High-speed aircraft cooperative guidance method and system under uncontrollable flight speed conditions

Abstract

The present invention discloses a method and system for cooperative guidance of high-speed aircraft under the condition of uncontrollable flight speed. The method comprises: constructing the velocity dynamics equation of the aircraft; designing the variable gain proportional guidance law under the three-dimensional guidance scenario; determining the dynamics equation of the guidance state relative to the remaining flight trajectory length based on the variable gain proportional guidance law and the velocity dynamics equation; predicting and correcting the remaining flight time based on the dynamics equation of the guidance state relative to the remaining flight trajectory length using the improved Euler method; determining the cooperative guidance instructions based on the remaining flight time; and controlling multiple aircraft based on the cooperative guidance instructions. The present invention can realize the precise and simultaneous arrival of multiple high-speed aircraft at a specified position in three-dimensional space under the condition of uncontrollable flight speed.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-aircraft cooperative guidance, and in particular to a method and system for cooperative guidance of high-speed aircraft under the condition that the flight speed is uncontrollable. Background Art

[0002] Collaborative guidance refers to a method that enables multiple aircraft to reach a designated location at the same time. In the military field, collaborative guidance can improve the survival probability and damage effectiveness of weapon systems by saturating enemy defense systems; in the civilian field, collaborative guidance can be used to achieve the simultaneous assembly of multiple drones in a designated area. Therefore, multi-aircraft collaborative guidance has broad application prospects in both military and civilian fields, and has received more and more attention and research in recent years.

[0003] The focus of multi-aircraft collaborative guidance is how to achieve consistency in arrival time based on the communication network. To this end, existing collaborative guidance methods mostly adopt the following two approaches: one is to assume that the flight speed can be adjusted autonomously as needed. In this case, the collaborative guidance problem can be simplified to a feedback control problem of an all-wheel drive system; the other is to assume that the flight speed remains unchanged throughout the guidance process. In this case, simultaneous arrival can be achieved by simply predicting and correcting the arrival time.

[0004] However, for many aircraft in practice, their flight speed usually cannot be adjusted autonomously as needed, and their size often changes significantly due to the influence of aerodynamic forces. Therefore, studying the problem of multi-aircraft collaborative guidance under conditions of uncontrollable speed has important practical significance. Summary of the invention

[0005] Based on this, the purpose of the present invention is to provide a high-speed aircraft collaborative guidance method and system under the condition of uncontrollable flight speed, so as to realize the precise and simultaneous arrival of multiple high-speed aircraft at a specified position in three-dimensional space under the condition of uncontrollable flight speed.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A high-speed aircraft cooperative guidance method under the condition of uncontrollable flight speed, comprising:

[0008] Construct the velocity dynamics equation of the aircraft;

[0009] Design a variable gain proportional guidance law for three-dimensional guidance scenarios;

[0010] Determining a dynamic equation of a guidance state relative to a remaining flight trajectory length based on the variable gain proportional guidance law and the velocity dynamic equation;

[0011] Based on the dynamic equation of the guidance state relative to the remaining flight trajectory length, the remaining flight time is predicted and corrected using the modified Euler method;

[0012] determining a coordinated guidance instruction based on the remaining flight time;

[0013] A plurality of aircraft are controlled based on the coordinated guidance instructions.

[0014] Optionally, the velocity dynamics equation is expressed as follows:

[0015]

[0016] in, is the velocity V of the ith aircraft i The derivative of S i is the aerodynamic reference area of ​​the ith aircraft, C D0,i is the zero-lift drag coefficient of the ith aircraft, q i is the dynamic pressure of the ith aircraft, m i is the mass of the ith aircraft, K D,i is the lift-induced drag coefficient of the ith aircraft at the aerodynamic drag D, a i is the acceleration vector of the ith aircraft, g i is the local gravitational acceleration of the ith aircraft, g i =[0,0,-g i ] T is the corresponding local gravity acceleration vector, θ i is the velocity height angle of the ith aircraft.

[0017] Optionally, the expression of the variable gain proportional guidance law in the three-dimensional guidance scenario is as follows:

[0018]

[0019] in, For variable gain proportional guidance instructions, is the field of view angle σ with the i-th aircraft i The related function, Ω i is the line of sight rotation velocity vector of the i-th aircraft, V i is the velocity vector of the ith aircraft.

