The Coupled Wing Morphing of Ornithopters Improves Attitude Control and Agile Flight

: Bird wings are exquisite mechanisms integrated with multiple morphological deformation joints. The larger avian species are particularly adept at utilizing their wings’ flapping, folding, and twisting motions to control the wing angle and area. These motions mainly involve different types of spanwise folding and chordwise twisting. It is wondered whether the agile maneuverability of birds is based on the complex coupling of these wing morphing changes. To investigate this issue, we designed a two-section wing structure ornithopter capable of simultaneously controlling both spanwise folding and chordwise twisting and applied it to research on heading control. The experimental data collected from outdoor flights describe the differing flight capabilities between the conventional and two-section active twist wing states, indicating that incorporating an active twist structure enhances the agility and maneuverability of this novel flapping aircraft. In the experiments on yaw control, we observed some peculiar phenomena: although the twisting motion of the active twist ornithopter wings resembles that of a fixed-wing aileron control, due to the intricate coupling of the wing flapping and folding, the ornithopter, under the control of active twist structures, exhibited a yaw direction opposite to the expected direction (directly applying the logic assumed by the fixed-wing aileron control). Addressing this specific phenomenon, we provide a plausible model explanation. In summary, our study with active twist mechanisms on ornithopters corroborates the positive impact of active deformation on their attitude agility, which is beneficial for the design of similar bio-inspired aircraft in the future.


