Employing Wing Morphing to Cooperate Aileron Deflection Improves the Rolling Agility of Drones

In the wild, gliding birds dodge obstacles or predators by folding and twisting their wings swiftly to perform a rapid roll. Accordingly, the authors strive to explore the feasibility of improving the roll rate of drones through this bird‐inspired morphing method, by using the asymmetric sweepback of wings to simulate the contraction of birds’ wings and the deflection of the aileron to imitate wing torsion. Moreover, the effects of wing morphing on the centroid, inertia matrix, and aerodynamic characteristics of the drone are explored herein, and a nonlinear dynamic model is established. Furthermore, a novel cooperative strategy that combines wing morphing with aileron deflection for roll control is introduced, and a flight controller based on this cooperative strategy is developed. Finally, the superiority of the cooperative strategy and the accuracy of the dynamic modeling have been validated in the outdoor flights of the morphing wing drone.


Introduction
The rapid development of morphing wing technology significantly improves the performance of winged aircraft and expands their application. [1,2]Morphing wing aircraft can accomplish different flight tasks by changing their aerodynamic shape, [3,4] including shifting from high-speed flight to high-efficiency flight, switching between maneuvering flight and conventional cruising, and adapting takeoff and landing modes and fixed-wing mode.Furthermore, morphing wings with a fast deformation capability can lead to significant and rapid changes in the drone's forces and moments, [5][6][7][8] resulting in an improvement in the maneuverability and agility of drones.
A higher roll rate can improve the roll agility and attitude control ability of drones.In complex wilderness, better agility enables unmanned aerial vehicles (UAVs) to have a stronger ability to avoid obstacles and abscond. [9]During crosswind or gusty conditions, a larger control margin can enhance the drone's ability to maintain attitude. [10]To make the winged UAV more flexible, researchers have explored the application of asymmetric wing morphing for roll control in drones, and some have even conducted flight tests on prototypes. [11]There are two types of roll control methods for existing morphing wing drones: 1) methods based on wing deformation alone, and 2) methods based on the cooperation of aerodynamic control surfaces and wing morphing.
][16][17] An example is the bionic flying robot designed by Luca et al., [11] where asymmetric wing sweeping was used to achieve turning maneuvers.Because of its excellent structural design, the wing's morphing speed was comparable to that of traditional ailerons, but it could not provide a sufficient rolling moment when flying at a small angle of attack (AOA).Another example is a multimission UAV that can perform asymmetric span deformation. [12]lthough the feasibility of attitude control by asymmetric telescopic wings has been proven, it is difficult for drones to adapt to some complex flight conditions due to the slow motion of the wings.The last example is a bionic drone named Lis-Eagle inspired by eagles. [16]Flight tests of this drone showed that asymmetrical wing twisting produces a higher roll rate than asymmetrical wing folding during flight, enabling the drone to reach the expected roll angle in a shorter time.
Recently, some scholars have tried to combine the wing deformation with an aerodynamic control surface to improve the rolling control ability of morphing wing drones.The first example is a telescopic wing UAV designed by Ting et al., [18] who used an aerodynamic control surface to assist wing telescoping control rolling.Due to the structure of the telescopic wing, the aerodynamic control surface could only be installed on the fixed inner wing segment.As a result, roll control could not perform to the full extent.Another example is a bioinspired drone developed by Zhang et al. that resembled large gliding birds. [19]Flight tests have shown that using a combination of wing morphing and aileron deflection improves the roll rates and the reduces adverse yaw compared to using only asymmetric wing control.The last example is a UAV named Pigeon-Bot that was designed with real bird feathers attached to the wings. [20]This design improved the rolling flexibility by incorporating wingtip contraction and asymmetric wing sweep.However, the wingtip can only produce a small additional control moment, which is not prominent for improving the rolling maneuverability of the UAV.
According to existing research results, some obvious problems occur when wing deformation is used to independently perform roll controls.For example, asymmetric wing sweepback provides an insufficient moment at a small AOA, [11,20] and the telescopic wing structure moves slowly. [12,13]Combined control has been proven to improve the roll control capability of morphing wing UAVs, [18][19][20] but there are still no research have proven superior to the control effect of traditional ailerons so far. [21]7][18]20] The main innovation of this article is to establish a cooperative strategy of wing deformation and aileron to maximize the roll rate of drones, and it is proven in flight experiments that this combination control can produce more than 2 times the roll rate of aileron control when cruising at an AOA of 4°.The roll rate is primarily influenced by two factors: the roll moment and the drone's inertia.Increasing the roll moment and reducing the inertia can make the UAV produce a larger rolling rate.Therefore, in Section 2, we analyzed the following two aspects of the prototype: 1) the impacts of the wing deformation on the change in the center of gravity (CG), inertia of the drone, and static moment, and 2) the aerodynamic coupling effect among the wing deformation, aileron, and flight conditions.In Section 3, we presented the dynamic modeling process of a morphing wing UAV.In Section4, we developed a cooperative strategy for maximizing the roll rate of the UAV through dynamic simulations.Additionally, we established a flight control system for the drone, in which the roll angle is controlled by this collaborative strategy.In Section5, several flight tests were conducted on the prototype.Outdoor open-loop dynamics tests of the combination of wing asymmetric morphing and aileron deflection confirmed that our proposed collaborative strategy significantly enhances the roll agility of the drone.These tests also provided evidence that supports the accuracy of the dynamic simulations.Furthermore, the circular trajectory tracking test validated the feasibility of applying the collaborative strategy to outdoor autonomous flight.