[0020] Optionally, the expression of the dynamic equation of the guidance state relative to the remaining flight trajectory length is as follows:

[0021]

[0022] Among them, x i In the guidance state, D go,i is the remaining flight trajectory length, f(x i ) represents the value of x i The function of is the tangential acceleration of the flight speed of the ith aircraft under the action of drag and gravity, V i is the speed of the ith aircraft, V i is the velocity vector of the ith aircraft, It is a variable gain proportional guidance instruction.

[0023] Optionally, the expression of the aircraft cooperative guidance instruction is as follows:

[0024]

[0025] Among them, a i is the coordinated guidance instruction of the ith aircraft, is the field of view angle σ with the i-th aircraft i The related function, V i is the velocity vector of the i-th aircraft, Ω i is the line of sight rotation velocity vector of the i-th aircraft, a t,i To adjust the bias command size of the remaining flight time, ν i is the unit vector of the bias instruction.

[0026] In view of the above method, the present invention further provides a high-speed aircraft cooperative guidance system under the condition that the flight speed is uncontrollable, comprising:

[0027] The first dynamic equation building module is used to build the velocity dynamic equation of the aircraft;

[0028] Design module, used to design variable gain proportional guidance law in three-dimensional guidance scenario;

[0029] A second dynamic equation building module is used to determine the dynamic equation of the guidance state relative to the remaining flight trajectory length based on the variable gain proportional guidance law and the speed dynamic equation;

[0030] A remaining flight time prediction and correction module, used to predict and correct the remaining flight time using a modified Euler method based on a dynamic equation of the guidance state relative to the remaining flight trajectory length;

[0031] A collaborative guidance instruction determination module, configured to determine a collaborative guidance instruction based on the remaining flight time;

[0032] A control module is used to control multiple aircraft based on the collaborative guidance instructions.

[0033] Optionally, the velocity dynamics equation is expressed as follows:

[0034]

[0035] in, is the velocity V of the ith aircraft i The derivative of S i is the aerodynamic reference area of ​​the ith aircraft, C D0,i is the zero-lift drag coefficient of the ith aircraft, q i is the dynamic pressure of the ith aircraft, m i is the mass of the ith aircraft, K D,i is the lift-induced drag coefficient of the ith aircraft at the aerodynamic drag D, a i is the acceleration vector of the ith aircraft, g i is the local gravitational acceleration of the ith aircraft, g i =[0,0,-g i ] T is the corresponding local gravity acceleration vector, θ i is the velocity height angle of the ith aircraft.

[0036] Optionally, the expression of the variable gain proportional guidance law in the three-dimensional guidance scenario is as follows:

[0037]

[0038] in, For variable gain proportional guidance instructions, is the field of view angle σ with the i-th aircraft i The related function, Ω i is the line of sight rotation velocity vector of the i-th aircraft, V i is the velocity vector of the ith aircraft.

[0039] Optionally, the expression of the dynamic equation of the guidance state relative to the remaining flight trajectory length is as follows:

[0040]

[0041] Among them, x i In the guidance state, D go,i is the remaining flight trajectory length, f(x i ) represents the value of x i The function of is the tangential acceleration of the flight speed of the ith aircraft under the action of drag and gravity, V i is the speed of the ith aircraft, V i is the velocity vector of the ith aircraft, It is a variable gain proportional guidance instruction.

[0042] Optionally, the expression of the aircraft cooperative guidance instruction is as follows:

[0043]

[0044] Among them, a i is the coordinated guidance instruction of the ith aircraft, is the field of view angle σ with the i-th aircraft i The related function, V i is the velocity vector of the i-th aircraft, Ω i is the line of sight rotation velocity vector of the i-th aircraft, a t,i To adjust the bias command size of the remaining flight time, ν i is the unit vector of the bias instruction.

