Unmanned aerial vehicle pull-type air recovery wing folding process anti-swing control method

Abstract

The invention discloses an unmanned aerial vehicle pull-type air recovery wing folding process anti-swing control method, and belongs to the field of unmanned aerial vehicle navigation, guidance and control. The method comprises the following steps: firstly, establishing a wing folding process aerodynamic model of the buoy-unmanned aerial vehicle assembly, and carrying out parametric modeling by taking a wing folding angle as a parameter; a non-constraint force vector and direction feedforward compensation controller is established based on the non-constraint force vector and direction control mechanism; and then a feedback controller is designed based on a specified time preset performance control theory, the feedback controller and a feedforward compensation controller jointly form a composite control frame, and the floating and swinging of the buoy-unmanned aerial vehicle assembly in the wing folding process are controlled. Under the initial conditions of different cables, the floating degree of the buoy-unmanned aerial vehicle combination can be greatly reduced, and the safety and the anti-floating characteristic of the pull-type aerial recovery process are improved.

Description

Technical Field

[0001] The present invention belongs to the field of unmanned aerial vehicle (UAV) navigation, guidance and control, and in particular relates to an anti-sway control method for the folding process of a towed aerial recovery wing of a UAV. Background Art

[0002] Drone towed aerial recovery refers to the process in which a drone docks and locks with a buoy towed by a cable in the air, the buoy and the drone form a buoy-drone combination, and the cable is recovered by the reel and the buoy-drone combination is retrieved into the cargo hold of a transport aircraft. Figure 1 As shown. UAV aerial recovery technology can eliminate the UAV's dependence on reliable land / ship bases and effectively expand the UAV's combat range. During the recovery process, the UAV needs to fold its wings. The process is as follows Figure 2 How to reduce the flutter of the drone's wings during folding is an urgent problem that needs to be solved.

[0003] The buoy-UAV combination faces two major challenges during the wing folding process. First, the buoy-UAV combination is subject to multiple disturbances during the wing folding process. The inertial properties of the buoy-UAV combination change during the wing folding process, resulting in additional torques. The aerodynamic forces of the UAV's wings undergo significant changes during the folding process, gradually reducing lift to zero and generating coupled lateral and longitudinal aerodynamic torques. During the process of driving the UAV's wings to fold, the buoy-UAV fuselage combination experiences a reaction torque. These disturbances cause the buoy-UAV combination to sway. Second, during the wing folding process, the buoy-UAV combination is pulled by the cable. These disturbances cause the cable's configuration to change, further altering the tension exerted on the buoy-UAV combination and exacerbating its sway. During the recovery process, if the wing folding process causes excessive sway, it could adversely affect the safety and stability of the recovery process. Therefore, the buoy-UAV combination needs to be controlled against sway during the wing folding process.

[0004] Because the buoy-UAV combination's control surface configuration differs significantly from that of conventional UAVs, the lift of the UAV's wings gradually decreases to zero during wing folding, rendering conventional UAV wing control surfaces such as ailerons incapable of providing control during wing folding. Therefore, the buoy-UAV combination does not have control surfaces on its wings. Instead, it uses grid rudders on the buoy and a fully movable tail fin at the rear of the UAV to provide control force and torque. The grid rudder on the buoy has a large equivalent rudder area and generates a large aerodynamic force. Furthermore, since the grid rudder is located close to the center of gravity of the buoy-UAV combination, it generates a small aerodynamic torque. In contrast, the fully movable tail fin at the rear of the UAV is located farther from the center of gravity, generating a large aerodynamic force that exerts a large control torque on the buoy-UAV combination. This strong control capability provides the foundation for the buoy-UAV combination's wing folding control.

[0005] Based on the dynamic characteristics of the buoy-UAV combination, combined with the non-constrained force vector sum control method and the specified time preset performance control theory, a way is provided for the anti-sway control of the buoy-UAV combination during the wing folding process. Summary of the Invention

[0006] In order to improve the anti-sway characteristics of a towed aerial recovery UAV during the wing folding process, the present invention proposes an anti-sway control method for the wing folding process of a towed aerial recovery UAV. By combining a feedforward compensation controller and a feedback controller, the degree of sway of the buoy-UAV combination during the wing folding process of aerial recovery is effectively reduced, thereby improving the safety and stability of the aerial recovery process.

[0007] A method for controlling the anti-swaying during the folding process of the wing of a towed aerial recovery drone comprises the following steps:

[0008] Step 1: Establish a nonlinear motion model of the cable and buoy-UAV combination for the UAV recovery system;

[0009] The details are as follows:

[0010] (1) Establish a cable motion model based on multi-rigid body theory;

[0011] Based on the multi-rigid body theory, the cable is discretized into N segments of cylindrical rigid links of equal length. Assuming that the weight of the link is equivalent to the nodes at both ends of the link, a multi-rigid body dynamic system is obtained, specifically:

[0012] In the dragging coordinate system S D (O D -X D Y D Z D ) to model the cable, p iis the position of the i-th node, r i =p i -p i-1 is the position vector of the i-th connecting rod, and the i-th connecting rod is relative to the plane X D O D Y D and plane X D O D Z D The deflection angle λ i and Describe the motion of the connecting rod.

[0013] r i The calculation formula is as follows:

[0014]

[0015] Where l = L0 / N is the length of the i-th link, L0 is the total length of the cable; n i is the unit direction vector of the i-th link. i and The second-order dynamic equation is expressed as:

[0016]

[0017] in, α D and ω D Drag system S D Relative inertial system S g (O g -X g Y g Z g )'s involved angular velocity and angular acceleration; and That is the cable retraction and extension speed and acceleration.

[0018] According to Newton's second law, the acceleration of node i is:

[0019]

[0020] Among them, m i is the mass of the connecting rod concentrated at node i, m d is the mass of the buoy; Q i is the total external force acting on node i, including aerodynamic force and gravity; t i is the tension on the i-th cable segment.

[0021] (2) Establish a six-degree-of-freedom buoy-UAV combination motion model considering cable tension;

[0022] First, establish the kinematic equation of the center of mass translation of the buoy-UAV combination in the ground coordinate system:

[0023]

[0024] Where x g ,y g ,z g is the three-axis position in the ground coordinate system; V K is the track velocity; γ,χ represent the track inclination and heading angle respectively.

[0025] Then, the translational dynamic equation considering the effects of cable tension and airflow disturbance is established:

[0026]

[0027] Where: R K / a ,R K / b and R K / d Represents the conversion matrix from airflow system, aircraft system and drag system to track system respectively; 0.5F N is half of the aerodynamic force of the Nth section of cable; t N is the tension of the cable; m is the sum of the mass of the buoy-UAV assembly and half of the mass of the Nth cable segment; g is the acceleration due to gravity; F A Represents the aerodynamic force acting on the buoy-UAV combination.

[0028] Step 2: Based on the CFD numerical simulation method, establish the aerodynamic model of the buoy-UAV combination.