Morphing Wing Drone Test Platform
To perform rolling, birds can adopt two strategies: asymmetric wing folding and wing twisting. [21,22]The asymmetric deformation of the wings causes an uneven distribution of lift along the wingspan, and twisting of the wings changes the camber of the wings.In this article, the asymmetric sweep of wings and the deflection of ailerons are used to imitate these two actions of birds.Figure 1 shows the drone rolling through the collaborative control of the wing and aileron in the flight test.It should be emphasized that in our previous research, we completed the design of the prototype. [19]Here, only a brief introduction to the mechanical structure of the morphing wing is provided.The morphing wing is actuated by a digital servo motor whose power is transferred by a pair of crossed helical involute gears, driving a group of wing skeletons composed of linkage mechanisms to achieve folding and unfolding.During the morphing process, the wing skeletons are stacked, resulting in an increased sweeping angle and reduced wing area (Figure 2c).To fully exploit the control abilities of the ailerons, we placed them on the outermost deformable wing of the drone rather than on the fixed inner wing.
The size and appearance of the bionic drone are depicted in Figure 2a.The drone in this article wields large-scale wing morphing to achieve attitude control, which will lead to CG, inertia, and static moment changes as the wings deform.Through computer-aided design (CAD) software, we obtained these changed parameters (Figure 2d-f ).The blue curves in Figure 2d,e represent the displacement of the CG during asymmetric and symmetric morphing processes of the wing, respectively.When the wings are symmetrically swept back, the CG of the drone moves in the negative x-axis direction.However, when only the left wing is swept back, the CG moves simultaneously in the negative x-axis and positive y-axis directions.Additionally, the displacement of the CG along the x-axis during symmetric morphing is twice that of asymmetric morphing, given the same morphing angle.The pink curves in Figure 2d,e show the changes in the moment of inertia during symmetric and asymmetric morphing, respectively.The morphing of the wings reduces the wingspan and inertia of the drone along each axis, and these changes are more pronounced during symmetrical deformation.Figure 2f shows the static torque change of the CG to the coordinate origin O b .
The avionics applied on the drone are shown in Figure 3. Regarding the propulsion system, we opted for two T-motor V505 brushless DC motors outfitted with 15 Â 8 GWS propellers to achieve a maximum thrust up to 12 kg.To ensure swift wing morphing, two KST 320 digital actuators were used for driving (mass: 320 g, torque: 150 kg cm at 24 V).Additionally, we employed four KST X08 digital servos (mass: 7.1 g, torque: 20 kg cm at 6 V) for aileron and elevator deflection.Under noload conditions, we tested that a response time of 0.2 s for wings   to deform from unfolded to 55°folded and almost the same for the aileron deflection from the middle position to 20°.PIXHAWK 4 was used as an autopilot and integrated sensors, including the IMU, GPS, AOA meter, and airspeed meter.The communication between the ground station and the UAV was carried out through a data transmission system.We monitored the flight data and flight status through the ground station, and operated the remote controller to drive the UAV, send instructions, and switch the flight mode.

