Insects control unsteady aerodynamic forces on flapping wings to navigate complex environments. While understanding these forces is vital for biology, physics, and engineering, existing evaluation methods face trade-offs: high-fidelity simulations are computationally or experimentally expensive and lack explanatory power, whereas theoretical models based on quasi-steady assumptions offer insights but exhibit low accuracy. To overcome these limitations and thus enhance the accuracy of quasi-steady aerodynamic models, we applied a data-driven approach involving discovery and formulation of previously overlooked critical mechanisms. Through selection from 5,000 candidate kinematic functions, we identified mathematical expressions for three key additional mechanisms -- the effect of advance ratio, effect of spanwise kinematic velocity, and rotational Wagner effect -- which had been qualitatively recognized but were not formulated. Incorporating these mechanisms considerably reduced the prediction errors of the quasi-steady model using the computational fluid dynamics results as the ground truth, both in hawkmoth forward flight (at high Reynolds numbers) and fruit fly maneuvers (at low Reynolds numbers). The data-driven quasi-steady model enables rapid aerodynamic analysis, serving as a practical tool for understanding evolutionary adaptations in insect flight and developing bio-inspired flying robots.

Accurate estimation of aerodynamic forces is essential for advancing the control, modeling, and design of flapping-wing aerial robots with dynamic morphing capabilities. In this paper, we investigate two distinct methodologies for force estimation on Aerobat, a bio-inspired flapping-wing platform designed to emulate the inertial and aerodynamic behaviors observed in bat flight. Our goal is to quantify aerodynamic force contributions during tethered flight, a crucial step toward closed-loop flight control. The first method is a physics-based observer derived from Hamiltonian mechanics that leverages the concept of conjugate momentum to infer external aerodynamic forces acting on the robot. This observer builds on the system's reduced-order dynamic model and utilizes real-time sensor data to estimate forces without requiring training data. The second method employs a neural network-based regression model, specifically a multi-layer perceptron (MLP), to learn a mapping from joint kinematics, flapping frequency, and environmental parameters to aerodynamic force outputs. We evaluate both estimators using a 6-axis load cell in a high-frequency data acquisition setup that enables fine-grained force measurements during periodic wingbeats. The conjugate momentum observer and the regression model demonstrate strong agreement across three force components (Fx, Fy, Fz).

These physical constraints cannot be fully addressed through advancements in control algorithms alone. Drawing inspiration from the winged flying squirrel, this paper proposes a highly maneuverable drone with agility-enhancing foldable wings. The additional air resistance generated by appropriately deploying these wings significantly improves the tracking performance of the proposed "flying squirrel" drone. By leveraging collaborative control between the conventional propeller system and the foldable wings--coordinated through the Thrust-Wing Coordination Control (TWCC) framework--the controllable acceleration set is expanded, allowing for the production of abrupt vertical forces unachievable with traditional wingless drones. The complex aerodynamics of the foldable wings are captured using a physics-assisted recurrent neural network (paRNN), which calibrates the angle of attack (AOA) to align with the real-world aerodynamic behavior of the wings. The model is trained on real-world flight data and incorporates flat-plate aerodynamic principles. Experimental results demonstrate that the proposed flying squirrel drone achieves a 13.1% improvement in tracking performance, as measured by root mean square error (RMSE), compared to a conventional wingless drone. A demonstration video is available on Y ouT ube: https://youtu.be/O8nrip18azY .

In systems control, the dynamics of a system are governed by modulating its inputs to achieve a desired outcome. For example, to control the thrust of a quad-copter propeller the controller modulates its rotation rate, relying on a straightforward mapping between the input rotation rate and the resulting thrust. This mapping can be inverted to determine the rotation rate needed to generate a desired thrust. However, in complex systems, such as flapping-wing robots where intricate fluid motions are involved, mapping inputs (wing kinematics) to outcomes (aerodynamic forces) is nontrivial and inverting this mapping for real-time control is computationally impractical. Here, we report a machine-learning solution for the inverse mapping of a flapping-wing system based on data from an experimental system we have developed. Our model learns the input wing motion required to generate a desired aerodynamic force outcome. We used a sequence-to-sequence model tailored for time-series data and augmented it with a novel adaptive-spectrum layer that implements representation learning in the frequency domain. To train our model, we developed a flapping wing system that simultaneously measures the wing's aerodynamic force and its 3D motion using high-speed cameras. We demonstrate the performance of our system on an additional open-source dataset of a flapping wing in a different flow regime. Results show superior performance compared with more complex state-of-the-art transformer-based models, with 11% improvement on the test datasets median loss. Moreover, our model shows superior inference time, making it practical for onboard robotic control. Our open-source data and framework may improve modeling and real-time control of systems governed by complex dynamics, from biomimetic robots to biomedical devices.

