Multi-vehicle cooperative terminal guidance method with cooperative detection configuration constraint

Abstract

This invention discloses a multi-vehicle cooperative terminal guidance method and related products with cooperative detection configuration constraints. The master vehicle, based on the finally determined control sequence, interpolates and generates real-time control quantities at time t after the initial terminal guidance time t0 to regulate its motion state; and combines the offline calculated and online iteratively calculated state quantity sequences and their corresponding time sequences [t1; ...; t] N Terminal guidance time t f The master aircraft sends the control sequence to the slave aircraft. Based on the final determined control sequence, at time t after the initial guidance time t0, the slave aircraft interpolates and generates real-time control quantities to regulate its motion state. This involves the offline and online iterative calculations of the state quantity sequences and their corresponding time sequences [t0; t1; ...; t] sent by the master aircraft. N Terminal guidance time t f And the system detects configuration constraints to determine the sequence of control quantities.

Description

Technical Field

[0001] This invention relates to a multi-vehicle cooperative terminal guidance method with cooperative detection configuration constraints and related products. Background Technology

[0002] In the context of high-tech, information-based warfare, precision-guided aircraft face an increasingly complex electromagnetic environment. Various electromagnetic signals—both man-made and natural, enemy and friendly, adversarial and non-adversarial—permeate the operational space, exhibiting characteristics such as signal density, diversity, intense confrontation, and dynamic change. This results in a complex and crisscrossing electromagnetic field distribution in the airspace, sudden and frequent changes in electromagnetic signals in the time domain, dense overlap of electromagnetic spectra in the frequency domain, and uneven power distribution in the energy domain, severely impacting the mission effectiveness of aircraft. Due to the limited resources of a single aircraft, it is difficult to counter enemy electronic warfare systems; therefore, multi-aircraft collaborative detection has become one of the main technical approaches to improve anti-jamming capabilities.

[0003] The working mechanism of multi-vehicle cooperative anti-jamming detection is as follows: First, the distribution patterns of target and interference features differ significantly from different detection perspectives. Fusion processing of multi-view detection data can effectively identify targets and suppress interference, forming a systemic anti-jamming advantage. Second, interference can only cover a limited spatial range with prior information; aircraft outside this range can normally detect, identify, and track targets. Therefore, the spatial configuration of multiple aircraft relative to the target has a decisive influence on the detection and anti-jamming performance of the entire system.

[0004] Existing terminal guidance methods fall into two main categories: proportional guidance laws and optimal guidance laws. Proportional guidance laws primarily consider terminal hit conditions, decoupling detection and guidance, but cannot handle cooperative terminal guidance problems with terminal state constraints and terminal configuration constraints. Optimal control laws generally lack analytical solutions, and numerical solutions have small convergence intervals and low solution efficiency, failing to meet the online guidance requirements of high-speed aircraft platforms. Therefore, there is a need to develop an efficient cooperative terminal guidance method that simultaneously satisfies terminal state constraints and process configuration constraints. Summary of the Invention

[0005] This invention provides a multi-vehicle cooperative terminal guidance method and related products with cooperative detection configuration constraints.

[0006] This invention adopts the following technical solution: a multi-vehicle cooperative terminal guidance method with cooperative detection configuration constraints, applied to the master vehicle in a multi-vehicle system, the multi-vehicle system including one master vehicle and at least one slave vehicle, the method comprising:

[0007] (1) Before entering the terminal guidance phase, based on the pre-designed Lagrange interpolation polynomial order N, the weight matrix R(t) of the linear quadratic performance functional, and the initial time t0 of terminal guidance, the terminal guidance time t0 is used to determine the terminal guidance time.f Control sequence at Lagrange interpolation nodes Given unknowns, and constrained by the position, trajectory inclination, and trajectory deflection at the terminal guidance moment, with the objective of minimizing control energy expenditure, an offline nonlinear programming problem is solved to obtain the initial terminal guidance moment t. f The initial time series [t1; ...; t N Initial control sequence and the initial state sequence As the nominal terminal guidance time, time series, corresponding control quantity series, and corresponding state quantity series, the Lagrange interpolation polynomial is defined at t0, t1 to t... N At a total of N+1 feature times, the weight matrix R(t) is either a constant or a function of time t;

[0008] (2) At the initial time t0 of terminal guidance, based on the current terminal guidance time t f The current time series [t1; ...; t N The current control sequence and the current state sequence The characteristic matrix required for guidance law iteration is calculated. and weight matrix Feature matrix It is a concatenated matrix of system matrices obtained by linearizing the nonlinear dynamic equations of the aircraft at different characteristic moments, and the characteristic matrix is... It is a concatenated matrix of control matrices obtained by linearizing the nonlinear dynamic equations of the aircraft at different characteristic moments, and a weight matrix. It is a concatenated matrix of weight matrices at different feature times; the current time series [t1; ...; t N The current control sequence and the current state sequence The nominal trajectory of the main aircraft;

[0009] (3) At the initial time t0 of final guidance, based on the current control sequence The real-time control quantity U is generated using the Lagrange interpolation method. M In the interval [t0, t f The current time series [t1; ...; t] is obtained by numerically integrating the nonlinear dynamic equations of the main aircraft. N The sequence of state variables on ] Current terminal guidance time t f State variable X Mf According to the state variable X Mf Determine the terminal state constraint value ΦMP If the terminal state constraint value Φ MP If the preset error threshold is met, proceed to (5); otherwise, proceed according to the terminal state constraint value Φ. MP and state variable X Mf Solving for the variational sequence of control inputs Terminal guidance time variation δt f Proceed to (4);

[0010] (4) Let t f =t f +δt f , Repeat steps (2) and (3);

[0011] (5) Based on the final determined control quantity sequence At time t after the initial time t0 of final guidance, real-time control quantities are generated by interpolation using the Lagrange method to regulate the motion state of the main aircraft.

[0012] It also includes: sequences of state variables computed offline and iteratively online. and its corresponding time series [t1; ...; t N Terminal guidance time t f Send to the aircraft.