Introduction
Birds can adjust the geometric morphology of their wings to alter their posture [1].Compared to insect wings, avian wings possess multiple joints and exhibit greater maneuverability [2].Therefore, investigating avian wing deformation offers inspiration for aircraft attitude control [3][4][5].Birds can alter their wing morphology through various muscular and joint movements, including spanwise folding [6], spanwise extension-retraction [7], and chordwise twist [8], as depicted in Figure 1a-d.These complex muscular joint configurations and wing deformation capabilities ensure the agility of avian flight [9].Figure 1 depicts the four representative geometric morphologies of avian wings during flight.Among these, the flapping motion typified by hummingbirds does not apparently alter the static geometric morphing of the wings [10], generating lift solely through up-anddown flapping (Figure 1a,e).As shown in Figure 1b,f, the spanwise extension-retraction exhibited by high-speed avian species (such as falcons) manifests as a slight forward and aft sweeping motion of the wings [11].It is reported that varying this in-plane morphing parameter enhances flight maneuverability [12].In Figure 1c,g, represented by albatrosses and other large-wingspan birds, the spanwise folding deformation involves an "M"-shaped up-and-down flapping motion of the wings; it is reported that it can enhance the flight stability during deceleration [13,14].Figure 1d,h illustrate the chordwise twist movement, which is typically studied in pigeons; the research has focused on the effect of chordwise twist on agile attitude control [8].
The study of morphological parameters and their impact on flapping flight is a research hotspot.Song pointed out that research on the static morphological characteristics of avian wings has been extensive in non-flapping states.However, there has been relatively little theoretical research on the morphological deformation coupled with flapping states [15].
The morphological research in non-flapping states can be summarized such that (1) altering the wing shape parameters at different angles of attack can affect the lift coefficient [16]; (2) actions similar to the spanwise folding movements observed in largewinged birds (Figure 1a) can enhance flight stability [13]; and (3) pigeons can improve flight agility through chordwise twist [8].However, the morphological variables of these studies are not coupled with flapping, thus underestimating the complex aerodynamic situations induced by the coupling of flapping motion and wing deformation.
Does the torsional ability of wing muscles along the chord differ during flapping motions (such as extension-folding or extension-retraction) compared to non-flapping states?
The research on the morphological variables of wings during the flapping states remains scarce [4].Only a few studies have focused on the influence of the aspect ratio on lift and thrust performance [15].For instance, seagull wings exhibit excellent lift characteristics during flapping flight due to spanwise folding [17].Some studies have effectively explained the advantages of large-winged birds in generating lift and saving power during flapping by describing the effects of wing folding on leading-edge vortices and Strouhal numbers [18].Thielicke, W. [19] and the team led by Song [20] have conducted relevant studies on active chordwise twist, demonstrating that chordwise twist can reduce the constraint of the wing on vortex streets, decrease the magnitude of the lift, and alter the distribution of the effective angles of attack.However, this literature solely comprises aerodynamic simulations without investigating the coupling effects of chordwise twists and the flapping motion on the attitude of flapping-wing aircraft.To the best of the authors' knowledge, this paper represents the first study regarding the coupling effect of chordwise twist (Figure 1c) and spanwise folding (Figure 1d) on attitude control during flapping.In the literature on biomimetic mechanical design, there are numerous studies focusing on the mechanical structures mimicking each of the three wing deformation modes depicted in Figure 1b-d individually.For instance, in studies on wing morphology resembling spanwise extension-retraction (achieving the motion depicted in Figure 1b), Chan from Stanford University improved upon a fixed-wing prototype by creating a drone with foldable wings.The research indicates that altering the wing area and angle of fixed-wing aircraft through joint unfolding movements can significantly enhance the operability, agility, and stability of the aircraft [12].Their study utilized a fixed-wing aircraft platform (with the lift generated by propellers rather than flapping) to investigate the effect of asymmetric spanwise retraction on aircraft attitude control.However, constrained by the nature of the fixed-wing platform, their wing deformations were not coupled with a flapping motion.In contrast, researchers at Northwestern Polytechnical University designed a mechanical structure that couples wing deformation with flapping motion.Their developed RoboFalcon flapping-wing aircraft replicated the effect of the asymmetric spanwise folding of wings on attitude control during the flapping states (an asymmetric form of the extension-folding depicted in Figure 1b).RoboFalcon achieves flight and attitude control through asymmetric forward and aft sweeping motions [21].Their study indicates that the morphing-coupled flapping mode exhibits higher lift effects compared to the single-wing flapping mode with unchanged static characteristics when increasing the downstroke duration [11].
The studies on wing morphology resembling spanwise folding (emulating the motion depicted in Figure 1c) began in 2011, and the two-section wing ornithopter mimicking the avian wing deformation mechanisms was first developed by the Festo Corporation.The flagship model, known as Smartbird, has gathered significant attention due to its remarkably realistic flight posture resembling that of actual birds [22].Based on the structure of Smartbird, Zhang et al. developed an avian ornithopter with feather covers and achieved reliable flight [23].
In the studies on wing morphology resembling chordwise twist (emulating the motion depicted in Figure 1d), both theoretical and experimental research have been limited to single-section wing ornithopters.For example, the team led by Xiao et al. designed a differential control mechanism for active chordwise twist, verifying that lateral control using wing differential torsion yields superior performance compared to rudder control [24].
The aforementioned studies have independently investigated the influence of altering certain morphological parameters of wings on their aerodynamic performance or attitude control.However, during avian flapping flight, various types of geometric parameters of wings should be coupled [15].Therefore, when studying flapping-wing aircraft, considering multiple geometric parameters of wings and studying the coupling effects of the morphology and flapping (morphing-coupled flapping) are essential.Due to the complexity of the flapping motion, it is currently impractical to fully replicate the combined actions of all the muscles in birds [9].However, it is feasible to gradually observe the combined effects of several morphological parameters on flapping-wing aircraft.We note the lack of studies investigating the coupling effects of spanwise folding and chordwise twisting, which becomes the focus of our study.Given the complexity of the flapping motion, the addition of each new mechanism may potentially render the existing motion model ineffective.Therefore, we have adopted a cautious approach and designed a two-section ornithopter that retains a vertical tail mechanism, active chordwise twist mechanisms, and spanwise folding mechanisms.Through extensive experimentation (initially encountering numerous uncontrollable phenomena due to insufficient analysis of the aerodynamic model), we ultimately propose a model and control principles that enhance the agility of attitude control.
To summarize, inspired by the control strategies of the complex morphing strategy of avians, this paper investigates the impact of chordwise active twist coupled with spanwise folding-induced flapping through a two-section wing ornithopter.The main contributions are as follows: • We designed a two-section wing ornithopter with a spanwise folding and chordwise active twist mechanism.This flapping vehicle achieved agile flight and attitude control in the open air.

•
We experimentally analyzed the impact of the chordwise active twist structure on the attitude control during flapping.The results demonstrated that the spanwise active twist structure can provide independent direction control for headings.Therefore, it can enhance the maneuverability and agility of the ornithopter.

•
The experimental findings revealed that, due to the complex coupling of chordwise folding and spanwise active twist, the attitude control phenomenon could not be predicted by the traditional fixed-wing aileron control mechanism.Therefore, a novel model analysis and explanation is proposed for this coupled wing-flapping pattern.
The proposed "M"-shaped model describes the particularly special phenomenon that the attitude control effect of a single spanwise active twist is contrary to that when it is coupled with chordwise folding.

