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The special aerodynamic characteristics of insects have attracted the interest of biologists and engineers. In this paper, aerodynamic modeling methods for flapping flight are systematically reviewed in detail, especially those methods developed in the past ten years. The differences among kinds of methods, the development of each type of methods,...
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... The complete details are added in Section 2. Steady models are not good at predicting loads on small insects, and unsteady models are not fully understood due to a lack of understanding of flow complexities at these low Reynolds numbers. As a result, the improved or modified quasi-steady models are preferred for preliminary analysis here, as they include all aerodynamic forces such as translational, rotational, added mass, and induced wake capture; however, it should be noted that these models must still be compared to data obtained from computational fluid dynamics and experiments (Xuan et al., 2020). ...
... Due to the complexity and unsteady flow characteristics of insect wings, aerodynamic modeling methods continue to face significant difficulties and challenges. The authors of the reference (Xuan et al., 2020) provided a beautiful explanation of these models, stating their classification into three types: steady-state, quasi-steady, and unsteady. Steady-state models are simple and inappropriate for predicting load in small insects during flight. ...
... Crowther, 2014b). According to reference (Xuan et al., 2020), the total instantaneous force, therefore, can be expressed as: ...
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.
... Previous studies on the aerodynamics of flapping wings mostly focused on the highlift generation of flies 1,2 , bees 3 , beetles 4 , hoverflies 5 , and hummingbirds 6 . They have uncovered the basic unsteady mechanisms accounting for the aerodynamic performance of flapping wings, including the Weis-Fogh mechanism, the delayed-stall mechanism, the Wake-capture mechanism, and so on [7][8][9] . Those related studies have provided the theoretical basis for designing wings and actuation mechanisms for bioinspired FWMAVs 10 , and therefore most of the existing FW-MAVs have two flapping wings, and each wing has the same attack angle during upstroke and downstroke flapping (namely symmetric flapping mode) 11 . ...
Dragonflies show impressive flight performance due to their unique tandem flapping wing configuration. While previous studies focused on forewing-hindwing interference in dragonfly-like flapping wings, few have explored the role of asymmetric pitching angle in tandem flapping wings. This paper compares the aerodynamic performance of asymmetric dragonfly-like wings with symmetric hummingbird-like wings, both arranged in tandem. Using a three-dimensional numerical model, we analyzed wing configurations with single/tandem wings, advance ratios (J) from 0 to 0.45, and forewing-hindwing phase differences from 0 to 180 at a Reynolds number of 7000. Results show that asymmetric flapping wings exhibit higher vertical force and flight efficiency in both single and tandem wing configurations. Increasing the phase difference improves flight efficiency with minimal loss of vertical force in the asymmetric flapping mode, while the symmetrical flapping mode significantly reduces vertical force at a 180 phase difference. Additionally, symmetric tandem flapping wings unexpectedly gain extra vertical force during in-phase flapping. This study uncovers the flow characteristics of dragonfly-like tandem flapping wings, providing a theoretical basis for the design of tandem flapping wing robots.
... This approach assumes that aerodynamic force production can be expressed as a function of the instantaneous wing kinematics only. 4,3,31 Quasi-steady modeling and computational fluid dynamics (CFD) are the two most common approaches in flapping wing force modeling. 3 The choice whether to use the quasi-steady approach or CFD depends on the application. ...
... 4,3,31 Quasi-steady modeling and computational fluid dynamics (CFD) are the two most common approaches in flapping wing force modeling. 3 The choice whether to use the quasi-steady approach or CFD depends on the application. Quasi-steady models usually employ simple analytic functions to compute force production from wing motion. ...
... 33,7 Quasi-steady models are well suited for comparison of different designs and operating conditions. 3,33 This work studies the effects of a design adaptation. The flight behavior is analyzed for multiple wing elevation settings and for variable initial conditions. ...
Maneuverability of flapping wing fliers inevitably goes with inherent system instability. Inherent instability means that flapping wing systems require a flight controller and that these vehicles are prone to crashing. This work proposes a design feature to stabilize the descent of a flapping wing aerial vehicle. The vehicle is based on the KUlibrie, a flapping wing nano robot that is under development at KU Leuven. A computational study indicates that upwardly elevated wings provide inherently stable descending flight. The vehicle performs a free flight starting from different initial conditions. The system dynamics display convergence towards a limit cycle. Wing elevation and center of gravity position determine pitch and roll stiffness with respect to vertical descent and climb. The same effects that stabilize descent also destabilize climbing flight.