[0013] This invention adopts the following technical solution: a multi-vehicle cooperative terminal guidance method with cooperative detection configuration constraints, applied to a slave vehicle in a multi-vehicle system, the multi-vehicle system including a master vehicle and at least one slave vehicle, the method comprising:

[0014] (1) Before entering the terminal guidance phase, receive the offline calculated terminal guidance time t sent by the main spacecraft. f Time series [t1; ...; t N ] and the state quantity sequence corresponding to the time series

[0015] (2) Before entering the terminal guidance phase, based on the pre-designed Lagrange interpolation polynomial order N, the weight matrix R(t) of the linear quadratic performance functional, and the terminal guidance time t sent by the main spacecraft. f Time series [t1; ...; t N and state quantity sequence Using time series [t1; ...; t N Control sequence on ] As unknowns, with the objective of minimizing control energy expenditure, and constrained by the position of the slave vehicle at the terminal guidance moment, the trajectory inclination angle, the trajectory deflection angle, and the cooperative detection configuration of the master and slave vehicles in the terminal phase, an offline nonlinear programming problem is solved to obtain the slave vehicle's corresponding time series [t1; ...; t N Control quantity sequence and state quantity sequence As the nominal time series, control quantity series, and state quantity series, the weight matrix R(t) is a constant or a function of time t;

[0016] (3) At the initial time t0 of the final guidance, receive the final guidance time t0 of the online iterative calculation completed by the main spacecraft. f Time series [t1; ...; t N ] and the state quantity sequence corresponding to the time series

[0017] (4) At the initial time t0 of final guidance, based on the current time sequence [t1; ...; t... N The current control sequence and the current state sequence The characteristic matrix required for guidance law iteration is calculated. and weight matrix Feature matrix It is a concatenated matrix of system matrices obtained by linearizing the nonlinear dynamic equations of the aircraft at different characteristic moments, and the characteristic matrix is... It is a concatenated matrix of control matrices obtained by linearizing the nonlinear dynamic equations of the aircraft at different characteristic moments, and a weight matrix. It is a concatenated matrix of weight matrices at different feature times; the current time series [t1; ...; t N The current control sequence and the current state sequence This is referred to as the nominal trajectory of the aircraft;

[0018] (5) At the initial time t0 of final guidance, based on the current control sequence The real-time control quantity U is generated using the Lagrange interpolation method. S The nonlinear dynamic equations of the aircraft in the interval [t0, t f Numerical integration yields the time series [t1; ...; t] N The sequence of state variables on ] t f The state variable X at time t is Sf Combined with the current state sequence of the main spacecraft Determine the constraint value Ψ, including the terminal state and the cooperative configuration at characteristic moments. SP If Ψ SP If the preset error threshold is met, proceed to (7); otherwise, calculate the required control variation based on the terminal state constraint function value of the aircraft and the master-slave aircraft cooperative detection configuration function value at the interpolation node. Go to (6);

[0019] (6) Order Repeat steps (4) and (5);

[0020] (7) Based on the final determined control quantity sequence At time t after the initial time t0 of final guidance, real-time control quantities are generated using the Lagrange interpolation method to regulate the motion state of the aircraft.

[0021] The present invention adopts the following technical solution: a program product that executes the above-described method when running.

[0022] The present invention adopts the following technical solution: a multi-vehicle system, including a master aircraft and at least one slave aircraft, the master aircraft including a controller, the controller of the master aircraft executing the aforementioned method applied to the master aircraft during operation, the slave aircraft including a controller, the controller of the slave aircraft executing the aforementioned method applied to the slave aircraft during operation.

[0023] This invention solves the problem of cooperative terminal guidance in master-slave cooperative multi-vehicle systems considering cooperative detection configuration constraints, and has the following advantages.

[0024] (1) This method introduces a general cooperative detection configuration constraint into the design of the terminal guidance law. This configuration constraint can be characterized by an arbitrary form function of multiple aircraft state variables, thus having strong versatility for cooperative guidance problems between the same type of aircraft and different types of aircraft.

[0025] (2) This method transforms the multi-vehicle cooperative detection configuration constraint into a multi-feature time point state variational constraint, and uses the property of Lagrange interpolation polynomial to ensure that the cooperative detection configuration constraint within the mission profile meets the accuracy. It provides a simple and easy-to-implement problem modeling framework with strong engineering feasibility.

[0026] (3) This method transforms the optimal control problem with quadratic performance index and complex interior point constraints into a set of linear algebraic equations. Based on the analytical solution of the linear approximate control quantity (see the expression of the variational control quantity and the variational end guidance time) and the iterative solution of the actual error of the nonlinear system (meaning that the solution process is iterative), it has high online solution efficiency. Attached Figure Description

[0027] Figure 1This is a schematic diagram of the cooperative configuration of master and slave aircraft M and S relative to the target point T at different times in a simulation example of the present invention.

[0028] Figure 2 yes Figure 1 The flight trajectories of the master and slave aircraft M and S in the simulation example shown.

[0029] Figure 3 yes Figure 1 The simulation example shown shows the curves of the control variables of the master and slave aircraft M and S changing over time.

[0030] Figure 4 This is a structural block diagram of the controller in the aircraft of the present invention. Detailed Implementation

[0031] The present invention will be further described below with reference to specific embodiments, but the scope of protection of the present invention is not limited thereto. The following sections sequentially present the design concept, operation process, simulation examples, and related product embodiments of the method of the present invention.

[0032] The design concept is as follows.

[0033] Step 1: Based on the master-slave cooperative guidance architecture, considering the nonlinear dynamic characteristics of the aircraft and the requirements of complex cooperative configuration, define a multi-aircraft cooperative terminal guidance mission with cooperative detection configuration constraints.

[0034] Definition 1.1: Assume that the master and slave aircraft move at uniform velocities, and both satisfy the following nonlinear dynamic equations with flight time t as the independent variable:

[0035]

[0036] Where x, y, and z are the coordinates of the aircraft along the three directions OXYZ of the inertial reference coordinate system; OX is the intersection of the firing surface and the horizontal plane, pointing towards the target as positive; OY lies in the vertical plane containing OX, perpendicular to OX and pointing upwards as positive; OZ is determined by the right-hand rule; θ and ψ... V These five variables are the trajectory inclination angle and trajectory deflection angle of the aircraft, respectively; n is a state variable. y n z Let V be the control variables for the aircraft, representing the normal overload and the lateral overload, respectively; V be the aircraft's velocity, and g be the gravitational acceleration, both of which are constants. The black dot above the symbol indicates the derivative with respect to time.

