Wei Xu

Wei Xu, Haowei Gu, Youming Qing et al.

In this paper, we present a full attitude control of an efficient quadrotor tail-sitter VTOL UAV with flexible modes. This control system is working in all flight modes without any control surfaces but motor differential thrusts. This paper concentrates on the design of the attitude controller and the altitude controller. For the attitude control, the controller's parameters and filters are optimized based on the frequency response model which is identified from the sweep experiment. As a result, the effect of system flexible modes is easily compensated in frequency-domain by using a notch filter, and the resulting attitude loop shows superior tracking performance and robustness. In the coordinated flight condition, the altitude controller is structured as the feedforward-feedback parallel controller. The feedforward thrust command is calculated based on the current speed and the pitch angle. Tests in hovering, forward accelerating and forward decelerating flights have been conducted to verify the proposed control system.

Wei Xu, Yixi Cai, Dongjiao He et al.

This paper presents FAST-LIO2: a fast, robust, and versatile LiDAR-inertial odometry framework. Building on a highly efficient tightly-coupled iterated Kalman filter, FAST-LIO2 has two key novelties that allow fast, robust, and accurate LiDAR navigation (and mapping). The first one is directly registering raw points to the map (and subsequently update the map, i.e., mapping) without extracting features. This enables the exploitation of subtle features in the environment and hence increases the accuracy. The elimination of a hand-engineered feature extraction module also makes it naturally adaptable to emerging LiDARs of different scanning patterns; The second main novelty is maintaining a map by an incremental k-d tree data structure, ikd-Tree, that enables incremental updates (i.e., point insertion, delete) and dynamic re-balancing. Compared with existing dynamic data structures (octree, R*-tree, nanoflann k-d tree), ikd-Tree achieves superior overall performance while naturally supports downsampling on the tree. We conduct an exhaustive benchmark comparison in 19 sequences from a variety of open LiDAR datasets. FAST-LIO2 achieves consistently higher accuracy at a much lower computation load than other state-of-the-art LiDAR-inertial navigation systems. Various real-world experiments on solid-state LiDARs with small FoV are also conducted. Overall, FAST-LIO2 is computationally-efficient (e.g., up to 100 Hz odometry and mapping in large outdoor environments), robust (e.g., reliable pose estimation in cluttered indoor environments with rotation up to 1000 deg/s), versatile (i.e., applicable to both multi-line spinning and solid-state LiDARs, UAV and handheld platforms, and Intel and ARM-based processors), while still achieving higher accuracy than existing methods. Our implementation of the system FAST-LIO2, and the data structure ikd-Tree are both open-sourced on Github.

Fanze Kong, Wei Xu, Fu Zhang

In practical applications, autonomous quadrotors are still facing significant challenges, such as the detection and avoidance of very small and even dynamic obstacles (e.g., tree branches, power lines). In this paper, we propose a compact, integrated, and fully autonomous quadrotor system, which can fly safely in cluttered environments while avoiding dynamic small obstacles. Our quadrotor platform is equipped with a forward-looking three-dimensional (3D) light detection and ranging (lidar) sensor to perceive the environment and an onboard embedded computer to perform all the estimation, mapping, and planning tasks. Specifically, the computer estimates the current pose of the UAV, maintains a local map (time-accumulated point clouds KD-Trees), and computes a safe trajectory using kinodynamic A* search to the goal point. The whole perception and planning system can run onboard at 50Hz with careful optimization. Various indoor and outdoor experiments show that the system can avoid dynamic small obstacles (down to 20mm diameter bar) while flying at 2m/s in cluttered environments. Our codes and hardware design are open-sourced on Github.

Jiarong Lin, Chunran Zheng, Wei Xu et al.

In this letter, we propose a robust, real-time tightly-coupled multi-sensor fusion framework, which fuses measurement from LiDAR, inertial sensor, and visual camera to achieve robust and accurate state estimation. Our proposed framework is composed of two parts: the filter-based odometry and factor graph optimization. To guarantee real-time performance, we estimate the state within the framework of error-state iterated Kalman-filter, and further improve the overall precision with our factor graph optimization. Taking advantage of measurement from all individual sensors, our algorithm is robust enough to various visual failure, LiDAR-degenerated scenarios, and is able to run in real-time on an on-board computation platform, as shown by extensive experiments conducted in indoor, outdoor, and mixed environment of different scale. Moreover, the results show that our proposed framework can improve the accuracy of state-of-the-art LiDAR-inertial or visual-inertial odometry. To share our findings and to make contributions to the community, we open source our codes on our Github.

Dongjiao He, Wei Xu, Fu Zhang

Kalman filter is presumably one of the most important and extensively used filtering techniques in modern control systems. Yet, nearly all current variants of Kalman filters are formulated in the Euclidean space $\mathbb{R}^n$, while many real-world systems (e.g., robotic systems) are really evolving on manifolds. In this paper, we propose a method to develop Kalman filters for such on-manifold systems. Utilizing $\boxplus$, $\boxminus$ operations and further defining an oplus operation on the respective manifold, we propose a canonical representation of the on-manifold system. Such a canonical form enables us to separate the manifold constraints from the system behaviors in each step of the Kalman filter, ultimately leading to a generic and symbolic Kalman filter framework that are naturally evolving on the manifold. Furthermore, the on-manifold Kalman filter is implemented as a toolkit in $C$++ packages which enables users to implement an on-manifold Kalman filter just like the normal one in $\mathbb{R}^n$: the user needs only to provide the system-specific descriptions, and then call the respective filter steps (e.g., predict, update) without dealing with any of the manifold constraints. The existing implementation supports full iterated Kalman filtering for systems on any manifold composed of $\mathbb{R}^n$, $SO(3)$ and $\mathbb{S}^2$, and is extendable to other types of manifold when necessary. The proposed symbolic Kalman filter and the developed toolkit are verified by implementing a tightly-coupled lidar-inertial navigation system. Results show that the developed toolkit leads to superior filtering performances and computation efficiency comparable to hand-engineered counterparts. Finally, the toolkit is opened sourced at https://github.com/hku-mars/IKFoM to assist practitioners to quickly deploy an on-manifold Kalman filter.