... In addition, another method is engineering design through surrogate modeling [19], which has been applied successfully to some specific optimization problems in various engineering fields. Recently, numerical simulations and phenomenology-based aerodynamic modeling [20][21][22][23] have been employed to directly relate the aerodynamic forces exerted on a flapping wing to its time-varying motion and geometry. The effects of the design parameters on the wing performance can be predicted quickly, which allows for combining it with the surrogate optimization method [24] to advance the design of the wing. ...
... A slight difference in the chordwise locations of the action point of resultant forces is estimated to have a weak influence on the total power consumption, as discussed in Ref. [23]. ...
Due to the complexity of tailoring the wing flexibility and selecting favorable kinematics, the design of flapping wings is a considerably challenging problem. Therefore, there is an urgent need to investigate methods that can be used to design wings with high energy efficiency. In this study, an optimization model was developed to improve energy efficiency by optimizing wing geometric and kinematic parameters. Then, surrogate optimization was used to solve the design optimization model. Finally, the optimal design parameters and the associated sensitivity were provided. The optimized flapping wing, inspired by hummingbirds, features large geometrical parameters, a moderate amplitude of the flapping angle, and low frequency. With the spanwise twisting deformation considered in the parameterization model, the optimization solver gave an optimized wing with a pitching amplitude of approximately 39 deg at the root and 76 deg at the tip. According to the sensitivity analysis, the length of the wing, flapping frequency, and flapping amplitude are the three critical parameters that determine both force generation and power consumption. The amplitude of the pitching motion at the wing root contributes to lowering power consumption. These results provide some guidance for the optimal design of flapping wings.
... Many simplified aerodynamic models have been developed to compute the aerodynamic forces and moments on a flapping wing for various wing kinematics and flight regimes. These models are essential tools for fast predictions, required for real-time model-based control or design optimization, and can be classified as steady, quasi-steady and unsteady 14,15 . ...
... Steady models are typically based on actuator disk or vortex-based approaches but can only provide time-averaged forces 5,15 . Quasi-steady models link instantaneous forces to instantaneous states of the wing's kinematics and flow field, thus missing history effects. ...
... A recent review of aerodynamic models focusing on QS models is given by Xuan et al. 15 . Spanwise discretization using Blade Element Models (BEM) is typically used to account for wing shape variability, with the total force decomposed in translational, rotational and added mass contributions. ...
Flapping Wing Micro Air Vehicles (FWMAV) are highly manoeuvrable, bio-inspired drones that can assist in surveys and rescue missions. Flapping wings generate various unsteady lift enhancement mechanisms challenging the derivation of reduced models to predict instantaneous aerodynamic performance. In this work, we propose a robust CFD data-driven, quasi-steady (QS) Reduced Order Model (ROM) to predict the lift and drag coefficients within a flapping cycle. The model is derived for a rigid ellipsoid wing with different parameterized kinematics in hovering conditions. The proposed ROM is built via a two-stage regression. The first stage, defined as `in-cycle' (IC), computes the parameters of a regression linking the aerodynamic coefficients to the instantaneous wing state. The second stage, defined as `out-of-cycle' (OOC), links the IC weights to the flapping features that define the flapping motion. The training and test dataset were generated via high-fidelity simulations using the overset method, spanning a wide range of Reynolds numbers and flapping kinematics. The two-stage regressor combines Ridge regression and Gaussian Process (GP) regression to provide estimates of the model uncertainties. The proposed ROM shows accurate aerodynamic predictions for a wide range of kinematics. The model performs best for smooth kinematics that generates a stable Leading Edge Vortex (LEV). Remarkably accurate predictions are also observed in dynamic scenarios where the LEV is partially shed, the non-circulatory forces are considerable, and the wing encounters its own wake.
... Many simplified aerodynamic models have been developed to compute the aerodynamic forces and moments on a flapping wing for various wing kinematics and flight regimes. These models are essential tools for fast predictions, required for real-time model based control or design optimization, and can be classified as steady, quasi-steady and unsteady 14,15 . ...
... Steady models are typically based on actuator disk or vortex-based approaches but can only provide time-averaged forces 5,15 . Quasi-steady models link instantaneous forces to instantaneous states of the wing's kinematics and flow field, thus missing history effects. ...