[0037] Let X = [x,y,z,θ,ψ] V ] T U = [n y ,n z ] T The following dynamic equation in vector form, F, is obtained:

[0038]

[0039] Definition 1.2: M represents the main aircraft, X M0 =[x M0 ,y M0 Z M0 ,θ M0 ,ψ VM0 ] T The state of the main aircraft M at the initial time t0 of terminal guidance; the state of the main aircraft M at each characteristic time t1, t2, ..., t N The states are X M1 ,X M2 ,...,X MN X Mi =[x Mi ,y Mi ,z Mi ,θ Mi ,ψ VMi ] T ,i=1,…,N represents t i The state of the main spacecraft M at time x Mi y Mi z Mi θ Mi ψ VMi They represent t respectively i Record the x, y, and z coordinates of the main aircraft M at any given time, as well as the ballistic tilt angle and ballistic deflection angle. This represents the state sequence of the main aircraft M at each characteristic moment.

[0040] Definition 1.3: S represents the aircraft, let X... S0 =[x S0 ,y S0 ,z S0 ,θ S0 ,ψ VS0 ] T Let S be the initial state of the spacecraft S at the initial time t0 of the final guidance; let S be the initial state of the spacecraft S at each characteristic time t1, t2, ..., t N The states are X S1 ,X S2 ,...,X SN X Si =[x Si ,y Si ,z Si ,θ Si ,ψ VSi ] T ,i=1,…,N represents t iThe motion state of aircraft S is recorded at all times, where the definition rules for each element are consistent with those of the main aircraft M, and the corresponding time points are also consistent. This represents the state sequence of the aircraft S at each characteristic moment.

[0041] Definition 1.4: For master and slave aircraft, the terminal state constraints determined by the terminal hit conditions have the following form:

[0042] Φ Mi (t f ,X Mf )=0,i=0,1,…,f M #(3)

[0043] Φ Si (t f ,X Sf )=0,i=0,1,…,f S #(4)

[0044] Where, Φ Mi The i-th terminal state constraint function of the main aircraft M, f M The number of terminal state constraint functions for the master aircraft M; Φ Si Let f be the terminal state constraint function of the aircraft S. S t represents the number of terminal state constraint functions from aircraft S; f At the terminal time, X Mf For the state of spacecraft M at the terminal moment, X Sf The terminal state is the state of the aircraft S at the end moment. Terminal state constraints include, for example, constraints on coordinate position, trajectory inclination angle, and trajectory deflection angle.

[0045] Definition 1.5: To ensure good guidance accuracy, the master and slave spacecraft must simultaneously meet the pre-designed relative positional relationship (i.e., cooperative detection configuration) in the terminal phase. Therefore, at t N-r ,…,t N-2 ,t N-1 ,t N At time r+1, a cooperative detection configuration constraint of the following form is imposed:

[0046] C i (t N-i ,X M(N-i) ,X S(N-i) )=0,i=0,1,…,r#(5)

[0047] Among them, C i Indicates t N-i The cooperative detection configuration constraint function at time t, where r represents the number of characteristic times at which the cooperative detection configuration constraint is applied.

[0048] Cooperative detection configuration constraints are, for example, ||X M(N-i) -X T ||=k N-i ||X S(N-i) -X T || represents the distance from the main aircraft to the target ||X M(N-i) -X T || is the distance from the aircraft to the target || X S(N-i) -X T ||of K N-i times; for example is Let θ represent the angle between the line of sight of the primary aircraft and the line of sight of the secondary aircraft. N-i In the two examples above, X... T Represents the target's coordinates, X M(N-i) and X S(N-i) The master and slave spacecraft are in t N-i The coordinates of the moment.

[0049] Definition 1.6: The terminal guidance task of the main aircraft M is to solve the control sequence N. M =[n yM1 ,n zM1 ,n yM2 ,n zM2 ,…,n yMi ,n zMi ,…,n yMN ,n zMN ] T It satisfies equations (1) and (3).

[0050] Definition 1.7: The terminal guidance mission of the slave aircraft S is based on the t shared by the master aircraft M. N-r ,…,t N-2 ,t N-1 ,t N Predicting state information at time t, and solving for the control sequence N. S =[n yS1 ,n zS1 ,n yS2 ,n zS2 ,…,n ySi ,n zSi ,…,n ySN ,n zSN ] T It satisfies equations (1), (4) and (5).

[0051] Step 2: Design the control model for the multi-vehicle system. At the Legendre-Gauss point (polynomial P... N+1 (t)+P N (t) has N+1 real roots on the interval [-1, 1], P N+1 (t), PN Using Lagrange interpolation to approximate the system state and control variables on (t) the N+1 and Nth order Legendre polynomials respectively, can guarantee fast convergence of the solution process. The time interval between interpolation points can also be equal.

[0052] Step 2.1: Select an initial trajectory (based on the terminal guidance time t). f Control sequence at Lagrange interpolation nodes As unknowns, the position, trajectory inclination angle, and trajectory deviation angle at the terminal guidance moment are used as constraints. The goal is to minimize the control energy expenditure. Interpolation methods are used to generate the control quantities at each moment, and mature software tools are used to solve the nonlinear programming problem to calculate the nominal trajectory. The nonlinear dynamic equation (1) is expanded using Taylor series along the nominal trajectory to obtain the time-varying linear dynamic equations concerning the variational states and control quantities:

[0053]

[0054] δX=XX P =[δx δy δz δθ δψ V ] T #(7)

[0055] δU=UU P =[δn y δn z ] T #(8)

[0056]

[0057]

[0058] The subscript P of the matrix indicates the value taken for the nominal state variable and the control variable. Where A... P B P It is the characteristic matrix calculated along the nominal trajectory, where δX is the actual state variable X relative to the nominal trajectory state variable X. P The variation, δU, is the actual control quantity U relative to the nominal ballistic control quantity U. P Variations of .

[0059]

[0060]

[0061] Step 2.2: Expand the constraints (5) on the cooperative detection configuration along the nominal trajectory using Taylor series. Given the state variables of the main aircraft M and the characteristic moments, obtain the linear equations of variation of the state variables of the secondary aircraft S:

[0062]

[0063] In the formula δC i (t N-i ,X M(N-i) ,X S(N-i) ) represents the variation of the cooperative detection configuration function, δX S(N-i) For the variation of the state variables of the aircraft S.

[0064] Step 2.3: Set the actual time t∈[t0,t... f Mapped to normalized time τ∈[-1,1], the state variation and control variation are approximated by an Nth-order Lagrange interpolation polynomial:

[0065]

[0066]

[0067]

[0068] In equations (15) and (16), τ l L has N+1 interpolation nodes, including -1 and N roots of Legendre polynomials. l (τ) is defined in τ l The Lagrange interpolation polynomial over t is given. t is the actual time with dimensions, τ is the normalized time, and N is the pre-designed order of the interpolation polynomial (equal to the number of characteristic times).