[0029] The specific steps are as follows:

[0030] Step 201: Use CFD numerical simulation method to solve the aerodynamic parameters of the buoy-UAV combination in normal flight state and wing folding process.

[0031] The static grid method is used to solve the aerodynamic parameters of the buoy-UAV combination in normal flight state, and the dynamic grid method is used to solve the aerodynamic parameters of the buoy-UAV combination during the wing folding process.

[0032] Aerodynamic parameters include aerodynamic force parameters and aerodynamic moment parameters. Aerodynamic force includes lift, drag and side force, and aerodynamic moment includes rolling moment, pitching moment and yaw moment.

[0033] Step 202: Perform polynomial fitting on the aerodynamic parameters of the buoy-UAV combination obtained by the CFD numerical simulation method, and establish an aerodynamic model of the buoy-UAV combination with the wing folding angle as a parameter.

[0034] The aerodynamic model is divided into an aerodynamic force model and an aerodynamic moment model. The aerodynamic force and aerodynamic moment of the buoy-UAV combination are synthesized by the wing, buoy-fuselage combination, tail fin, and grid rudder. Based on the changes in aerodynamic parameters during the wing folding process, the following aerodynamic force model and aerodynamic moment model are established:

[0035] (1) Establish an aerodynamic model of the buoy-UAV combination with the wing folding angle as a parameter;

[0036]

[0037] Where: Q is the dynamic pressure; ρ is the air density; S is the reference area; L, D, and Y represent the lift, drag, and side force, respectively; V is the flight speed of the UAV; C Lw ,C Lf ,C Lt ,C LG are the lift coefficients of the wing, buoy-fuselage assembly, tail fin, and grid rudder, respectively; C Dw ,C Df ,C Dt ,C DG are the drag coefficients of the wing, buoy-fuselage assembly, tail fin, and grid rudder, respectively; C Yw ,C Yf ,C Yt ,C YG are the side force coefficients of the wing, buoy-fuselage assembly, tail fin, and grid rudder, respectively; their expanded formula is:

[0038]

[0039] Where: is the lift coefficient at zero angle of attack; is the derivative of the lift coefficient with respect to the angle of attack; is the drag coefficient at zero angle of attack; is the derivative of the lift coefficient with respect to the angle of attack; is the derivative of the side force coefficient with respect to the sideslip angle; subscripts * = w, f correspond to the wing and float-fuselage assembly, respectively; K Lηn ,K Dηn ,K Yηn , n=1,2,3 are the nth-order coefficients of η; α and β are the angle of attack and sideslip angle of the buoy-UAV combination respectively; η is the wing folding angle; are the derivatives of the tail wing lift coefficient, drag coefficient, and side force coefficient with respect to the tail wing deflection angle; δ1, δ2, δ3, and δ4 represent the deflection angles of the four all-moving tail wing of the UAV, and the deflection range of the all-moving tail wing is -25° to 25°; is the derivative of the grid rudder lift coefficient, drag coefficient and side force coefficient with respect to the grid rudder deflection angle; δ G1 ,δ G2 ,δG3 ,δ G4 They represent the deflection angles of the four grid rudders respectively, and the deflection range of the grid rudder is -20° to 20°.

[0040] (2) Establish an aerodynamic torque model of the buoy-UAV combination with the wing folding angle as a parameter;

[0041]

[0042] Where: are the rolling moment coefficients of the wing, buoy-fuselage assembly, tailplane, and grid rudder, respectively; are the pitching moment coefficients of the wing, buoy-fuselage assembly, tailplane, and grid rudder, respectively; are the yaw moment coefficients of the wing, buoy-fuselage assembly, tail fin, and grid rudder, respectively; their expanded formula is:

[0043]

[0044] Where: is the derivative of the rolling moment coefficient with respect to the sideslip angle; is the pitching moment coefficient at zero angle of attack; is the derivative of the pitching moment coefficient with respect to the angle of attack; K is the derivative of the yaw moment coefficient with respect to the sideslip angle; * = w, f subscripts correspond to the wing and the assembly respectively. Lηn ,K Dηn ,K Yηn ,n=0,1,2,3 is the coefficient of nth order term of η; is the derivative of the tail wing rolling moment coefficient, pitching moment coefficient and yaw coefficient with respect to the tail wing deflection angle; is the derivative of the grid rudder rolling moment coefficient, pitching moment coefficient and yaw coefficient with respect to the grid rudder deflection angle.

[0045] Step 3: Based on the unconstrained force vector and direction control mechanism and the rudder configuration of the buoy-UAV combination, a unconstrained force vector and direction feedforward compensation controller is designed to control the grid rudder deflection to compensate for the unconstrained force vector and direction;

[0046] The specific steps for establishing the feedforward compensation controller are as follows:

[0047] Step 301: Calculate the difference in the unconstrained force vector and direction of the buoy-UAV assembly before and after wing folding.

[0048] First, the sum of the unconstrained force vectors on the buoy-UAV combination before and after wing folding is calculated based on the nominal aerodynamic parameters of the buoy-UAV combination:

[0049]

[0050] Where: L η＝0 and D η＝0 are the nominal lift and drag before wings are folded, G is the weight of the buoy-UAV combination; L η＝90 and D η＝90 The nominal lift and drag with the wings folded.

[0051] Then, the difference in the unconstrained force vector and direction of the buoy-UAV combination before and after the wing folding is calculated as follows:

[0052]

[0053] F G is the sum of the non-constraint force vectors of the buoy-UAV combination itself, θ0 and θ are the sum of the non-constraint force vectors of the buoy-UAV combination before and after the wing is folded, respectively;

[0054] Step 302, calculating the grid rudder deflection angle based on the change in the non-constrained force vector and direction before and after the wing is folded, and controlling the grid rudder deflection angle by establishing a feedforward compensation controller;

[0055] The goal of the feedforward compensation controller is to minimize the difference between the non-constrained force vector and direction after folding and the non-constrained force vector and direction before folding by controlling the grid rudder deflection angle;

[0056] The lift force L generated by the deflection of the grid rudder G and resistance D G The following conditions must be met:

[0057]

[0058] According to the aerodynamic model, F G ,F0,F can be expanded to obtain the formula:

[0059]

[0060] Where: δ G is the grid rudder deflection angle, C Dw,η＝0 is the drag coefficient of the wing before folding, C Dw,η＝90 is the drag coefficient of the folded wing, C Lw,η＝0 is the lift coefficient of the folded front wing, C Lw,η＝90 is the lift coefficient of the folded wing, C Df is the drag coefficient of the buoy-fuselage combination, C Lf is the lift coefficient of the buoy-fuselage combination.

[0061] Furthermore, substituting Equation (19) into Equation (17), the grid rudder deflection angle optimization equation can be obtained as follows:

[0062]

[0063] Solving the above optimization problem yields the grid rudder deflection angle δ G , so that the changes in the non-constrained force vector and direction before and after the wing folding are minimized, achieving the purpose of establishing a feedforward compensation controller.

