A CPG-based formation control method for a biomimetic flapping-wing robot

Abstract

The application discloses a formation control method of a bionic flapping-wing flying robot based on a CPG, and the method comprises the following steps: an improved CPG network of the bionic flapping-wing flying robot is used to adjust the upstroke time and the downstroke time of wings, and the influence of the upstroke resistance during flight is reduced; the multi-mode motion of the flapping-wing robot in the modes of level flight, climbing, descending and turning is realized by changing the oscillator parameters of the CPG network; a second-order consensus algorithm is used to estimate the target pose of the bionic flapping-wing flying robot; a fuzzy controller is used to convert the difference between the target pose and the actual pose of the flapping-wing robot into the input parameters of the CPG control network, the flight mode of the flapping-wing robot is changed, and thus the formation control of the flapping-wing robot is realized. The formation control effect of the bionic flapping-wing flying robot is improved by the robustness and adaptability of the CPG control.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of flapping-wing robot control, in particular to a CPG-based formation control method of a bionic flapping-wing robot. BACKGROUND

[0002] A bionic flapping-wing robot is a kind of bionic robot designed according to the flight mechanism of birds or insects in nature, which has the advantages of high concealment, high mobility and long endurance time, and has wide application in the fields of national defense and military, disaster relief and forest bird driving. With the rapid development of bionic flapping-wing robots, formation control of bionic flapping-wing robots has gradually become a more interesting research direction for research teams at home and abroad. On the one hand, formation control research helps to improve human understanding of bird formation transformation; on the other hand, formation control research can make multiple bionic flapping-wing robots more efficiently complete more complex tasks.

[0003] Due to the unsteady and large time-varying characteristics of the flight control of bionic flapping-wing robots, the control effect of traditional control methods is often not ideal, and the formation control of bionic flapping-wing robots is closely related to the flight control. The patent "Flapping-wing robot formation control method" (application number 202111065723.6) determines the formation shape switching scheme of the flapping-wing robot according to the wake vortex generation mechanism, energy saving principle and wake vortex attenuation mechanism of the formation flight of the large goose cluster from the perspective of energy consumption. The patent realizes the maintenance and reconstruction of the formation shape by controlling the position of the flapping-wing robot, but does not propose a specific implementation method of the position control of the flapping-wing robot. The document "Unmanned aerial vehicle formation controller design based on levi flight pigeon group optimization" (Chinese science and technology) proposes a PID control-based imitation goose group formation controller, which improves the stability and reliability of the formation and reduces the fuel consumption during long-distance formation. Although the traditional PID control method has good stability and robustness, it cannot simulate the biological rhythm movement. The central pattern generator (CPG) is a kind of bionic control method that can generate periodic signals to realize the rhythm movement of biology, such as flight, walking and swimming. CPG control has strong robustness and adaptability, and by changing the parameters of the CPG network, smooth transition between different modes of bionic robots can be realized. Therefore, CPG control can be used for flight control of bionic flapping-wing robots to improve the formation control effect. SUMMARY

[0004] To solve the above problems, the present application proposes a CPG-based formation control method of a bionic flapping-wing robot to improve the formation control effect of the bionic flapping-wing robot.

[0005] To achieve the above purpose, the technical solution adopted by the present application is:

[0006] A formation control method of a CPG-based biomimetic flapping-wing robot, comprising the following steps:

[0007] Step one, build a CPG control network of a biomimetic flapping-wing robot, the input parameters of the CPG controller are converted by a fuzzy controller, and the output signal is converted into a control signal for wing flapping and tail swinging;

[0008] The CPG control network of the biomimetic flapping-wing robot adopts Hopf oscillators, and the mathematical model of the CPG control network of the flapping-wing robot is:

[0009]

[0010] In the formula, i = 1, 2, 3 represents the i th Hopf oscillator, the first oscillator corresponds to the wing unit, and the second and third oscillators correspond to the left and right tail units respectively; the state variables x i and y i are the outputs of the i th oscillator, wherein x1, x2 and x3 are the control signals of the wing, the left tail and the right tail respectively; and are the reciprocals of the state variables x i and y i respectively; ω i is the inherent oscillation frequency of the i th oscillator; A i > 0 is the amplitude of the i th oscillator; α > 0 is the speed of convergence to the limit cycle with a radius of A i ; μ i is the offset; a ij and b ik are the coupling coefficients between each oscillator;

