Recent advances in deep learning have enabled the development of autonomous systems that use deep neural networks for perception. Formal verification of these systems is challenging due to the size and complexity of the perception DNNs as well as hard-to-quantify, changing environment conditions. To address these challenges, we propose a probabilistic verification framework for autonomous systems based on the following key concepts: (1) Scenario-based Modeling: We decompose the task (e.g., car navigation) into a composition of scenarios, each representing a different environment condition. (2) Probabilistic Abstractions: For each scenario, we build a compact abstraction of perception based on the DNN's performance on an offline dataset that represents the scenario's environment condition. (3) Symbolic Reasoning and Acceleration: The abstractions enable efficient compositional verification of the autonomous system via symbolic reasoning and a novel acceleration proof rule that bounds the error probability of the system under arbitrary variations of environment conditions. We illustrate our approach on two case studies: an experimental autonomous system that guides airplanes on taxiways using high-dimensional perception DNNs and a simulation model of an F1Tenth autonomous car using LiDAR observations.

Recent advancements in LiDAR-Inertial Odometry (LIO) have boosted a large amount of applications. However, traditional LIO systems tend to focus more on localization rather than mapping, with maps consisting mostly of sparse geometric elements, which is not ideal for downstream tasks. Recent emerging neural field technology has great potential in dense mapping, but pure LiDAR mapping is difficult to work on high-dynamic vehicles. To mitigate this challenge, we present a new solution that tightly couples geometric kinematics with neural fields to enhance simultaneous state estimation and dense mapping capabilities. We propose both semi-coupled and tightly coupled Kinematic-Neural LIO (KN-LIO) systems that leverage online SDF decoding and iterated error-state Kalman filtering to fuse laser and inertial data. Our KN-LIO minimizes information loss and improves accuracy in state estimation, while also accommodating asynchronous multi-LiDAR inputs. Evaluations on diverse high-dynamic datasets demonstrate that our KN-LIO achieves performance on par with or superior to existing state-of-the-art solutions in pose estimation and offers improved dense mapping accuracy over pure LiDAR-based methods. The relevant code and datasets will be made available at https://**.

Fault diagnosis is crucial for complex autonomous mobile systems, especially for modern-day autonomous driving (AD). Different actors, numerous use cases, and complex heterogeneous components motivate a fault diagnosis of the system and overall system integrity. AD systems are composed of many heterogeneous components, each with different functionality and possibly using a different algorithm (e.g., rule-based vs. AI components). In addition, these components are subject to the vehicle's driving state and are highly dependent. This paper, therefore, faces this problem by presenting the concept of a modular fault diagnosis framework for AD systems. The concept suggests modular state monitoring and diagnosis elements, together with a state- and dependency-aware aggregation method. Our proposed classification scheme allows for the categorization of the fault diagnosis modules. The concept is implemented on AD shuttle buses and evaluated to demonstrate its capabilities.

Due to the advantages of high computational efficiency and small memory requirements, filter-based visual inertial odometry (VIO) has a good application prospect in miniaturized and payload-constrained embedded systems. However, the filter-based method has the problem of insufficient accuracy. To this end, we propose the State transformation and Pose-only VIO (SP-VIO) by rebuilding the state and measurement models, and considering further visual deprived conditions. In detail, we first proposed a system model based on the double state transformation extended Kalman filter (DST-EKF), which has been proven to have better observability and consistency than the models based on extended Kalman filter (EKF) and state transformation extended Kalman filter (ST-EKF). Secondly, to reduce the influence of linearization error caused by inaccurate 3D reconstruction, we adopt the Pose-only (PO) theory to decouple the measurement model from 3D features. Moreover, to deal with visual deprived conditions, we propose a double state transformation Rauch-Tung-Striebel (DST-RTS) backtracking method to optimize motion trajectories during visual interruption. Experiments on public (EuRoC, Tum-VI, KITTI) and personal datasets show that SP-VIO has better accuracy and efficiency than state-of-the-art (SOTA) VIO algorithms, and has better robustness under visual deprived conditions.

For robots with low rigidity, determining the robot's state based solely on kinematics is challenging. This is particularly crucial for a robot whose entire body is in contact with the environment, as accurate state estimation is essential for environmental interaction. We propose a method for simultaneous articulated robot posture estimation and environmental mapping by integrating data from proximity sensors distributed over the whole body. Our method extends the discrete-time model, typically used for state estimation, to the spatial direction of the articulated structure. The simulations demonstrate that this approach significantly reduces estimation errors.

The Kalman Filter (KF) is a powerful mathematical tool widely used for state estimation in various domains, including Simultaneous Localization and Mapping (SLAM). This paper presents an in-depth introduction to the Kalman Filter and explores its several extensions: the Extended Kalman Filter (EKF), the Error-State Kalman Filter (ESKF), the Iterated Extended Kalman Filter (IEKF), and the Iterated Error-State Kalman Filter (IESKF). Each variant is meticulously examined, with detailed derivations of their mathematical formulations and discussions on their respective advantages and limitations. By providing a comprehensive overview of these techniques, this paper aims to offer valuable insights into their applications in SLAM and enhance the understanding of state estimation methodologies in complex environments.