[0064] Step 4: Design a feedback controller based on the specified time preset control theory, and use the full-moving tail of the buoy-UAV combination to control the attitude of the buoy-UAV combination.

[0065] The specific steps are as follows:

[0066] Step 401: Design a track angle loop controller based on a specified time preset performance control theory;

[0067] First, given the desired track angle, define the track angle error:

[0068] e1=X 1c -X1

[0069] where X 1c =[χ c ,γ c ] T is the desired track angle instruction of the assembly, and X1 is the actual track angle of the assembly.

[0070] Then, make the track angle error meet the preset boundary

[0071] Define the preset performance function as follows:

[0072]

[0073] Where: i = γ, χ, r i and k 0i ∈[0,1) is the parameter to be designed, k fi Determines the maximum value of the steady-state error, T ai Specifies the convergence time.

[0074] Define the error transfer function Υ i (t) are as follows:

[0075]

[0076] Derivative of track angle tracking error for:

[0077]

[0078] Define Υ1=[Υ χ , Υ γ ] T ,ζ1=diag(ζ χ ,ζγ ), k1=diag(k χ , k γ ).

[0079] Substituting equation (23) into the error conversion function yields:

[0080]

[0081] In order to achieve track angle error stabilization, the track angle loop virtual control law is designed as follows:

[0082]

[0083] Where: X 2c =[α c ,β c ,σ c ] T is the airflow angle loop command signal, K1=diag(K χ ,K γ ) is the controller gain. Is F1=[F χ ,F γ ] T The estimated value of is obtained by the extended state observer ESO; is the first-order differential value of the desired track angle, obtained by the tracking differentiator TD shown in equation (26):

[0084]

[0085] Where r1 and h1 are the parameters of the tracking differentiator to be designed, h1 is the tracking step size, r1 is the acceleration factor, and a larger r1 value results in a faster tracking process but greater sensitivity to noise. Adjust r1 based on the tracking characteristics of the system. fhan(x1, x2, r, h) is the comprehensive function for the fastest control.

[0086] Step 402: Design an airflow angle loop and an angular rate controller based on backstepping and an “observe-compensate” architecture.

[0087] Define the airflow angle tracking error e2 = X 2c -X2, airflow angle loop instruction X 2c According to the track angle loop controller, the differential of the airflow angle tracking error e2 is:

[0088]

[0089] The airflow angle loop control law is designed as follows:

[0090]

[0091] Where: X 3c=[p c ,q c ,r c ] T is the angular rate loop command signal, K2=diag(K α ,K β ,K σ ) is the controller gain. is the estimated value of F2, obtained by ESO shown in formula (29).

[0092]

[0093] Where: K 2o,1 and K 2o,2 is the bandwidth parameter of the observer to be designed. is the first-order differential value of the desired airflow angle, obtained by TD shown in equation (30).

[0094]

[0095] Where: r2 and h2 are the parameters of the tracking differentiator to be designed.

[0096] Define angular velocity tracking error e3 = X 3c -X3, the differential of the angular velocity tracking error e3 is:

[0097]

[0098] The angular velocity loop control law is designed as follows:

[0099]

[0100] Where: δ c =[δ 1c δ 2c δ 3c δ 4c ] T is the desired full-movable tail rudder deflection angle; K3 = diag (K p ,K q ,K r ) is the controller gain. Similarly, is the estimated value of F3, obtained by ESO shown in formula (33); is the first-order differential value of the desired airflow angle, which is obtained by TD as shown in equation (34):

[0101]

[0102] Where: K 3o,1 and K 3o,2The observer bandwidth parameter to be designed, r3 and h3 are the tracking differentiator parameters to be designed. B1, B2, and B3 are the control matrices for each loop. The observer bandwidth and tracking differentiator parameters for each of the three loops need to be tuned individually based on the system characteristics.

[0103] Step 5: A composite controller is constructed based on the feedback controller with preset performance at a specified time, the unconstrained force vector and the feedforward controller to realize the anti-sway control of the wing folding process of the buoy-UAV.

[0104] Based on the six-degree-of-freedom nonlinear model of the buoy-UAV combination, during the wing folding process of the aerial recovery of the UAV, when there is airflow disturbance in the atmosphere, the feedforward compensation controller first adjusts the grid rudder deflection angle according to the wing folding angle; at the same time, according to the desired track angle of the buoy-UAV combination, the feedback controller gives the full-moving tail deflection angle; by controlling the grid rudder and the full-moving tail deflection angle, the buoy-UAV combination's swing degree is reduced, so that the buoy-UAV combination can complete a stable recovery process within the specified time.

[0105] The advantages of the present invention are:

[0106] (1) A method for anti-sway control of the wing folding process of an aerial recovery aircraft can realize anti-sway control of the wing folding process of a buoy-UAV combination under different initial states and complex airflow disturbances.

[0107] (2) An anti-sway control method for the wing folding process of aerial recovery is designed based on the non-constrained force vector and direction control mechanism. A non-constrained force vector and direction feedforward compensation controller is designed to reduce the initial sway of the cable during the wing folding process, speed up the control response speed, and reduce the sway of the buoy-UAV combination.

[0108] (3) A method for anti-sway control during the wing folding process of aerial recovery is developed. Based on the specified time preset performance control theory, backstepping method and "observation-compensation" architecture, the track angle loop controller, airflow angle loop controller and angular velocity loop controller are designed respectively, so that the buoy-UAV combination can be stabilized within a pre-specified range within the specified time. BRIEF DESCRIPTION OF THE DRAWINGS

[0109] Figure 1 Schematic diagram of the towed aerial recovery system for unmanned aerial vehicles of the present invention;

[0110] Figure 2 This is a schematic diagram of the wing folding process of the buoy-UAV combination of the present invention;

[0111] Figure 3 Schematic diagram of the non-constrained force vector and change before and after wing folding and grid rudder compensation effect of the present invention;

[0112] Figure 4 It is a schematic diagram of the cable dynamics modeling of the present invention;

[0113] Figure 5 This is a structural block diagram of the anti-sway control method of the present invention;

[0114] Figure 6 The present invention shows the curves of additional torque, reaction torque and rotational angular velocity during the wing folding process at different wing folding speeds;

[0115] Figure 7 1 is a curve showing the longitudinal drift distance variation of the buoy-UAV combination during the UAV recovery process using the proposed method and the comparative method in the embodiment of the present invention;

[0116] Figure 8 is the projection of the motion trajectory of the buoy-UAV combination on the YOZ plane during the UAV recovery process using the proposed method and the comparative method in the embodiment of the present invention;

[0117] Figure 9 : is a diagram showing the cable configuration changes during the wing folding process of the UAV recovery process using the proposed method and the comparative method in the embodiment of the present invention, wherein Figure 9 a is the comparison method 1, Figure 9 b is comparison method 2, Figure 9 c is the anti-sway control method proposed in the present invention. DETAILED DESCRIPTION

[0118] In order to facilitate those skilled in the art to understand and implement the present invention, the present invention is further described in detail below with reference to the accompanying drawings and examples.