Design of Active Twist Two-Section Wing Ornithopter
To investigate the influence of wing deformation on avian posture control for potential application in unmanned aerial vehicle (UAV) design, we developed a two-section wing with an active twist structure inspired by the morphology of seagulls, as illustrated in Figure 2a and parameter specifications are listed in Table 1.The propulsion architecture of this flapping wing mechanism resembles Festo's Smartbird design.This model's outer and inner wing segments are composed of two four-bar linkage structures; the outer segment and the inner segment are driven by a single motor, resulting in a coupled motion between the outer segment and the inner segment.Therefore, it is an actuated system with one degree of freedom [22]; the motor only provides lift and thrust without posture control capability.During flight, birds can generate rolling moments by altering the posture and shape of their two wings differently.To achieve a similar effect, we propose a mechanism wherein servo motors are positioned at the joints of the outer and inner wing segments (as depicted in Figure 2b).The rotation of the outer wing's twist servo motor can induce the rotation of the wing spar.Under remote control, the servo motors of the left and right wings can execute opposite directional twists, thereby inducing different deformation effects in the outer wing segments on either side (as illustrated in Figure 2d).This generates an asymmetric moment on the fuselage, thereby achieving posture control.To obtain controlled experimental results without active twist, our aircraft retained the commonly observed vertical tail structure for posture control, as depicted in Figure 2c.Through simulation analysis conducted using SolidWorks 2024 and MATLAB R2024a software, it has been observed that, compared to single-wing flapping-wing aircraft, the two-section wing structure exhibits minimal variation in the center of gravity position, as illustrated in Figure 2e, which is advantageous for the design of flapping-wing aircraft controllers.This observation is consistent with the conclusions drawn by Lee JS and colleagues regarding the research on folding-wing and flapping-wing aircraft [25].A dynamic demonstration of the special wing-morphing (flapping-twisting) mechanism, can be found in the video of the suplymentary material.

Aerodynamic Analysis
The factors influencing the lift and thrust of an aircraft are numerous, including the air density coefficient ρ, the horizontal projected wing area S, the incoming flow velocity v L , the cruising velocity v T , the lift coefficient C L , and the thrust coefficient C T .The mathematical expressions are represented as shown in Equations ( 1) and ( 2): Thus, the lift and thrust coefficients can be represented by Equations ( 3) and (4): The horizontal projected area of the flapping wing dominates the trend of lift variation, where the local tangential velocity (v) and horizontal projected area determine the instantaneous lift of the flapping wing mechanism, which is closely related to the development of leading-edge vortices [6].
Experimental testing of the aerodynamic performance of the bi-plane flapping-wing aircraft was conducted without yaw control.The experiments involved measuring the lift and thrust of the aircraft using an ANIPRO RL4 turntable system [26], as illustrated in Figure 3a.From Figure 3b, it can be observed that, at a certain relative airspeed, the thrust coefficient of the flapping-wing aircraft is directly proportional to the wing flapping frequency [27].Furthermore, as shown in Figure 3c, the thrust coefficient of the two-section flapping-wing aircraft is maximally affected by the relative airspeed at low frequencies.These results and analysis guarantee the basic flight safety of our outdoor real-flight experiments.

Outdoor Real Flight Experiments on Horizontal Maneuverability
As depicted in Figure 4, multiple stable flight tests were conducted outdoors, during which the attitude data and control signals were recorded using onboard sensors (more information of the outdoor flight can be found in the suplymentary material).These experiments encompassed both pre-modification flight trials and flights after installing the active twist mechanism.Due to the lack of historical literature and prior knowledge on the aeroelastic testing of wingtip twist, to ensure flight safety, we incorporate an active wingtip twist structure onto a relatively mature scheme with a vertical tail.During the experimental exploration of the influence of the active twist structure on the flight attitudes, the control of the vertical tail is disabled to ensure the uniqueness of the variable.The ability of an aircraft to change its flight direction is referred to as horizontal maneuverability [28,29].During the actual flight, it was observed that discrepancies between the left and right wings were inevitable due to manufacturing variations, resulting in an imbalance of the forces on both sides of the aircraft.In this case, relying solely on the tail fin cannot effectively control the aircraft's roll to a neutral position, leading to the torpid climbing performance of the aircraft.Human pilots have repeatedly observed this occurrence during outdoor experiments.It indicates that relying solely on tail control for the heading direction control of a flapping-wing aircraft can lead to a deficiency in the aircraft's horizontal maneuverability.

