A 4D Radar Camera Extrinsic Calibration Tool Based on 3D Uncertainty Perspective N Points
School of Automation and Intelligent Sensing, Institute of Medical Robotics, Shanghai Jiao Tong University（自动化与智能感知学院、医疗机器人研究院、上海交通大学）；Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240（系统控制与信息处理重点实验室、中华人民共和国教育部、上海200240）；Ruijin Hospital, Shanghai Jiao Tong University School of Medicine（瑞金医院、上海交通大学医学院）；Renji hospital, Shanghai Jiao Tong University School of Medicine（仁济医院、上海交通大学医学院）
Chuan Cao, Xiaoning Wang, Wenqian Xi, Han Zhang, Weidong Chen, Jingchuan Wang
4D imaging radar is a type of low-cost millimeter-wave radar(costing merely 10-20$\%$ of lidar systems) capable of providing range, azimuth, elevation, and Doppler velocity information. Accurate extrinsic calibration between millimeter-wave radar and camera systems is critical for robust multimodal perception in robotics, yet remains challenging due to inherent sensor noise characteristics and complex error propagation. This paper presents a systematic calibration framework to address critical challenges through a spatial 3d uncertainty-aware PnP algorithm (3DUPnP) that explicitly models spherical coordinate noise propagation in radar measurements, then compensating for non-zero error expectations during coordinate transformations. Finally, experimental validation demonstrates significant performance improvements over state-of-the-art CPnP baseline, including improved consistency in simulations and enhanced precision in physical experiments. This study provides a robust calibration solution for robotic systems equipped with millimeter-wave radar and cameras, tailored specifically for autonomous driving and robotic perception applications.
University of Toronto Institute for Aerospace Studies（多伦多大学航空航天研究所）；University of Zagreb Faculty of Electrical Engineering and Computing（萨格勒布大学电气工程与计算学院）；Vector Institute（Vector研究所）
Reliable operation in inclement weather is essential to the deployment of safe autonomous vehicles (AVs). Robustness and reliability can be achieved by fusing data from the standard AV sensor suite (i.e., lidars, cameras) with weather robust sensors, such as millimetre-wavelength radar. Critically, accurate sensor data fusion requires knowledge of the rigid-body transform between sensor pairs, which can be determined through the process of extrinsic calibration. A number of extrinsic calibration algorithms have been designed for 2D (planar) radar sensors - however, recently-developed, low-cost…
Accurate LiDAR-camera extrinsic calibration is a precondition for many multi-sensor systems in mobile robots. Most calibration methods rely on laborious manual operations and calibration targets. While working online, the calibration methods should be able to extract information from the environment to construct the cross-modal data association. Convolutional neural networks (CNNs) have powerful feature extraction ability and have been used for calibration. However, most of the past methods solve the extrinsic as a regression task, without considering the geometric constraints involved. In thi…
Accurate and reliable sensor calibration is critical for fusing LiDAR and inertial measurements in autonomous driving. This paper proposes a novel three-stage extrinsic calibration method between LiDAR and GNSS/INS for autonomous driving. The first stage can quickly calibrate the extrinsic parameters between the sensors through point cloud surface features so that the extrinsic can be narrowed from a large initial error to a small error range in little time. The second stage can further calibrate the extrinsic parameters based on LiDAR-mapping space occupancy while removing motion distortion. …
Sensor-based environmental perception is a crucial step for autonomous driving systems, for which an accurate calibration between multiple sensors plays a critical role. For the calibration of LiDAR and camera, the existing method is generally to calibrate the intrinsic of the camera first and then calibrate the extrinsic of the LiDAR and camera. If the camera's intrinsic is not calibrated correctly in the first stage, it isn't easy to calibrate the LiDAR-camera extrinsic accurately. Due to the complex internal structure of the camera and the lack of an effective quantitative evaluation method…