Environment awareness is crucial for enhancing walking safety and stability of amputee wearing powered prosthesis when crossing uneven terrains such as stairs and obstacles. However, existing environmental perception systems for prosthesis only provide terrain types and corresponding parameters, which fails to prevent potential collisions when crossing uneven terrains and may lead to falls and other severe consequences. In this paper, a visual-inertial motion estimation approach is proposed for prosthesis to perceive its movement and the changes of spatial relationship between the prosthesis and uneven terrain when traversing them. To achieve this, we estimate the knee motion by utilizing a depth camera to perceive the environment and align feature points extracted from stairs and obstacles. Subsequently, an error-state Kalman filter is incorporated to fuse the inertial data into visual estimations to reduce the feature extraction error and obtain a more robust estimation. The motion of prosthetic joint and toe are derived using the prosthesis model parameters. Experiment conducted on our collected dataset and stair walking trials with a powered prosthesis shows that the proposed method can accurately tracking the motion of the human leg and prosthesis with an average root-mean-square error of toe trajectory less than 5 cm. The proposed method is expected to enable the environmental adaptive control for prosthesis, thereby enhancing amputee's safety and mobility in uneven terrains.

We report results obtained and insights gained while answering the following question: how effective is it to use a simulator to establish path following control policies for an autonomous ground robot? While the quality of the simulator conditions the answer to this question, we found that for the simulation platform used herein, producing four control policies for path planning was straightforward once a digital twin of the controlled robot was available. The control policies established in simulation and subsequently demonstrated in the real world are PID control, MPC, and two neural network (NN) based controllers. Training the two NN controllers via imitation learning was accomplished expeditiously using seven simple maneuvers: follow three circles clockwise, follow the same circles counter-clockwise, and drive straight. A test randomization process that employs random micro-simulations is used to rank the ``goodness'' of the four control policies. The policy ranking noted in simulation correlates well with the ranking observed when the control policies were tested in the real world. The simulation platform used is publicly available and BSD3-released as open source; a public Docker image is available for reproducibility studies. It contains a dynamics engine, a sensor simulator, a ROS2 bridge, and a ROS2 autonomy stack the latter employed both in the simulator and the real world experiments.

Due to the state trajectory-independent features of invariant Kalman filtering (InEKF), it has attracted widespread attention in the research community for its significantly improved state estimation accuracy and convergence under disturbance. In this paper, we formulate the full-source data fusion navigation problem for fixed-wing unmanned aerial vehicle (UAV) within a framework based on error state right-invariant extended Kalman filtering (ES-RIEKF) on Lie groups. We merge measurements from a multi-rate onboard sensor network on UAVs to achieve real-time estimation of pose, air flow angles, and wind speed. Detailed derivations are provided, and the algorithm's convergence and accuracy improvements over established methods like Error State EKF (ES-EKF) and Nonlinear Complementary Filter (NCF) are demonstrated using real-flight data from UAVs. Additionally, we introduce a semi-aerodynamic model fusion framework that relies solely on ground-measurable parameters. We design and train an Long Short Term Memory (LSTM) deep network to achieve drift-free prediction of the UAV's angle of attack (AOA) and side-slip angle (SA) using easily obtainable onboard data like control surface deflections, thereby significantly reducing dependency on GNSS or complicated aerodynamic model parameters. Further, we validate the algorithm's robust advantages under GNSS denied, where flight data shows that the maximum positioning error stays within 30 meters over a 130-second denial period. To the best of our knowledge, this study is the first to apply ES-RIEKF to full-source navigation applications for fixed-wing UAVs, aiming to provide engineering references for designers. Our implementations using MATLAB/Simulink will open source.

Visual-inertial initialization can be classified into joint and disjoint approaches. Joint approaches tackle both the visual and the inertial parameters together by aligning observations from feature-bearing points based on IMU integration then use a closed-form solution with visual and acceleration observations to find initial velocity and gravity. In contrast, disjoint approaches independently solve the Structure from Motion (SFM) problem and determine inertial parameters from up-to-scale camera poses obtained from pure monocular SLAM. However, previous disjoint methods have limitations, like assuming negligible acceleration bias impact or accurate rotation estimation by pure monocular SLAM. To address these issues, we propose EDI, a novel approach for fast, accurate, and robust visual-inertial initialization. Our method incorporates an Error-state Kalman Filter (ESKF) to estimate gyroscope bias and correct rotation estimates from monocular SLAM, overcoming dependence on pure monocular SLAM for rotation estimation. To estimate the scale factor without prior information, we offer a closed-form solution for initial velocity, scale, gravity, and acceleration bias estimation. To address gravity and acceleration bias coupling, we introduce weights in the linear least-squares equations, ensuring acceleration bias observability and handling outliers. Extensive evaluation on the EuRoC dataset shows that our method achieves an average scale error of 5.8% in less than 3 seconds, outperforming other state-of-the-art disjoint visual-inertial initialization approaches, even in challenging environments and with artificial noise corruption.