A CFD-informed quasi-steady model of flapping wing aerodynamics

Quasi-steady aerodynamic modeling and dynamic stability of mosquito-inspired flapping wing pico aerial vehicle

Recent exploration in insect-inspired robotics has generated considerable interest. Among insects navigating at low Reynolds numbers, mosquitoes exhibit distinct flight characteristics, including higher wingbeat frequencies, reduced stroke amplitudes, and slender wings. This leads to unique aerodynamic traits such as trailing edge vortices via wake capture, diminished reliance on leading vortices, and rotational drag. This paper shows the energetic analysis of a mosquito-inspired flapping-wing Pico aerial vehicle during hovering, contributing insights to its future design and fabrication. The investigation relies on kinematic and quasi-steady aerodynamic modeling of a symmetric flapping-wing model with a wingspan of approximately 26 mm, considering translational, rotational, and wake capture force components. The control strategy adapts existing bird flapping wing approaches to accommodate insect wing kinematics and aerodynamic features. Flight controller design is grounded in understanding the impact of kinematics on wing forces. Additionally, a thorough analysis of the dynamic stability of the mosquito-inspired PAV model is conducted, revealing favorable controller response and maneuverability at a small scale. The modified model, incorporating rigid body dynamics and non-averaged aerodynamics, exhibits weak stability without a controller or sufficient power density. However, the controller effectively stabilizes the PAV model, addressing attitude and maneuverability. These preliminary findings offer valuable insights for the mechanical design, aerodynamics, and fabrication of RoboMos, an insect-inspired flapping wing pico aerial vehicle developed at UPM Malaysia.

Closed-loop nonlinear optimal control design for flapping-wing flying robot (1.6 m wingspan) in indoor confined space: Prototyping, modeling, simulation, and experiment

The flapping-wing technology has emerged recently in the application of unmanned aerial robotics for autonomous flight, control, inspection, monitoring, and manipulation. Despite the advances in applications and outdoor manual flights (open-loop control), closed-loop control is yet to be investigated. This work presents a nonlinear optimal closed-loop control design via the state-dependent Riccati equation (SDRE) for a flapping-wing flying robot (FWFR). Considering that the dynamic modeling of the flapping-wing robot is complex, a proper model for the implementation of nonlinear control methods is demanded. This work proposes an alternative approach to deliver an equivalent dynamic for the translation of the system and a simplified model for orientation, to find equivalent dynamics for the whole system. The objective is to see the effect of flapping (periodic oscillation) on behavior through a simple model in simulation. Then the SDRE controller is applied to the derived model and implemented in simulations and experiments. The robot bird is a 1.6 m wingspan flapping-wing system (six-degree-of-freedom robot) with four actuators, three in the tail, and one as the flapping input. The underactuated system has been controlled successfully in position and orientation. The control loop is closed by the motion capture system in the indoor test bed where the experiments of flight have been successfully done.

Computational Fluid Dynamics Analysis in Biomimetics Applications: A Review from Aerospace Engineering Perspective

In many modern engineering fields, computational fluid dynamics (CFD) has been adopted as a methodology to solve complex problems. CFD is becoming a key component in developing updated designs and optimization through computational simulations, resulting in lower operating costs and enhanced efficiency. Even though the biomimetics application is complex in adapting nature to inspire new capabilities for exciting future technologies, the recent CFD in biomimetics is more accessible and practicable due to the availability of high-performance hardware and software with advances in computer sciences. Many simulations and experimental results have been used to study the analyses in biomimetics applications, particularly those related to aerospace engineering. There are numerous examples of biomimetic successes that involve making simple copies, such as the use of fins for swimming or the mastery of flying, which became possible only after the principles of aerodynamics were better understood. Therefore, this review discusses the essential methodology of CFD as a reliable tool for researchers in understanding the technology inspired by nature and an outlook for potential development through simulations. CFD plays a major role as decision support prior to undertaking a real commitment to execute any design inspired by nature and providing the direction to develop new capabilities of technologies.