[0069] At each interpolation node, the values ​​of the Lagrange interpolation polynomial are consistent with the original system parameter values. Differentiation at the interpolation nodes yields:

[0070]

[0071]

[0072] Where τ k It is the k-th normalized interpolation node, D kl It is defined in τ l The Lagrange interpolation polynomial on τ k The differential approximation matrix at point .

[0073] Step 2.4: Using equations (15), (16), and (17), transform equation (6) into an algebraic equation concerning the variational variables of the interpolation node state variables and the variational variables of the control variables:

[0074]

[0075] By combining the algebraic equations at each interpolation node, we obtain the following global algebraic equation system in matrix form:

[0076]

[0077] in It is composed of the differential approximation matrix at each interpolation node and the characteristic matrix of the linear system, and has the following form:

[0078]

[0079]

[0080]

[0081]

[0082]

[0083] It is a globally differential approximation matrix defined on the nominal trajectory. It is a global feature matrix defined on the nominal trajectory. It is a variational sequence of state variables. It is a variational sequence of control variables.

[0084] From equation (20), the analytical relationship between the state variable variation and the control variable variation can be obtained:

[0085]

[0086] Step 2.5: Integrate the Lagrange interpolation polynomial along the time interval [-1, 1] to obtain the variational expression for the terminal state variable:

[0087]

[0088]

[0089] ω k It is defined in τ k The integral of the Lagrange interpolation polynomial over the time interval [-1, 1] is a constant.

[0090] Equation (27) can be rearranged into the following matrix form:

[0091]

[0092]

[0093]

[0094] W n It is the global integration constant matrix. It is related to the integration constant ωk The corresponding local integral constant matrix.

[0095] Substituting equation (26) into equation (29), we can obtain the relationship between the variational values ​​of the terminal state variables and the variational values ​​of the control variables:

[0096]

[0097] Where I nN It is an n×N dimensional identity matrix.

[0098] Step 2.6: Similar to Step 2.5, use the Lagrange interpolation polynomial along the time interval [-1, τ] N-i Integrating, we obtain the analytical expression for the variational state of the aircraft at the constraint point:

[0099]

[0100] It is defined in τ k The Lagrange interpolation polynomial on the time interval [-1, τ] is given by the polynomial. N-i The integral over ] is a constant:

[0101]

[0102] The relationship between the variational states and control variables at the constraint points is further obtained as follows:

[0103]

[0104] Is with τ N-i The corresponding global integration constant matrix, It is related to the integration constant ω k The corresponding local integral constant matrix:

[0105]

[0106]

[0107] Substituting equation (35) into equation (13), we obtain the variational relation of the cooperative detection configuration function in terms of control variable variation:

[0108]

[0109] in It is derived from the global feature matrix of aircraft S (refer to formulas 22 and 23). It is the variational sequence of control variables from aircraft S.

[0110] Step 3: For the main aircraft M, solve the independent guidance problem to obtain the optimal control quantity in analytical form for terminal state correction.

[0111] Step 3.1: For the main aircraft, the quadratic performance index functional is established as follows:

[0112]

[0113] In the formula J M It refers to the performance indicators of the main aircraft M, U M R is the control input of the main aircraft, and R is the weight matrix.

[0114] Utilizing the orthogonality of interpolation polynomials, the above performance index functional can be rearranged into a relationship between the control quantity and the terminal time variation:

[0115]

[0116]

[0117]

[0118]

[0119] It is the variational sequence of the main spacecraft control variables, and it is the terminal time variation, J MP It is the performance indicator of the nominal ballistics. It is the sequence of control quantities at each characteristic moment of the nominal ballistic trajectory, U MPf It is the control quantity at the terminal moment, W q It is the global integration constant matrix. Is with ω k The relevant local integral constant matrix, It is the global weight matrix, R f It is the weight matrix at the terminal time.

[0120] Step 3.2: Based on the analytical expression shown in equation (44), solve for the variational values ​​of the control sequence and the terminal time variation, substitute them into the nonlinear dynamic equation, integrate to obtain the terminal constraint satisfaction, and iterate until the terminal error is sufficiently small:

[0121]

[0122]

[0123]

[0124] In the formula, Φ MP It is the value of the master aircraft terminal state constraint function using the nominal control quantity. The partial derivative of the terminal state constraint function of the master aircraft with respect to its control sequence. The partial derivative of the terminal state constraint function of the master aircraft with respect to the terminal time. The partial derivative of the terminal state constraint function of the master aircraft with respect to its terminal state. The partial derivative of the terminal state constraint function of the master aircraft with respect to the terminal time. The partial derivative of the terminal state of the master aircraft with respect to its control sequence. The partial derivative of the terminal state of the master aircraft with respect to the terminal time, F M (X Mpf U MPf ,t f ) is the state differential of the main spacecraft at the terminal moment, υ M It is an auxiliary variable.

[0125] Step 4: Solve the cooperative guidance problem for the aircraft to obtain the optimal analytical control quantity that takes into account both the terminal state and cooperative configuration correction.

[0126] Step 4.1: For the aircraft, establish the quadratic performance index functional as follows:

[0127]

[0128] In the formula J S From the performance indicators of the aircraft, U S It is the control quantity from the aircraft.

[0129] Considering terminal time t f Given the variables, and utilizing the orthogonality of interpolation polynomials, the above performance index functional can be rearranged into a relationship with respect to the control variables:

[0130]

[0131] From the variational sequence of aircraft control variables, J SP It is the performance indicator of the nominal ballistics. It is a sequence of control quantities at each characteristic moment of the nominal ballistic trajectory.

[0132] Step 4.2: Solve for the variational control sequence according to the analytical expression shown in equation (49), and iterate until the terminal error is sufficiently small:

[0133]

[0134]

[0135] In the formula, Ψ SP =[Φ SP C 0P ,...,C rP ] TIt uses the nominal control quantities from the aircraft terminal state constraint function value and the terminal cooperative detection configuration constraint function value. This is the partial derivative of the aircraft's terminal state constraint function with respect to its control sequence. υ is the partial derivative of the aircraft's terminal state constraint function with respect to its terminal state. S It is an auxiliary variable.

