This paper addresses the problem of choosing a sparse subset of measurements for quick calibration parameter estimation. A standard solution to this is selecting a measurement only if its utility -- the difference between posterior (with the measurement) and prior information (without the measurement) -- exceeds some threshold. Theoretically, utility, a function of the parameter estimate, should be evaluated at the estimate obtained with all measurements selected so far, hence necessitating a recalibration with each new measurement. However, we hypothesize that utility is insensitive to changes in the parameter estimate for many systems of interest, suggesting that evaluating utility at some initial parameter guess would yield equivalent results in practice. We provide evidence supporting this hypothesis for extrinsic calibration of multiple inertial measurement units (IMUs), showing the reduction in calibration time by two orders of magnitude by forgoing recalibration for each measurement.
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）
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We present a method of extrinsic calibration for a system of multiple inertial measurement units (IMUs) that estimates the relative pose of each IMU on a rigid body using only measurements from the IMUs themselves, without the need to prescribe the trajectory. Our method is based on solving a nonlinear least-squares problem that penalizes inconsistency between measurements from pairs of IMUs. We validate our method with experiments both in simulation and in hardware. In particular, we show that it meets or exceeds the performance -- in terms of error, success rate, and computation time -- of a…
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 …
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…
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.
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）
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…
School of Artificial Intelligence and Automation, Huazhong University of Science and Technology（华中科技大学人工智能与自动化学院）；School of Automation, SouthEast University（东南大学自动化学院）
Mobile robot positioning, mapping, and navigation systems generally employ an inertial measurement unit (IMU) to obtain the acceleration and angular velocity of the robot. However, errors in the internal and external parameters of an IMU arising from defective calibration directly affect the accuracy of robot positioning and pose estimation. While this issue has been addressed by the mature internal reference calibration methods available for IMUs, external reference calibration methods between the IMU and the chassis of a mobile robot are lacking. This study addresses this issue by proposing …
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…
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…
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…
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…
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）
GMMCalib: Extrinsic Calibration of LiDAR Sensors using GMM-based Joint Registration
Technical University of Munich（慕尼黑工业大学）；TUM School of Engineering and Design（慕尼黑工业大学工程与设计学院）；TUM School of Computation, Information and Technology（慕尼黑工业大学计算、信息与技术学院）
In this paper, we discuss an imitation learning based method for reducing the calibration error for a mixed reality system consisting of a vision sensor and a projector. Unlike a head mounted display, in this setup, augmented information is available to a human subject via the projection of a scene into the real world. Inherently, the camera and projector need to be calibrated as a stereo setup to project accurate information in 3D space. Previous calibration processes require multiple recording and parameter tuning steps to achieve the desired calibration, which is usually time consuming proc…
Observability-Aware Active Calibration of Multi-Sensor Extrinsics for Ground Robots via Online Trajectory Optimization
Shenzhen Key Laboratory of Control Theory and Intelligent Systems（深圳控制理论与智能系统重点实验室）；Guangdong Provincial Key Laboratory of Fully Actuated System Control Theory and Technology（广东省全驱动系统控制理论与技术省级重点实验室）；Southern University of Science and Technology（南方科技大学）
University of Toronto Institute for Aerospace Studies（多伦多大学航空航天研究所）
We present a certifiably globally optimal algorithm for determining the extrinsic calibration between two sensors that are capable of producing independent egomotion estimates. This problem has been previously solved using a variety of techniques, including local optimization approaches that have no formal global optimality guarantees. We use a quadratic objective function to formulate calibration as a quadratically constrained quadratic program (QCQP). By leveraging recent advances in the optimization of QCQPs, we are able to use existing semidefinite program (SDP) solvers to obtain a certifi…
We propose a solution for sensor extrinsic self-calibration with very low time complexity, competitive accuracy and graceful handling of often-avoided corner cases: drift in calibration parameters and unobservable directions in the parameter space. It consists of three main parts: 1) information-theoretic based segment selection for constant-time estimation; 2) observability-aware parameter update through a rank-revealing decomposition of the Fisher information matrix; 3) drift-correcting self-calibration through the time-decay of segments. At the core of our FastCal algorithm is the loosely-c…
Texas A&M University（德克萨斯农工大学）；Ford Motor Company（福特汽车公司）
This work presents an extrinsic parameter estimation algorithm between a 3D LIDAR and a Projective Camera using a marker-less planar target, by exploiting Planar Surface Point to Plane and Planar Edge Point to back-projected Plane geometric constraints. The proposed method uses the data collected by placing the planar board at different poses in the common field of view of the LIDAR and the Camera. The steps include, detection of the target and the edges of the target in LIDAR and Camera frames, matching the detected planes and lines across both the sensing modalities and finally solving a cos…
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 …
Hong Kong University of Science and Technology（香港科技大学）；City University of Hong Kong（香港城市大学）
Fusion of heterogeneous extroceptive sensors is the most effient and effective way to representing the environment precisely, as it overcomes various defects of each homogeneous sensor. The rigid transformation (aka. extrinsic parameters) of heterogeneous sensory systems should be available before precisely fusing the multisensor information. Researchers have proposed several approaches to estimating the extrinsic parameters. These approaches require either auxiliary objects, like chessboards, or extra help from human to select correspondences. In this paper, we proposed a novel extrinsic cali…
The University of Tokyo（东京大学）；Southeast University（东南大学）
Recently, multi-sensors fusion has achieved significant progress in the field of automobility to improve navigation and position performance. As the prerequisite of the fusion algorithm, the demand for the extrinsic calibration of multi-sensors is growing. To calculate the extrinsic parameter, many researches have been dedicated to the two-step method, which integrates the respective calibration in pairs. It is inefficient and incompact because of losing sight of the constrain of all sensors. With regard to remove this burden, an optimization-based IMU/Lidar/Camera co-calibration method is pro…
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）
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…