[0011] The wing oscillator unit of the flapping-wing robot is improved, and a frequency adjustment factor η is introduced to change the proportion relationship of the downstroke time and the upstroke time in a flapping cycle, and the relationship between the wing oscillator frequency ω1 and the adjustment factor η is:

[0012]

[0013] In the formula, ω up and ω down are the upstroke frequency and the downstroke frequency of the wing respectively; λ determines the speed of ω1 changing between ω up and ω down ; y1 is one of the outputs of the wing oscillator, and the improved control network of the biomimetic flapping-wing robot is:

[0014]

[0015] Step two, the multi-mode motion and smooth transition between modes of the bionic flapping-wing flying robot are realized through the CPG control network;

[0016] Step three, a distributed formation control method based on consistency theory is designed to estimate the target attitude of the bionic flapping-wing flying robot.

[0017] Step four, a fuzzy controller is used to convert the deviation between the actual pose and the target pose of the flapping-wing robot into input parameters of the CPG control network, and height and heading angle fuzzy controllers are designed.

[0018] As a further improvement of the application, step two is specifically controlled as follows

[0019] The lift and thrust of the flapping-wing robot during flight are generated by the flapping of the wings, and the attitude adjustment is realized through the differential control of the left and right tail wings;

[0020] During straight flight, the same input parameters are controlled for the oscillator units of the left and right tail wings, and the same waveform signals are output, so that the flapping-wing robot does not generate a deflection force;

[0021] During ascent or descent, the flapping frequency of the wings is adjusted by changing the frequency parameter ω up of the wing oscillator unit, thereby changing the lift of the flapping-wing robot and adjusting the flight height;

[0022] During turning, the left and right tail wings are made to swing with an angle difference by changing the amplitude, frequency and phase of the oscillator units of the left and right tail wings, thereby generating horizontal acceleration and deflecting the flapping-wing robot.

[0023] As a further improvement of the application, step three is specifically controlled as follows

[0024] The directed communication of the bionic flapping-wing flying robot is represented by a graph G={V,E,C}, where V={ν1,ν2,…ν n} represents the vertex set of the directed graph; E={(ν i ,ν j )} represents the edge set of the directed graph, where i,j∈n,i≠j; C=[c ij ] represents the adjacency matrix of the directed graph, where c ij is the weight of the edge (ν i ,ν j ), c ij =1 only when the jth flapping-wing robot can receive the state information of the ith flapping-wing robot, otherwise c ij =0;

[0025] The dynamics model of the ith flapping-wing robot is described as a second-order integrator system:

[0026]

[0027] where i = 1, 2,..., n, and are the i-th ornithopter's estimation of the virtual leader's pose and velocity, respectively, where and are the estimated three-dimensional coordinates, and are the estimated heading and pitch angles, respectively; u i is the input of the model, assuming the virtual leader's dynamics model is also a second-order integrator system:

[0028]

[0029] where and v l are the virtual leader's pose and velocity, respectively, where x l , y l , and z l are the virtual leader's three-dimensional coordinates, φ l and are the virtual leader's heading and pitch angles, respectively; f(t, s l , v l ) is a function of t, s l , and v l . The controller based on second-order consensus is:

[0030]

[0031] where and are the i-th and j-th ornithopter's estimation of the virtual leader's pose; and are the i-th and j-th ornithopter's estimation of the virtual leader's velocity; c ij is the weight of the adjacent element of the system directed graph; β and γ are tuning parameters, respectively. From the position relationship between the ornithopter and the virtual leader, the target pose of the i-th ornithopter is:

[0032]

[0033] where and are the i-th ornithopter's target position three-dimensional coordinates; and are the i-th ornithopter's target heading and pitch angles, respectively; is the distance between the i-th ornithopter's estimated virtual leader's pose and the target pose. for The angle between it and its projection onto the xoy plane; φ is The projection of the target pose onto the robot coordinate system in the xoy plane. r The angle between the target and actual poses of the i-th flapping-wing robot is:

