A Comprehensive Introduction of Visual-Inertial Navigation

In this article, a tutorial introduction to visual-inertial navigation(VIN) is presented. Visual and inertial perception are two complementary sensing modalities. Cameras and inertial measurement units (IMU) are the corresponding sensors for these two modalities. The low cost and light weight of camera-IMU sensor combinations make them ubiquitous in robotic navigation. Visual-inertial Navigation is a state estimation problem, that estimates the ego-motion and local environment of the sensor platform. This paper presents visual-inertial navigation in the classical state estimation framework, first illustrating the estimation problem in terms of state variables and system models, including related quantities representations (Parameterizations), IMU dynamic and camera measurement models, and corresponding general probabilistic graphical models (Factor Graph). Secondly, we investigate the existing model-based estimation methodologies, these involve filter-based and optimization-based frameworks and related on-manifold operations. We also discuss the calibration of some relevant parameters, also initialization of state of interest in optimization-based frameworks. Then the evaluation and improvement of VIN in terms of accuracy, efficiency, and robustness are discussed. Finally, we briefly mention the recent development of learning-based methods that may become alternatives to traditional model-based methods.Comment: 35 pages, 10 figure

Keyframe-based visual–inertial odometry using nonlinear optimization

Combining visual and inertial measurements has become popular in mobile robotics, since the two sensing modalities offer complementary characteristics that make them the ideal choice for accurate visual–inertial odometry or simultaneous localization and mapping (SLAM). While historically the problem has been addressed with filtering, advancements in visual estimation suggest that nonlinear optimization offers superior accuracy, while still tractable in complexity thanks to the sparsity of the underlying problem. Taking inspiration from these findings, we formulate a rigorously probabilistic cost function that combines reprojection errors of landmarks and inertial terms. The problem is kept tractable and thus ensuring real-time operation by limiting the optimization to a bounded window of keyframes through marginalization. Keyframes may be spaced in time by arbitrary intervals, while still related by linearized inertial terms. We present evaluation results on complementary datasets recorded with our custom-built stereo visual–inertial hardware that accurately synchronizes accelerometer and gyroscope measurements with imagery. A comparison of both a stereo and monocular version of our algorithm with and without online extrinsics estimation is shown with respect to ground truth. Furthermore, we compare the performance to an implementation of a state-of-the-art stochastic cloning sliding-window filter. This competitive reference implementation performs tightly coupled filtering-based visual–inertial odometry. While our approach declaredly demands more computation, we show its superior performance in terms of accuracy

Continuous-Time Vs. Discrete-Time Vision-Based SLAM: A Comparative Study

Robotic practitioners generally approach the vision-based SLAM problem through discrete-time formulations. This has the advantage of a consolidated theory and very good understanding of success and failure cases. However, discrete-time SLAM needs tailored algorithms and simplifying assumptions when high-rate and/or asynchronous measurements, coming from different sensors, are present in the estimation process. Conversely, continuous-time SLAM, often overlooked by practitioners, does not suffer from these limitations. Indeed, it allows integrating new sensor data asynchronously without adding a new optimization variable for each new measurement. In this way, the integration of asynchronous or continuous high-rate streams of sensor data does not require tailored and highly-engineered algorithms, enabling the fusion of multiple sensor modalities in an intuitive fashion. On the down side, continuous time introduces a prior that could worsen the trajectory estimates in some unfavorable situations. In this work, we aim at systematically comparing the advantages and limitations of the two formulations in vision-based SLAM. To do so, we perform an extensive experimental analysis, varying robot type, speed of motion, and sensor modalities. Our experimental analysis suggests that, independently of the trajectory type, continuous-time SLAM is superior to its discrete counterpart whenever the sensors are not time-synchronized. In the context of this work, we developed, and open source, a modular and efficient software architecture containing state-of-the-art algorithms to solve the SLAM problem in discrete and continuous time

GNSS/Multi-Sensor Fusion Using Continuous-Time Factor Graph Optimization for Robust Localization

Accurate and robust vehicle localization in highly urbanized areas is challenging. Sensors are often corrupted in those complicated and large-scale environments. This paper introduces GNSS-FGO, an online and global trajectory estimator that fuses GNSS observations alongside multiple sensor measurements for robust vehicle localization. In GNSS-FGO, we fuse asynchronous sensor measurements into the graph with a continuous-time trajectory representation using Gaussian process regression. This enables querying states at arbitrary timestamps so that sensor observations are fused without requiring strict state and measurement synchronization. Thus, the proposed method presents a generalized factor graph for multi-sensor fusion. To evaluate and study different GNSS fusion strategies, we fuse GNSS measurements in loose and tight coupling with a speed sensor, IMU, and lidar-odometry. We employed datasets from measurement campaigns in Aachen, Duesseldorf, and Cologne in experimental studies and presented comprehensive discussions on sensor observations, smoother types, and hyperparameter tuning. Our results show that the proposed approach enables robust trajectory estimation in dense urban areas, where the classic multi-sensor fusion method fails due to sensor degradation. In a test sequence containing a 17km route through Aachen, the proposed method results in a mean 2D positioning error of 0.19m for loosely coupled GNSS fusion and 0.48m while fusing raw GNSS observations with lidar odometry in tight coupling.Comment: Revision of arXiv:2211.0540