... A recent review of aerodynamic models focusing on QS models is given by Xuan et al. 15 . Spanwise discretization using Blade Element Models (BEM) is typically used to account for wing shape variability, with the total force decomposed in translational, rotational and added mass contributions. ...
Flapping Wing Micro Air Vehicles (FWMAV) are highly manoeuvrable, bio-inspired drones that can assist in surveys and rescue missions. Flapping wings generate various unsteady lift enhancement mechanisms challenging the derivation of reduced models to predict instantaneous aerodynamic performance. In this work, we propose a robust CFD data-driven, quasi-steady (QS) Reduced Order Model (ROM) to predict the lift and drag coefficients within a flapping cycle. The model is derived for a rigid ellipsoid wing with different parameterized kinematics in hovering conditions. The proposed ROM is built via a two-stage regression. The first stage, defined as `in-cycle' (IC), computes the parameters of a regression linking the aerodynamic coefficients to the instantaneous wing state. The second stage, `out-of-cycle' (OOC), links the IC weights to the flapping features that define the flapping motion. The training and test dataset were generated via high-fidelity simulations using the overset method, spanning a wide range of Reynolds numbers and flapping kinematics. The two-stage regressor combines Ridge regression and Gaussian Process (GP) regression to provide estimates of the model uncertainties. The proposed ROM shows accurate aerodynamic predictions for widely varying kinematics. The model performs best for smooth kinematics that generate a stable Leading Edge Vortex (LEV). Remarkably accurate predictions are also observed in dynamic scenarios where the LEV is partially shed, the non-circulatory forces are considerable, and the wing encounters its own wake.
... A variety of new concept aircraft have been designed and built to meet different mission requirements. [1][2][3][4] In the search for efficient micro-aircraft designs, researchers have taken inspiration from maple seeds, discovering that such samaras spontaneously enter a spin state when they fall from their tree. People have designed some special unmanned aerial vehicles (UAVs) based on the principles of a samara, 5-7 called samarai monocopters. ...
... Here, ρ is the air density, and dA is the annular disk area. According to Eqs. (2) and (3), the formula for downwash flow can be obtained. Finally, according to the spanwise integral of Eq. (2), the aerodynamic force of the six components acting on the wing can be calculated. ...
A monocopter, which is a biology-inspired aircraft based on the samara, has been proved to have passive flight stability. However, due to the asymmetry of its configurations and the constant rotation during flight, its flight dynamics equation is complex. In this paper, the longitudinal stability of a monocopter is systematically analyzed. The longitudinal motion of the monocopter is used as the main research object in this paper. By transforming the body axis coordinate frame to the semi-body axis coordinate frame, its longitudinal dynamics equation is greatly simplified. Then, a fourth-order state space matrix of the longitudinal motion of the monocopter is established, and its longitudinal stability is analyzed at different pitch angles of the wing. Furthermore, the fourth-order state space matrix is simplified into a third-order matrix, and the Rouse criterion is used to analyze the stability of the simplified state space. A set of sufficient conditions is obtained as the criterion for longitudinal stability. Based on this criterion, it is found that the product of inertia [Formula: see text] is a very important factor affecting the stability. Then, the inertial parameters of the aircraft are modified, which greatly expands the range of the pitch angle that maintains longitudinal stability. Finally, the six-degree-of-freedom nonlinear flight dynamic simulation is performed to verify the rationality of the longitudinal stability criterion.
... The hover maneuverability of flapping-wing aircraft can be attributed to their unsteady high-lift mechanisms which cannot be explained by traditional steady aerodynamic theories for fixed-wing aircraft due to their low Reynolds number regime and unsteady characteristics [7]. Great achievements have been made in the unsteady aerodynamic study of flapping flight in the past decades [7][8][9][10], among which, Dickinson et al. [7] summarized these mechanisms as delayed stall, rotational lift, added mass and wake capture. They investigated the aerodynamic force generation of a fruit fly by using a dynamically scaled robotic model and various instantaneous force measuring experiments were conducted. ...