[0045] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0046] (1) According to the variable gain proportional guidance law proposed by the present invention, the remaining flight trajectory length of the aircraft can be explicitly given, and it has higher control efficiency compared with the classical proportional guidance law;

[0047] (2) When the flight speed of the aircraft is affected by external aerodynamic forces and undergoes a large range of passive changes, the present invention can provide an accurate prediction value of the remaining flight time in real time;

[0048] (3) According to the high-speed aircraft collaborative guidance method proposed in the present invention, multiple aircraft can achieve online precise synchronization of the remaining flight time without the need for active control of the flight speed, thereby ensuring simultaneous arrival in three-dimensional space while having better terminal arrival accuracy and less control energy consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0050] Figure 1 A flow chart of a high-speed aircraft cooperative guidance method under the condition of uncontrollable flight speed provided by the present invention;

[0051] Figure 2 It is a three-dimensional collaborative guidance geometric relationship diagram;

[0052] Figure 3 It is the communication topology relationship between the four aircraft in the experimental example;

[0053] Figure 4 are the flight trajectory curves of the four aircraft in the three-dimensional space in the experimental example;

[0054] Figure 5It is the speed change curve of the four aircraft in the experimental example;

[0055] Figure 6 The remaining flight time variation curve of the four aircraft in the experimental example;

[0056] Figure 7 is the field of view angle change curve of the four aircraft in the experimental example;

[0057] Figure 8 This is the change curve of the coordinated guidance instructions of the four aircraft in the experimental example. DETAILED DESCRIPTION

[0058] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0059] The purpose of the present invention is to provide a high-speed aircraft collaborative guidance method and system under the condition of uncontrollable flight speed, so as to realize the precise and simultaneous arrival of multiple high-speed aircraft at a specified position in three-dimensional space under the condition of uncontrollable flight speed.

[0060] The present invention first proposes a variable gain proportional guidance law with an explicit remaining flight trajectory length, then converts the guidance model independent variable into the remaining flight trajectory length, realizes efficient and accurate prediction of the remaining flight time by improving the Euler method, and finally synchronizes the remaining flight time online as a coordination variable based on consistency theory, thereby realizing the precise and simultaneous arrival of multiple high-speed aircraft at a specified position in three-dimensional space, thereby completing the present invention.

[0061] Specifically, the purpose of the present invention is to provide a method for coordinated precision guidance of high-speed aircraft that can achieve simultaneous arrival at designated positions under the condition of uncontrollable flight speed. In this method, a novel variable gain proportional guidance law is first proposed, the remaining flight trajectory length of the law can be explicitly given, and its gain is only related to the field of view angle between the current aircraft and the target position; the independent variable in the guidance model is converted from flight time to the remaining flight trajectory length, and the remaining flight time prediction problem is converted into an initial value problem of an ordinary differential equation, which is efficiently solved online using an improved Euler algorithm; the variable gain proportional guidance law is used as the basic guidance law, and the design of the coordinated guidance law is completed by introducing a bias term for the remaining flight time feedback based on the consistency theory.

[0062] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0063] Embodiment 1

[0064] like Figure 1 As shown, the high-speed aircraft cooperative guidance method under the condition of uncontrollable flight speed provided by the present invention comprises the following steps:

[0065] Step 101: Construct the velocity dynamics equation of the aircraft.

[0066] The present invention considers a scenario in which M high-speed aircrafts cooperate to reach the same target location. Figure 2 The guidance geometry relationship between the i-th aircraft and the target position is given, where XYZ and X′Y′Z′ represent the inertial coordinate system and the quasi-inertial coordinate system, respectively. i represents the velocity vector of the i-th aircraft, and the corresponding velocity height angle and azimuth angle are denoted as θ i and φ i . R i represents the sight vector between the i-th aircraft and the target position, and the field of view angle σ i is the speed V i and sight R i The guidance command of the aircraft is a i , direction and speed V i vertical, whose components in the yaw and pitch channels are a y,i and a z,i .

[0067] In order to facilitate the design of cooperative guidance methods, the communication topology between aircraft is composed of an undirected graph describe, It is a collection of aircraft. is a collection of communication connections. Definition graph The adjacency matrix of If aircraft i can receive information from aircraft j, then a ij =1, otherwise a ij = 0. For an undirected graph, the adjacency matrix is ​​symmetric. In the present invention, it is assumed that the undirected graph The communication topology is connected, that is, there is at least one path between any two aircraft.