[0119] The present invention provides an anti-flutter control method for the wing folding process of a towed drone aerial recovery aircraft. This method proposes a composite control framework that combines an unconstrained force vector and direction feedforward compensation controller with a feedback controller based on a specified time preset performance control theory. First, a feedforward compensation controller is designed based on the unconstrained force vector and direction control mechanism. A grid rudder is used to compensate for changes in the unconstrained force vector and direction of the buoy-drone assembly before and after wing folding, reducing disturbances caused by the wing folding process and improving the control system's response speed. Subsequently, a feedback controller is designed based on the specified time preset performance control theory to stabilize the buoy-drone assembly within a reasonable range within a specified time.

[0120] A method for controlling the anti-swaying of the wing folding process of a towed aerial recovery drone includes the following steps:

[0121] Step 1: Establish a nonlinear motion model of the cable and buoy-UAV combination for the UAV recovery system;

[0122] The specific steps are as follows:

[0123] Step 101: Establish a cable motion model based on multi-rigid body theory;

[0124] The cable is discretized into N equal-length cylindrical rigid links, connected by frictionless spherical hinges. The ductility and flexibility of the links are neglected, and the weight of the links is assumed to be concentrated at the nodes at both ends. That is, half the mass of the i-th link and half the mass of the i+1th link are assumed to be concentrated at the hinge nodes at the ends of the i-th link. Based on these assumptions and approximations, the cable can be considered a multi-rigid-body dynamic system.

[0125] like Figure 4 As shown, in the dragging coordinate system S D (O D -X D Y D Z D ) to model the cable, p i is the position of the i-th node, r i =p i -p i-1 is the position vector of the i-th connecting rod. Since the rolling motion of the cable can be ignored, the present invention adopts the position vector of the i-th connecting rod relative to the plane X D O D Y D and plane X D O D Z D The deflection angle λ i and Describe the motion of the connecting rod.

[0126] r i It can be calculated by the following formula:

[0127]

[0128] Where l = L0 / N is the length of the i-th link, L0 is the total length of the cable (variable), and n i is the unit direction vector of the i-th link.

[0129] λ i and The second-order dynamic equation can be expressed as:

[0130]

[0131] in, a i is the acceleration of node i, α D and ω D Drag system S D Relative inertial system S g (O g -Xg Y g Z g )'s involved angular velocity and angular acceleration; and That is the cable retraction and extension speed and acceleration.

[0132] According to Newton's second law, the acceleration of node i can be calculated as follows:

[0133]

[0134] Among them, m i is the mass of the connecting rod concentrated at node i, m d is the mass of the buoy; Q i is the total external force acting on node i, including aerodynamic force and gravity; t i is the tension on the i-th cable segment.

[0135] According to (1)-(3), the kinematic model of the cable can be established.

[0136] Step 102: Establish a six-degree-of-freedom buoy-UAV combination dynamic model taking into account cable tension;

[0137] After the drone and buoy are docked and locked, the gravity and aerodynamic forces of the buoy-drone combination, acting as the end point of the cable, significantly influence the cable's motion, which in turn affects the cable's tension. This tension, in turn, affects the motion of the buoy-drone combination. Therefore, the buoy-drone combination and the cable are tightly coupled in dynamics. To more accurately describe the motion of the buoy-drone combination, this paper draws on the six-degree-of-freedom dynamic modeling method for aircraft to model it.

[0138] Combined with the general fixed-wing aircraft modeling method, a six-degree-of-freedom nonlinear dynamic model of the assembly is established. First, the center of mass translation kinematic equation in the ground coordinate system is established:

[0139]

[0140] Where x g ,y g ,z g is the three-axis position in the ground coordinate system; V K is the track velocity; γ,χ represent the track inclination and heading angle respectively.

[0141] Then, the translational dynamic equation considering the effects of cable tension and airflow disturbance is established:

[0142]

[0143] Where: R K / a ,RK / b and R K / d Represents the conversion matrix from airflow system, aircraft system and drag system to track system respectively; 0.5F N is half of the aerodynamic force of the Nth section of cable; t N is the tension of the cable; m is the sum of the masses of the buoy-UAV combination and half of the Nth section of the cable; g is the acceleration due to gravity.

[0144] Step 2: Based on the CFD numerical simulation method, the aerodynamic parameters of the buoy-UAV combination in normal flight state and wing folding process are solved.

[0145] The specific steps are as follows:

[0146] Step 201: Use CFD (Computational Fluid Dynamics) numerical simulation method to solve the aerodynamic parameters of the buoy-UAV combination in normal flight state and wing folding process.

[0147] The static grid method is used to solve the aerodynamic parameters of the buoy-UAV combination in normal flight state, and the dynamic grid method is used to solve the aerodynamic parameters of the buoy-UAV combination during the wing folding process.

[0148] Step 202: Perform polynomial fitting on the aerodynamic parameters of the buoy-UAV combination obtained by the CFD numerical simulation method, and establish an aerodynamic model of the buoy-UAV combination with the wing folding angle as a parameter.

[0149] The aerodynamic forces and aerodynamic moments of the buoy-UAV combination are synthesized by the wings, buoy-fuselage combination, tail, and grid rudder. During the wing folding process, the changes in the aerodynamic parameters of the buoy-UAV combination are mainly caused by the changes in the aerodynamic parameters of the wings. Therefore, in order to accurately describe the changes in aerodynamic parameters during the wing folding process, the following aerodynamic force model and aerodynamic moment model are established:

[0150] (1) Establish an aerodynamic model of the buoy-UAV combination with the wing folding angle as a parameter;

[0151] The CFD method is used to solve the aerodynamic parameters of the buoy-UAV combination in normal flight state and wing folding process. The polynomial fitting is performed on the solution results to obtain the aerodynamic model of the buoy-UAV combination with wing folding as the parameter:

[0152]

[0153] Where: Q is the dynamic pressure; ρ is the air density; S is the reference area; C Lw ,C Lf ,C Lt ,C LGare the lift coefficients of the wing, buoy-fuselage assembly, tail fin, and grid rudder, respectively; C Dw ,C Df ,C Dt ,C DG are the drag coefficients of the wing, buoy-fuselage assembly, tail fin, and grid rudder, respectively; C Yw ,C Yf ,C Yt ,C YG are the side force coefficients of the wing, buoy-fuselage assembly, tail fin and grid rudder, respectively, and their expanded formula is:

[0154]

[0155] Where: is the lift coefficient at zero angle of attack; is the derivative of the lift coefficient with respect to the angle of attack; is the drag coefficient at zero angle of attack; is the derivative of the lift coefficient with respect to the angle of attack; is the derivative of the side force coefficient with respect to the sideslip angle; subscripts * = w, f correspond to the wing and float-fuselage assembly, respectively; K Lηn ,K Dηn ,K Yηn , n=1,2,3 are the coefficients of the nth order term of η; are the derivatives of the tail wing lift coefficient, drag coefficient, and side force coefficient with respect to the tail wing deflection angle; δ1, δ2, δ3, and δ4 represent the deflection angles of the four all-moving tail wing of the UAV, and the deflection range of the all-moving tail wing is -25° to 25°; is the derivative of the grid rudder lift coefficient, drag coefficient and side force coefficient with respect to the grid rudder deflection angle; δ G1 ,δ G2 ,δ G3 ,δ G4 They represent the deflection angles of the four grid rudders respectively, and the deflection range of the grid rudder is -20° to 20°.

