Efficient Right‐Decoupled Composite Manifold Optimization for Visual Inertial Odometry

In filtering-based global navigation satellite system (GNSS) / inertial navigation system (INS) integrated navigation systems, the precise INS mechanization has fully considered the impact of the Earth rotation, Coriolis acceleration, etc. However, most inertial measurement unit (IMU) preintegration models in factor graph optimization (FGO)-based integrated navigation systems are rough and ignore these factors. We propose an FGO-based GNSS/INS integrated navigation system to analyze and evaluate the impact of the Earth rotation on MEMS-IMU preintegration. The proposed FGO-based integration is based on a refined IMU preintegration, in which the Earth rotation is compensated. The proposed GNSS/INS integration is a sliding-window optimizer in which the GNSS positioning and the IMU preintegration are tightly fused within the FGO framework. The simulated GNSS outage in field tests, an effective method, is adopted to evaluate the IMU preintegration quantitatively. The results demonstrate that the refined IMU preintegration can achieve the same accuracy as the precise INS mechanization. In contrast, the rough IMU preintegration and INS mechanization without compensating for the Earth rotation yields notable accuracy degradation. When the GNSS-outage time is 60 seconds, the degradation can be 200% for the industrial-grade MEMS module and more than 10% for the consumer-grade MEMS chip. Besides, the degradation can be more significant if the GNSS-outage time is longer. The proposed FGO-based GNSS/INS integration ( <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/i2Nav-WHU/OB_GINS</uri> ) and the employed datasets ( <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/i2Nav-WHU/awesome-gins-datasets</uri> ) are open-sourced on GitHub.

Direct visual-inertial odometry with semi-dense mapping

The inertial measurement unit (IMU) preintegration approach nowadays is widely used in various robotic applications. In this article, we revisit the preintegration theory and propose a novel interpretation to understand it from a nonlinear observer perspective, specifically the parameter estimation-based observer (PEBO). We demonstrate that the preintegration approach can be viewed as a recursive implementation of PEBO in moving horizons, and that the two approaches are equivalent with perfect measurements. We then discuss how these findings can be used to tackle practical challenges in estimation problems. As byproducts, our results lead to a novel hybrid sampled-data observer design and an approach to address statistical optimality for PEBO in the presence of noise.

Two novel nonlinear pose (i.e, attitude and position) filters developed directly on the Special Euclidean Group SE(3)able to guarantee prescribed characteristics of transient and steady-state performance are proposed. The position error and normalized Euclidean distance of attitude error are trapped to arbitrarily start within a given large set and converge systematically and asymptotically to the origin from almost any initial condition. The transient error is guaranteed not to exceed a prescribed value while the steady-state error is bounded by a predefined small value. The first pose filter operates based on a set of vectorial measurements coupled with a group of velocity vectors and requires preliminary pose reconstruction. The second filter, on the contrary, is able to perform its function using a set of vectorial measurements and a group of velocity vectors directly. Both proposed filters provide reasonable pose estimates with superior convergence properties while being able to use measurements obtained from low-cost inertial measurement, landmark measurement, and velocity measurement units. Simulation results demonstrate effectiveness and robustness of the proposed filters considering large error in initialization and high level of uncertainties in velocity vectors as well as in the set of vector measurements. Attitude, position, pose estimation, nonlinear observer, estimate, special orthogonal group, special Euclidean group, SO(3), SE(3), prescribed performance function, transient, steady-state error, transformed error, Landmark, feature measurement, PPF, IMU, Lie algebra, Lie group, projection, Gyroscope, Inertial measurement units, rigid body, micro electromechanical systems, sensor, IMUs, MEMS, Roll, Pitch, Yaw, UAVs, QUAV, SVD, Fixed, Moving, Vehicles, Robot, Robotic System, Spacecraft, submarine, Underwater vehicle.

