Global Existence and Aggregation of Chemotaxis-fluid Systems in dimension two

To describe the cellular self-aggregation phenomenon, some strongly coupled PDEs named as Patlak--Keller--Segel (PKS) systems were proposed in 1970s. Since PKS systems possess relatively simple structures but admit rich dynamics, plenty of scholars have studied them and obtained many significant results. However, the cells or bacteria in general direct their movement in liquid. As a consequence, it seems more realistic to consider the influence of ambient fluid flow on the chemotactic mechanism. Motivated by this, we consider the chemotaxis-fluid model proposed by He et al. (SIAM J. Math. Anal., Vol. 53, No. 3, 2021) in the two-dimensional bounded domain. It is well-known that the PKS system admits the critical mass phenomenon in 2D and for the whole space $\mathbb R^2$, He et al. also showed there exists the same phenomenon in the chemotaxis-fluid system. In this paper, we first study the global well-posedness of two-dimensional chemotaxis-fluid model in the bounded domain and prove the solution exists globally with the subcritical mass. Then concerning the critical mass case, we construct the boundary spot steady states rigorously via the inner-outer gluing method. While studying the concentration phenomenon with the critical mass, we develop the global $W^{2,p}$ theory of the stationary Stokes operator in 2D

Trajectory Generation and Tracking Control for Aggressive Tail-Sitter Flights

We address the theoretical and practical problems related to the trajectory generation and tracking control of tail-sitter UAVs. Theoretically, we focus on the differential flatness property with full exploitation of actual UAV aerodynamic models, which lays a foundation for generating dynamically feasible trajectory and achieving high-performance tracking control. We have found that a tail-sitter is differentially flat with accurate aerodynamic models within the entire flight envelope, by specifying coordinate flight condition and choosing the vehicle position as the flat output. This fundamental property allows us to fully exploit the high-fidelity aerodynamic models in the trajectory planning and tracking control to achieve accurate tail-sitter flights. Particularly, an optimization-based trajectory planner for tail-sitters is proposed to design high-quality, smooth trajectories with consideration of kinodynamic constraints, singularity-free constraints and actuator saturation. The planned trajectory of flat output is transformed to state trajectory in real-time with consideration of wind in environments. To track the state trajectory, a global, singularity-free, and minimally-parameterized on-manifold MPC is developed, which fully leverages the accurate aerodynamic model to achieve high-accuracy trajectory tracking within the whole flight envelope. The effectiveness of the proposed framework is demonstrated through extensive real-world experiments in both indoor and outdoor field tests, including agile SE(3) flight through consecutive narrow windows requiring specific attitude and with speed up to 10m/s, typical tail-sitter maneuvers (transition, level flight and loiter) with speed up to 20m/s, and extremely aggressive aerobatic maneuvers (Wingover, Loop, Vertical Eight and Cuban Eight) with acceleration up to 2.5g

Joint Intrinsic and Extrinsic LiDAR-Camera Calibration in Targetless Environments Using Plane-Constrained Bundle Adjustment

This paper introduces a novel targetless method for joint intrinsic and extrinsic calibration of LiDAR-camera systems using plane-constrained bundle adjustment (BA). Our method leverages LiDAR point cloud measurements from planes in the scene, alongside visual points derived from those planes. The core novelty of our method lies in the integration of visual BA with the registration between visual points and LiDAR point cloud planes, which is formulated as a unified optimization problem. This formulation achieves concurrent intrinsic and extrinsic calibration, while also imparting depth constraints to the visual points to enhance the accuracy of intrinsic calibration. Experiments are conducted on both public data sequences and self-collected dataset. The results showcase that our approach not only surpasses other state-of-the-art (SOTA) methods but also maintains remarkable calibration accuracy even within challenging environments. For the benefits of the robotics community, we have open sourced our codes

Swashplateless-elevon Actuation for a Dual-rotor Tail-sitter VTOL UAV

In this paper, we propose a novel swashplateless-elevon actuation (SEA) for dual-rotor tail-sitter vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs). In contrast to the conventional elevon actuation (CEA) which controls both pitch and yaw using elevons, the SEA adopts swashplateless mechanisms to generate an extra moment through motor speed modulation to control pitch and uses elevons solely for controlling yaw, without requiring additional actuators. This decoupled control strategy mitigates the saturation of elevons' deflection needed for large pitch and yaw control actions, thus improving the UAV's control performance on trajectory tracking and disturbance rejection performance in the presence of large external disturbances. Furthermore, the SEA overcomes the actuation degradation issues experienced by the CEA when the UAV is in close proximity to the ground, leading to a smoother and more stable take-off process. We validate and compare the performances of the SEA and the CEA in various real-world flight conditions, including take-off, trajectory tracking, and hover flight and position steps under external disturbance. Experimental results demonstrate that the SEA has better performances than the CEA. Moreover, we verify the SEA's feasibility in the attitude transition process and fixed-wing-mode flight of the VTOL UAV. The results indicate that the SEA can accurately control pitch in the presence of high-speed incoming airflow and maintain a stable attitude during fixed-wing mode flight. Video of all experiments can be found in youtube.com/watch?v=Sx9Rk4Zf7sQComment: 8 pages, 13 figure