Analysis on Hover Control Performance of T- and Cross-Shaped Tail Fin of X-Wing Single-Bar Biplane Flapping Wing

+e current flapping wing adopts T-shaped or cross-shaped tail fin to adjust its flight posture. However, how the tail fin will affect the hover control is not very clear. So, the effects of the two types of tail on flight will be analyzed and compared by actual flight tests in this paper. Firstly, we proposed a new X-wing single-bar biplane flapping-wing mechanism with two pairs of wings. +ereafter, the overall structure, gearbox structure, tail, frame, and control system of the flapping wing were designed and analyzed. Secondly, the control mechanism of hover is analyzed to describe the effect of two-tail fin on posture control.+irdly, the Beetle was used as the control unit to achieve a controllable flight of flapping wing.+eMPU6050 electronic gyroscope was used to monitor the drone’s posture in real time, and the Bluetooth BLE4.0 wireless communication module was used to receive remote control instructions. At last, to verify the flight effect, two actual flapping wings were fabricated and flight experiments were conducted. +e experiments show that the cross-shaped tail fin has a better controllable performance than the T-shaped tail fin. +e flapping wing has a high lift-to-mass ratio and good maneuverability. +e designed control system can achieve the controllable flight of the flapping wing.


Introduction
Flying creatures of nature all use a flapping wing to fly. ey flap wings and change the angle and shape of their wing and tail fin, to create lift and propulsion, and change the direction of flight and flight mode. By doing these, they can easily realize the rapid and flexible flight movements [1], such as flying, gliding, and hovering. en, they can have very high mobility and flexibility of the flight and realize a high structural pattern of a pair of wings with multiple functions. Especially, hummingbirds have good hovering flight performance, as shown in Figure 1. is inspired us to design a small, smart, and flexible drone.
At present, the flapping-wing drone that can successfully fly can be divided into forward flight and hover flight from the flight function and can be divided into two categories from the presence or absence of the tail: the tailless ( Figure 2) and the tailed. e tailed flapping-wing drone can be divided into three types: horizontal tail fin (Figures 3(e), 3(g), 3(h), and 3(k)), T-shaped tail fin (Figures 3(a), 3(b), 3(f ), 3(i), 3(j), and 3(l)), and cross-shaped tail fin (Figures 3(c) and 3(d)).
ese research studies provide great contribution and innovation for making flapping wing to successfully fly. If the tail structure is too complicated, it will increase the weight of the tail and make the drone difficult to fly. So, the tail of the actual flapping-wing drone will not be too complicated, and for easy control, most of the flapping-wing drones use Tand cross-shaped tail fin.   [20]. (h) Robotic Hummingbird developed by Purdue University [21]. (i) Quad-thopter developed by Delft University of Technology [22]. (j) NUS-Robobird developed by the National University of Singapore [23]. (k) DelFly Nimble developed by the Delft University of Technology [24]. (l) Butterfly-type ornithopter developed by Beihang University [25].
For ornithopter, it is more difficult to hover like a hummingbird, since its aerodynamic [36,37] and mechanism [38] are more complex. Moreover, it should produce more drag force to balance gravity and be controlled better than flying forwards only [39][40][41][42]. And the hovering flapping wing has more flying potential. erefore, many researchers carry out stability analysis of near-hovering [43] or hovering [44,45] and use various control strategies, such as adaptive control [46], passive stability enhancement [47], Spiking Neural Network (SNN) control [48], sliding-mode approach [49,50], and adaptive feedforward schemes [51]. However, these make the ornithopter adopt more powerful control unit and more expensive.
Moreover, at present, the ornithopter adopts mostly the structure of imitating birds' wings [52]-the whole ornithopter only has one pair of wings. Due to the great difference in the freedom and flexibility between the ornithopter and birds' wings, the lift of the ornithopter will decrease when the wings are flapped upwards. erefore, special structures need to be designed to compensate, resulting in complex wing structures [53][54][55] and increased weight of the ornithopter.
In addition, few papers have analyzed the influence of the tail fin shape on the hovering effect. erefore, in this paper, we designed a new X-wing single-bar biplane flapping-wing flight vehicle to imitate the hummingbird vertical hovering flight. en, we analyzed and compared hover performance of two kinds of tail fin. e remaining sections of this article are organized as follows: in the second section, the structure of the X-wing flapping-wing drone is designed. It can further enhance flight thrust through the synchronization of two pairs of wings beat-up and squeeze the air vortex flow. erefore, it can both generate thrust while flapping up and down. In the third section, the control mechanism of the T-shaped and cross-shaped tail fin is analyzed. en, the control variables and implementation are proposed. In the fourth section, control circuit and software modules are designed. e fly control system can get the gyroscope data in the flapping wing and receive the operator's command via Bluetooth. In the fifth section, hovering experiments are conducted and analyzed to verify the flight performance. Finally, conclusions of this article are presented in the sixth section.
Since the left wing and right wing do not use the same bar, there should be other components to connect the left bar and right bar. is will increase the weight. We designed a new single-bar wing ( Figure 5). e wings were improved from double-bar to single-bar, simplifying the structure and enhancing the strength. e two pairs of wings of the new X-wing ornithopter are arranged in an X-shaped cross using two single-bar wings, with a total of four wings. By doing this, we can simplify the flapping support structure. e ornithopter is composed of gearbox, tail fin, body frame, and control system, as shown in Figure 6. Figure 7 illustrates the gearbox structure composition. e gearbox is an important mechanism to reduce the speed of the motor, increase the torque of the motor, and convert the rotary motion of the motor into the reciprocating flapping motion of the wings. When the brushless motor rotates, it drives the swing arm gear to rotate via the two-stage reduction of the motor gear and the middle gear. e two swing arm gears mesh with each other to realize the transmission of power from the right swing arm gear to the left. e swing arm gear drives the eccentric cam to rotate. e eccentric cam drives the tie rod to turn the rotary motion into a reciprocating motion of the tie rod. e tie rod then drives the elastic support on the wings to swing up and down through the small lifting lugs to achieve flapping motion. e elastic support and the body frame are connected through an elastic hinge to achieve both rotation restraint and certain energy recovery. e entire gearbox system is fixed on the body frame through a gearbox plate.