(b) (a)
To evaluate the control performance, the correlation between the roll angle and the control signals (from the remote controller) is calculated using the root mean squared error (RMSE).This evaluation is feasible because the control signals provided by the remote controller are proportional to the mechanism's rotational angles, and its effects on attitude control can be measured by the Inertial Measurement Unit directly.Data points are recorded by the onboard processor at 25 Hz and represented in a two-dimensional coordinate system as P(controlinput, attitudeangle).
The calculation of RMSE is provided as follows: where n is the total number of recorded data points, Roll represents the roll angle of the aircraft, Roll is the mean obtained from the regression equation, Pitch represents the pitch angle of the aircraft, and Pitch is the mean obtained from the regression equation.

Horizontal Maneuverability without Active Twist
Before installing the active twist structure, the aircraft's attitude control relies solely on the T-tail.The tail is capable of rotation about the Z-axis and the Y-axis (as shown in Figure 2a,c).The control principle is as follows: rotation about the Z-axis increases the force on the horizontal surface of the tail, thereby increasing the aircraft's angle of attack; rotation about the Y-axis alters the force on the vertical surface of the tail, thereby modifying the aircraft's yaw and roll angles.During the actual flight experiment, the relationship between the T-tail control input and the aircraft's attitude is illustrated in Figure 5.It can be observed that there is a strong correlation between the aircraft's roll angle and the control signal along the Z-axis of the tail surface (Figure 5a), as well as the correlation between the pitch angle and the control signal along the Y-axis (Figure 5c).In comparison to the linear regression equations between the attitude angles and the control signals, the root mean square errors (RMSEs) are 1.1530 for the roll angle and 3.1161 for the pitch angle, as depicted in Figure 5b,d.
In this configuration, the aircraft cannot fully control all three degrees of freedom due to only two servos acting as active control mechanisms on two degrees of freedom.However, the control signal along the Z-axis influences both the yaw and roll angles.According to [30], this coupling phenomenon in the control effectiveness of roll and yaw angles is attributed to the T-tail configuration, which causes the center of pressure of the horizontal control surface to deviate from the xoz plane where the aircraft's center of mass is located, resulting in a rolling moment.Consequently, the tilting lift generates a lateral force in the horizontal direction, providing the centripetal force required for the aircraft's yaw rotation [28].Comparing the data for roll and yaw (Figure 6), it is evident that there is a significant coupling effect between them in terms of control.

Horizontal Maneuverability with Active Twist Mechanism
Birds adjust their flight posture by flexibly changing the shape of their wings during flight.Wing deformation causes the displacement of the vortices on the wing surface, so the deformation of the outer wing of a two-section ornithopter can result in changes in lift and thrust [31].We aim to install an active twist wing structure to enable the ornithopter to also have the capability to adjust its aircraft attitude through imbalanced wing deformation.
In actual flight experiments, the control effect of the active twist mechanism is illustrated in Figure 7.The magnitude of the control signal (Signal) is directly proportional to the active twisting angle of the ornithopter's outer wing sections.This mechanical structure is somewhat similar to the ailerons on fixed-wing aircraft.On a fixed-wing aircraft, when the ailerons undergo differential deflection as indicated by the signal, different lift distributions are generated on the two wing surfaces, resulting in a rolling moment, as depicted in Figure 7a.According to the theory of aileron control on fixed-wing aircraft [32], the roll angle change of the aircraft should be as shown in Figure 7a (a fake curve generated by inverting the roll data in Figure 7b), demonstrating that the higher side of the aileron on the fixed-wing aircraft rolls downward.However, as shown in Figure 7b, the experimental data contradict this expectation.In comparison to the linear regression equation between attitude angles and control signals, the root mean square error (RMSE) is RMSE 3 = 9.0975, as depicted in Figure 7e.The active twist wing mechanism causes the roll situation of the ornithopter to be the opposite, with the side of the outer wing twisting upward, resulting in the aircraft rolling upward.During actual flight, it was observed that, when the ornithopter's wings are higher than the fuselage, the reversal effect of the roll angle becomes significant.When the wings are level with or lower than the fuselage, the roll angle control effect tends to resemble that of a fixed-wing aircraft.In the experiments with the installed active twist wing mechanism, the rolling induced by wing deformation has alleviated the previously encountered climbing difficulties and the manufacturing asymmetry issue.The ornithopter can now achieve left or right turns or adjust the bias caused by left-right asymmetry through the imbalance active twisting of the outer wing.Comparative experiments indicate that, by solely controlling the twisting of the ailerons, it is possible to change the aircraft's yaw angle, as shown in Figure 7c.In Figure 7c, the roll angle deviates from the direction away from 0 • , causing the aircraft to continuously circle in one direction, while the value of the yaw angle increases in the negative direction in an integrated form.Under these circumstances, does the coupling phenomenon still exist between the roll angle and yaw angle control?By extracting the high-frequency components of the yaw angle, filtering out the low-frequency fundamental signal of yaw (0.0185 Hz), and comparing it with the roll angle control signal, as shown in Figure 7d, it can be observed that the high-frequency part of the yaw angle changes synchronously with the roll angle, indicating that the coupling effect still exists in the control.This result suggests that the active wing-warping mechanism can provide the required torque for attitude changes, achieving control over both the roll and yaw angles.The experiential feedback from pilots is that, during horizontal directional control, the phenomenon of aircraft center of mass drift is significantly reduced, making turning more flexible and easier.Therefore, the significance of the active twist wing in ornithopters lies in adjusting the imbalance wing deformation, enhancing the control strategies, compensating for the shortcomings of tail control, and making ornithopter flight more agile.