[0156] (2) Establish an aerodynamic torque model of the buoy-UAV combination with the wing folding angle as a parameter;

[0157] The CFD method is used to solve the aerodynamic torque parameters of the buoy-UAV combination in normal flight state and wing folding process. The polynomial fitting is performed on the solution results to obtain the aerodynamic torque model of the buoy-UAV combination with wing folding as the parameter:

[0158]

[0159] Where: are the rolling moment coefficients of the wing, buoy-fuselage assembly, tailplane, and grid rudder, respectively; are the pitching moment coefficients of the wing, buoy-fuselage assembly, tailplane, and grid rudder, respectively; are the yaw moment coefficients of the wing, buoy-fuselage assembly, tail fin and grid rudder, respectively, and their expanded formula is:

[0160]

[0161] Where: is the derivative of the rolling moment coefficient with respect to the sideslip angle; is the pitching moment coefficient at zero angle of attack; is the derivative of the pitching moment coefficient with respect to the angle of attack; K is the derivative of the yaw moment coefficient with respect to the sideslip angle; * = w, f subscripts correspond to the wing and the assembly respectively. Lηn ,K Dηn ,K Yηn ,n=0,1,2,3 is the coefficient of nth order term of η; is the derivative of the tail wing rolling moment coefficient, pitching moment coefficient and yaw coefficient with respect to the tail wing deflection angle; is the derivative of the grid rudder rolling moment coefficient, pitching moment coefficient and yaw coefficient with respect to the grid rudder deflection angle.

[0162] Step 3: Based on the unconstrained force vector and direction control method and the rudder configuration of the buoy-UAV combination, a unconstrained force vector and direction feedforward compensation controller is designed to control the grid rudder deflection to compensate for the unconstrained force vector and direction;

[0163] The specific steps for establishing the feedforward compensation controller are as follows:

[0164] Step 301: Calculate the difference in the unconstrained force vector and direction of the buoy-UAV assembly before and after wing folding.

[0165] Based on the nominal aerodynamic parameters of the buoy-UAV combination, the sum of the unconstrained force vectors on the buoy-UAV combination before and after the wing folding can be calculated. The sum of the unconstrained force vectors before and after the folding can be expressed as the following vector form:

[0166]

[0167] Where: L η＝0 and D η＝0 are the nominal lift and drag before wings are folded, G is the weight of the buoy-UAV combination; L η＝90 and D η＝90 are the nominal lift and drag after the wing is folded. The difference in the unconstrained force vector and direction before and after the wing is folded is:

[0168]

[0169] Take the buoy-UAV combination of some UAV towed aerial recovery systems as an example. The comparison of the non-constrained force vector before and after wing folding and the grid rudder deflection compensation effect are shown as follows: Figure 3 shown.

[0170] Step 302, calculating the grid rudder deflection angle based on the change in the non-constrained force vector and direction before and after the wing is folded, and controlling the grid rudder deflection angle by establishing a feedforward compensation controller;

[0171] According to the difference between the non-constrained force vector and direction after compensation and the non-constrained force vector and direction before folding is the smallest (or 0), the lift L generated by the deflection of the grid rudder is G and resistance D G The following conditions must be met:

[0172]

[0173] According to the aerodynamic model, F G ,F0,F can be expanded to obtain the formula:

[0174]

[0175] Where: δ G is the grid rudder deflection angle, C Dw,η＝0 is the drag coefficient of the wing before folding, C Dw,η＝90 is the drag coefficient of the folded wing, C Lw,η＝0 is the lift coefficient of the folded front wing, C Lw,η＝90 is the lift coefficient of the folded wing, C Df is the drag coefficient of the buoy-fuselage combination, C Lf is the lift coefficient of the buoy-fuselage combination.

[0176] Further substituting formula (19) into formula (17) yields:

[0177]

[0178] Solving the above equations, we can get the grid rudder deflection angle δ G , so that the changes in the non-constrained force vector and direction before and after the wing folding are minimized, and the feedforward compensation controller is established.

[0179] Step 4: Design a feedback controller based on the specified time preset control theory, and use the full-moving tail of the buoy-UAV combination to control the attitude of the buoy-UAV combination.

[0180] like Figure 5 As shown in the feedback loop, the specific steps are as follows:

[0181] Step 401: Design a track angle loop controller based on a specified time preset performance control theory;

[0182] According to the design idea of ​​the preset performance control method at a specified time, first define the tracking error e1 = X 1c -X1, where X 1c =[χ c ,γ c ] T is the desired track angle command of the assembly. To ensure that the output of the track angle keeps up with the preset command and that the tracking error e1 is within the preset limit, it is necessary to pre-define a preset performance function that meets the requirements before designing the controller. The preset performance function is defined as follows:

[0183]

[0184] Where: i = γ, χ, r i and k 0i ∈[0,1) is the parameter to be designed, k fi Determines the maximum value of the steady-state error, T ai Specifies the convergence time.

[0185] In order to make the track angle error meet the preset limit The error conversion function Y is defined i (t) are as follows:

[0186]

[0187] Derivative of track angle tracking error for:

[0188]

[0189] Define Υ1=[Υ χ , Υ γ ] T ,ζ1=diag(ζ χ ,ζ γ ), k1=diag(k χ , k γ ). Substituting formula (23) into the error conversion function, we get:

[0190]

[0191] In order to achieve track angle error stabilization, the track angle loop virtual control law is designed as follows:

[0192]

[0193] Where: X 2c =[α c ,β c ,σ c ] Tis the airflow angle loop command signal, K1=diag(K χ ,K γ ) is the controller gain. Is F1=[F χ ,F γ ] T The estimated value of is obtained by the extended state observer ESO; is the first-order differential value of the desired track angle, obtained by the tracking differentiator TD shown in equation (26):

[0194]

[0195] Where r1 and h1 are the parameters of the tracking differentiator to be designed, h1 is the tracking step size, and r1 is the acceleration factor. A larger r1 results in faster tracking but also greater sensitivity to noise. Adjusting r1 based on the system's tracking characteristics can rationally schedule the transition of the command signal and reduce tracking overshoot. fhan(x1, x2, r, h) is the comprehensive function for the fastest control.

[0196] Step 402: Design an airflow angle loop and an angular rate controller based on backstepping and an “observe-compensate” architecture.

