utilize an adaptive decay-based Time Surface to extract texture information from asynchronous events, which adapts to the dynamic characteristics of the event stream and enhances the representation of environmental textures. However, polarity-weighted time surfaces suffer from event polarity shifts during changes in motion direction. To mitigate its adverse effects on feature tracking, we optimize the feature tracking by incorporating an additional polarity-inverted time surface to enhance the robustness. Comparative analysis with visual-inertial and event-inertial odometry methods shows that our approach outperforms state-of-the-art techniques, with competitive results across various datasets.

Gaussian-LIC: Photo-realistic LiDAR-Inertial-Camera SLAM with 3D Gaussian Splatting

We present a real-time LiDAR-Inertial-Camera SLAM system with 3D Gaussian Splatting as the mapping backend. Leveraging robust pose estimates from our LiDAR-Inertial-Camera odometry, Coco-LIC, an incremental photo-realistic mapping system is proposed in this paper. We initialize 3D Gaussians from colorized LiDAR points and optimize them using differentiable rendering powered by 3D Gaussian Splatting. Meticulously designed strategies are employed to incrementally expand the Gaussian map and adaptively control its density, ensuring high-quality mapping with real-time capability. Experiments conducted in diverse scenarios demonstrate the superior performance of our method compared to existing radiance-field-based SLAM systems.

Coco-LIC: Continuous-Time Tightly-Coupled LiDAR-Inertial-Camera Odometry using Non-Uniform B-spline

In this paper, we propose an efficient continuous-time LiDAR-Inertial-Camera Odometry, utilizing non-uniform B-splines to tightly couple measurements from the LiDAR, IMU, and camera. In contrast to uniform B-spline-based continuous-time methods, our non-uniform B-spline approach offers significant advantages in terms of achieving real-time efficiency and high accuracy. This is accomplished by dynamically and adaptively placing control points, taking into account the varying dynamics of the motion. To enable efficient fusion of heterogeneous LiDAR-Inertial-Camera data within a short sliding-window optimization, we assign depth to visual pixels using corresponding map points from a global LiDAR map, and formulate frame-to-map reprojection factors for the associated pixels in the current image frame. This way circumvents the necessity for depth optimization of visual pixels, which typically entails a lengthy sliding window with numerous control points for continuous-time trajectory estimation. We conduct dedicated experiments on real-world datasets to demonstrate the advantage and efficacy of adopting non-uniform continuous-time trajectory representation. Our LiDAR-Inertial-Camera odometry system is also extensively evaluated on both challenging scenarios with sensor degenerations and large-scale scenarios, and has shown comparable or higher accuracy than the state-of-the-art methods. The codebase of this paper will also be open-sourced at https://github.com/APRIL-ZJU/Coco-LIC.

Correlation Pyramid Network for 3D Single Object Tracking

3D LiDAR-based single object tracking (SOT) has gained increasing attention as it plays a crucial role in 3D applications such as autonomous driving. The central problem is how to learn a target-aware representation from the sparse and incomplete point clouds. In this paper, we propose a novel Correlation Pyramid Network (CorpNet) with a unified encoder and a motion-factorized decoder. Specifically, the encoder introduces multi-level self attentions and cross attentions in its main branch to enrich the template and search region features and realize their fusion and interaction, respectively. Additionally, considering the sparsity characteristics of the point clouds, we design a lateral correlation pyramid structure for the encoder to keep as many points as possible by integrating hierarchical correlated features. The output features of the search region from the encoder can be directly fed into the decoder for predicting target locations without any extra matcher. Moreover, in the decoder of CorpNet, we design a motion-factorized head to explicitly learn the different movement patterns of the up axis and the x-y plane together. Extensive experiments on two commonly-used datasets show our CorpNet achieves state-of-the-art results while running in real-time.

Continuous-Time Fixed-Lag Smoothing for LiDAR-Inertial-Camera SLAM

Localization and mapping with heterogeneous multi-sensor fusion have been prevalent in recent years. To adequately fuse multi-modal sensor measurements received at different time instants and different frequencies, we estimate the continuous-time trajectory by fixed-lag smoothing within a factor-graph optimization framework. With the continuous-time formulation, we can query poses at any time instants corresponding to the sensor measurements. To bound the computation complexity of the continuous-time fixed-lag smoother, we maintain temporal and keyframe sliding windows with constant size, and probabilistically marginalize out control points of the trajectory and other states, which allows preserving prior information for future sliding-window optimization. Based on continuous-time fixed-lag smoothing, we design tightly-coupled multi-modal SLAM algorithms with a variety of sensor combinations, like the LiDAR-inertial and LiDAR-inertial-camera SLAM systems, in which online timeoffset calibration is also naturally supported. More importantly, benefiting from the marginalization and our derived analytical Jacobians for optimization, the proposed continuous-time SLAM systems can achieve real-time performance regardless of the high complexity of continuous-time formulation. The proposed multi-modal SLAM systems have been widely evaluated on three public datasets and self-collect datasets. The results demonstrate that the proposed continuous-time SLAM systems can achieve high-accuracy pose estimations and outperform existing state-of-the-art methods. To benefit the research community, we will open source our code at ~\url{https://github.com/APRIL-ZJU/clic}.