Batch optimization based inertial measurement unit (IMU) and visual sensor fusion enables high rate localization for many robotic tasks. However, it remains a challenge to ensure that the batch optimization is computationally efficient while being consistent for high rate IMU measurements without marginalization. In this paper, we derive inspiration from maximum likelihood estimation with partial-fixed estimates to provide a unified approach for handing both IMU preintegration and time-offset calibration. We present a modularized analytic combined IMU integrator (ACI2) with elegant derivations for IMU integrations, bias Jabcobians and related covariances. To simplify our derivation, we also prove that the right Jacobians for Hamilton quaterions and SO(3) are equivalent. Finally, we present a time offset calibrator that operates by fixing the linearization point for a given time offset. This reduces re-integration of the IMU measurements and thus improve efficiency. The proposed ACI2 and time-offset calibration is verified by intensive Monte-Carlo simulations generated from real world datasets. A proof-of-concept real world experiment is also conducted to verify the proposed ACI2 estimator.

Traditional Micro-Aerial Vehicles (MAVs) are usually equipped with a low-cost Inertial Measurement Unit (IMU) and monocular cameras, how to achieve high precision and high reliability navigation under the framework of low computational complexity is the main problem for MAVs. To this end, a novel semi-direct point-line visual inertial odometry (SDPL-VIO) has been proposed for MAVs. In the front-end, point and line features are introduced to enhance image constraints and increase environmental adaptability. At the same time, the semi-direct method combined with IMU pre-integration is used to complete motion estimation. This hybrid strategy combines the accuracy and loop closure detection performance of the feature-based method with the rapidity of the direct method, and tracks keyframes and non-keyframes, respectively. In the back-end, the sliding window mechanism is adopted to limit the computation, while the improved marginalization method is used to decompose the high-dimensional matrix corresponding to the cost function to reduce the computational complexity in the optimization process. The comparison results in the EuRoC datasets demonstrate that SDPL-VIO performs better than the other state-of-the-art visual inertial odometry (VIO) methods, especially in terms of accuracy and real-time performance.

Accurate positional estimation is an essential prerequisite for the regular operation of an autonomous rotary-wing Unmanned Aerial Vehicles (UAV). However, the field of view (FOV) limitation problem of lidar makes it more challenging to locate the rotary-wing UAV in an unknown environment. To address rotor drones with an insufficient FOV and the observation blindness of lidar in complex environments, this paper designs a rotorcraft UAV system based on rotating 3D lidar and proposes a simultaneous localization and mapping algorithm for rotating 3D lidar. The algorithm distinguishes between planar and edge features based on the curvature value of the point cloud first. Then, to reduce the impact caused by the UAV motion and lidar rotation, messages about the Inertial Measurement Unit (IMU) and real-time rotation angles are used to compensate for these motions twice, while the IMU measurements are used for state prediction, and the error-sate iterative extended Kalman filter is used to update the residuals after matching line and surface features with sub-map. Finally, Smoother high-rate odometer data was obtained through IMU pre-integration and a first-order low-pass filter. The experimental results show that the proposed rotating lidar unit in indoor and outdoor conditions makes the rotorcraft UAV have a larger FOV, which not only improves the environmental perception capability and positional estimation accuracy of the rotorcraft but enhances the positioning reliability and flight stability of the rotorcraft UAV in complex environments.

Abstract. Simultaneous Localization and Mapping (SLAM), as one of the core technologies in autonomous driving, provides environment perception, decision-making, and path planning to ensure safe vehicle operation. This paper proposes a tightly-coupled fusion mapping method based on LiDAR and Inertial Measurement Unit (IMU). By introducing IMU, performing extrinsic calibration, and time synchronization with the LiDAR, the issue of mapping drift caused by inconsistent coordinate systems is addressed, leading to improved mapping accuracy. Furthermore, to compensate for IMU zero-bias errors, IMU preintegration is employed to calibrate the point cloud and optimize the initial values of the LiDAR odometry. A novel iVox voxel-based point cloud registration method is used to enhance registration efficiency without compromising mapping accuracy. Lastly, the Iterative Extended Kalman Filter (IEKF) is incorporated into the back-end state estimation to propagate and correct the estimated state using IMU data, enabling precise state estimation and map updates. This research is of significant importance in addressing the challenges of low mapping accuracy and real-time performance in single-sensor SLAM, providing an effective solution for environment perception and path planning in autonomous driving systems.