[0136] In the above design process, the aircraft dynamics equation shown in equation (1) can be modified and any form of continuous differentiable function can be applied.

[0137] Based on the above design concept, the operation process of the main aircraft can be obtained as follows.

[0138] (1) Before entering the terminal guidance phase, based on the pre-designed Lagrange interpolation polynomial order N, the weight matrix R(t) of the linear quadratic performance functional, and the initial time t0 of terminal guidance, the terminal guidance time t0 is used to determine the terminal guidance time. f Control sequence at Lagrange interpolation nodes Given unknowns, and constrained by the position, trajectory inclination, and trajectory deflection at the terminal guidance moment, with the objective of minimizing control energy expenditure, an offline nonlinear programming problem is solved to obtain the initial terminal guidance moment t. f The initial time series [t1; ...; t N Initial control sequence and the initial state sequence As the nominal terminal guidance time, time series, corresponding control quantity series, and corresponding state quantity series, the Lagrange interpolation polynomial is defined at t0, t1 to t... N At a total of N+1 feature times, the weight matrix R(t) is either a constant or a function of time t;

[0139] (2) At the initial time t0 of terminal guidance, based on the current terminal guidance time t f The current time series [t1; ...; t N The current control sequence and the current state sequence The characteristic matrix required for guidance law iteration is calculated. and weight matrix Feature matrix It is a concatenated matrix of system matrices obtained by linearizing the nonlinear dynamic equations of the aircraft at different characteristic moments, and the characteristic matrix is... It is a concatenated matrix of control matrices obtained by linearizing the nonlinear dynamic equations of the aircraft at different characteristic moments, and a weight matrix. It is a concatenated matrix of weight matrices at different feature times;

[0140] (3) At the initial time t0 of final guidance, based on the current control sequence The real-time control quantity U is generated using the Lagrange interpolation method. M In the interval [t0, t f The current time series [t1; ...; t] is obtained by numerically integrating the nonlinear dynamic equations of the main aircraft. N ;t f The sequence of state variables on ] Current terminal guidance time t f State variable X Mf According to the state variable X Mf Determine the terminal state constraint value Φ MP If the terminal state constraint value Φ MP If the preset error threshold is met, proceed to (5); otherwise, proceed according to the terminal state constraint value Φ. MP and state variable X Mf Solving for the variational sequence of control inputs Terminal guidance time variation δt f Proceed to (4);

[0141] (4) Let t f =t f +δt f , Repeat steps (2) and (3);

[0142] (5) Based on the final determined control quantity sequence At time t after the initial time t0 of final guidance, real-time control quantities are generated by interpolation using the Lagrange method to regulate the motion state of the main aircraft.

[0143] It also includes: sequences of state variables computed offline and iteratively online. and its corresponding time series [t0; t1; ...; t N Terminal guidance time t f Send to the aircraft.

[0144] Optionally, step (2) is based on the currently determined terminal guidance time t. f Time series [t1; ...; t N Control sequence and state quantity sequence The global characteristic matrix required for guidance law iteration is obtained using the following method. and weight matrix

[0145]

[0146]

[0147]

[0148] Where A MP (t1),...,A MP (t N ),B MP (t1),...,B MP (t N (a) is a nonlinear system The characteristic matrix of the linearized system at each interpolation node, where X is the state vector, U is the control vector, t is time, and F(·) is the dynamic equation of the nonlinear system.

[0149] The aforementioned time-varying characteristic matrix is ​​obtained by performing a Taylor expansion of the nonlinear system state differential function along the nominal trajectory:

[0150]

[0151]

[0152] Optionally, in step (3), the real-time control quantity U is generated by interpolation using the following formula. M :

[0153]

[0154] Among them, L l (τ) is defined at the l-th interpolation node τ l The Lagrange interpolation polynomial on U M (τ l ) represents the l-th interpolation node τ l The control variable τ is the dimensionless time corresponding to the actual time t.

[0155]

[0156] Optionally, step (3) modifies the nonlinear dynamic equations In the interval [t0, t] f The terminal state constraint function value Φ obtained by integration MP The correction values ​​for both the control quantity and the final guidance time are obtained according to the following formula. δt f :

[0157]

[0158] Among them, W q U is the global integration constant matrix.MPf It is through t obtained by interpolation f Time control quantity, R f =R(t) f ) is t f The weight matrix at time step, The partial derivative of the terminal state constraint function of the master aircraft with respect to its control sequence. The partial derivative of the main aircraft terminal state constraint function with respect to the terminal time; υ M It is an auxiliary variable;

[0159]

[0160]

[0161] Among them W n This is the global integration constant matrix. The differential approximation matrix is ​​related to the order of the Lagrange interpolation polynomial and remains a constant matrix during the iteration process. nN It is an n×N dimensional identity matrix, where n is the number of system state variables; The partial derivative of the terminal state constraint function of the master aircraft with respect to its terminal state. F is the partial derivative of the master aircraft terminal state constraint function with respect to the terminal time. M (X Mpf U MPf ,t f The state differential of the main aircraft at the end of terminal guidance.

[0162] Based on the above design concept, the operation process of the aircraft can be obtained as follows.

[0163] (1) Before entering the terminal guidance phase, receive the offline calculated terminal guidance time t sent by the main spacecraft. f Time series [t1; ...; t N ] and the state quantity sequence corresponding to the time series

[0164] (2) Before entering the terminal guidance phase, based on the pre-designed Lagrange interpolation polynomial order N, the weight matrix R(t) of the linear quadratic performance functional, and the terminal guidance time t sent by the main spacecraft. f Time series [t1; ...; t N and state quantity sequence Using time series [t1; ...; t N Control sequence on ] As unknowns, with the objective of minimizing control energy expenditure, and constrained by the position of the slave vehicle at the terminal guidance moment, the trajectory inclination angle, the trajectory deflection angle, and the cooperative detection configuration of the master and slave vehicles in the terminal phase, an offline nonlinear programming problem is solved to obtain the slave vehicle's corresponding time series [t1; ...; t N Control quantity sequence and state quantity sequence As the nominal time series, control quantity series, and state quantity series, the weight matrix R(t) is a constant or a function of time t;

[0165] (3) At the initial time t0 of the final guidance, receive the final guidance time t0 of the online iterative calculation completed by the main spacecraft. f Time series [t1; ...; t N ] and the state quantity sequence corresponding to the time series