L2Calib: $SE(3)$-Manifold Reinforcement Learning for Robust Extrinsic Calibration with Degenerate Motion Resilience
Institute of Cyber-Systems and Control, Zhejiang University, China（浙江大学控制科学与工程学院）；State Key Laboratory of Industrial Control Technology, Zhejiang University, China（浙江大学工业控制技术状态重点实验室）；Zhejiang Guozi Robotics Technology Co., Ltd.（浙江国智机器人科技有限公司）
Accurate extrinsic sensor calibration is essential for both autonomous vehicles and robots. Traditionally this is an involved process requiring calibration targets, known fiducial markers and is generally performed in a lab. Moreover, even a small change in the sensor layout requires recalibration. With the anticipated arrival of consumer autonomous vehicles, there is demand for a system which can do this automatically, after deployment and without specialist human expertise. To solve these limitations, we propose a flexible framework which can estimate extrinsic parameters without an explicit…
Biomedical Research Institute of Malaga (IBIMA)（马拉加生物医学研究所（IBIMA））；University of Malaga（马拉加大学）
In order to fuse measurements from multiple sensors mounted on a mobile robot, it is needed to express them in a common reference system through their relative spatial transformations. In this paper, we present a method to estimate the full 6DoF extrinsic calibration parameters of multiple heterogeneous sensors (Lidars, Depth and RGB cameras) suitable for automatic execution on a mobile robot. Our method computes the 2D calibration parameters (x, y, yaw) through a motion-based approach, while for the remaining 3 parameters (z, pitch, roll) it requires the observation of the ground plane for a …
For an autonomous vehicle, the ability to sense its surroundings and to build an overall representation of the environment by fusing different sensor data streams is fundamental. To this end, the poses of all sensors need to be accurately determined. Traditional calibration methods are based on: 1) using targets specifically designed for calibration purposes in controlled environments, 2) optimizing a quality metric of the point clouds collected while traversing an unknown but static environment, or 3) optimizing the match among per-sensor incremental motion observations along a motion path fu…
As neuromorphic technology is maturing, its application to robotics and autonomous vehicle systems has become an area of active research. In particular, event cameras have emerged as a compelling alternative to frame-based cameras in low-power and latency-demanding applications. To enable event cameras to operate alongside staple sensors like lidar in perception tasks, we propose a direct, temporally-decoupled extrinsic calibration method between event cameras and lidars. The high dynamic range, high temporal resolution, and low-latency operation of event cameras are exploited to directly regi…
A Target-based Multi-LiDAR Multi-Camera Extrinsic Calibration System
Research \& Development, Toyota Material Handling Manufacturing, Bologna Italy Department of Information Engineering, University of Pisa, Pisa, Italy School of Engineering；Materials Science, Queen Mary University of London, London, United Kingdom
4D-CAAL: 4D Radar-Camera Calibration and Auto-Labeling for Autonomous Driving
School of Information Engineering, Yancheng Institute of Technology（信息工程学院，盐城职业技术学院）；School of Navigation, Wuhan University of Technology（导航学院，武汉理工大学）；The Hong Kong University of Science and Technology (Guangzhou)（香港科学与技术大学（广州））；School of Information Engineering, Yancheng Institute Technology（信息工程学院，盐城职业技术学院）；School of Advanced Technology, Xi’an Jiaotong-Liverpool University（先进技术学院，西安交通大学利物浦大学）；School of Information Science and Technology, Nantong University（信息科学与技术学院，南通大学）；State Key Laboratory of Maritime Technology and Safety（船舶技术与安全国家重点实验室）
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；Hong Kong University of Science and Technology（香港科技大学）；HKUST Shenzhen-Hong Kong Collaborative Innovation Research Institute（香港科技大学深港协同创新研究院）；CWB Institute of Autonomous Driving（CWB自动驾驶研究院）