Video-driven simulation of lower limb mechanical loading during aquatic exercises

Understanding the mechanical demands of an exercise on the musculoskeletal system is crucial to prescribe effective training or therapeutic interventions. Yet, that knowledge is currently limited in water, mostly because of the difficulty in evaluating external resistance. Here I reconcile recent advances in 3D markerless pose and mesh estimation, biomechanical simulations, and hydrodynamic modeling, to predict lower limb mechanical loading during aquatic exercises. Simulations are driven exclusively from a single video. Fluid forces were estimated within 12.5±4.1% of the peak forces determined through computational fluid dynamics analyses, at a speed three orders of magnitude greater. In silico hip and knee resultant joint forces agreed reasonably well with in vivo instrumented implant recordings (R²=0.74) downloaded from the OrthoLoad database, both in magnitude (RMSE =251±125 N) and direction (cosine similarity = 0.92±0.09). Hip flexors, glutes, adductors, and hamstrings were the main contributors to hip joint compressive forces (40.4±12.7%, 25.6±9.7%, 14.2±4.8%, 13.0±8.2%, respectively), while knee compressive forces were mostly produced by the gastrocnemius (39.1±15.9%) and vasti (29.4±13.7%). Unlike dry-land locomotion, non-hip- and non-knee-spanning muscles provided little to no offloading effect via dynamic coupling. This noninvasive method has the potential to standardize the reporting of exercise intensity, inform the design of rehabilitation protocols and improve their reproducibility.

Review of insect-inspired wing micro air vehicle

Micro air vehicles (MAVs) have wide application prospects in environmental monitoring, disaster rescue and other civil fields because of their flexibility and maneuverability. Compared with fixed wing and rotary wing aircraft, flapping wing micro air vehicles (FWMAVs) have higher energy utilization efficiency and lower cost and have attracted extensive attention from scientists. Insects have become excellent bionic objects for the study of FWMAVs due to their characteristics of low Reynolds number, low noise, hoverability, small size and light weight. By mimicking flying insects, it may be possible to create highly efficient biomimetic FWMAVs. In this paper, insect flight aerodynamics are reviewed, and the mechanism designs of insect-inspired FWMAVs and their aerodynamics are summarized, including the wing type effect, vibration characteristics and aerodynamic characteristics of the flapping wing.

Dynamic experimental rigs for investigation of insect wing aerodynamics

This paper provides a systematic and critical review of dynamic experimental rigs used for insect wing aerodynamics research. The goal is to facilitate meaningful comparison of data from existing rigs and provide insights for designers of new rigs. The scope extends from simple one degree of freedom rotary rigs to multi degrees of freedom rigs allowing various rotation and translation motions. Experimental methods are characterized using a consistent set of parameters that allows objective comparison of different approaches. A comprehensive catalogue is presented for the tested flow conditions (assessed through Reynolds number, Rossby number and advance ratio), wing morphologies (assessed through aspect ratio, planform shape and thickness to mean chord ratio) and kinematics (assessed through motion degrees of freedom). Links are made between the type of aerodynamic characteristics being studied and the type of experimental set-up used. Rig mechanical design considerations are assessed, and the aerodynamic measurements obtained from these rigs are discussed.