Aerodynamic Modeling
The aerodynamic modeling process for the combined control of wing morphing and aileron is much more complex compared to the individual control of either of them.In addition to the mutual impacts between the two kinds of control surfaces, the control efficiency of the wing deformation is also affected by the AOA.In this section, an aerodynamic simulation of the drone is performed through the computational fluid dynamics (CFD) method, to explore the interaction between wing morphing and conventional control surfaces.Equations of the aerodynamic parameters are determined according to the simulation results.
By using Fluent 19.0 commercial software, we performed a numerical simulation for the UAV.The flow field in the computational domain is set as a cuboid, with a length, width, and height of 30, 20, and 20 m, respectively.Moreover, the flow field is divided by an unstructured grid, and the number of grids is 2.2 Â 10 8 .The specific parameter settings in the software were described in detail in our previous research, [19] and the accuracy of the aerodynamic simulation method was also validated by comparing it with the results of the wind tunnel tests. [23]o estimate aerodynamic derivatives, we utilized the aerodynamic vortex lattice (AVL) method by employing XFRL 5 software. [24]o investigate the aerodynamic effects of the asymmetric wing sweep on the drone, four configurations with asymmetric morphing angles of 15°, 30°, 45°, and 55°were numerically simulated, and aerodynamic data before stall are shown in Figure 4.The aerodynamic forces and moments obtained from CFD are converted into aerodynamic coefficients using the following equations: where L, D, l, and M are the lift force, drag force, roll moment, and pitching moment of the drone, respectively.C L , C D , C l , and C m are the coefficients of lift, drag, roll moment, and pitch moment, respectively.V is the air speed, S is the wing area, ρ is the air density, c is the mean aerodynamic chord, and b is the wingspan.
Different colored curves in Figure 4b represent their corresponding configurations in Figure 4a.As the wing sweeps back, the slopes of the lift curve and drag curve (Figure 4b) will decrease, while that of the roll moment curve will increase.An increase in the asymmetric morphing angle leads to a reduction in both the lift force and drag force of the folded wing.Therefore, the distribution of the lift force becomes more uneven along the wingspan, which ultimately leads to an increase in the rolling moment.With wing asymmetric morphing, the pitching moment coefficient first decreases (Figure 4b) first and then increases, and it is smaller than other configurations at a morphing angle of 30°.As the wing asymmetrically deforms from the fully unfolded state, the aerodynamic center will move backward, thus generating a pitching down moment (Figure 4b) of the UAV.However, if the wing deformation angle exceeds 30°, it will lead to a significant reduction in the wing area, thereby weakening the pitch down moment generated by the wing swept-back.
The impacts of aileron deflection on the aerodynamic moments under different wing morphing angles are depicted in Figure 5a,b.Figure 5a illustrates the results at a morphing angle of 55°, while Figure 5b shows the results at a morphing angle of 30°.In the simulation, the right wing was folded while the left wing expanded.Simultaneously, the right aileron deflected upward, and the left aileron deflected downward.All these actions were implemented to ensure a consistent direction of the roll moments generated by the aileron and wing morphing, thereby improving the aircraft's rolling performance.With a fixed morphing angle, the aileron deflection has almost no effect on the slope of the roll moment curve, but it improves the control moment of the UAV by increasing the intercept of the moment curve (Figure 5a,b).However, the roll moments generated by the aileron under these two morphing angle configurations are different.When the wing morphing angle is 55°, the roll moment coefficient increases by approximately 0.011 as each 10°of the aileron deflection occurs, while this number is approximately 0.018 at a morphing angle of 30°.Therefore, the asymmetric sweeping back of the wings weakens the aileron control.Additionally, the asymmetric morphing of wings also reduces the drag force exerted on the folded wing by the aileron, thus generating a reverse yaw moment (Figure 5a).Furthermore, operating the aileron at a fixed wing morphing angle induces a downward pitching moment (Figure 5a), resulting in a decrease in the AOA during flight.
The pitch attitude of the drone is independently controlled by the elevator on the tail.Figure 6 shows the aerodynamic effects of the elevator deflection on the deployed configuration and the asymmetric deformation 55°configuration.When the elevator  deflects upward 20°from the neutral position, the lift coefficient and drag coefficient will decrease, the pitching moment coefficient will increase (Figure 6), and the changes in the aerodynamic parameters for the two configurations are very similar.This indicates that the control effect of the elevator does not change with the deformation of the wing.
Obviously, the control efficiency of asymmetric wing morphing is mainly related to the AOA of the drone.The effectiveness of the aileron is affected by the wing morphing angle.However, almost no interaction occurs between the elevator and wing morphing.Based on the aerodynamic simulation results mentioned above, the expressions of the aerodynamic coefficients affected by the joint input of the wing and aileron can be depicted as follows: where C Y and C n are the coefficients of the side force and yaw moment, respectively.The subscript "0" represents the zero-lift coefficient.C ij denotes the aerodynamic derivative, where C ij ¼ ∂C i = ∂C j .α and β represent the AOA and sideslip angle of the drone, respectively.δ a stands the aileron deflection, with the left aileron downward and the right aileron upward as the positive direction.θ m is the wing morphing angle, which is defined as positive when the right wing sweeps back and the left wing unfolds.δ e is the deflection of the elevator, where the downward rotation of the trailing edge is defined as positive.