Kinetic Model of the Active Twist Wing Ornithopter
As described above, during flight experiments, it was observed that the principle of fixed-wing aileron control could not explain the performance of the yaw control of the ornithopter with active twist.The actual yaw deviation of the ornithopter is opposite to the expected deviation direction based on the principle of fixed-wing aileron control.Moreover, this reverse control phenomenon becomes more pronounced as the outer wing's folding degree increases.Additionally, it was found during experiments that, the higher the flapping position of the ornithopter, the more significant its inverted turning control effect becomes.
The inverted control phenomenon induced by outer segment flapping, which was unexpected at the outset of the experiments, was not explained in the literature citations.Additionally, the existing studies have not provided a kinetic model for two-section wing twisting, necessitating a new model to explain the current control phenomenon and its underlying principles.This paper proposes an M-shaped model to analyze and elucidate this control phenomenon, guiding the controller in understanding this new control characteristic.As illustrated in Figure 8a, considering the limit position when the ornithopter is folded by 90 • , the inverted control effect can be explained intuitively at this limit position.The thrust acting on the outer wing is denoted as Thrust(F T ), expressed by Equation ( 2), which can be decomposed into forces in the X and Y directions: Comparing Figure 8b with Figure 8a, it is noted that the rotation axis of the ailerons on a fixed-wing aircraft remains aligned with the Y-axis throughout the flight process, and, when the wings of the ornithopter do not fold, the direction of the wing warping rotation axis aligns with that of the ailerons on a fixed-wing aircraft.Additionally, the rotation axes on both sides of the wings are aligned (Axis − L = Axis − R).However, when the wings of the ornithopter fold by 90 • during flapping, the direction of the wing warping rotation axis changes, becoming oriented in opposite directions along the Z-axis (Axis − L = −Axis − R).Under the influence of differential control signals, the initially opposite rotations of the wing warping on both sides around the Y-axis gradually transform into rotations in the same direction around the Z-axis.
As the center of pressure of the outer wing is consistently positioned above and aft of the aircraft's center of mass, the resulting torque exerted on the fuselage can be expressed as follows: In the above expressions, M X represents the rolling moment caused by wing twisting, M Y denotes the pitching moment, and M Z signifies the yawing moment.The agility of an aircraft is employed to quantify its capability for attitude rotation.The control of the rotational angular acceleration of a flapping-wing aircraft by wing twisting is as follows: where Ω represents the angular acceleration vector of the airframe influenced by the wing twisting, ṗ denotes the roll acceleration, q denotes the pitch acceleration, and ṙ denotes the yaw acceleration.I xx is the moment of inertia of the fuselage about the X-axis, I yy is the moment of inertia of the fuselage about the Y-axis, and I zz is the moment of inertia of the fuselage about the Z-axis.The yawing moment is not directly influenced by wing warping.However, the rolling motion induced by wing twisting causes a change in the lift direction of the ornithopter, resulting in a lateral force in the horizontal direction, leading to a change in the heading of the ornithopter.Additionally, due to the transition of the active twist wing rotation axis from parallel to opposite directions during the flapping process of the ornithopter, the aircraft exhibits a directional control characteristic that is completely opposite to that of fixed-wing aircraft, as analyzed in the model.