Ctrl-VIO: Continuous-Time Visual-Inertial Odometry for Rolling Shutter Cameras

In this paper, we propose a probabilistic continuous-time visual-inertial odometry (VIO) for rolling shutter cameras. The continuous-time trajectory formulation naturally facilitates the fusion of asynchronized high-frequency IMU data and motion-distorted rolling shutter images. To prevent intractable computation load, the proposed VIO is sliding-window and keyframe-based. We propose to probabilistically marginalize the control points to keep the constant number of keyframes in the sliding window. Furthermore, the line exposure time difference (line delay) of the rolling shutter camera can be online calibrated in our continuous-time VIO. To extensively examine the performance of our continuous-time VIO, experiments are conducted on publicly-available WHU-RSVI, TUM-RSVI, and SenseTime-RSVI rolling shutter datasets. The results demonstrate the proposed continuous-time VIO significantly outperforms the existing state-of-the-art VIO methods. The codebase of this paper will also be open-sourced at \url{https://github.com/APRIL-ZJU/Ctrl-VIO}.

Observability-Aware Intrinsic and Extrinsic Calibration of LiDAR-IMU Systems

Accurate and reliable sensor calibration is essential to fuse LiDAR and inertial measurements, which are usually available in robotic applications. In this paper, we propose a novel LiDAR-IMU calibration method within the continuous-time batch-optimization framework, where the intrinsics of both sensors and the spatial-temporal extrinsics between sensors are calibrated without using calibration infrastructure such as fiducial tags. Compared to discrete-time approaches, the continuous-time formulation has natural advantages for fusing high rate measurements from LiDAR and IMU sensors. To improve efficiency and address degenerate motions, two observability-aware modules are leveraged: (i) The information-theoretic data selection policy selects only the most informative segments for calibration during data collection, which significantly improves the calibration efficiency by processing only the selected informative segments. (ii) The observability-aware state update mechanism in nonlinear least-squares optimization updates only the identifiable directions in the state space with truncated singular value decomposition (TSVD), which enables accurate calibration results even under degenerate cases where informative data segments are not available. The proposed LiDAR-IMU calibration approach has been validated extensively in both simulated and real-world experiments with different robot platforms, demonstrating its high accuracy and repeatability in commonly-seen human-made environments. We also open source our codebase to benefit the research community: {\url{https://github.com/APRIL-ZJU/OA-LICalib}}.

CLINS: Continuous-Time Trajectory Estimation for LiDAR-Inertial System

In this paper, we propose a highly accurate continuous-time trajectory estimation framework dedicated to SLAM (Simultaneous Localization and Mapping) applications, which enables fuse high-frequency and asynchronous sensor data effectively. We apply the proposed framework in a 3D LiDAR-inertial system for evaluations. The proposed method adopts a non-rigid registration method for continuous-time trajectory estimation and simultaneously removing the motion distortion in LiDAR scans. Additionally, we propose a two-state continuous-time trajectory correction method to efficiently and efficiently tackle the computationally-intractable global optimization problem when loop closure happens. We examine the accuracy of the proposed approach on several publicly available datasets and the data we collected. The experimental results indicate that the proposed method outperforms the discrete-time methods regarding accuracy especially when aggressive motion occurs. Furthermore, we open source our code at \url{https://github.com/APRIL-ZJU/clins} to benefit research community.

LIC-Fusion 2.0: LiDAR-Inertial-Camera Odometry with Sliding-Window Plane-Feature Tracking

Multi-sensor fusion of multi-modal measurements from commodity inertial, visual and LiDAR sensors to provide robust and accurate 6DOF pose estimation holds great potential in robotics and beyond. In this paper, building upon our prior work (i.e., LIC-Fusion), we develop a sliding-window filter based LiDAR-Inertial-Camera odometry with online spatiotemporal calibration (i.e., LIC-Fusion 2.0), which introduces a novel sliding-window plane-feature tracking for efficiently processing 3D LiDAR point clouds. In particular, after motion compensation for LiDAR points by leveraging IMU data, low-curvature planar points are extracted and tracked across the sliding window. A novel outlier rejection criterion is proposed in the plane-feature tracking for high-quality data association. Only the tracked planar points belonging to the same plane will be used for plane initialization, which makes the plane extraction efficient and robust. Moreover, we perform the observability analysis for the LiDAR-IMU subsystem and report the degenerate cases for spatiotemporal calibration using plane features. While the estimation consistency and identified degenerate motions are validated in Monte-Carlo simulations, different real-world experiments are also conducted to show that the proposed LIC-Fusion 2.0 outperforms its predecessor and other state-of-the-art methods.