In this paper, based on Inertial Measurement Unit (IMU) preintegration, a pose estimation algorithm for Visual-Inertial Odometry (VIO) system has been investigated. Firstly, we developed the kinematic equation of acceleration and angular velocity of IMU. To avoid the re-integration caused by the change of the system states, the IMU measurements are preintegrated on the Riemannian manifold of rotation. Furthermore, we studied the propagation characteristic of noise and derived the state transition equation of the noise. So the influence of noise on pose estimation can be dramatically reduced. Compared with the famous Okvis algorithm, experimental results on two public datasets of EuRoC show that the proposed IMU preintegration algorithm achieves good estimation median of translation error with 0.14 m, which is better than Okvis with 0.24 m.

Multisource information fusion is a major area of interest within the field of unmanned technology. In comparison with utilizing the Kalman filter (KF)-based method, the factor graph optimization (FGO)-based method has recently been proposed as an innovative approach. However, the traditional FGO-based inertial measurement unit (IMU) preintegration process is designed for low-accuracy inertial sensors, which leads to insufficient utilization of information and a decrease in positioning accuracy, in the case of tactical-grade or higher accuracy IMUs. Therefore, this article refines the process on the manifold model and utilizes the equivalent rotation vector to accumulate IMU measurements. The main contribution of our work is the refined on-manifold IMU preintegration theory and the application of the multisample algorithm based on the equivalent rotation vector for obtaining more precise preintegrated IMU measurements. The refined on-manifold IMU preintegration theory is applied based on the FGO algorithm in the global navigation satellite system (GNSS)/inertial navigation system (INS) loosely integrated navigation system. The experiments based on simulated and real-world data were conducted and demonstrate that, compared to a high-precision extended KF (EKF) algorithm and optimization methods, the proposed method achieves more accuracy in a dynamic environment.

Recently, visual-inertial odometry (VIO) has been widely adopted for tracking the movement of robots in simultaneous localization and mapping (SLAM). In this paper, a low-cost and highly accurate depth-added VIO framework is proposed for robots in indoor environments by taking advantage of an RGB-D camera and a micro-electromechanical system (MEMS) inertial measurement unit (IMU). Movement estimation is achieved by IMU pre-integration and visual tracking in this tightly coupled framework. Meanwhile, an empirical IMU model is developed by using Allan variance analysis to guarantee the accuracy of the estimated errors. Images with depth information are deployed during initialization to achieve a fast response. Extensive experiments are conducted to validate the effectiveness and its performance by comparing it with other advanced schemes in indoor scenarios. The results show that the scale drift error is reduced to 2.6 % and the response time of the initialization process is improved by about 124 % compared to its counterpart.

A Least Squares Estimate of Satellite Attitude

Aiming at the problems of insufficient accuracy and serious computational time-consumption of mainstream laser odometry schemes, this paper proposes an innovative solution, where the front end is based on the idea of iterative Kalman filtering, which realizes the tight coupling of inertial measurement unit (IMU) and LiDAR to obtain high-precision position and attitude estimation. The back-end optimization employs a factor graph approach, incorporating laser odometry, IMU preintegration, and loop closure detection factors. In comparison with state-of-the-art laser SLAM algorithms, the SLAM algorithm proposed in this paper reduces the absolute position error of trajectories by 9.61%, 91.03%, and 94.89% compared to Fast-lio2, Lego-loam, and a-loam, respectively.

Inertial measurement units (IMUs) enable orientation, velocity, and position estimation in several application domains ranging from robotics and autonomous vehicles to human motion capture and rehabilitation engineering. Errors in orientation estimation greatly affect any of those motion parameters. The present work explains the main challenges in inertial orientation estimation (IOE) and presents an extensive benchmark dataset that includes 3D inertial and magnetic data with synchronized optical marker-based ground truth measurements, the Berlin Robust Orientation Estimation Assessment Dataset (BROAD). The BROAD dataset consists of 39 trials that are conducted at different speeds and include various types of movement. Thereof, 23 trials are performed in an undisturbed indoor environment, and 16 trials are recorded with deliberate magnetometer and accelerometer disturbances. We furthermore propose error metrics that allow for IOE accuracy evaluation while separating the heading and inclination portions of the error and introduce well-defined benchmark metrics. Based on the proposed benchmark, we perform an exemplary case study on two widely used openly available IOE algorithms. Due to the broad range of motion and disturbance scenarios, the proposed benchmark is expected to provide valuable insight and useful tools for the assessment, selection, and further development of inertial sensor fusion methods and IMU-based application systems.

An improved SLAM based on RK-VIF: Vision and inertial information fusion via Runge-Kutta method