State-space aerodynamic model reveals high force control authority and predictability in flapping flight

Flying animals resort to fast, large-degree-of-freedom motion of flapping wings, a key feature that distinguishes them from rotary or fixed-winged robotic fliers with limited motion of aerodynamic surfaces. However, flapping-wing aerodynamics are characterized by highly unsteady and three-dimensional flows difficult to model or control, and accurate aerodynamic force predictions often rely on expensive computational or experimental methods. Here, we developed a computationally efficient and data-driven state-space model to dynamically map wing kinematics to aerodynamic forces/moments. This model was trained and tested with a total of 548 different flapping-wing motions and surpassed the accuracy and generality of the existing quasi-steady models. This model used 12 states to capture the unsteady and nonlinear fluid effects pertinent to force generation without explicit information of fluid flows. We also provided a comprehensive assessment of the control authority of key wing kinematic variables and found that instantaneous aerodynamic forces/moments were largely predictable by the wing motion history within a half-stroke cycle. Furthermore, the angle of attack, normal acceleration and pitching motion had the strongest effects on the aerodynamic force/moment generation. Our results show that flapping flight inherently offers high force control authority and predictability, which can be key to developing agile and stable aerial fliers.

A semi-empirical model of the aerodynamics of manoeuvring insect flight

Blade element modelling provides a quick analytical method for estimating the aerodynamic forces produced during insect flight, but such models have yet to be tested rigorously using kinematic data recorded from free-flying insects. This is largely because of the paucity of detailed free-flight kinematic data, but also because analytical limitations in existing blade element models mean that they cannot incorporate the complex three-dimensional movements of the wings and body that occur during insect flight. Here, we present a blade element model with empirically fitted aerodynamic force coefficients that incorporates the full three-dimensional wing kinematics of manoeuvring Eristalis hoverflies, including torsional deformation of their wings. The two free parameters were fitted to a large free-flight dataset comprising N = 26 541 wingbeats, and the fitted model captured approximately 80% of the variation in the stroke-averaged forces in the sagittal plane. We tested the robustness of the model by subsampling the data, and found little variation in the parameter estimates across subsamples comprising 10% of the flight sequences. The simplicity and generality of the model that we present is such that it can be readily applied to kinematic datasets from other insects, and also used for the study of insect flight dynamics.

Data-driven CFD Scaling of Bioinspired Mars Flight Vehicles for Hover

One way to improve our model of Mars is through aerial sampling and surveillance, which could provide information to augment the observations made by ground-based exploration and satellite imagery. Flight in the challenging ultra-low-density Martian environment can be achieved with properly scaled bioinspired flapping wing vehicle configurations that utilize the same high lift producing mechanisms that are employed by insects on Earth. Through dynamic scaling of wings and kinematics, we investigate the ability to generate solutions for a broad range of flapping wing flight vehicles masses ranging from insects O(10-3) kg to the Mars helicopter Ingenuity O(100) kg. A scaling method based on a neural-network trained on 3D Navier-Stokes solutions is proposed to determine approximate wing size and kinematic values that generate bioinspired hover solutions. We demonstrate that a family of solutions exists for designs that range from 1 to 1000 grams, which are verified and examined using a 3D Navier-Stokes solver. Our results reveal that unsteady lift enhancement mechanisms, such as delayed stall and rotational lift, are present in the bioinspired solutions for the scaled vehicles hovering in Martian conditions. These hovering vehicles exhibit payloads of up to 1 kg and flight times on the order of 100 minutes when considering the respective limiting cases of the vehicle mass being comprised entirely of payload or entirely of a battery and neglecting any transmission inefficiencies. This method can help to develop a range of Martian flying vehicle designs with mission viable payloads, range, and endurance.

Review on System Identification and Mathematical Modeling of Flapping Wing Micro-Aerial Vehicles

This paper presents a thorough review on the system identification techniques applied to flapping wing micro air vehicles (FWMAVs). The main advantage of this work is to provide a solid background and domain knowledge of system identification for further investigations in the field of FWMAVs. In the system identification context, the flapping wing systems are first categorized into tailed and tailless MAVs. The most recent developments related to such systems are reported. The system identification techniques used for FWMAVs can be classified into time-response based identification, frequency-response based identification, and the computational fluid-dynamics based computation. In the system identification scenario, least mean square estimation is used for a beetle mimicking system recognition. In the end, this review work is concluded and some recommendations for the researchers working in this area are presented.