The combination of LiDARs and cameras enables a mobile robot to perceive environments with multi-modal data, becoming a key factor in achieving robust perception. Traditional frame cameras are sensitive to changing illumination conditions, motivating us to introduce novel event cameras to make LiDAR-camera fusion more complete and robust. However, to jointly exploit these sensors, the challenging extrinsic calibration problem should be addressed. This paper proposes an automatic checkerboard-based approach to calibrate extrinsics between a LiDAR and a frame/event camera, where four contributio…
ETH Zürich（苏黎世联邦理工学院）；Czech Technical University in Prague（布拉格捷克理工大学）；Microsoft Mixed Reality & AI Zürich Lab（微软混合现实与人工智能苏黎世实验室）；Chalmers University of Technology（查尔姆斯理工大学）
Multi-camera systems are an important sensor platform for intelligent systems such as self-driving cars. Pattern-based calibration techniques can be used to calibrate the intrinsics of the cameras individually. However, extrinsic calibration of systems with little to no visual overlap between the cameras is a challenge. Given the camera intrinsics, infrastucture-based calibration techniques are able to estimate the extrinsics using 3D maps pre-built via SLAM or Structure-from-Motion. In this paper, we propose to fully calibrate a multi-camera system from scratch using an infrastructure-based a…
Vellore Institute of Technology, Chennai（金奈韦洛尔理工大学）；Birla Institute of Technology and Science, Hyderabad（海得拉巴比尔拉理工学院）；Veermata Jijabai Technological Institute, Mumbai（孟买韦尔马塔·吉贾拜技术学院）；International Institute of Information and Technology, Hyderabad（海得拉巴国际信息技术学院）
With the advent of autonomous vehicles, LiDAR and cameras have become an indispensable combination of sensors. They both provide rich and complementary data which can be used by various algorithms and machine learning to sense and make vital inferences about the surroundings. We propose a novel pipeline and experimental setup to find accurate rigid-body transformation for extrinsically calibrating a LiDAR and a camera. The pipeling uses 3D-3D point correspondences in LiDAR and camera frame and gives a closed form solution. We further show the accuracy of the estimate by fusing point clouds fro…
For autonomous vehicles, an accurate calibration for LiDAR and camera is a prerequisite for multi-sensor perception systems. However, existing calibration techniques require either a complicated setting with various calibration targets, or an initial calibration provided beforehand, which greatly impedes their applicability in large-scale autonomous vehicle deployment. To tackle these issues, we propose a novel method to calibrate the extrinsic parameter for LiDAR and camera in road scenes. Our method introduces line features from static straight-line-shaped objects such as road lanes and pole…
4D Millimeter-Wave Radar in Autonomous Driving: A Survey
School of Vehicle and Mobility, Tsinghua University（清华大学车辆与 mobility学院）；Xingjian College, Tsinghua University（清华大学行健书院）；Changan Automobile Co., Ltd.（长安汽车股份有限公司）
Determining the extrinsic parameter between multiple LiDARs and cameras is essential for autonomous robots, especially for solid-state LiDARs, where each LiDAR unit has a very small Field-of-View (FoV), and multiple units are often used collectively. The majority of extrinsic calibration methods are proposed for 360$^\circ$ mechanical spinning LiDARs where the FoV overlap with other LiDAR or camera sensors is assumed. Few research works have been focused on the calibration of small FoV LiDARs and cameras nor on the improvement of the calibration speed. In this work, we consider the problem of …
Radar-Inertial Odometry with Online Spatio-Temporal Calibration via Continuous-Time IMU Modeling
University of Zagreb Faculty of Electrical Engineering and Computing, Laboratory for Autonomous Systems and Mobile Robotics (LAMOR)（泽格布大学电子工程与计算学院，自主系统与移动机器人实验室）；Calirad d.o.o.（Calirad公司）
In this work we present a novel method to jointly calibrate a sensor suite consisting a 3D-LiDAR, Inertial Measurement Unit (IMU) and Camera under an Extended Kalman Filter (EKF) framework. We exploit pairwise constraints between the 3 sensor pairs to perform EKF update and experimentally demonstrate the superior performance obtained with joint calibration as against individual sensor pair calibration.