Dynamic Modeling of the Morphing Wing Drone
Compared to traditional fixed-wing UAVs, the introduction of the asymmetric wing deformation in the attitude control will result in changes in the inertia matrix and the movement of the CG.27] To obtain a more accurate model, we took these factors into account when establishing dynamic equations for the drone.The establishment process of the coordinate system is shown in Figure 2b.The origin of the body coordinate system O b x b y b z b is set as the CG of the drone when the wings are fully expanded, the ground coordinate system is described as O g x g y g z g , and the CG of the deformable wing segments on both sides is The dynamic equation of the morphing wing UAV can be explained using vector form as [28] where F and M are the forces and moments on the drone, m and m i are the masses of the UAV and its deformed wings, I is the inertial matrix, V is the flight speed of the UAV, ω and ω i are fuselage angular velocity and sweep rotational speed of outer wing, and i = 1, 2 represent the deformable part of the left wing and right wing.As the wings can only rotate about the Z axis, The static moments of the left and right deformed wings are as follows: The static moment of UAV is described as The angular velocity of two deformed wings can be formed as The angular velocity and speed of drone in body coordinate system can be expressed as Equation ( 4)-( 7) are substituted into Equation (3) and simplified to obtain the dynamics equation of UAV in scalar form as follows: where F x , F y , and F z are the forces along the three coordinate axes of the airframe, respectively, and l, m, and n are the roll, pitch, and yaw moments, respectively.In the nonlinear Equation ( 8) and ( 9), the terms including S represent the additional forces/moments produced by the CG shift as the wing sweeping, and the terms including first and second derivatives of static moment are the additional forces and moments produced by the velocity and acceleration of aircraft's CG shift in wing asymmetric sweeping progress.The aerodynamic model is introduced, and the forces and moments exert on the drone are as follows: (10)   where g refers to the gravitational acceleration, P indicates the pull of propeller, L, D, and Y correspond to the lift, drag, and lateral force of the UAV, respectively.And l A , m A , and n A , respectively, stand for the roll, pitch, and yaw aerodynamic moment.φ and θ are the bank angle and pitch angle, respectively; According to Equation ( 8)-( 10), we can further sort out the nonlinear dynamic model as where x = [u, v, w, p, q, r] T is the state variable, and u = [δ e , θ m , δ T ] T is the control variable of the UAV.g is a configuration matrix of the mass, static moment, and inertia moment, and its value varies as the control input u changes.Meanwhile, the flight status will also affect the control input u.The control input in conventional fixed-wing UAVs usually only affects the control moment, and its influence on the configuration matrix is usually ignored.This also reflects the differences between the deformation wing control in this article and the traditional control.