A Modified Quasisteady Aerodynamic Model for a Sub-100 mg Insect-Inspired Flapping-Wing Robot

This study proposes a modified quasisteady aerodynamic model for the sub-100-milligram insect-inspired flapping-wing robot presented by the authors in a previous paper. The model, which is based on blade-element theory, considers the aerodynamic mechanisms of circulation, dissipation, and added-mass, as well as the inertial effect. The aerodynamic force and moment acting on the wing are calculated based on the two-degree-of-freedom (2-DOF) wing kinematics of flapping and rotating. In order to validate the model, we used a binocular high-speed photography system and a customized lift measurement system to perform simultaneous measurements of the wing kinematics and the lift of the robot under different input voltages. The results of these measurements were all in close agreement with the estimates generated by the proposed model. In addition, based on the model, this study analyzes the 2-DOF flapping-wing dynamics of the robot and provides an estimate of the passive rotation—the main factor in generating lift—from the measured flapping kinematics. The analysis also reveals that the calculated rotating kinematics of the wing under different input voltages accord well with the measured rotating kinematics. We expect that the model presented here will be useful in developing a control strategy for our sub-100 mg insect-inspired flapping-wing robot.

Effects of timing and magnitude of wing stroke-plane tilt on the escape maneuverability of flapping wing

Hummingbirds perform a variety of agile maneuvers, and one of them is the escape maneuver, in which the birds can steer away from threats using only 3-4 wingbeats in less than 150 ms. A distinct kinematic feature that enables the escape maneuver is the rapid backward tilt of the wing stroke plane at the beginning of the maneuver. This feature results in a simultaneous nose-up pitching and backward acceleration. In this work, we investigated how the magnitude and timing of the wing stroke-plane tilt (relative to the phase of flapping cycle) affected the generation of backward thrust, lift, and pitching moment and therefore the maneuverability of escape flight. Investigations were performed using experiments on dynamically scaled robotic wings and computational fluid dynamic simulation based on a simplified harmonic wing stroke and rotation kinematics at Re = 1000 and hummingbird wing kinematics at Re ≈ 10 000. Results showed that the wing stroke-plane tilt timing exerted a strong influence on the aerodynamic force generation. Independent of the tilt magnitude, the averaged backward thrust and pitching moment were maximized when the stroke plane tilt occurred near the end of the half strokes (e.g., upstroke and downstroke). Relative to the other timings of stroke-plane tilt, the 'optimal' timings led to a maximal backward tilt of the total aerodynamic force during the wing upstroke; hence, the backward thrust and nose-up pitching moment increased. The 'optimal' timings found in this work were in good agreement with those identified in the escape maneuvers of four species of hummingbirds. Therefore, hummingbirds may use a similar strategy in the beginning of their escape maneuver.

Reconstructing full-field flapping wing dynamics from sparse measurements

Flapping insect wings deform during flight. This deformation benefits the insect's aerodynamic force production as well as energetic efficiency. However, it is challenging to measure wing displacement field in flying insects. Many points must be tracked over the wing's surface to resolve its instantaneous shape. To reduce the number of points one is required to track, we propose a physics-based reconstruction method called system equivalent reduction expansion processes to estimate wing deformation and strain from sparse measurements. Measurement locations are determined using a weighted normalized modal displacement method. We experimentally validate the reconstruction technique by flapping a paper wing from 5-9 Hz with 45° and measuring strain at three locations. Two measurements are used for the reconstruction and the third for validation. Strain reconstructions had a maximal error of 30% in amplitude. We extend this methodology to a more realistic insect wing through numerical simulation. We show that wing displacement can be estimated from sparse displacement or strain measurements, and that additional sensors spatially average measurement noise to improve reconstruction accuracy. This research helps overcome some of the challenges of measuring full-field dynamics in flying insects and provides a framework for strain-based sensing in insect-inspired flapping robots.