[0034]

[0035] In the formula, and These are the three-dimensional coordinates of the actual position of the i-th flapping-wing robot; and Let be the actual heading angle and pitch angle of the i-th flapping-wing robot, respectively; ψ is... Its projection onto the xoz plane and the x-axis of the robot coordinate system of the target pose r The included angle; e xi ,e yi and e zi These represent the deviations of the three-dimensional coordinates of the i-th flapping-wing robot; e φi and These are the deviations of the heading angle and pitch angle of the i-th flapping-wing robot, respectively.

[0036] As a further improvement to the present invention, step four is as follows:

[0037] The height deviation e in formula (8) zi Taking the derivative, we obtain the rate of change of height deviation, ec. zi :

[0038]

[0039] For height deviation e zi and height deviation change rate ec zi For fuzzification, seven membership degrees are set: positive large PB, positive middle PM, zero ZE, negative small NS, negative middle NM, and negative large NB.

[0040] The height control variable U is obtained according to the fuzzy control rule. z Then, the output u of the highly fuzzy controller is obtained using the centroid method. z :

[0041]

[0042] In the formula, m is the number of activated fuzzy rules in the fuzzy rule base; ξ i (U iz ) represents the membership degree output of the i-th rule, expressed by ω. up =ω upm (1-u z) / 2 will output u of the highly fuzzy controller z This is converted into frequency parameters of the wing oscillator unit, thereby changing the lift and altitude of the flapping-wing robot, where ω upm This represents the maximum upward flapping frequency of the wing oscillation unit;

[0043] For the heading angle deviation e in formula (8) φi Taking the derivative, we obtain the rate of change of heading angle deviation, ec. φi :

[0044]

[0045] For heading angle deviation e φi and the rate of change of heading angle deviation (ec) φi Fuzzy logic is applied, with seven membership degrees set: positive large (PB), positive middle (PM), zero (Z), negative small (NS), negative middle (NM), and negative large (NB). The height control variable U is obtained according to the fuzzy control rules. φ Then, the output u of the highly fuzzy controller is obtained using the centroid method. φ ,pass The heading angle fuzzy controller output u φ The amplitude parameters of the left and right tail fin oscillator units are converted to change the tail fin swing angle, causing the flapping-wing robot to deflect. Where A... m This represents the maximum value of the amplitude of the tail fin oscillation unit.

[0046] Beneficial effects:

[0047] 1. The improved CPG control network of the biomimetic flapping-wing flying robot makes the proportion of the wing flapping time to the descent time in a flapping cycle smaller, reducing the impact of drag during the flapping-wing robot's flight and making it more in line with the flight mechanism of birds.

[0048] 2. In the formation control of biomimetic flapping-wing flying robots, maintaining the formation requires continuous adjustment of the robots' posture. Using a CPG control network to generate rhythmic signals enables smooth transitions between different motion modes of the flapping-wing robots even during parameter abrupt changes, improving the stability and adaptability of formation control. Attached Figure Description

[0049] Figure 1 It is a biomimetic flapping-wing flight robot formation control framework;

[0050] Figure 2 This is the output curve of the wing oscillator of a biomimetic flapping-wing flying robot;

[0051] Figure 3 This is the multimodal conversion output curve of the CPG control system for a biomimetic flapping-wing flying robot;

[0052] Figure 4 It is a directed communication topology between biomimetic flapping-wing flying robots;

[0053] Figure 5 It is the relationship between the actual pose, target pose, and virtual navigator of the i-th bionic flapping-wing flying robot in the xoy plane;

[0054] Figure 6 It is the relationship between the actual pose, target pose, and virtual navigator of the i-th bionic flapping-wing flying robot in the xoz plane;

[0055] Figure 7 This is the fuzzy controller structure of the present invention;

[0056] Figure 8 This is the linguistic variable membership function of this invention. Detailed Implementation

[0057] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0058] To improve the formation control performance of biomimetic flapping-wing flying robots, a formation control method based on CPG control and a second-order consensus algorithm is proposed. (See attached...) Figure 1 The diagram shows the control framework for the formation of a biomimetic flapping-wing flying robot. The specific steps are as follows:

[0059] Step 1: Build the CPG control network for the biomimetic flapping-wing flying robot. The input parameters of the CPG controller are converted by the fuzzy controller, and the output signals are converted into control signals for wing flapping and tail wing oscillation.