[0197] Define the airflow angle tracking error e2 = X 2c -X2, airflow angle command X 2c According to the track angle loop controller, the differential of the airflow angle tracking error e2 is:

[0198]

[0199] The airflow angle loop control law is designed as follows:

[0200]

[0201] Where: X 3c =[p c ,q c ,r c ] T is the angular rate loop command signal, K2=diag(K α ,K β ,K σ ) is the controller gain. is the estimated value of F2, obtained by ESO shown in formula (29).

[0202]

[0203] Where: K 2o,1 and K 2o,2 is the bandwidth parameter of the observer to be designed. is the first-order differential value of the desired airflow angle, obtained by TD shown in equation (30).

[0204]

[0205] Where: r2 and h2 are the parameters of the tracking differentiator to be designed.

[0206] Define angular velocity tracking error e3 = X 3c -X3, the differential of the angular velocity tracking error e3 is:

[0207]

[0208] The angular velocity loop control law is designed as follows:

[0209]

[0210] Where: δ c =[δ 1c δ 2c δ 3c δ 4c ] T is the desired full-motion tail deflection angle; K3 = diag (K p ,K q ,K r ) is the controller gain. Similarly, is the estimated value of F3, obtained by ESO shown in formula (34); is the first-order differential value of the desired airflow angle, which is obtained by TD as shown in equation (34):

[0211]

[0212] Where: K 3o,1 and K 3o,2 is the observer bandwidth parameter to be designed, r3 and h3 are the tracking differentiator parameters to be designed.

[0213] Step 5: A composite controller is constructed based on the feedback controller with preset performance at a specified time, the unconstrained force vector and the feedforward controller to achieve anti-sway control of the wing folding process of the buoy-UAV.

[0214] After the above design, the overall anti-sway control structure of the wing folding process of the aerial recovery UAV is as follows Figure 5Based on the six-degree-of-freedom nonlinear model of the buoy-UAV combination, when there is airflow disturbance in the atmosphere during the wing-folding process of aerial recovery of the UAV, the feedforward compensation controller first adjusts the grid rudder deflection angle according to the wing folding angle. At the same time, the feedback controller provides the full-moving tail deflection angle based on the desired track angle of the buoy-UAV combination. By controlling the grid rudder and full-moving tail deflection angles, the buoy-UAV combination's sway is reduced, allowing the buoy-UAV combination to complete a stable recovery process within the specified time.

[0215] Example

[0216] In order to verify the effectiveness and superiority of the present invention, a simulation verification is carried out using a certain type of UAV air recovery system as an example. The comparison methods are as follows: Comparison method 1 adopts the ADRC control method without using feedforward compensation control; Comparison method 2 adopts the ADRC control method. The control command input of the comparison method is the same as that of the proposed method. During the wing folding process, the command track inclination angle is 0°, and the PID control law parameters in the track deflection angle command generation are The buoy-UAV combination is stabilized using the ADRC control method in normal flight. After entering the stable state, the wings begin to fold. The start moment of wing folding is used as the initial moment of the simulation to conduct a comparative simulation of the three control methods.

[0217] Comparison of control methods The simulation conditions used in the proposed method and the comparison method are shown in Table 1.

[0218] Table 1

[0219] parameter Numerical parameter Numerical Flight altitude H / m 3000 <![CDATA[Initial heading angle χ0 / °]]> 0 Buoy-UAV combination mass m / kg 400 <![CDATA[Initial sideslip angle β0 / °]]> 0 Flight speed V / (m / s) 120 <![CDATA[Initial roll angle μ0 / °]]> 0

[0220] There are three wing folding speeds. In all three cases, the wing folding starts from 0s from the normal flight state. When the maximum folding speed is 60° / s, the total folding time is 2.5s. The maximum folding speed is 50° / The total folding time is 2.8s, and the maximum folding speed is 40° / The total time is 3.25s. The additional torque change curves, reaction torque change curves and wing folding angular velocity change curves during the folding process of the three folding speeds are shown as follows: Figure 6 shown.

[0221] When the wings are folded at a maximum folding speed of 60° / s, the additional torque and reaction torque on the buoy-UAV combination are the largest. If the wing folding anti-sway control can be achieved under such a disturbance intensity, it will be beneficial to speed up the recovery speed and improve the overall efficiency of the recovery mission while ensuring the stability of the wing folding process. Therefore, the maximum folding speed of 60° is selected. / The proposed method was validated using a folding scheme. A comparison was performed between the proposed control method and the comparative method, assuming the same control gains, ESO parameters, and TD parameters. The controller parameters of the ADRC method used in the comparative method are shown in Table 2. The control gains, ESO parameters, and TD parameters of each control loop in the proposed method are the same as those in the comparative method. The preset performance function parameters of the proposed anti-sway control method are shown in Table 3.

[0222] Table 2

[0223] parameter Numerical Control gain <![CDATA[K1=diag(1,1),K2=diag(3,5,5),K3=diag(10,20,20)]]> ESO parameters <![CDATA[k 1o,1 =1,k 1o,2 =1,k 2o,1 =6,k 2o,2 =9,k 3o,1 =40,k 3o,2 =400]]> TD parameters <![CDATA[r1=1,h1=0.01,r2=10,h2=0.01,r1=20,h1=0.01]]>

[0224] Table 3

[0225] parameter Numerical Preset performance functions <![CDATA[T ai =5,k fi =0.1,r i =0.7,k 0i =0.1]]>

[0226] The distance that the assembly deviates from the initial position of the Z axis is defined as the longitudinal drift distance, and the distance that the assembly deviates from the initial position of the Y axis is defined as the lateral drift distance. The longitudinal drift distance change curves of the proposed method and the two comparison methods are shown in Figure 2. Figure 7 As shown; the projection of the motion trajectory of the buoy-UAV combination on the YOZ plane is as follows Figure 8 As shown in the figure, the dot represents the end position of the buoy-UAV combination; the cable configuration change curve is shown in Figure 9 As shown, Figure 9 a is the cable configuration change diagram of comparison method 1, Figure 9 b is the cable configuration change diagram of comparison method 2, Figure 9 c is the cable configuration change diagram of the proposed method.

[0227] from Figure 7 and Figure 8 It can be seen that the maximum longitudinal drift distance using the proposed stabilization control method is 0.18m, the maximum longitudinal drift distance using Comparative Method 1 is 0.44m, and the maximum longitudinal drift distance using Comparative Method 2 is 0.30m. The changes in longitudinal drift distance for the three methods show that the proposed method and Comparative Method 2, which use an unconstrained force vector and feedforward compensation controller, deviate less from the initial position in the longitudinal direction, while the stable position of Comparative Method 1, which does not use a feedforward compensation controller, deviates further from the initial position. The maximum longitudinal drift distances for the proposed method and Comparative Method 2 are smaller than those for Comparative Method 1, which does not use a feedforward compensation controller. Comparative Method 1 is still oscillating with a relatively large amplitude after 15 seconds, while Comparative Method 2 is still oscillating after 15 seconds, but the oscillation amplitude is slightly smaller than that of Comparative Method 1. The oscillation amplitude of the proposed method has reached a relatively low level after approximately 5 seconds. This shows that the proposed anti-drift control method can effectively reduce the longitudinal drift distance during the wing folding process and reduce the oscillation amplitude of the buoy-UAV combination.