Birds repurpose the role of drag and lift to take off and land

The lift that animal wings generate to fly is typically considered a vertical force that supports weight, while drag is considered a horizontal force that opposes thrust. To determine how birds use lift and drag, here we report aerodynamic forces and kinematics of Pacific parrotlets (Forpus coelestis) during short, foraging flights. At takeoff they incline their wing stroke plane, which orients lift forward to accelerate and drag upward to support nearly half of their bodyweight. Upon landing, lift is oriented backward to contribute a quarter of the braking force, which reduces the aerodynamic power required to land. Wingbeat power requirements are dominated by downstrokes, while relatively inactive upstrokes cost almost no aerodynamic power. The parrotlets repurpose lift and drag during these flights with lift-to-drag ratios below two. Such low ratios are within range of proto-wings, showing how avian precursors may have relied on drag to take off with flapping wings.

Recent work has suggested that lift and drag may be employed differently in slow, flapping flight compared to classic flight aerodynamics. Here the authors develop a method to measure vertical and horizontal aerodynamic forces simultaneously and use it to quantify lift and drag during slow flight.

A chordwise offset of the wing-pitch axis enhances rotational aerodynamic forces on insect wings: a numerical study

Most flying animals produce aerodynamic forces by flapping their wings back and forth with a complex wingbeat pattern. The fluid dynamics that underlies this motion has been divided into separate aerodynamic mechanisms of which rotational lift, that results from fast wing pitch rotations, is particularly important for flight control and manoeuvrability. This rotational force mechanism has been modelled using Kutta-Joukowski theory, which combines the forward stroke motion of the wing with the fast pitch motion to compute forces. Recent studies, however, suggest that hovering insects can produce rotational forces at stroke reversal, without a forward motion of the wing. We have conducted a broad numerical parametric study over a range of wing morphologies and wing kinematics to show that rotational force production depends on two mechanisms: (i) conventional Kutta-Joukowski-based rotational forces and (ii) a rotational force mechanism that enables insects with an offset of the pitch axis relative to the wing's chordwise symmetry axis to generate rotational forces in the absence of forward wing motion. Because flying animals produce control actions frequently near stroke reversal, this pitch-axis-offset dependent aerodynamic mechanism may be particularly important for understanding control and manoeuvrability in natural flyers.

UAV-Borne Dual-Band Sensor Method for Monitoring Physiological Crop Status

Unmanned aerial vehicles (UAVs) equipped with dual-band crop-growth sensors can achieve high-throughput acquisition of crop-growth information. However, the downwash airflow field of the UAV disturbs the crop canopy during sensor measurements. To resolve this issue, we used computational fluid dynamics (CFD), numerical simulation, and three-dimensional airflow field testers to study the UAV-borne multispectral-sensor method for monitoring crop growth. The results show that when the flying height of the UAV is 1 m from the crop canopy, the generated airflow field on the surface of the crop canopy is elliptical, with a long semiaxis length of about 0.45 m and a short semiaxis of about 0.4 m. The flow-field distribution results, combined with the sensor's field of view, indicated that the support length of the UAV-borne multispectral sensor should be 0.6 m. Wheat test results showed that the ratio vegetation index (RVI) output of the UAV-borne spectral sensor had a linear fit coefficient of determination (R²) of 0.81, and a root mean square error (RMSE) of 0.38 compared with the ASD Fieldspec2 spectrometer. Our method improves the accuracy and stability of measurement results of the UAV-borne dual-band crop-growth sensor. Rice test results showed that the RVI value measured by the UAV-borne multispectral sensor had good linearity with leaf nitrogen accumulation (LNA), leaf area index (LAI), and leaf dry weight (LDW); R² was 0.62, 0.76, and 0.60, and RMSE was 2.28, 1.03, and 10.73, respectively. Our monitoring method could be well-applied to UAV-borne dual-band crop growth sensors.