The Hong Kong University of Science and Technology（香港科技大学）
Stereo cameras and dense stereo matching algorithms are core components for many robotic applications due to their abilities to directly obtain dense depth measurements and their robustness against changes in lighting conditions. However, the performance of dense depth estimation relies heavily on accurate stereo extrinsic calibration. In this work, we present a real-time markerless approach for obtaining high-precision stereo extrinsic calibration using a novel 5-DOF (degrees-of-freedom) and nonlinear optimization on a manifold, which captures the observability property of vision-only stereo …
Texas A&M University（得克萨斯农工大学）；Ford Motor Company（福特汽车公司）
This work presents a novel target-free extrinsic calibration algorithm for a 3D Lidar and an IMU pair using an Extended Kalman Filter (EKF) which exploits the \textit{motion based calibration constraint} for state update. The steps include, data collection by motion excitation of the Lidar Inertial Sensor suite along all degrees of freedom, determination of the inter sensor rotation by using rotational component of the aforementioned \textit{motion based calibration constraint} in a least squares optimization framework, and finally, the determination of inter sensor translation using the \text…
University of Toronto Institute for Aerospace Studies（多伦多大学航空航天研究所）；University of Zagreb（萨格勒布大学）
We present a novel approach for mobile manipulator self-calibration using contact information. Our method, based on point cloud registration, is applied to estimate the extrinsic transform between a fixed vision sensor mounted on a mobile base and an end effector. Beyond sensor calibration, we demonstrate that the method can be extended to include manipulator kinematic model parameters, which involves a non-rigid registration process. Our procedure uses on-board sensing exclusively and does not rely on any external measurement devices, fiducial markers, or calibration rigs. Further, it is full…
Texas A&M University（德克萨斯A&M大学）；Ford Motor Company（福特汽车公司）
In this paper we perform an experimental comparison of three different target based 3D-LIDAR camera calibration algorithms. We briefly elucidate the mathematical background behind each method and provide insights into practical aspects like ease of data collection for all of them. We extensively evaluate these algorithms on a sensor suite which consists multiple cameras and LIDARs by assessing their robustness to random initialization and by using metrics like Mean Line Re-projection Error (MLRE) and Factory Stereo Calibration Error. We also show the effect of noisy sensor on the calibration r…
Fast Extrinsic Calibration for Multiple Inertial Measurement Units in Visual-Inertial System
Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences（中国科学院上海微系统与信息技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）
In the context of robotics, accurate ground-truth positioning is the cornerstone for the development of mapping and localization algorithms. In outdoor environments and over long distances, total stations provide accurate and precise measurements, that are unaffected by the usual factors that deteriorate the accuracy of Global Navigation Satellite System (GNSS). While a single robotic total station can track the position of a target in three Degrees Of Freedom (DOF), three robotic total stations and three targets are necessary to yield the full six DOF pose reference. Since it is crucial to ex…
Joint Optimization-based Targetless Extrinsic Calibration for Multiple LiDARs and GNSS-Aided INS of Ground Vehicles
Institute of Systems Engineering and Collaborative Laboratory for Intelligent Science and Systems, Macau University of Science and Technology（系统工程研究院和智能科学与系统联合实验室，澳门科学技术大学）；Institute for AI Industry Research (AIR), Tsinghua University（人工智能产业研究院（AIR），清华大学）
National Institute of Advanced Industrial Science and Technology（产业技术综合研究所）
This paper presents an open source LiDAR-camera calibration toolbox that is general to LiDAR and camera projection models, requires only one pairing of LiDAR and camera data without a calibration target, and is fully automatic. For automatic initial guess estimation, we employ the SuperGlue image matching pipeline to find 2D-3D correspondences between LiDAR and camera data and estimate the LiDAR-camera transformation via RANSAC. Given the initial guess, we refine the transformation estimate with direct LiDAR-camera registration based on the normalized information distance, a mutual information…
The University of Hong Kong（香港大学）；Southern University of Science and Technology（南方科技大学）
In this letter, we present a novel method for automatic extrinsic calibration of high-resolution LiDARs and RGB cameras in targetless environments. Our approach does not require checkerboards but can achieve pixel-level accuracy by aligning natural edge features in the two sensors. On the theory level, we analyze the constraints imposed by edge features and the sensitivity of calibration accuracy with respect to edge distribution in the scene. On the implementation level, we carefully investigate the physical measuring principles of LiDARs and propose an efficient and accurate LiDAR edge extra…
Zhejiang University（浙江大学）；University of Delaware（特拉华大学）；Huzhou Institute of Zhejiang University（浙江大学湖州研究院）
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 improv…
Institute of Measurement, Control and Microtechnology, Ulm University（乌尔姆大学测量、控制与微技术研究所）
In this work, we propose an approach for extrinsic sensor calibration from per-sensor ego-motion estimates. Our problem formulation is based on dual quaternions, enabling two different online capable solving approaches. We provide a certifiable globally optimal and a fast local approach along with a method to verify the globality of the local approach. Additionally, means for integrating previous knowledge, for example, a common ground plane for planar sensor motion, are described. Our algorithms are evaluated on simulated data and on a publicly available dataset containing RGB-D camera images…
MFCalib: Single-shot and Automatic Extrinsic Calibration for LiDAR and Camera in Targetless Environments Based on Multi-Feature Edge
College of Mechatronics and Control Engineering, Shenzhen University（深圳大学机电与控制工程学院）；Peng Cheng Laboratory（鹏城实验室）；Manifold Tech Limited（万孚科技有限公司）；The University of Hong Kong（香港大学）