[0060] The CPG control network of the biomimetic flapping-wing flying robot adopts a Hopf oscillator. The Hopf oscillator is characterized by its simplicity, few parameters, low computational cost, and good adaptability and robustness. The mathematical model of the CPG control network for the flapping-wing robot is as follows:

[0061]

[0062] In the formula, i = 1, 2, 3 represents the i-th Hopf oscillator, the first oscillator corresponds to the wing element, and the second and third oscillators correspond to the left and right tail wing elements, respectively; the state variable x i and y i is the output of the i-th oscillator, where x1, x2 and x3 are the control signals for the wings, left tail fin and right tail fin, respectively; and The state variables x are respectively i and y i The reciprocal of ω; i Let A be the natural oscillation frequency of the i-th oscillator; i>0 represents the amplitude of the i-th oscillator; α>0 represents the convergence to a radius of A. i The velocity of the limiting cycle; μ i This is the offset; a ij and b ik These are the coupling coefficients between each oscillator.

[0063] The wing oscillator unit of the flapping-wing robot was improved by introducing a frequency adjustment factor η to change the ratio of the descent time to the ascent time within one flapping cycle. This simulates the faster ascent motion compared to the descent motion during bird flight, reducing the impact of drag on flight during the ascent. The relationship between the wing oscillator frequency ω1 and the adjustment factor η is as follows:

[0064]

[0065] In the formula, ω up and ω down These are the flapping and drooping frequencies of the wings, respectively; λ determines ω1 in ω up and ω down The rate of change between; y1 is one of the output quantities of the wing oscillator. (See attached...) Figure 2 As shown, the parameters of the wing oscillator unit are set as η = 0.75, λ = 500, ω up =1.5π, A1=1, α=100, the ratio of the upward flapping time to the downward flapping time within one flapping cycle is 1:3. The improved control network of the biomimetic flapping-wing flight robot is:

[0066]

[0067] Step two: The biomimetic flapping-wing flying robot achieves multimodal motion and smooth transitions between modes through the CPG control network.

[0068] The main flight modes of the biomimetic flapping-wing flying robot include straight flight, ascent, descent, and turning. The lift and thrust of the flapping-wing robot during flight are primarily generated by wing flapping, while attitude adjustment is achieved through differential control of the left and right tail fins. During straight flight, by controlling the oscillator units of the left and right tail fins to have identical input parameters and output signals of the same waveform, the flapping-wing robot does not generate yaw force. During ascent or descent, the frequency parameter ω of the wing oscillator unit is changed... up The flapping frequency of the wings is adjusted to change the lift of the flapping-wing robot and thus adjust its flight altitude. When turning, the amplitude, frequency, and phase of the left and right tail fin oscillation units can be changed to create an angle difference in the left and right tail fin swing, thereby generating horizontal acceleration and causing the flapping-wing robot to deflect.

[0069] As attached Figure 3As shown, the parameters ω2=ω3=6π, α=100, A1=1, A3=0.25, η=0.75, and λ=50 are kept constant. From 0-5s, the biomimetic flapping-wing flying robot flies in a straight line, A2=A3=0.25, ω up =4.5π; at the 5th second, increase ω up The frequency of the flapping wing robot is increased to 6π, causing it to climb upwards; at the 10th second, A2 is decreased to 0.09, causing the flapping wing robot to turn right. The output curve can also smoothly transition when the CPG input parameters change abruptly.

[0070] Step 3: Design a distributed formation control law based on consistency theory to estimate the attitude of the biomimetic flapping-wing flying robot.