Conclusions
(1) The active twist wing ornithopter, redesigned based on the prototype of a vertical-tail ornithopter, has been systematically analyzed and reliably validated through actual flight experiments.(2) The field flight experiment results demonstrate that the active twist wing can provide independent horizontal control capability and enhance the maneuverability and agility of the ornithopter.(3) The observed phenomenon in the experiment, where the roll angle and yaw control effect of the ornithopter after using the active twist wing function are opposite to the common control phenomenon of the fixed-wing aileron control, indicates that the active twist wing structure introduces complex aeroelastic changes that the existing models cannot describe to explain its control principles.Therefore, this paper presents an initial model to analyze and describe this new yaw control principle.
Overall, measuring the attitude control effect of the active twist on the two-section wing ornithopter during actual flight is of great significance for studying the agility and maneuverability of folding-wing birds, providing some insights for future experiments investigating this behavior.To further explore the flight attitude control of birds, our laboratory will establish wind tunnel experiments to investigate the magnitude of the rolling moment under the active deformation of the two-section wing ornithopter.In the future, we aim to develop a two-section wing ornithopter that is completely independent of vertical tail control, aiming to more closely replicate the flight mode of birds.

Figure 1 .
Figure 1.Geometric morphology of bird wing motion, where the first row depicts simplified schematic diagrams of motion, and the second row shows corresponding bird flight forms.(a) The up-and-down flapping of the wings without static geometric deformation.(b) Spanwise extension-retraction of the wings.(c) Spanwise folding of the wings, folding upwards and downwards.(d) Chordwise twisting of the wings.(e) Flapping flight mode, exemplified by hummingbirds, where the wings do not undergo static deformation.(f) Spanwise extension-retraction flight mode, exemplified by peregrine falcons.(g) Spanwise folding flight mode, represented by albatrosses with large wing spans.(h) Flight mode of pigeons, enhancing agility through chordwise twisting during flight [8].

Figure 2 .
Figure 2. (a) Skeletal structure of an ornithopter.The power system motor and variable speed gears form a set of variable speed systems.The left wing has a three-stage transmission, and the right wing has a four-stage transmission.(b) Diagram of the effect of the twisted wing structure in action (with fuselage coordinates, originating at the center of mass of the ornithopter).(c) Twisted wing structure, a four-bar linkage servo arm (blue), linkage on the wing spar (green), connecting bar (light blue), and virtual linkage between wing spar and servo arm root.(d) Diagram of the change in the center position of the flapping wing craft with the flapping of the wings.The blue color is for a two-section wing flap ornithopter, and the red color is for a single-ended wing flap of the same size.(e) Definition of the coordinates of the tail-fuselage junction.

Figure 3 .
Figure 3. (a) Experimental force analysis of ornithopters under ANIPRO RL4 turntable system allows for the measurement of the lift and thrust forces experienced by the ornithopters under specific conditions, accompanied by a dynamic capture system to measure the flapping frequency of the ornithopters.(b) The relationship between flapping frequency and thrust coefficient (C T ) of ornithopters at different airspeeds.(c) The relationship between relative airspeed and lift coefficient (C L ) of the ornithopter at various flapping frequencies.

Figure 4 .
Figure 4. (a,b) The outdoor flight experiments of two-section wing ornithopter.

Figure 5 .
Figure 5. Graph of the relationship between the attitude of an ornithopter and control signals.(a) Roll angle and tail wing Z-axis control signal for the ornithopter.(b) The linear regression plot of roll angle against Z-axis control signal.(c) Pitch angle and tail wing Y-axis control signal for the ornithopter.(d) The linear regression plot of pitch angle against the Y-axis control signal.

Figure 6 .
Figure 6.The coupling relationship diagram between pitch angle and roll angle under tail control.

Figure 7 .
Figure 7.The control relationship between the wing twist control signal and the aircraft's roll and yaw angles.(a) The twist wing signal's anticipated control effect on the ornithopter's roll angle (similar to the aileron's control effect on fixed-wing aircraft).(b) The twist wing signal's actual control effect on the ornithopter's roll angle is completely opposite to the anticipated effect.(c) The coupling relationship between the yaw and roll angles during actual flight.(d) The coupling relationship between the yaw angle signal filtered by low frequency and the roll angle.(e) The linear regression curve between wing twist signal and the roll angle.

Figure 8 .
Figure 8.Comparison diagram between fixed-wing aircraft and two-section wing ornithopter.(a) Schematic illustration of aileron twisting in fixed-wing aircraft.(b) Schematic illustration of outer wing twisting in two-section wing ornithopter, along with its corresponding force analysis.

Table 1 .
Main properties of ornithopter.