Quasi-Steady versus Navier–Stokes Solutions of Flapping Wing Aerodynamics

Various tools have been developed to model the aerodynamics of flapping wings. In particular, quasi-steady models, which are considerably faster and easier to solve than the Navier–Stokes equations, are often utilized in the study of flight dynamics of flapping wing flyers. However, the accuracy of the quasi-steady models has not been properly documented. The objective of this study is to assess the accuracy of a quasi-steady model by comparing the resulting aerodynamic forces against three-dimensional (3D) Navier–Stokes solutions. The same wing motion is prescribed at a fruit fly scale. The pitching amplitude, axis, and duration are varied. Comparison of the aerodynamic force coefficients suggests that the quasi-steady model shows significant discrepancies under extreme pitching motions, i.e., the pitching motion is large, quick, and occurs about the leading or trailing edge. The differences are as large as 1.7 in the cycle-averaged lift coefficient. The quasi-steady model performs well when the kinematics are mild, i.e., the pitching motion is small, long, and occurs near the mid-chord with a small difference in the lift coefficient of 0.01. Our analysis suggests that the main source for the error is the inaccuracy of the rotational lift term and the inability to model the wing-wake interaction in the quasi-steady model.

The comparative hydrodynamics of rapid rotation by predatory appendages

Countless aquatic animals rotate appendages through the water, yet fluid forces are typically modeled with translational motion. To elucidate the hydrodynamics of rotation, we analyzed the raptorial appendages of mantis shrimp (Stomatopoda) using a combination of flume experiments, mathematical modeling and phylogenetic comparative analyses. We found that computationally efficient blade-element models offered an accurate first-order approximation of drag, when compared with a more elaborate computational fluid-dynamic model. Taking advantage of this efficiency, we compared the hydrodynamics of the raptorial appendage in different species, including a newly measured spearing species, Coronis scolopendra The ultrafast appendages of a smasher species (Odontodactylus scyllarus) were an order of magnitude smaller, yet experienced values of drag-induced torque similar to those of a spearing species (Lysiosquillina maculata). The dactyl, a stabbing segment that can be opened at the distal end of the appendage, generated substantial additional drag in the smasher, but not in the spearer, which uses the segment to capture evasive prey. Phylogenetic comparative analyses revealed that larger mantis shrimp species strike more slowly, regardless of whether they smash or spear their prey. In summary, drag was minimally affected by shape, whereas size, speed and dactyl orientation dominated and differentiated the hydrodynamic forces across species and sizes. This study demonstrates the utility of simple mathematical modeling for comparative analyses and illustrates the multi-faceted consequences of drag during the evolutionary diversification of rotating appendages.

Wing-wake interaction destabilizes hover equilibrium of a flapping insect-scale wing

Wing-wake interaction is a characteristic nonlinear flow feature that can enhance unsteady lift in flapping flight. However, the effects of wing-wake interaction on the flight dynamics of hover are inadequately understood. We use a well-validated 2D Navier-Stokes equation solver and a quasi-steady model to investigate the role of wing-wake interaction on the hover stability of a fruit fly scale flapping flyer. The Navier-Stokes equations capture wing-wake interaction, whereas the quasi-steady models do not. Both aerodynamic models are tightly coupled to a flight dynamic model, which includes the effects of wing mass. The flapping amplitude, stroke plane angle, and flapping offset angle are adjusted in free flight for various wing rotations to achieve hover equilibrium. We present stability results for 152 simulations which consider different kinematics involving the pitch amplitude and pitch axis as well as the duration and timing of pitch rotation. The stability of all studied motions was qualitatively similar, with an unstable oscillatory mode present in each case. Wing-wake interaction has a destabilizing effect on the longitudinal stability, which cannot be predicted by a quasi-steady model. Wing-wake interaction increases the tendency of the flapping flyer to pitch up in the presence of a horizontal velocity perturbation, which further destabilizes the unstable oscillatory mode of hovering flight dynamics.