Bird-sized flapping-wing robots offer significant potential for agile flight in complex environments, but achieving agile and robust trajectory tracking remains a challenge due to the complex aerodynamics and highly nonlinear dynamics inherent in flapping-wing flight. In this work, a learning-based control approach is introduced to unlock the versatility and adaptiveness of flapping-wing flight. We propose a model-free reinforcement learning (RL)-based framework for a high degree-of-freedom (DoF) bird-inspired flapping-wing robot that allows for multimodal flight and agile trajectory tracking. Stability analysis was performed on the closed-loop system comprising of the flapping-wing system and the RL policy. Additionally, simulation results demonstrate that the RL-based controller can successfully learn complex wing trajectory patterns, achieve stable flight, switch between flight modes spontaneously, and track different trajectories under various aerodynamic conditions.

Nonlinear aeroelastic reduced-order models (ROMs) based on machine learning or artificial intelligence algorithms can be complex and computationally demanding to train, meaning that for practical aeroelastic applications, the conservative nature of linearization is often favored. Therefore, there is a requirement for novel nonlinear aeroelastic model reduction approaches that are accurate, simple and, most importantly, efficient to generate. This paper proposes a novel formulation for the identification of a compact multi-input Volterra series, where Orthogonal Matching Pursuit is used to obtain a set of optimally sparse nonlinear multi-input ROM coefficients from unsteady aerodynamic training data. The framework is exemplified using the Benchmark Supercritical Wing, considering; forced response, flutter and limit cycle oscillation. The simple and efficient Optimal Sparsity Multi-Input ROM (OSM-ROM) framework performs with high accuracy compared to the full-order aeroelastic model, requiring only a fraction of the tens-of-thousands of possible multi-input terms to be identified and allowing a 96% reduction in the number of training samples.

Tail-sitters, with the advantages of both the fixed-wing unmanned aerial vehicles (UAVs) and vertical take-off and landing UAVs, have been widely designed and researched in recent years. With the change in modern UAV application scenarios, it is required that UAVs have fast maneuverable three-dimensional flight capabilities. Due to the highly nonlinear aerodynamics produced by the fuselage and wings of the tail-sitter, how to quickly generate a smooth and executable trajectory is a problem that needs to be solved urgently. We constrain the speed of the tail-sitter, eliminate the differential dynamics constraints in the trajectory generation process of the tail-sitter through differential flatness, and allocate the time variable of the trajectory through the state-of-the-art trajectory generation method named MINCO. By discretizing the trajectory in time, we convert the speed constraint on the vehicle into a soft constraint, thereby achieving the time-optimal trajectory for the tail-sitter to fly through any given waypoints.

The 3D flight control of a flapping wing robot is a very challenging problem. The robot stabilizes and controls its pose through the aerodynamic forces acting on the wing membrane which has complex dynamics and it is difficult to develop a control method to interact with such a complex system. Bats, in particular, are capable of performing highly agile aerial maneuvers such as tight banking and bounding flight solely using their highly flexible wings. In this work, we develop a control method for a bio-inspired bat robot, the Aerobat, using small low-powered actuators to manipulate the flapping gait and the resulting aerodynamic forces. We implemented a controller based on collocation approach to track a desired roll and perform a banking maneuver to be used in a trajectory tracking controller. This controller is implemented in a simulation to show its performance and feasibility.

Neglecting complex aerodynamic effects hinders high-speed yet high-precision multirotor autonomy. In this paper, we present a computationally efficient learning-based model predictive controller that simultaneously optimizes a trajectory that can be tracked within the physical limits (on thrust and orientation) of the multirotor system despite unknown aerodynamic forces and adapts the control input. To do this, we leverage the well-known differential flatness property of multirotors, which allows us to transform their nonlinear dynamics into a linear model. The main limitation of current flatness-based planning and control approaches is that they often neglect dynamic feasibility. This is because these constraints are nonlinear as a result of the mapping between the input, i.e., multirotor thrust, and the flat state. In our approach, we learn a novel representation of the drag forces by learning the mapping from the flat state to the multirotor thrust vector (in a world frame) as a Gaussian Process (GP). Our proposed approach leverages the properties of GPs to develop a convex optimal controller that can be iteratively solved as a second-order cone program (SOCP). In simulation experiments, our proposed approach outperforms related model predictive controllers that do not account for aerodynamic effects on trajectory feasibility, leading to a reduction of up to 55% in absolute tracking error.

This paper presents a novel VTOL UAV that owns a link connecting four rotors and a fuselage by a passive joint, allowing the control of the rotor's tilting angle by adjusting the rotors' thrust. This unique structure contributes to eliminating additional actuators, such as servo motors, to control the tilting angles of rotors, resulting in the UAV's weight lighter and simpler structure. We first derive the dynamical model of the newly designed UAV and analyze its controllability. Then, we design the controller that leverages the tiltable link with four rotors to accelerate the UAV while suppressing a deviation of the UAV's angle of attack from the desired value to restrain the change of the aerodynamic force. Finally, the validity of the proposed control strategy is evaluated in simulation study.