Gearbox.
In this way, the gearbox plate, the eccentric cam, the tie rod, and the elastic support constitute a crank rocker mechanism, as shown in Figure 8. By optimizing the size of each component, on the premise that the optimal working range (speed, torque) of the motor and the flapping frequency of the wings are met, the angle range of the elastic support movement can be controlled. When the amplitude of the elastic support is 54.32°, the angle between the upper and lower wings is maximized when the wings are deployed. It reaches 111.5°. e minimum angle between the upper and lower wings is 2.86°when the wings are folded together. ey both meet the requirements of wing motion amplitude. Figure 8 shows the curve of the wing angle with time when the wings are flapped up and down after optimization. Figure 6 illustrates the tail fin structure composition. e tail fin is an important part of controlling the flying pose of the flapping-wing drone. Its main function is to control the angle of the rudder wing and the elevator wing  Journal of Robotics through the servo motor and then change the pitching and leftright flight direction of the flapping-wing drone. e tail fin is mainly composed of a tail fixed bracket, a cross-directional stabilizer, a rudder, an elevator, a rudder wing, an elevator wing, a rudder swing arm, and a reinforced carbon fiber rod. When the flapping-wing machine needs to change the direction of the pitching motion, the rudder (or elevator) will drive the swing arm. Since the swing arm and the rudder wing (or the elevator wing) are fixed together, the swing arm of the servo will drive the rudder wing (or the elevator wing) to rotate around the connection axle between the stabilizer wing and the rudder wing (or the elevator wing). en the drone will change the direction of the airflow flowing through the tail fin and realize the change of the direction of the flapping-wing drone.

Body Frame.
e body frame is a rod-shaped structure with a rectangular cross section, and its main function is to fix the entire structural assembly of the flapping-wing drone.
Since carbon fiber has the lightest mass among the materials that can be selected with the same strength and stiffness, the carbon fiber material is selected as the body material.