Asymmetries in wing inertial and aerodynamic torques contribute to steering in flying insects

Maneuvering in both natural and artificial miniature flying systems is assumed to be dominated by aerodynamic phenomena. To explore this, we develop a flapping wing model integrating aero and inertial dynamics. The model is applied to an elliptical wing similar to the forewing of the Hawkmoth Manduca sexta and realistic kinematics are prescribed. We scrutinize the stroke deviation phase, as it relates to firing latency in airborne insect steering muscles which has been correlated to various aerial maneuvers. We show that the average resultant force production acting on the body largely arises from wing pitch and roll and is insensitive to the phase and amplitude of stroke deviation. Inclusion of stroke deviation can generate significant averaged aerodynamic torques at steady-state and adjustment of its phase can facilitate body attitude control. Moreover, averaged wing angular momentum varies with stroke deviation phase, implying a non-zero impulse during a time-dependent phase shift. Simulations show wing inertial and aerodynamic impulses are of similar magnitude during short transients whereas aerodynamic impulses dominate during longer transients. Additionally, inertial effects become less significant for smaller flying insects. Body yaw rates arising from these impulses are consistent with biologically measured values. Thus, we conclude (1) modest changes in stroke deviation can significantly affect steering and (2) both aerodynamic and inertial torques are critical to maneuverability, the latter of which has not widely been considered. Therefore, the addition of a control actuator modulating stroke deviation may decouple lift/thrust production from steering mechanisms in flapping wing micro aerial vehicles and increase vehicle dexterity through inertial trajectory shaping.

Smart wing rotation and trailing-edge vortices enable high frequency mosquito flight

Mosquitoes exhibit unusual wing kinematics; their long, slender wings flap at remarkably high frequencies for their size (>800 Hz)and with lower stroke amplitudes than any other insect group. This shifts weight support away from the translation-dominated, aerodynamic mechanisms used by most insects, as well as by helicopters and aeroplanes, towards poorly understood rotational mechanisms that occur when pitching at the end of each half-stroke. Here we report free-flight mosquito wing kinematics, solve the full Navier-Stokes equations using computational fluid dynamics with overset grids, and validate our results with in vivo flow measurements. We show that, although mosquitoes use familiar separated flow patterns, much of the aerodynamic force that supports their weight is generated in a manner unlike any previously described for a flying animal. There are three key features: leading-edge vortices (a well-known mechanism that appears to be almost ubiquitous in insect flight), trailing-edge vortices caused by a form of wake capture at stroke reversal, and rotational drag. The two new elements are largely independent of the wing velocity, instead relying on rapid changes in the pitch angle (wing rotation) at the end of each half-stroke, and they are therefore relatively immune to the shallow flapping amplitude. Moreover, these mechanisms are particularly well suited to high aspect ratio mosquito wings.

Aerodynamics, sensing and control of insect-scale flapping-wing flight

There are nearly a million known species of flying insects and 13 000 species of flying warm-blooded vertebrates, including mammals, birds and bats. While in flight, their wings not only move forward relative to the air, they also flap up and down, plunge and sweep, so that both lift and thrust can be generated and balanced, accommodate uncertain surrounding environment, with superior flight stability and dynamics with highly varied speeds and missions. As the size of a flyer is reduced, the wing-to-body mass ratio tends to decrease as well. Furthermore, these flyers use integrated system consisting of wings to generate aerodynamic forces, muscles to move the wings, and sensing and control systems to guide and manoeuvre. In this article, recent advances in insect-scale flapping-wing aerodynamics, flexible wing structures, unsteady flight environment, sensing, stability and control are reviewed with perspective offered. In particular, the special features of the low Reynolds number flyers associated with small sizes, thin and light structures, slow flight with comparable wind gust speeds, bioinspired fabrication of wing structures, neuron-based sensing and adaptive control are highlighted.