[0068] In engineering practice, due to the influence of drag and gravity, the flight speed of the aircraft is uncontrollable. Define the speed of aircraft i as V i =||V i ||, its dynamic equation can be expressed as:

[0069]

[0070] Among them, m irepresents the mass of aircraft i, g i represents the local gravitational acceleration of aircraft i, which is usually related to the flight altitude, D i =C D,i q i S i represents the aerodynamic drag on aircraft i, S i is the aerodynamic reference area, C D,i is the aerodynamic drag coefficient, q i =0.5ρ i V i 2 is the dynamic pressure, ρ i is the local atmospheric density. For a side-slip turn controlled aircraft, its space guidance command is achieved through the simultaneous action of lift and gravity, so the lift is required to satisfy:

[0071] L i =m i ||a i -g i || (2)

[0072] Among them, L i =C L,i q i S i represents the required lift of aircraft i, C L,i is the lift coefficient, g i =[0,0,-g i ] T is the local gravity acceleration vector pointing vertically downward. According to the drag polar curve model, the relationship between the drag coefficient and the lift coefficient can be expressed as:

[0073]

[0074] Among them, C D0,i Indicates the zero-lift drag coefficient, K D,i represents the lift-induced drag coefficient. According to equations (1) to (3), the dynamic equation of the aircraft speed can be summarized as:

[0075]

[0076] Step 102: Design a variable gain proportional guidance law in a three-dimensional guidance scenario.

[0077] In order to enable multiple high-speed aircraft to arrive at the same target position at the same time, the present invention first proposes a novel variable gain proportional guidance law to give priority to the purpose of reaching the target position, and then accurately predicts the remaining flight time of the variable gain proportional guidance law by converting the model independent variable into the remaining flight trajectory length. On this basis, the remaining flight time is synchronized online based on the consistency theory to complete the design of the three-dimensional collaborative guidance law.

[0078] The variable gain proportional guidance law in the three-dimensional guidance scenario is designed as:

[0079]

[0080] in, is the field of view of aircraft i, is the field of view angle σ i Related functions, N>2 is the guidance parameter; is the line of sight rotation velocity vector, R i =||R i || is the relative distance between the aircraft i and the target position. According to formula (5), the gain of the improved proportional guidance law is is time-varying and only depends on the field of view angle σ i In addition, under the action of the time-varying gain proportional guidance law, the aircraft will always contain R i and V i Movement on the guidance plane.

[0081] Step 103: Based on the variable gain proportional guidance law and the speed dynamics equation, determine the dynamics equation of the guidance state relative to the remaining flight trajectory length.

[0082] For the variable gain proportional guidance law of formula (5), the remaining flight trajectory length D go,i It can be calculated by the following formula:

[0083]

[0084] Since the flight speed is always tangent to the flight trajectory, the remaining flight time t go,i It can be expressed as:

[0085]

[0086] However, since the dynamic equation (4) for velocity magnitude is highly coupled and nonlinear, the above equation cannot be solved analytically. Therefore, we will seek to design an efficient numerical prediction method for the remaining flight time.

[0087] Define the guidance state as Then, under the variable gain proportional guidance law of formula (5), the guidance state x i Relative to the remaining flight path length D go,i The kinetic equation can be expressed as:

[0088]

[0089] Among them, f(x i ) represents the value of x iThe function of According to formula (5), the guidance state x i To obtain, represents the tangential acceleration of the flight speed under the action of drag and gravity, The a in formula (4) can be i Replace with To obtain.

[0090] Step 104: Based on the dynamic equation of the guidance state relative to the remaining flight trajectory length, the remaining flight time is predicted and corrected using the improved Euler method.

[0091] The guidance state of aircraft i at the current moment is expressed as The remaining flight path length at the current moment It can be calculated by formula (6), so the remaining flight time prediction problem under speed change can be transformed into the initial value problem of ordinary differential equation (8), which can be solved by a variety of different numerical integration methods. Considering the trade-off between calculation accuracy and solution efficiency, the present invention adopts the improved Euler method to predict the remaining flight time online. To this end, the continuous remaining flight trajectory length is The interval is discretized into K equal parts, and the step length between adjacent discrete points is Then the remaining flight trajectory length after discretization can be expressed as And meet Accordingly, the aircraft guidance state at the discrete point can be expressed as And meet The improved Euler method includes two steps: prediction and correction. In the prediction step, the Euler method is used according to predict Right now:

[0092]

[0093] In the correction step, the trapezoidal method is used to calculate The corrected value is:

[0094]

[0095] According to equations (9) and (10), given the current guidance state It is possible to obtain the value of any k∈{1,...,K} by iterative calculation. Finally, the remaining time of the variable gain proportional guidance law can be predicted as:

[0096]

[0097] According to equations (6) and (7), the remaining flight time t can be obtained go,i The derivative of is:

[0098]

[0099] Step 105: Determine a coordinated guidance instruction based on the remaining flight time.