[0228] from Figure 9It can be seen that compared with Comparative Method 1, the cable configuration changes more smoothly and with smaller swing amplitudes when using Comparative Method 2 due to the effect of the NCFVSD feedforward compensation controller. The proposed method further reduces the cable configuration changes based on Comparative Method 2, and its change amplitude is the smallest among the three methods.

[0229] The above simulation verification of the embodiments proves the effectiveness of the anti-flutter control method for folding the wing of a towed aerial recovery drone of the present invention.

[0230] The contents not described in detail in the specification of the present invention belong to the prior art known to those skilled in the art.

Claims

1. A method for controlling the anti-swaying of the wing folding process of a towed aerial recovery drone, characterized in that: The specific steps include: Step 1: Establish a nonlinear motion model of the cable and buoy-UAV combination for the UAV recovery system; First, a cable motion model is established based on multi-rigid body theory, and then a six-degree-of-freedom buoy-UAV combination dynamic model is established considering the cable tension. Step 2: Based on the CFD numerical simulation method, establish the aerodynamic model of the buoy-UAV combination; Firstly, the aerodynamic parameters of the buoy-UAV combination in normal flight state and during wing folding are solved respectively; Then, based on the aerodynamic parameters of the buoy-UAV combination, an aerodynamic force model and an aerodynamic moment model with the wing folding angle as a parameter were established. Step 3: Based on the unconstrained force vector and direction control mechanism and the rudder configuration of the buoy-UAV combination, a unconstrained force vector and direction feedforward compensation controller is designed to control the grid rudder deflection to compensate for the unconstrained force vector and direction; The specific process of establishing the feedforward compensation controller is as follows: First, the unconstrained force vector and direction difference of the buoy-UAV combination before and after wing folding are calculated; Then, the grid rudder deflection angle is calculated according to the changes in the non-constrained force vector and direction before and after the wing is folded, and the grid rudder deflection angle is controlled by establishing a feedforward compensation controller. The goal of the feedforward compensation controller is to minimize the difference between the non-constrained force vector and direction after folding and the non-constrained force vector and direction before folding by controlling the grid rudder deflection angle; The lift force L generated by the deflection of the grid rudder G and resistance D G The following conditions must be met: Among them, F G is the sum of the non-constraint force vectors of the buoy-UAV combination itself, θ0 and θ are the sum of the non-constraint force vectors of the buoy-UAV combination before and after the wing is folded, respectively; According to the aerodynamic model, F G ,F0,F can be expanded to obtain the formula: Where: δ G is the grid rudder deflection angle, C Dw,η＝0 is the drag coefficient of the wing before folding, C Dw,η＝90 is the drag coefficient of the folded wing, C Lw,η＝0 is the lift coefficient of the folded front wing, C Lw,η＝90 is the lift coefficient of the folded wing, C Df is the drag coefficient of the buoy-fuselage combination, C Lf is the lift coefficient of the buoy-fuselage combination; Furthermore, the grid rudder deflection angle optimization equation is: Finally, solving the above optimization problem yields the grid rudder deflection angle δ G , so that the changes in the non-constrained force vector and direction before and after the wing folding are minimized, achieving the purpose of establishing a feedforward compensation controller; Step 4: Design a feedback controller based on the specified time preset control theory, and use the full-moving tail of the buoy-UAV combination to control the attitude of the buoy-UAV combination; The specific steps are as follows: Step 401: Design a track angle loop controller based on a specified time preset performance control theory; First, given the desired track angle, define the track angle error: e1=X 1c -X1 where X 1c =[χ c ,γ c ] T is the desired track angle instruction of the assembly, and X1 is the actual track angle of the assembly; Then, make the track angle error meet the preset boundary Define the preset performance function as follows: Where: i = γ, χ, r i and k 0i ∈[0,1) is the parameter to be designed, k fi Determines the maximum value of the steady-state error, T ai To specify the convergence time; Define the error transfer function Υ i (t) are as follows: Derivative of track angle tracking error for: definitionY1=[Y χ ,Y γ ] T ,ζ1=diag(ζ χ ,g γ ), k1=diag(k χ ,k γ ); Substituting equation (6) into the error conversion function yields: In order to achieve track angle error stabilization, the track angle loop virtual control law is designed as follows: Where: X 2c =[α c ,β c ,σ c ] T is the airflow angle loop command signal, K1=diag(K χ ,K γ ) is the controller gain; Is F1=[F χ ,F γ ] T The estimated value of is obtained by the extended state observer ESO; is the first-order differential value of the desired track angle, obtained by the tracking differentiator TD shown in equation (9): Where: r1 and h1 are the parameters of the tracking differentiator to be designed, h1 is the tracking step size; r1 is the acceleration factor. The larger r1 is, the faster the tracking process is, but the more sensitive it is to noise. r1 should be adjusted according to the tracking characteristics of the system; fhan(x1,x2,r,h) is the fastest control synthesis function; Step 402: Design an airflow angle loop and an angular rate controller based on backstepping and an "observe-and-compensate" architecture. Define the airflow angle tracking error e2 = X 2c -X2, airflow angle loop instruction X 2c According to the track angle loop controller, the differential of the airflow angle tracking error e2 is: The airflow angle loop control law is designed as follows: Where: X 3c =[p c ,q c ,r c ] T is the angular rate loop command signal, K2=diag(K α ,K β ,K σ ) is the controller gain; is the estimated value of F2, obtained by ESO shown in formula (13): Where: K 2o,1 and K 2o,2 is the bandwidth parameter of the observer to be designed; is the first-order differential value of the desired airflow angle, which is obtained by TD as shown in formula (15): Where: r2 and h2 are the parameters of the tracking differentiator to be designed; Define angular velocity tracking error e3 = X 3c -X3, the differential of the angular velocity tracking error e3 is: The angular velocity loop control law is designed as follows: Where: δ c =[δ 1c δ 2c δ 3c δ 4c ] T is the desired full-movable tail rudder deflection angle; K3 = diag (K p ,K q ,K r ) is the controller gain. Similarly, is the estimated value of F3, obtained by ESO shown in formula (19); is the first-order differential value of the desired airflow angle, which is obtained by TD shown in formula (20): Where: K 3o,1 and K 3o,2 is the observer bandwidth parameter to be designed, r3 and h3 are the tracking differentiator parameters to be designed; B1, B2, B3 are the control matrices of each loop; Step 5: A composite controller is constructed based on the feedback controller with preset performance at a specified time, the unconstrained force vector controller, and the feedforward controller to achieve anti-sway control of the buoy-UAV's wing folding process. Based on the six-degree-of-freedom nonlinear model of the buoy-UAV combination, during the wing folding process of the aerial recovery of the UAV, when there is airflow disturbance in the atmosphere, the feedforward compensation controller first adjusts the grid rudder deflection angle according to the wing folding angle; at the same time, according to the desired track angle of the buoy-UAV combination, the feedback controller gives the full-moving tail deflection angle; by controlling the grid rudder and the full-moving tail deflection angle, the buoy-UAV combination's swing degree is reduced, so that the buoy-UAV combination can complete a stable recovery process within the specified time.