[0071] As attached Figure 4 As shown, the directed communication of the biomimetic flapping-wing flying robot is represented by the graph G = {V, E, C}, where V = {ν1, ν2, ..., ν}. n} represents the vertex set of a directed graph; E = {(ν i ,ν j )} represents the edge set of a directed graph, where i,j∈n, i≠j; C=[c ij ] represents the adjacency matrix of a directed graph, where c ij For edge (ν) i ,ν j The weight of c is determined if and only if the j-th flapping-wing robot can receive the state information of the i-th flapping-wing robot. ij =1, otherwise c ij =0.

[0072] The dynamic model of the i-th flapping-wing robot is described as a second-order integrator system:

[0073]

[0074] In the formula, i = 1, 2, ..., n, and Let be the pose and velocity estimates of the virtual navigator by the i-th flapping-wing robot, respectively. and These are the estimated three-dimensional coordinates. and These are the estimated heading angle and pitch angle, respectively; u i This serves as the input to the model. Assume the virtual navigator's dynamics model is also a second-order integrator system:

[0075]

[0076] In the formula, and v lThese represent the pose and velocity of the virtual navigator, where x... l ,y l and z l These are the three-dimensional coordinates of the virtual navigator, φ l and These are the heading and pitch angles of the virtual navigator, respectively; f(t,s) l ,v l ) for t,s l and v l The function. The controller based on second-order consistency formation is:

[0077]

[0078] In the formula, s l and v l These are the virtual navigator's position and speed, respectively. and These are the pose estimates of the virtual navigator by the i-th and j-th flapping-wing robots, respectively; and c represents the speed estimates of the virtual navigator by the i-th and j-th flapping-wing robots, respectively; ij β represents the weight of the adjacency elements in the directed graph of the system; β and γ are the adjustment parameters, respectively. The relationship between the actual pose, target pose, and virtual navigator pose of the flapping-wing robot is shown in the appendix. Figure 5 and attached Figure 6 As shown, the target pose of the i-th flapping-wing robot can be obtained based on geometric relationships:

[0079]

[0080] In the formula, and These are the three-dimensional coordinates of the target position of the i-th flapping-wing robot; and These are the heading angle and pitch angle of the i-th flapping-wing robot target, respectively; The distance between the estimated virtual navigator pose and the target pose for the i-th flapping-wing robot; for The angle between it and its projection onto the xoy plane; φ is The projection of the target pose onto the robot coordinate system in the xoy plane. r The angle between the actual pose and the target pose of the i-th flapping-wing robot is:

[0081]

[0082] In the formula, and These are the three-dimensional coordinates of the actual position of the i-th flapping-wing robot; and These are the actual heading angle and pitch angle of the i-th flapping-wing robot, respectively; ψ is L l i Its projection onto the xoz plane and the x-axis of the robot coordinate system of the target pose r The included angle; e xi ,e yi and e zi These represent the deviations of the three-dimensional coordinates of the i-th flapping-wing robot; e φi and These are the deviations of the heading angle and pitch angle of the i-th flapping-wing robot, respectively.

[0083] Step four involves using fuzzy controllers to convert the deviation between the actual pose and the target pose of the flapping-wing robot into input parameters for the CPG control network. Fuzzy controllers for altitude and heading angle can be designed accordingly. (See attached...) Figure 7 The fuzzy controller structure shown illustrates the controller design process:

[0084] The height deviation e in formula (8) zi Taking the derivative, we obtain the rate of change of height deviation, ec. zi :

[0085]

[0086] For height deviation e zi and height deviation change rate ec zi For fuzzification, seven membership degrees are set: positive large (PB), positive medium (PM), zero (Z), negative small (NS), negative medium (NM), and negative large (NB). For example... Figure 8 As shown, the membership functions are selected from trigonometric functions and the Z-function. The height control variable U is obtained by looking up the 49 fuzzy control rules in Table 1. z Then, the output u of the highly fuzzy controller is obtained using the centroid method. z :

[0087]

[0088] In the formula, m is the number of activated fuzzy rules in the fuzzy rule base; ξ i (U iz ) is the membership degree output for the i-th rule. (This is achieved through ω...) up =ω upm (1-u z ) / 2 will output u of the highly fuzzy controller z This is converted into frequency parameters of the wing oscillator unit, thereby changing the lift and altitude of the flapping-wing robot, where ω upm This represents the maximum upward flapping frequency of the wing oscillation unit.