Body Dynamics.
e positive directions of the coordinates are displayed in Figure 9. e x-axis is perpendicular to the flapping-wing surface and points forward, the y-axis is pointing to the left of the flapping-wing drone, and the z-axis is vertically upward. e dynamics of the ornithopter can be described, under rigid body assumption, by Newton-Euler motion equations. Similar to a drone, we obtain 12 ordinary differential equations with 12 unknown coordinates: velocity (u, v, w), angular velocity (p, q, r), position (x, y, z), and orientation expressed by Roll-Pitch-Yaw angles (φ, θ, δ) by omitting the equations for position and heading (yaw) [20,[57][58][59].
Here, m is the body mass, and I xx , I yy , I zz , and I xz are both nonzero moments and product of inertia in body frame (products I xy and I yz are both zero due to body symmetry). Aerodynamic forces and moments are represented by vectors (X, Y, Z) and (L, M, N), respectively [60][61][62].
e wing forces and tail fin forces are transformed into the body frame as follows: Here, F Fly is the drag force produced by flapping wings, θ Fly is the angle between F Fly and z-axis, θ Flyxz and θ Flyyz are the projection of angle θ Fly on x-z plane and y-z plane, respectively, F Rud and F Ele are the rudder force and elevator force produced by rudder wings and elevator wings, respectively, l E is the projection of the distance the tail fin and the center of gravity of the ornithopter onto the z-axis, ρ is air density, V is airflow velocity, S WR and S WE are the area of the rudder wings and elevator wings, respectively, C Yθ Rud and C Yθ Ele are the rudder lateral force derivative and the elevator longitudinal force derivative, and θ Rud and θ Ele are the rudder and elevator rotation angles, respectively.
Since the rudder wing of the T-shaped tail fin is not plane-symmetrical about y-z surface, the flapping wing of T-shaped tail fin has one more N torque than the crossshaped tail fin: (3) Here, l R is the projection of the distance between F Rud and the center of gravity of the ornithopter onto the y-axis.
So, N torque will cause hovering flapping-wing extra yaw movement of the T-shaped tail fin. It should be compensated by appropriate control mechanism. Hence, the flapping wing of the cross-shaped tail fin will hover in a more controllable manner than the T-shaped tail fin, because its rudder wing is plane-symmetrical about y-z surface.
From these equations, we can see that the flapping-wing posture can be controlled by the rudder rotation angles θ Rud and elevator rotation angles θ Ele . Figure 9 also shows the control mechanism integrated in our present flapping wing; when the rudder wing is moved by a rudder servo as shown in Figures 9(b) and 9(e), the ornithopter will create a rolling moment to rotate about the x-axis. e T-shaped ornithopter will also create a yawing moment to rotate about the z-axis. Similarly, when the elevator wing is moved by an elevator servo as shown in Figures 9(c) and 9(f ), the ornithopter will create a pitching moment to rotate about the y-axis.
e two degrees of control allow us to effectively control the ornithopter. erefore, if we want the ornithopter to have a good hover flight performance, the tail fin must be symmetrical about the longitudinal axis (z-axis) of the ornithopter.

Control Strategy.
e servo output off-angle position is Here, K p , K d , and K i are the parameters of the PID, respectively; T A and Act A are the target posture angle from a remote control and actual posture angle from a gyroscope. e gyroscope can output precise angle velocity, so it is unnecessary to derive Δ A in single-chip microcomputer; then, Here, Act ω are actual posture angle velocity from gyroscope.
So, the servo output off-angle position changes to By doing this, the requirements for the control system can be decreased. It can improve PID strategy speed. And the hovering can be controlled better.
Since the servo position is 90 when the flapping wing in hover balance, the new servo position after PID being controlled is According to the signal from a gyroscope and remote control, we can calculate the new rudder servo position and elevator servo position, respectively. By using this strategy, we can control the ornithopter hovering. Currently, there is no control over the yaw axis, which is passively stable by adjusting the fixed angle of two elevator wings manually. Because if we control the yaw, we will need two servos to adjust two elevator wings, respectively, not one currently.
is will add weight to the flapping wing and make it fly difficultly.