[0166] (4) At the initial time t0 of final guidance, based on the current time sequence [t1; ...; t... N The current control sequence and the current state sequence The characteristic matrix required for guidance law iteration is calculated. and weight matrix Feature matrix It is a concatenated matrix of system matrices obtained by linearizing the nonlinear dynamic equations of the aircraft at different characteristic moments, and the characteristic matrix is... It is a concatenated matrix of control matrices obtained by linearizing the nonlinear dynamic equations of the aircraft at different characteristic moments, and a weight matrix. It is a concatenated matrix of weight matrices at different feature times;

[0167] (5) At the initial time t0 of final guidance, based on the current control sequence The real-time control quantity U is generated using the Lagrange interpolation method. S The nonlinear dynamic equations of the aircraft in the interval [t0, t f Numerical integration yields the time series [t1; ...; t] N The sequence of state variables on ] t f The state variable X at time t is Sf Combined with the current state sequence of the main spacecraft Determine the constraint value Ψ, including the terminal state and the cooperative configuration at characteristic moments. SP If Ψ SPIf the preset error threshold is met, proceed to (7); otherwise, calculate the required control variation based on the terminal state constraint function value of the aircraft and the master-slave aircraft cooperative detection configuration function value at the interpolation node. Go to (6);

[0168] (6) Order Repeat steps (4) and (5);

[0169] (7) Based on the final determined control quantity sequence At time t after the initial time t0 of final guidance, real-time control quantities are generated using the Lagrange interpolation method to regulate the motion state of the aircraft.

[0170] Optionally, step (4) is based on the currently determined control quantity sequence. and state quantity sequence The global characteristic matrix required for guidance law iteration is obtained using the following method. and weight matrix

[0171]

[0172]

[0173]

[0174] Where A SP (t1),...,A SP (t N ),B SP (t1),...,B SP (t N (a) is a nonlinear system The characteristic matrix of the linearized system at each interpolation node, where X is the state vector, U is the control vector, t is time, and F(·) is the dynamic equation of the nonlinear system.

[0175] The aforementioned time-varying characteristic matrix is ​​obtained by performing a Taylor expansion of the nonlinear system along the nominal trajectory:

[0176]

[0177]

[0178] Optionally, in step (5), the real-time control quantity U is generated by interpolation using the following formula. S :

[0179]

[0180] Among them, U S (τl ) represents the l-th interpolation node τ l The control quantity on L l (τ) is defined at the l-th interpolation node τ l The Lagrange interpolation polynomial on τ is the dimensionless time corresponding to the actual time t:

[0181]

[0182] Optionally, step (5) modifies the nonlinear dynamic equations In the interval [t0, t] f The integrated constraint function value Ψ obtained by integration SP =[Φ SP C 0P ,...,C rP ] T The correction amount of the control quantity is obtained according to the following formula.

[0183]

[0184] Where, Φ SP To obtain the value of the constraint function from the terminal state of the aircraft, C 0P ,...,C rP To be defined in t respectively N-0 ,…,t N-r The master and slave spacecraft cooperate to detect configuration function values ​​at these interpolation nodes. This is the partial derivative of the comprehensive constraint function with respect to the sequence of aircraft control variables. This includes constraint functions for the terminal state of the aircraft and constraint functions for the cooperative detection configuration of the master and slave aircraft; S As an auxiliary variable;

[0185]

[0186] in, Is with τ N-i The corresponding global integration constant matrix, i = 0, ..., r, Let be the partial derivative of the aircraft's terminal state constraint function with respect to its terminal state. Let be the partial derivative of the i-th cooperative detection configuration function with respect to the (Ni)-th interpolation node from the spacecraft state. The differential approximation matrix is ​​related to the order of the Lagrange interpolation polynomial and remains a constant matrix during the iteration process. nN It is an n×N dimensional identity matrix, where n is the number of system state variables.

[0187] This invention aims to propose a cooperative terminal guidance method with cooperative detection configuration constraints for multi-vehicle systems. It overcomes the shortcomings of traditional terminal guidance methods, such as difficulty in handling spatial configuration constraints during flight or low solution efficiency, by comprehensively considering various constraints including the relative position configuration of the vehicle and target at multiple characteristic time points during the terminal guidance phase, zero miss distance at the time of impact, and desired attack angle. This ensures the normal performance of precision-guided vehicle missions.

[0188] The zero miss distance and the desired attack angle constraint can be reflected in the variational solution of the control variable, Φ M Φ S The convergence to zero through iteration indicates that zero off-target error and the desired attack angle have been achieved.

[0189] Because the distribution patterns of target and interference characteristics differ significantly across different detection perspectives, fusing multi-view detection data can effectively identify targets and suppress interference, creating a systemic advantage against interference. Simultaneously, interference can only cover a limited spatial range with prior information; aircraft outside this range can still detect, identify, and track targets normally. Therefore, through the rational design of multi-aircraft spatial configurations, electromagnetic interference can be effectively addressed.

[0190] The following detailed description of the specific implementation of the present invention, with reference to the accompanying drawings, takes a cooperative terminal guidance mission involving two spacecraft as an example. The master and slave spacecraft M and S begin their movements from positions M0 and S0, respectively. The terminal guidance mission is to solve for the control sequence N of the master and slave spacecraft M and S. M N S This ensures that both aircraft hit the target simultaneously, and that the cooperative configuration in the terminal phase meets the requirements (specifically, the ratio of the distances between the two aircraft and the target is a constant).

[0191] For simplicity, consider the scenario where two aircraft are moving in the same vertical plane and performing terminal guidance for a stationary target. Figure 1 As shown, a rectangular coordinate system is established with the target point T as the origin. The main aircraft M has a flight speed of 400 m / s, an initial position of (-2400, 3200) m, and an initial trajectory inclination of -48.13°. The secondary aircraft S has a flight speed of 260 m / s, an initial position of (-2400, 1000) m, and an initial trajectory inclination of -22.52°. The flight time for both aircraft to reach the target is approximately 10 seconds.

[0192] The terminal state constraints considered for the main aircraft M are as follows:

[0193]

[0194] The terminal state constraints considered from the perspective of aircraft S are as follows:

[0195]

[0196] Based on the 8th-order Lagrange interpolation method, the 9 interpolation nodes in the interval [-1,1] (the interpolation nodes are the 9 real roots of the polynomial P9(t)+P8(t) in the interval [-1,1], where P9(t) and P8(t) are the 9th and 8th order Legendre polynomials, respectively) are {-1.0000,-0.9107,-0.7113,-0.4264,-0.0904,0.2561,0.5714,0.8174,0.9644}. The ratio of the distances between the two spacecraft and the target point at the 7th to 9th node times is selected as the cooperative detection configuration constraint function, where l in equation (48) is 0.65.