[0089] For the heading angle deviation e in formula (8) φi Taking the derivative, we obtain the rate of change of heading angle deviation, ec. φi :

[0090]

[0091] For heading angle deviation e φi and the rate of change of heading angle deviation (ec) φi Fuzzy control was applied, with seven membership degrees set: positive large (PB), positive medium (PM), zero (ZE), negative small (NS), negative medium (NM), and negative large (NB). The height control variable U was obtained by looking up the 49 fuzzy control rules in Table 1. φ Then, the output u of the highly fuzzy controller is obtained using the centroid method. φ .pass The heading angle fuzzy controller output u φ The amplitude parameters of the left and right tail fin oscillator units are converted to change the tail fin swing angle, causing the flapping-wing robot to deflect. Where A... m This represents the maximum value of the amplitude of the tail fin oscillation unit.

[0092] Table 1: Fuzzy Control Rules for Altitude and Yaw Angle

[0093]

[0094] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A formation control method for a CPG-based biomimetic flapping-wing flying robot, characterized in that, Includes the following steps: Step 1: Build the CPG control network for the biomimetic flapping-wing flying robot. The input parameters of the CPG controller are converted by the fuzzy controller, and the output signals are converted into control signals for wing flapping and tail wing oscillation. The CPG control network of the biomimetic flapping-wing flying robot adopts a Hopf oscillator. The mathematical model of the CPG control network of the flapping-wing robot is as follows: （1） In the formula, i = 1, 2, 3 represents the i-th Hopf oscillator, the first oscillator corresponds to the wing element, and the second and third oscillators correspond to the left and right tail wing elements, respectively; the state variable x i and y i is the output of the i-th oscillator, where x1, x2 and x3 are the control signals for the wings, left tail fin and right tail fin, respectively; and The state variables x are respectively i and y i The reciprocal of ω; i Let be the inherent oscillation frequency of the i-th oscillator; A i > 0 represents the amplitude of the i-th oscillator; α > 0 represents the convergence to a radius of A. i The velocity of the limiting cycle; μ i This is the offset; a ij and b ik These are the coupling coefficients between each oscillator; The wing oscillator unit of the flapping-wing robot is improved by introducing a frequency adjustment factor η to change the ratio of the descent time and the ascent time within one flapping cycle. The relationship between the wing oscillator frequency ω1 and the adjustment factor η is as follows: （2） In the formula, ω up and ω down These are the flapping and drooping frequencies of the wings, respectively; λ determines ω1 in ω up and ω down The rate of change between them; y1 is one of the outputs of the wing oscillator, and the improved control network of the biomimetic flapping-wing flying robot is: （3） Step two: The multimodal motion and smooth transitions between modes of the biomimetic flapping-wing flying robot are realized through the CPG control network; Step 3: Design a distributed formation control method based on consistency theory to estimate the target attitude of the biomimetic flapping-wing flying robot; Step four: Use a fuzzy controller to convert the deviation between the actual pose and the target pose of the flapping-wing robot into input parameters for the CPG control network, and design fuzzy controllers for altitude and heading angle.

2. The formation control method for a CPG-based biomimetic flapping-wing flying robot according to claim 1, characterized in that, Step two is controlled as follows: The lift and thrust of the flapping-wing robot during flight are generated by the flapping of its wings, while attitude adjustment is achieved through differential control of the left and right tail fins. When flying in a straight line, the oscillator units of the left and right tail wings are controlled to have the same input parameters and output signals with the same waveform, so that the flapping-wing robot does not generate a deflection force. During ascent or descent, the frequency parameter ω of the wing oscillator unit is changed. up This is done by adjusting the flapping frequency of the wings, thereby changing the lift of the flapping-wing robot and adjusting its flight altitude. When turning, the amplitude, frequency and phase of the left and right tail wing oscillation units are changed to make the left and right tail wings swing at an angle difference, thereby generating horizontal acceleration and causing the flapping-wing robot to deflect.