Flying System
Hardware.
e control system mainly consists of a control module, a brushless motor drive module (BMDM), a wireless communication module, a gyroscope, and a lithium battery, as shown in Figure 6. e control module uses Beetle single-chip microcomputer as the core control board. It can receive the target control instructions from the remote control via the Bluetooth wireless module and then generates a PWM signal based on the actual posture of the flapping-wing machine detected by a gyroscope. e PWM signal can control the servo to dynamically adjust the position of the tail fin. And Beetle also generates a PWM signal to control the speed of the brushless motor, so the flapping frequency of wings can be controlled.
Because the flapping-wing machine is very small in volume and mass, to ensure the life of the motor and meet the requirements of power-volume ratio and power-mass ratio, brushless motors and corresponding drive modules are selected here to realize the rotary drive of the flapping wing. Here, we use Hobby King AP-03 7000 kV Brushless Micro Motor (3.1 g). Table 1 illustrates the parameters of the brushless motor. e wireless communication module is mainly used for receiving the instructions of the remote control and transmitting them to the control unit to realize the controllable flight of the flapping-wing drone. To save power and reduce the volume, the Bluetooth 4.0 BLE module of Cypress's CYBL series chip is selected here. It can not only save power but also simplify the wiring and programming of the main control module by using the serial communication interface protocol. e gyroscope is used to detect the posture of the ornithopter in real time. We use the GY 901 chip. It uses an MPU6050 electronic gyroscope chip with a built-in Kalman filter algorithm. It can output various motion state parameters of the ornithopter in real time, such as angle, angular velocity, and linear velocity. e lithium battery is 3.7 V 70 mAh, which can extend the flight time as much as possible without increasing too much weight of the drone. e total weight of the system is 17.79 g, and each part of the system is shown in Figure 10. e hardware circuit connection is shown in Figure 11. Figure 12 illustrates the ornithopter, control system, and remote control prototype.

Flying System Software.
e system control program is mainly composed of the initialization subprogram, wireless Journal of Robotics communication subprogram, posture control subprogram, and execution subprogram. e control block diagram is shown in Figure 13.

Flapping-Wing Drone Experimental Verification
To verify the structural performance and flight control effect of the designed flapping-wing drone, two flappingwing drone prototypes were produced. One has a T-shaped tail fin as shown in Figure 14 and is only controlled manually. Another is controlled by PID strategy and has a cross-directional tail fin as shown in Figure 12. ey both performed a vertical flight test as shown in Figures 15 and  16 to simulate the hummingbirds' hovering as shown in Figure 1.
In supplemental files, T-shape Tail Flight Test.mp4 is the flight test video of T-shaped tail fin, and Cross Tail Fly FromTable.mp4 is the flight test video of cross-shaped tail fin.
It can be seen that the ornithopter without control has a larger swing angle than the ornithopter with control. e ornithopter without control has also more lateral displacement and less hovering time. e hovering time of the ornithopter without control is 6.9s and the hovering time with control is 15s. Moreover, there is a more obvious spin flight in the T-shaped flapping-wing drone.
is is completely consistent with the previous analysis.
It can be seen from Figures 16-18 that the ornithopter with a control system can hover frequently in a fixed area. Figure 19 shows the angle between the body frame and plumb line. e change frequency of the angle of the crossshaped tail is higher than that of the T-shaped tail, and the amplitude is smaller than that of the T-shaped tail. is indicates that the improved PID strategy can adjust timely the ornithopter posture to hold hovering.  Since the spin flight or yaw in the T-shaped flappingwing drone is more obvious than that of the cross-shaped one. Moreover, the improved PID strategy can only adjust the ornithopter pitch and roll to hold hovering and does not control yaw. So, the cross-shaped tail fin is better than the T-shaped one from the perspective of spin flight.
ey also indicate that the designed remote control system and flight control system can achieve a better flight effect in ornithopter's pitch and roll.
At the same time, the flapping-wing drone has a large upward flight acceleration, which proves that the developed flapping-wing drone has a large lift-mass ratio. And  flapping-wing drone can simulate hummingbirds to achieve a certain hover flight. However, it can be seen from Figures 17-19 that the tail also sways, and there is a little spin flight in the flappingwing drone. erefore, further measures need to be taken to ensure a well controllable flight.

Conclusions
In this research, a new X-shaped flapping-wing drone was proposed, and the specific mechanism of each part of the flapping-wing drone was designed and analyzed. e control mechanism of T-shaped and cross-shaped tail fin of flapping      wing was analyzed. At the same time, to realize the controllable flight of the flapping-wing drone, a corresponding remote control and flight control system was developed. e hardware circuit and control algorithm were compiled, and two actual flapping-wing drones were produced, and flight experiments were carried out. e experimental results show that the designed flapping-wing drone has a large lift-mass ratio and good maneuverability. e developed control system and control method can realize the controllable flight of flapping-wing drone and lay the foundation for future research. e crossshaped tail fin is better than the T-shaped tail fin in yawcontrolling performance. e cross-shaped tail fin has a better controllable hovering performance than the T-shape tail fin.
In the next stage, this study will focus on the spin flight and flight stability of the flapping-wing drone and further correct it through structural improvements and algorithm improvements to achieve good flapping-wing flight control.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest regarding the publication of this paper.