Dynamic Characteristics Analyses and Collaborative Strategy of the Wing and Aileron
In Section 4.1, we conducted dynamic analyses to assess the impact of utilizing wing morphing in conjunction with ailerons on the flight attitude.In Section 4.2, we developed a collaborative strategy between the wing and ailerons that maximizes the roll rate by analyzing the dynamic characteristics.Moreover, we established an effective collaborative expression.The main content of Section 4.3 is the application of the collaborative strategy to the roll control in a closed-loop flight control system.We also demonstrated the advantages of the collaborative control over using aileron control alone through the flight control simulation for tracking a 90°yaw angle.

Dynamic Characteristics Analyses
According to the aerodynamic simulation results (Figure 5), the drone exhibits the highest roll agility when the aileron deflects at its peak value.Therefore, we conducted dynamic simulations to explore the impact of wing morphing on the drone performance when the ailerons are set at their maximum deflection angle.
In the following dynamic simulations, the peak deflection of ailerons was set to 20°, the wing on the side of the upwarddeflecting aileron folded, and the wing on the side of the downward-deflecting aileron expanded.The position of the elevator remains stationary in the trimmed state.The dynamic performance of the combination of asymmetric wing morphing and aileron deflection was tested using three permutations (Figure 7a): an aileron with a 20°deflection and wing at a 55°d eformation (green configuration); an aileron with a 20°deflection and wing at a 30°deformation (blue configuration); and an aileron with a 20°deflection alone (red configuration).How the angles of the two kinds of control surfaces changed over time is recorded in Figure 7a.As the wing morphing and aileron deflection take place in an extremely short time, it can be assumed that the motor rotation angle is in the form of a ramp signal. [11,29]igure 7b exhibits the recorded changes in the attitude occurring within a span of 1 s after the action input under different trimmed conditions of horizontal straight flight.These include (α = 2°, V = 20 m s À1 ), (α = 4°, V = 17 m s À1 ), and (α = 6°, V = 15.5 m s À1 ).
Figure 7b illustrates that, at an AOA of 2°, the synergy of 30°a symmetric wing morphing and 20°aileron deflection resulted in a larger roll angle and roll rate compared to the other two configurations.However, at AOAs of 4°and 6°, the combination of the wing full asymmetric contraction and 20°aileron deflection can produce stronger roll agility.Therefore, a single configuration could not bring out the best effect of the collaborative control.Based on the roll angle curves shown in Figure 7b, the larger the AOA is, the more significant the advantage of utilizing a combination of full wing contraction and aileron deflection for roll control in drones becomes.We also found some adverse effects caused by wing asymmetric deformation.First, the wing morphing increased the roll angle and reduced the wing area, so the lift to overcome gravity was reduced, which led the drone to descend.In addition, compared with independent aileron control, the wing's asymmetric morphing aggravated the adverse yaw when the drone begins to turn.However, these problems can be solved by elevator and rudder during flight.