Wei Xu, Fu Zhang

This paper presents a computationally efficient and robust LiDAR-inertial odometry framework. We fuse LiDAR feature points with IMU data using a tightly-coupled iterated extended Kalman filter to allow robust navigation in fast-motion, noisy or cluttered environments where degeneration occurs. To lower the computation load in the presence of large number of measurements, we present a new formula to compute the Kalman gain. The new formula has computation load depending on the state dimension instead of the measurement dimension. The proposed method and its implementation are tested in various indoor and outdoor environments. In all tests, our method produces reliable navigation results in real-time: running on a quadrotor onboard computer, it fuses more than 1,200 effective feature points in a scan and completes all iterations of an iEKF step within 25 ms. Our codes are open-sourced on Github.

Jiacheng Wang, Zhedong Zheng, Wei Xu et al.

Given a single image of a target object, image-to-3D generation aims to reconstruct its texture and geometric shape. Recent methods often utilize intermediate media, such as multi-view images or videos, to bridge the gap between input image and the 3D target, thereby guiding the generation of both shape and texture. However, inconsistencies in the generated multi-view snapshots frequently introduce noise and artifacts along object boundaries, undermining the 3D reconstruction process. To address this challenge, we leverage 3D Gaussian Splatting (3DGS) for 3D reconstruction, and explicitly integrate uncertainty-aware learning into the reconstruction process. By capturing the stochasticity between two Gaussian models, we estimate an uncertainty map, which is subsequently used for uncertainty-aware regularization to rectify the impact of inconsistencies. Specifically, we optimize both Gaussian models simultaneously, calculating the uncertainty map by evaluating the discrepancies between rendered images from identical viewpoints. Based on the uncertainty map, we apply adaptive pixel-wise loss weighting to regularize the models, reducing reconstruction intensity in high-uncertainty regions. This approach dynamically detects and mitigates conflicts in multi-view labels, leading to smoother results and effectively reducing artifacts. Extensive experiments show the effectiveness of our method in improving 3D generation quality by reducing inconsistencies and artifacts.

Guozheng Lu, Wei Xu, Fu Zhang

We consider the problem of bridging the gap between geometric tracking control theory and implementation of model predictive control (MPC) for robotic systems operating on manifolds. We propose a generic on-manifold MPC formulation based on a canonical representation of the system evolving on manifolds. Then, we present a method that solves the on-manifold MPC formulation by linearizing the system along the trajectory under tracking. There are two main advantages of the proposed scheme. The first is that the linearized system leads to an equivalent error system represented by a set of minimal parameters without any singularity. Secondly, the process of system modeling, error-system derivation, linearization and control has the manifold constraints completely decoupled from the system descriptions, enabling the development of a symbolic MPC framework that naturally encapsulates the manifold constraints. In this framework, users need only to supply system-specific descriptions without dealing with the manifold constraints. We implement this framework and test it on a quadrotor unmanned aerial vehicle (UAV) operating on $SO(3) \times \mathbb{R}^n$ and an unmanned ground vehicle (UGV) moving on a curved surface. Real-world experiments show that the proposed framework and implementation achieve high tracking performance and computational efficiency even in highly aggressive aerobatic quadrotor maneuvers.

Yixi Cai, Wei Xu, Fu Zhang

This paper proposes an efficient data structure, ikd-Tree, for dynamic space partition. The ikd-Tree incrementally updates a k-d tree with new coming points only, leading to much lower computation time than existing static k-d trees. Besides point-wise operations, the ikd-Tree supports several features such as box-wise operations and down-sampling that are practically useful in robotic applications. In parallel to the incremental operations (i.e., insert, re-insert, and delete), ikd-Tree actively monitors the tree structure and partially re-balances the tree, which enables efficient nearest point search in later stages. The ikd-Tree is carefully engineered and supports multi-thread parallel computing to maximize the overall efficiency. We validate the ikd-Tree in both theory and practical experiments. On theory level, a complete time complexity analysis is presented to prove the high efficiency. On experiment level, the ikd-Tree is tested on both randomized datasets and real-world LiDAR point data in LiDAR-inertial odometry and mapping application. In all tests, ikd-Tree consumes only 4% of the running time in a static k-d tree.

Youming Qin, Yihang Li, Xu Wei et al.

Exploiting contacts with environment structures provides extra force support to a UAV, often reducing the power consumption and hence extending the mission time. This paper investigates one such way to exploit flat surfaces in the environment by a novel aerial-ground hybrid locomotion. Our design is a single passive wheel integrated at the UAV bottom, serving a minimal design to date. We present the principle and implementation of such a simple design as well as its control. Flight experiments are conducted to verify the feasibility and the power saving caused by the ground locomotion. Results show that our minimal design allows successful aerial-ground hybrid locomotion even with a less-controllable bi-copter UAV. The ground locomotion saves up to 77% battery without much tuning effort.