2. The anti-sway control method for the wing folding process of a towed aerial recovery UAV according to claim 1 is characterized in that: The cable motion model described in step 1 is established based on the multi-rigid body theory, specifically: In the dragging coordinate system S D (O D -X D Y D Z D ) to model the cable, p i is the position of the i-th node, r i =p i -p i-1 is the position vector of the i-th connecting rod; the i-th connecting rod is relative to the plane X D O D Y D and plane X D O D Z D The deflection angle λ i and Describe the motion of the connecting rod; r i The calculation formula is as follows: Where l = L0 / N is the length of the i-th link, L0 is the total length of the cable, N is the N discrete cylindrical rigid links of equal length in the cable; n i is the unit direction vector of the i-th link; λ i and The second-order dynamic equation is expressed as: in, α D and ω D Drag system S D Relative inertial system S g (O g -X g Y g Z g )'s involved angular velocity and angular acceleration; and That is, the cable retraction speed and acceleration; According to Newton's second law, the acceleration of node i is obtained as follows: Among them, m i is the mass of the connecting rod concentrated at node i, m d is the mass of the buoy; Q i is the total external force acting on node i, including aerodynamic force and gravity; t i is the tension on the i-th cable segment.

3. The anti-sway control method for the wing folding process of a towed aerial recovery UAV according to claim 1 is characterized in that: The dynamic model of the six-degree-of-freedom buoy-UAV combination considering the cable tension described in step 1 is as follows: First, establish the kinematic equation of the center of mass translation in the ground coordinate system: Where x g ,y g ,z g is the three-axis position in the ground coordinate system; V K is the track speed; γ,χ represent the track inclination and heading angle respectively; Then, the translational dynamics equation considering the influence of airflow disturbance is established: Where: R K / a ,R K / b and R K / d Represents the conversion matrix from airflow system, aircraft system and drag system to track system respectively; 0.5F N is half of the aerodynamic force of the Nth section of cable; t N is the tension of the cable; m is the sum of the mass of the buoy-UAV assembly and half of the mass of the Nth cable segment; g is the acceleration due to gravity; F A Represents the aerodynamic force acting on the buoy-UAV combination.

4. The anti-sway control method for the wing folding process of a towed aerial recovery UAV according to claim 1 is characterized in that: The aerodynamic model of the buoy-UAV combination with the wing folding angle as a parameter in step 2 is as follows: Where: Q is the dynamic pressure; ρ is the air density; S is the reference area; C Lw ,C Lf ,C Lt ,C LG are the lift coefficients of the wing, buoy-fuselage assembly, tail fin, and grid rudder, respectively; C Dw ,C Df ,C Dt ,C DG are the drag coefficients of the wing, buoy-fuselage assembly, tail fin, and grid rudder, respectively; C Yw ,C Yf ,C Yt ,C YG Side force coefficients of the wing, buoy-fuselage assembly, tailplane and grid rudder, respectively.

5. The anti-sway control method for the wing folding process of a towed aerial recovery UAV according to claim 4 is characterized in that: The calculation formulas for the lift coefficient, drag coefficient and side force coefficient of the wing, buoy-fuselage combination, tail and grid rudder are: Where: is the lift coefficient at zero angle of attack; is the derivative of the lift coefficient with respect to the angle of attack; is the drag coefficient at zero angle of attack; is the derivative of the lift coefficient with respect to the angle of attack; is the derivative of the side force coefficient with respect to the sideslip angle; subscripts * = w, f correspond to the wing and float-fuselage assembly, respectively; K Lηn ,K Dηn ,K Yηn , n=1,2,3 are the coefficients of the nth order term of η; are the derivatives of the tail wing lift coefficient, drag coefficient, and side force coefficient with respect to the tail wing deflection angle; δ1, δ2, δ3, and δ4 represent the deflection angles of the four all-moving tail wing of the UAV, respectively; is the derivative of the grid rudder lift coefficient, drag coefficient and side force coefficient with respect to the grid rudder deflection angle; δ G1 ,δ G2 ,δ G3 ,δ G4 Represent the deflection angles of the four grid rudders respectively.

6. The anti-sway control method for the wing folding process of a towed aerial recovery UAV according to claim 1 is characterized in that: The aerodynamic torque model of the buoy-UAV combination with the wing folding angle as a parameter in step 2 is as follows: Where: are the rolling moment coefficients of the wing, buoy-fuselage assembly, tailplane, and grid rudder, respectively; are the pitching moment coefficients of the wing, buoy-fuselage assembly, tailplane, and grid rudder, respectively; are the yaw moment coefficients of the wing, buoy-fuselage assembly, tailplane, and grid rudder, respectively.

7. The anti-sway control method for the wing folding process of a towed aerial recovery UAV according to claim 6 is characterized in that: The formulas for calculating the rolling moment coefficient, pitching moment coefficient and yaw moment coefficient of the wing, buoy-fuselage combination, tail and grid rudder are: Where: is the derivative of the rolling moment coefficient with respect to the sideslip angle; is the pitching moment coefficient at zero angle of attack; is the derivative of the pitching moment coefficient with respect to the angle of attack; K is the derivative of the yaw moment coefficient with respect to the sideslip angle; * = w, f subscripts correspond to the wing and the assembly respectively. Lηn ,K Dηn ,K Yηn ,n=0,1,2,3 is the coefficient of nth order term of η; is the derivative of the tail wing rolling moment coefficient, pitching moment coefficient and yaw coefficient with respect to the tail wing deflection angle; is the derivative of the grid rudder rolling moment coefficient, pitching moment coefficient and yaw coefficient with respect to the grid rudder deflection angle.

8. The anti-sway control method for the wing folding process of a towed aerial recovery UAV according to claim 1 is characterized in that: The method for calculating the difference in the non-constrained force vector and direction of the buoy-UAV combination before and after the wings are folded is: First, the sum of the unconstrained force vectors on the buoy-UAV combination before and after wing folding is calculated based on the nominal aerodynamic parameters of the buoy-UAV combination: Where: L η＝0 and D η＝0 are the nominal lift and drag before wings are folded, G is the weight of the buoy-UAV combination; L η＝90 and D η＝90 are the nominal lift and drag with the wings folded; Then, the difference in the unconstrained force vector and direction of the buoy-UAV combination before and after the wing folding is calculated as follows: F G is the non-constraint force vector and direction of the buoy-UAV combination itself, θ0 and θ are the non-constraint force vector and direction of the buoy-UAV combination before and after the wing folding, respectively.

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