Establishment of the Collaborative Strategy
Next, we fine-tuned the drone by adjusting the AOAs within the range of 0°-8°.We then conducted dynamic response tests using various wing morphing angles in combination with a 20°aileron deflection.For each test, the action command is to deflect the aileron by 20°and sweep back the wing to the intended angle.Once all actuators have deflected from their initial position to the corresponding position, we reset the actuators and proceeded to measure the roll rate of the drone.In Figure 8a, the wing sweep angles corresponding to the maximum roll rates of the drone at various AOAs are depicted by the distinctive red solid line.At an AOA over 4.4°, the wing is fully folded, which will produce better roll agility.Regarding an AOA smaller than 0.4°, it is better to only use aileron for control.At AOAs between 0.4°and 4.4°, the wing morphing angle that generates the maximum roll rate demonstrates an almost linear growth pattern as the AOA increases.To simplify the representation, we approximated this curve (0.4°-4.4°) by employing a straight line with a slope denoted as K.The cooperative strategy expressions for maximizing the roll rate of the drone in dynamic simulation are as follows: where δ aðmaxÞ = 20°, which is the maximum value of δ a , and δ θm ðαÞ is the wing morphing angle that produces the maximum roll rate.K is the slope of the wing morphing angle varying with the AOA in the corresponding equation, with a value of 12.5.θ mðmaxÞ is the amplitude of the wing morphing angle, and its value is 55°.The red dotted line in Figure 8b shows that when the aileron controls the roll independently, the roll rate significantly decreases as the AOA increases.This is because the rolling moment generated by the aileron is weakened due to the low flight speed under a high AOA.The red solid line in Figure 8b clearly demonstrates that when utilizing a 55°asymmetric wing folding combined with a 20°aileron deflection, the range of fluctuations in the roll rate caused by varying the AOAs is limited.By introducing wing morphing and aileron cooperation, the roll moment coefficient increases as the AOA becomes larger (Figure 5a), thus mitigating the weakening effect of the decreasing flight speed on the roll moment.Therefore, this combination consistently generates a relatively stable roll control moment across a wide range of AOAs.

Flight Controller Design and Simulation Using the Collaborative Strategy
The flight controller operates in a cascaded loop, [30] including the longitudinal autopilot and the lateral autopilot.The specific controller structure is shown in Figure 9.The lateral autopilot takes the course controller as the outer loop and the roll attitude controller as its inner loop.The course controller calculates the error between the set value and the real value of the course attitude, and uses a proportional-integral (PI) controller to generate a required roll angle.The roll controller consists of two parts.First, it calculates the deviation between the roll attitude set value and the real value and generates the set value of the angular rate by multiplying the error and a gain proportional (P) controller.Then, it also calculates the deviation between the set value and the true value of angular rate, and the PI controller is used to generate a desired roll angular acceleration, which is used to calculate the angular offset of the actuators (aileron, wings).The longitudinal autopilot takes the altitude controller as the  outer loop and integrates the pitch attitude controller as the inner loop.The structure of the longitudinal autopilot is similar to that of the lateral autopilot, so it is not described in this article.
Wing morphing and aileron inputs are redundant for the roll control of the drone, so a reasonable allocation strategy of the two surfaces is crucial.We used the cooperative strategy in Equation ( 12) as the maximum angle of the wing sweep and aileron deflection for roll control.Meanwhile, the wing deformation angle δ θ1 is obtained by linear interpolation, that is, the position of δ θ1 in the interval ½Àδ θm ðαÞ, δ θm ðαÞ is equal to the corresponding position of δ a1 in the interval ½Àδ aðmaxÞ , δ aðmaxÞ .The combined control function (Figure 9) for roll control in the closedloop system is expressed as follows: 8 > < > : where δ is the actuator output parameter calculated by the roll control solver in the flight controller; δ a1 and δ θ1 are the corresponding outputs of the aileron and wing, respectively, and δ aðmaxÞ is the amplitude of δ a1 and is set to 20°.
Notably, the "combined control function" in Figure 9 refers to Equation (13), which is based on Equation (12).According to the variables of Equation ( 12) and ( 13), the input parameters of this function are the flight AOA α and the driver output parameter δ.The output parameters are the wing deformation angle δ θ1 and aileron deflection angle δ a1 .In the simulation, the roll angle of the UAV is controlled by the collaborative strategy, while the pitch angle is controlled by the elevator.
Figure 10 shows the attitude change and response of the control surfaces of the drone while tracking a 90°yaw angle at an AOA of 4°.Moreover, the red and blue curves represent roll control using the aileron alone and the collaborative strategy of the wing and aileron, respectively.The maximum roll angle of the drone was limited to 50°.
Based on the flight simulation results, we compared and analyzed the flight attitude changes and control surface movement generated by two roll control methods.By employing the collaborative strategy, the drone achieved a 90°yaw angle 0.83 s earlier and a 50°roll angle 0.78 s earlier compared to using ailerons alone (Figure 10b,c).Furthermore, Figure 10e demonstrates that the collaborative strategy reduced the maximum output angle of the aileron by 5.2°in comparison to using the aileron alone.Although the aileron deflection angle is smaller, the cooperative control enables better roll control by increasing the wing deformation angle (Figures 10d).The simulation results provide compelling evidence that the synergistic strategy enhances both the roll agility and roll control margin for the drone.To reduce the impact of the external environment on flight tests, all tests were completed under calm or breeze conditions.We adopted PIXHAWK 4 as the autopilot and combined it with sensors, such as the IMU, airspeed meter, and GPS, to measure and record the attitude change, flight speed, and trajectory information of the UAV.In addition, an AOA sensor was also equipped to monitor the change in the AOA during the flight test. [31]t should be noted that the autopilot does not participate in the flight control during the open-loop dynamic tests, and is only used to record the outputs of each drive and flight data.