[0197]

[0198] Tables 1 and 2 show the normal overloads calculated for the master and slave aircraft at the interpolation nodes, and Table 3 shows the cooperative configuration satisfaction of the master and slave aircraft. The control law obtained by the method of this invention can effectively control the cooperative detection configuration constraint function at the constraint time point within the specified level.

[0199] Table 1. Calculation results of the main aircraft

[0200]

[0201] Table 2 shows the calculation results from the aircraft.

[0202]

[0203]

[0204] Table 3. Cooperative configuration satisfaction status

[0205]

[0206] Figure 2 and Figure 3 The flight trajectories and control variables of the master and slave aircraft obtained by the method of the present invention are given. M0 and S0 are the positions of the master and slave aircraft at the initial moment of terminal guidance. M6 and S6 are the positions of the master and slave aircraft at time τ6. M7 and S7 are the positions of the master and slave aircraft at time τ7. M8 and S8 are the positions of the master and slave aircraft at time τ8.

[0207] Based on the same inventive concept, embodiments of the present invention also provide a program product that executes the aforementioned multi-vehicle cooperative terminal guidance method with cooperative detection configuration constraints during runtime.

[0208] Based on the same inventive concept, embodiments of the present invention also provide a multi-vehicle system, including a master vehicle and at least one slave vehicle. The master vehicle includes a controller, which executes the aforementioned multi-vehicle cooperative terminal guidance method with cooperative detection configuration constraints for the master vehicle during operation. The slave vehicle includes a controller, which executes the aforementioned multi-vehicle cooperative terminal guidance method with cooperative detection configuration constraints for the slave vehicle during operation.

[0209] refer to Figure 4 The controller's structure may include, for example, a memory and a processor, with the memory storing programs for executing the aforementioned multi-aircraft cooperative terminal guidance method with cooperative detection configuration constraints. The controller may also be other hardware types, such as application-specific integrated circuits (ASICs) or field-programmable arrays (FPGAs).

[0210] The aircraft also includes, for example, inertial measurement units and satellite navigation and positioning devices, and obtains the state at each moment through navigation calculations by the controller.

[0211] The various embodiments in this invention are described in a progressive manner. For the same or similar parts between the various embodiments, please refer to each other. Each embodiment focuses on describing the differences from other embodiments.

[0212] The scope of protection of this invention is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its scope and spirit. If these modifications and variations fall within the scope of the claims of this invention and their equivalents, then the intent of this invention also includes these modifications and variations.

Claims

1. A multi-vehicle cooperative terminal guidance method with cooperative detection configuration constraints, applied to the master vehicle in a multi-vehicle system, the multi-vehicle system comprising one master vehicle and at least one slave vehicle, characterized in that, The method includes: (1) Before entering the final guidance phase, based on the pre-designed Lagrange interpolation polynomial order N Weight matrix of linear quadratic performance functional R ( t ) and the initial moment of final guidance t 0, terminal guidance time t f Control sequence at Lagrange interpolation nodes Given the unknowns, and constrained by the position, trajectory inclination, and trajectory deflection at the terminal guidance moment, with the objective of minimizing the control energy expenditure, an offline nonlinear programming problem is solved to obtain the initial terminal guidance moment. t f Initial time series [ t 1;...; t N Initial control sequence and the initial state sequence As the nominal terminal guidance time, time series, corresponding control sequence, and corresponding state sequence, the Lagrange interpolation polynomial is defined in t 0、 t 1 to t N total N At +1 feature time step, the weight matrix R ( t ) is a constant or a constant with respect to time t The function; (2) At the initial moment of terminal guidance t 0, based on the current terminal guidance time. t f The current time series [ t 1;...; t N The current control sequence and the current state sequence The characteristic matrix required for guidance law iteration is calculated. and Weight matrix , characteristic matrix It is a concatenated matrix of system matrices obtained by linearizing the nonlinear dynamic equations of the aircraft at different characteristic moments, and the characteristic matrix is... It is a concatenated matrix of control matrices obtained by linearizing the nonlinear dynamic equations of the aircraft at different characteristic moments, and a weight matrix. It is a concatenated matrix of weight matrices at different feature times; the current time series [ t 1;...; t N The current control sequence and the current state sequence The nominal trajectory of the main aircraft; (3) At the initial moment of terminal guidance t 0, based on the current control sequence Real-time control quantities are generated using the Lagrange interpolation method. In the interval [ t 0, t f The current time series is obtained by numerically integrating the nonlinear dynamic equations of the main aircraft. t 1;...; t N The sequence of state variables on ] Current terminal guidance time t f state variables According to the state variables Determine terminal state constraint values If the terminal state constraint value If the preset error threshold is met, proceed to (5); otherwise, proceed according to the terminal state constraint value. and state variables Solving for the variational sequence of control input Terminal guidance time variation , then proceed to (4); (4) Let , Repeat (2) and (3); (5) Based on the final determined control quantity sequence At the initial moment of terminal guidance t The moment after 0 t Real-time control quantities are generated by interpolation using the Lagrange method to regulate the motion state of the main aircraft. It also includes: control quantity sequences calculated offline and iteratively online. and its corresponding time series [ t 0; t 1;...; t N ; t f Send to the aircraft.