The periodically time-varying forces make the equilibrium state of Beihawk, an X-shaped flapping-wing aircraft, to be a periodic limit cycle oscillation. However, traditional controllers based on averaging theory fail to suppress this oscillation and the derived stability result may be inaccurate. In this study, a period-based method is proposed to design the oscillation suppression controller, locate the corresponding cycle and analyze its stability. A periodically time-varying wing-tail interaction model is built and Discrete Fourier Transform is applied to adapt the model for controller design. The harmonics less than quintuple flapping frequency account for more than 96 percent of the total harmonics and are reserved to present a concise model. Based on this model, active disturbance rejection controller (ADRC) is designed and its Extended State Observer can observe the disturbance to suppress the oscillation. Poincaré map is introduced to convert the stability analysis of the cycle to a fixed point. A multiple shooting method is adopted to locate several points on the cycle and the map is obtained by calculating the submaps between the adjacent points with the Floquet theory. The located points are proved to be accurate compared with the numerical solved cycle and the stability analysis result of the cycle is verified by the dynamic evolution. Compared with the State Feedback Controller, the ADRC performs better in suppressing the limit cycle oscillation and eliminating the attitude control error. The oscillation suppression is meaningful in maintaining a stable flight and capturing high quality images.
... The hover maneuverability of flapping-wing aircraft can be attributed to their unsteady high-lift mechanisms which cannot be explained by traditional steady aerodynamic theories for fixed-wing aircraft due to their low Reynolds number regime and unsteady characteristics [7]. Great achievements have been made in the unsteady aerodynamic study of flapping flight in the past decades [7][8][9][10], among which, Dickinson et al. [7] summarized these mechanisms as delayed stall, rotational lift, added mass and wake capture. They investigated the aerodynamic force generation of a fruit fly by using a dynamically scaled robotic model and various instantaneous force measuring experiments were conducted. ...
The periodically time-varying forces make the equilibrium state of Beihawk, an X-shaped flapping-wing aircraft, to be a periodic limit cycle oscillation. However, traditional controllers based on averaging theory fail to suppress this oscillation and the derived stability result may be inaccurate. In this study, a period-based method is proposed to design the oscillation suppression controller, locate the corresponding cycle and analyze its stability. A periodically time-varying wing-tail interaction model is built and Discrete Fourier Transform is applied to adapt the model for controller design. The harmonics less than quintuple flapping frequency account for more than 96 percent of the total harmonics and are reserved to present a concise model. Based on this model, active disturbance rejection controller (ADRC) is designed and its Extended State Observer can observe the disturbance to suppress the oscillation. Poincaré map is introduced to convert the stability analysis of the cycle to a fixed point. A multiple shooting method is adopted to locate several points on the cycle and the map is obtained by calculating the submaps between the adjacent points with the Floquet theory. The located points are proved to be accurate compared with the numerical solved cycle and the stability analysis result of the cycle is verified by the dynamic evolution. Compared with the State Feedback Controller , the ADRC performs better in suppressing the limit cycle oscillation and eliminating the attitude control error. The oscillation suppression is meaningful in maintaining a stable flight and capturing high quality images.
... In contrast, basic QS aerodynamic models suggest that the instantaneous forces on the wings are fully dependent on the instantaneous flapping velocity, rotational angle, and wing's design, regardless of the flow field. Xuan et al. [40] reviewed these aerodynamic models and categorized them as Osborne, Walker, and Dickinson models, which are based on blade element theory that ignores span wise flows and wake-related unsteady effects. However, the modified QS model in the current study considered the additional lift from leading edge vortex (LEV) and the effects of wing rotation as discussed in previous studies [41,42]. ...
This paper proposes an approach to analyze the dynamic stability and develop trajectory-tracking controllers for flapping-wing micro air vehicle (FWMAV). A multibody dynamics simulation framework coupled with a modified quasi-steady aerodynamic model was implemented for stability analysis, which was appended with flight control block for accomplishing various flight objectives. A gradient-based trim search algorithm was employed to obtain the trim conditions by solving the fully coupled nonlinear equations of motion at various flight speeds. Eigenmode analysis showed instability that grew with the flight speed in longitudinal dynamics. Using the trim conditions, we linearized dynamic equations of FWMAV to obtain the optimal gain matrices for various flight speeds using the linear-quadratic regulator (LQR) technique. The gain matrices from each of the linearized equations were used for gain scheduling with respect to forward flight speed. The reference tracking augmented LQR control was implemented to achieve transition flight tracking that involves hovering, acceleration, and deceleration phases. The control parameters were updated once in a wingbeat cycle and were changed smoothly to avoid any discontinuities during simulations. Moreover, trajectories tracking control was achieved successfully using a dual loop control approach. Control simulations showed that the proposed controllers worked effectively for this fairly nonlinear multibody system.