3. The formation control method for a CPG-based biomimetic flapping-wing flying robot according to claim 1, characterized in that, Step three is specifically controlled as follows; Directed communication of biomimetic flapping-wing flying robots is shown in the figure. It means that, among them, Represents the set of vertices in a directed graph; Let f(x) represent the edge set of a directed graph, where f(x) = ... ; Let the adjacency matrix of a directed graph be denoted as , where For the edge The weight is determined if and only if the j-th flapping-wing robot can receive the state information of the i-th flapping-wing robot. ,otherwise ; The dynamic model of the i-th flapping-wing robot is described as a second-order integrator system: （4） In the formula, , and Let be the pose and velocity estimates of the virtual navigator by the i-th flapping-wing robot, respectively. and These are the estimated three-dimensional coordinates. and These are the estimated heading angle and pitch angle, respectively; Assuming the virtual navigator's dynamics model is also a second-order integrator system, as the input to the model: （5） In the formula, and These represent the virtual navigator's pose and velocity, respectively. and These are the three-dimensional coordinates of the virtual navigator. and These are the heading angle and pitch angle of the virtual navigator, respectively. For about and The function, based on the second-order consistency array controller, is: （6） In the formula, and These are the pose estimates of the virtual navigator by the i-th and j-th flapping-wing robots, respectively; and These are the speed estimates of the virtual navigator by the i-th and j-th flapping-wing robots, respectively; The weights of the adjacent elements in the directed graph of the system; and The parameters are adjusted, and the target pose of the i-th flapping-wing robot is determined by the positional relationship between the flapping-wing robot and the virtual navigator. （7） In the formula, and These are the three-dimensional coordinates of the target position of the i-th flapping-wing robot; and These are the heading angle and pitch angle of the i-th flapping-wing robot target, respectively; The distance between the estimated virtual navigator pose and the target pose for the i-th flapping-wing robot; for The angle between it and its projection onto the xoy plane; for Projection in the xoy plane and the robot coordinate system of the target pose The angle between the target and actual poses of the i-th flapping-wing robot is: （8） In the formula, and These are the three-dimensional coordinates of the actual position of the i-th flapping-wing robot; and These are the actual heading angle and pitch angle of the i-th flapping-wing robot, respectively; for Its projection onto the xoz plane and the robot coordinate system of the target pose. The included angle; and These represent the deviations of the three-dimensional coordinates of the i-th flapping-wing robot; and These are the deviations of the heading angle and pitch angle of the i-th flapping-wing robot, respectively.

4. The formation control method for a CPG-based biomimetic flapping-wing flying robot according to claim 3, characterized in that, Step four is as follows: Deviation of height in formula (8) Differentiating, we obtain the rate of change of height deviation. : （9） For height deviation and height deviation rate For fuzzification, seven membership degrees are set: positive large PB, positive middle PM, zero ZE, negative small NS, negative middle NM, and negative large NB. The height control quantity is obtained based on the fuzzy control rule. Then, the output of the highly fuzzy controller is obtained using the centroid method. : (10) In the formula, m is the number of fuzzy rules activated in the fuzzy rule base; Output the membership degree of the i-th rule, through Output of the high fuzzy controller The frequency parameters of the wing oscillator unit are converted to change the lift and altitude of the flapping-wing robot. This represents the maximum upward flapping frequency of the wing oscillation unit; For the heading angle deviation in formula (8) Differentiating, we obtain the rate of change of heading angle deviation. : (11) For heading angle deviation and the rate of change of heading angle deviation Fuzzification was performed, and seven membership degrees were set: positive large (PB), positive middle (PM), zero (Z), negative small (NS), negative middle (NM), and negative large (NB). The height control value was obtained according to the fuzzy control rules. Then, the output of the highly fuzzy controller is obtained using the centroid method. ,pass Output of the heading angle fuzzy controller The amplitude parameters of the left and right tail fin oscillator units are converted to change the tail fin swing angle, causing the flapping-wing robot to deflect. This represents the maximum value of the amplitude of the tail fin oscillation unit.

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