2. The method according to claim 1, characterized in that, Step (2) Based on the currently determined terminal guidance time t f Time series t 1;...; t N Control sequence and state quantity sequence The global characteristic matrix required for guidance law iteration is obtained using the following method. and Weight matrix : ； ； ； in ,..., , ,..., Nonlinear system The characteristic matrix of the linearized system at each interpolation node For state vectors, For control vectors, For time, The dynamic equations of a nonlinear system; The above time-varying characteristic matrix ,..., , ,..., The result is obtained by Taylor expansion of the state differential function of the nonlinear system along the nominal trajectory: ； 。 3. The method according to claim 1, characterized in that, In step (3), the following interpolation formula is used to generate the real-time control quantity. : ； in, For the definition in the first l interpolation nodes Lagrange interpolation polynomial on, For the first l interpolation nodes Control quantity on, To match actual time t Corresponding dimensionless time: 。 4. The method according to claim 1, characterized in that, The nonlinear dynamic equation of the main aircraft is: , For state vectors, For control vectors, For time, The dynamic equations of a nonlinear system; Step (3) for the nonlinear dynamic equation In the interval [ t 0, t f The terminal state constraint function value obtained by integration The correction values ​​for both the control quantity and the final guidance time are obtained according to the following formula. , : ； in, This is the global integration constant matrix. It is through Interpolation t f Control the amount at all times. yes t f The weight matrix at time step, The partial derivative of the terminal state constraint function of the master aircraft with respect to its control sequence. The partial derivative of the terminal state constraint function of the main aircraft with respect to the terminal time; It is an auxiliary variable; ； ； in This is the global integration constant matrix. It is a differential approximation matrix, related to the order of the Lagrange interpolation polynomial, and remains a constant matrix during the iteration process. for n × N 3D identity matrix n The number of system state variables; The partial derivative of the terminal state constraint function of the master aircraft with respect to its terminal state. The partial derivative of the terminal state constraint function of the master aircraft with respect to the terminal time. The state differential of the main aircraft at the end of terminal guidance.

5. A multi-vehicle cooperative terminal guidance method with cooperative detection configuration constraints, applied to a slave vehicle in a multi-vehicle system, the multi-vehicle system comprising a master vehicle and at least one slave vehicle, characterized in that, The method includes: (1) Before entering the terminal guidance phase, receive the offline calculated terminal guidance time sent by the main spacecraft. t f Time series t 1;...; t N ], the state quantity sequence corresponding to the time series ; (2) Before entering the final guidance phase, based on the pre-designed Lagrange interpolation polynomial order N Weight matrix of linear quadratic performance functional R ( t ) and the terminal guidance time sent by the main spacecraft t f Time series t 1;...; t N and state quantity sequence In time series [ t 1;...; t N Control sequence on ] As unknowns, with the objective of minimizing control energy expenditure, and constrained by the position of the slave vehicle at the terminal guidance moment, the trajectory inclination angle, the trajectory deflection angle, and the cooperative detection configuration of the master and slave vehicles in the terminal phase, an offline nonlinear programming problem is solved to obtain the slave vehicle's corresponding time series for the current time period. t 1;...; t N Control quantity sequence and state quantity sequence As the nominal time series, control quantity series, and state quantity series, the weight matrix R ( t ) is a constant or a constant with respect to time t The function; (3) At the initial moment of terminal guidance t 0, Receive the terminal guidance time when the online iterative calculation is completed, sent by the main spacecraft. t f Time series t 1;...; t N ] and the state quantity sequence corresponding to the time series ; (4) At the initial moment of terminal guidance t 0, based on the current time series [ t 1;...; t N The current control sequence and the current state sequence The characteristic matrix required for guidance law iteration is calculated. and Weight matrix , characteristic matrix It is a concatenated matrix of system matrices obtained by linearizing the nonlinear dynamic equations of the aircraft at different characteristic moments, and the characteristic matrix is... It is a concatenated matrix of control matrices obtained by linearizing the nonlinear dynamic equations of the aircraft at different characteristic moments, and a weight matrix. It is a concatenated matrix of weight matrices at different feature times; the current time series [ t 1;...; t N The current control sequence and the current state sequence This is referred to as the nominal trajectory of the aircraft; (5) At the initial moment of terminal guidance t 0, based on the current control sequence Real-time control quantities are generated using the Lagrange interpolation method. The nonlinear dynamic equations of the aircraft in the interval [ t 0, t f Numerical integration yields the time series. t 1;...; t N The sequence of state variables on ] , t f state quantity at time 1 Combined with the current state sequence of the main spacecraft Determine constraint values ​​including terminal state and characteristic moment co-configuration. ,if If the preset error threshold is met, proceed to (7); otherwise, calculate the required control variation based on the terminal state constraint function value of the aircraft and the master-slave aircraft cooperative detection configuration function value at the interpolation node. , then proceed to (6); (6) Order , Repeat steps (4) and (5); (7) Based on the final determined control quantity sequence At the initial moment of terminal guidance t The moment after 0 t The Lagrange interpolation method is used to generate real-time control quantities to regulate the motion state of the aircraft.

6. The method according to claim 5, characterized in that, Step (4) Based on the currently determined control quantity sequence and state quantity sequence The global characteristic matrix required for guidance law iteration is obtained using the following method. and Weight matrix : ； ； ； in ,..., , ,..., Nonlinear system The characteristic matrix of the linearized system at each interpolation node For state vectors, For control vectors, For time, The dynamic equations of a nonlinear system; The above time-varying characteristic matrix ,..., , ,..., The result is obtained by Taylor expansion of the nonlinear system along the nominal trajectory: ； 。 7. The method according to claim 5, characterized in that, In step (5), the following interpolation formula is used to generate the real-time control quantity. : ； in, For the first l interpolation nodes Control quantity on, For the definition in the first l interpolation nodes Lagrange interpolation polynomial on, To match actual time t Corresponding dimensionless time: 。 8. The method according to claim 5, characterized in that, Combined with the comprehensive constraint function value obtained in step (5) The correction amount of the control quantity is obtained according to the following formula. : ； in, To obtain the value of the constraint function from the terminal state of the aircraft, To be defined separately in The master and slave spacecraft cooperate to detect configuration function values ​​at these interpolation nodes. This is the partial derivative of the comprehensive constraint function with respect to the sequence of aircraft control variables. This includes constraint functions for the terminal state of the aircraft and constraint functions for the cooperative detection configuration of the master and slave aircraft. As an auxiliary variable; ； in, Is with The corresponding global integration constant matrix, =0、……、 , Let be the partial derivative of the aircraft's terminal state constraint function with respect to its terminal state. For the first i The cooperative detection configuration function is relative to the ( ) N- i The partial derivatives from the aircraft state at each interpolation node, It is a differential approximation matrix, related to the order of the Lagrange interpolation polynomial, and remains a constant matrix during the iteration process. for n × N 3D identity matrix n The number of system state variables.

9. A computer program product, characterized in that, Includes a computer program that, when run, performs the method according to any one of claims 1 to 8.

10. A multi-vehicle system, characterized in that, It includes a master aircraft and at least one slave aircraft, the master aircraft including a controller, the controller of the master aircraft performing the method according to any one of claims 1 to 4 during operation, and the slave aircraft including a controller, the controller of the slave aircraft performing the method according to any one of claims 5 to 8 during operation.

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