Flight Experiment
The open-loop dynamics were investigated using three different experimental configurations (Figure 11a): an aileron with a 20°deflection and a 55°wing morphing (red); an aileron with a 20°deflection and the wing deformation according to Equation (12) (green); and an independent aileron with a 20°d eflection (blue).In each flight test, the action signal input (Figure 11b) was carried out in the level flight state trimmed with a flight speed of 17 m s À1 at an AOA of 4°.Furthermore, the attitude changes of the UAV within 0.7 s were recorded (Figure 11c).During the flight tests conducted to assess the roll ability, a constant 70% throttle was maintained throughout the tests.To avoid any interference with the experimental results, the position of the elevator was locked in the trimmed position and not manipulated during the tests.Moreover, under the same trimmed status and command input conditions as the outdoor flight tests, we conducted open-loop dynamic simulation tests to verify the accuracy of the dynamic modeling.
Figure 11c illustrates the drone's attitude response.In each attitude subfigure, the solid line represents the average value of the repeated experiments, the shaded portion represents the error range of the flight attitude, and the dotted line denotes the result of the dynamic simulation.The attitude changes observed in the simulation align closely with the experimental results, confirming the consistency between the two.Meanwhile, Figure11c shows that the combined strategy of Equation ( 12) (green curve) generates a greater roll angle and roll angular rate, compared with the other two configurations.More importantly, in a short time of 0.7 s, the roll angle generated by this strategy is almost twice that of traditional aileron control.According to the yaw angle curve depicted in Figure 11c, the green configuration initially generated more reverse yaw compared to the blue configuration during the start of the turn.However, due to the higher roll angle obtained by the green configuration, it began to turn at a faster yaw rate from 0.4 s onward.To assess the flight controller's performance, we proceeded with an outdoor experiment in which the UAV's mission was to circle above a fixed point.The flight path, roll attitude, attitude error, and control signal input are recorded in Figure 12.The real flight track almost coincided with the expected track (Figure 12b), and the roll attitude control error was no more than 3°after the circling started (Figure 12d).In order to obtain a roll angle (0-2 s) to enter the turning as shown (Figure 12d), the servo actions were obvious, with a maximum aileron deflection of 16°and a maximum wing deformation of 20°(0-2 s), as illustrated in Figure 12f.Due to the influence of wind, the roll angle of the UAV continuously fluctuated (Figure 12d), so the servos were also fine-tuned with the flight state to ensure track accuracy.The UAV successfully completed the circling command, and the servos were far from reaching the control margin (wing morphing: 55°, aileron: 20°) during the attitude maintenance process.According to the flight test results, the flight controller based on the cooperative strategy has a good control effect and is suitable for automatic pilot missions.

Conclusions
In this study, we explored the application of coordinated wing morphing and aileron deflection as a novel control input to improve the roll agility of the morphing drone.Aerodynamic coupling effects between the wing deformation and aileron deflection cannot be neglected.Wing deformations can generate a roll moment while also decreasing that of the ailerons.
We developed nonlinear dynamic equations for the morphing wing drone, which consider the effects of wing morphing on the aircraft's inertia, CG position, and aerodynamic forces/ moments.Based on dynamic simulation testing, we established the collaborative strategy that produces the maximum roll rate of the drone at different AOAs.Flight experiments were performed to verify that the roll rate of the drone under this cooperative strategy is almost twice that under sole aileron control at an AOA of 4°.We also developed a flight controller based on the collaborative strategy.Compared to conventional aileron control, this method has a faster tracking speed and stronger control margin.
The cooperative strategy is applicable not only to the drone in this article but also to any other morphing wing aircraft with its fast morphing capability and equipped with ailerons, even if their wing and aileron sizes are different.

Figure 1 .
Figure 1.Roll control achieved by the combination of wing morphing and aileron.

Figure 2 .
Figure 2. Bioinspired platform architecture.a) Appearance of the drone.b) Establishment of the coordinate system.c) Mechanical structure of the deformed wing.d) Changes in the CG and moment of inertia with wing asymmetric morphing.e) Changes in the CG and moment of inertia with wing symmetric morphing.f ) Shift in the static moment caused by wing asymmetric/symmetric morphing.

Figure 4 .
Figure 4. Analysis on aerodynamics of asymmetrical wing morphing.a) Five configurations in the aerodynamic simulation.b) Aerodynamic data of the drone under five different asymmetric morphing angles.The four subgraphs from left to right represent the lift coefficient, drag coefficient, rolling moment coefficient, and pitching moment coefficient changes with the AOA, respectively.

Figure 5 .
Figure 5. Aileron deflection effects on the aerodynamic moments under different wing morphing angles.a) Configuration of wings at a 55°asymmetric deformation.b) Configuration of wings at a 30°asymmetric deformation.

Figure 6 .
Figure 6.The effects of elevator deflection on aerodynamic forces and moments under different wing morphing angles.

Figure 7 .
Figure 7. Open-loop dynamic response test of three permutations of wing and aileron.a) Three control inputs of wing and aileron.The curve color corresponding to the drone color in each subgraph represents the angle output of the morphing wing driver, and the yellow curve represents the deflection angle of the aileron driver.b) Open-loop dynamic response caused by asymmetrical deformation at 2°, 4°, and 6°AOAs.Moreover, the roll angle, roll rate, yaw angle, and flight height were recorded within 1 s of the signal input.

Figure 9 .
Figure 9. Flight controller of the morphing wing UAV.

Figure 8 .
Figure 8. Roll rate response of different wing morphing angles, coupled with a 20°aileron deflection.a) The wing sweep angles that correspond to the maximum roll rates at different AOAs.b) Variation in the roll rate with the wing morphing angle and AOA.

Figure 10 .
Figure 10.Tracking response to a 90°left yaw angle under an AOA of 4°.a) Curve of angle of attack with time, b) curve of yaw angle with time, c) curve of roll angle with time, d) curve of wing morphing angle with time, e) curve of aileron deflection with time, and f ) curve of elevator deflection with time.

First, we
conducted outdoor open-loop dynamics tests of the combination of wing asymmetric morphing and aileron deflection to validate the accuracy of the dynamic simulations and the superiority of the collaborative strategy.Next, the drone was ordered to track a circle trajectory outdoors to test the feasibility of the flight controller designed in 4.3 for autonomous driving.

Figure 11 .
Figure 11.Open-loop flight tests of the roll agility.a) The three configurations in the flight tests.b) Time-resolved wing and aileron position for the control input.c) Attitude responses to the three cases.