[0100] In order to achieve the consistency of the remaining flight time, the cooperative guidance instruction is designed as a variable gain proportional guidance law additional bias instruction, that is:

[0101]

[0102] Among them, a t,i To adjust the bias command size of the remaining flight time, ν i is the unit vector of the offset command. In order to make the aircraft still move on the original guidance plane under the action of the cooperative guidance law, the direction of the offset command should be consistent with the direction of the variable gain proportional guidance command, that is:

[0103]

[0104] Under the action of the collaborative guidance instruction (13), the field of view angle σ can be obtained i The derivative of is:

[0105]

[0106] According to equations (12) and (14), we can get t go,i The derivative of is:

[0107]

[0108] For the i-th aircraft, the local error of the remaining flight time is defined as:

[0109]

[0110] According to the remaining flight time prediction value obtained by formula (11) and the remaining flight time dynamic equation of formula (15), the bias instruction a is designed t,i for:

[0111]

[0112] Among them, κ>3 is the guidance parameter, ψ(σ i ) is about σ i The function is of the form:

[0113]

[0114] Among them, μ>1, σ m >0 is a positive constant. In the present invention, the function ψ(σ i) is to avoid the field angle σ i When it is close to zero, the singularity of guidance instructions may be caused. According to L’Hôpital’s rule, we can get:

[0115]

[0116] Therefore, when the field angle σ i When approaching zero, the bias command a t,i tends to zero, at which point the cooperative guidance law (13) degenerates into the variable gain proportional guidance law (5). The closed-loop stability of the designed cooperative guidance law can be guaranteed by the consistency theory, and the consistency convergence time of the residual flight time error can be adjusted by changing the value of κ. The larger the value of κ, the faster the convergence time.

[0117] The cooperative guidance command calculated according to formula (13) is in the form of a space vector. From the perspective of engineering practice, it needs to be further decomposed into yaw and pitch channels to obtain the cooperative guidance command components under each channel:

[0118]

[0119] Among them, a i It is calculated by equation (13) and equation (17). So far, the calculation of the coordinated guidance command is completed.

[0120] Step 106: Control multiple aircraft based on the coordinated guidance instructions.

[0121] By applying the calculated guidance instructions to each aircraft, multiple high-speed aircraft will be able to accurately reach the designated target position simultaneously along their respective flight trajectories.

[0122] Embodiment 2

[0123] In order to execute the method corresponding to the above embodiment 1 to achieve the corresponding functions and technical effects, a high-speed aircraft cooperative guidance system under the condition of uncontrollable flight speed is provided below, including:

[0124] The first dynamic equation building module is used to build the velocity dynamic equation of the aircraft;

[0125] Design module, used to design variable gain proportional guidance law in three-dimensional guidance scenario;

[0126] A second dynamic equation building module is used to determine the dynamic equation of the guidance state relative to the remaining flight trajectory length based on the variable gain proportional guidance law and the speed dynamic equation;

[0127] A remaining flight time prediction and correction module, used to predict and correct the remaining flight time using a modified Euler method based on a dynamic equation of the guidance state relative to the remaining flight trajectory length;

[0128] A collaborative guidance instruction determination module, configured to determine a collaborative guidance instruction based on the remaining flight time;

[0129] A control module is used to control multiple aircraft based on the collaborative guidance instructions.

[0130] Experimental example

[0131] Table 1 Initial conditions of the four aircraft in the experimental example

[0132]

[0133] A numerical simulation is performed on a guidance scenario in which four high-speed aircraft numbered 1-4 cooperate to reach the origin position in three-dimensional space. The guidance instructions of each aircraft are calculated according to the high-speed aircraft cooperative precision guidance method under the condition of uncontrollable flight speed provided in the present invention. The communication topology relationship between the four aircraft is as follows: Figure 3 In this experimental example, the initial conditions of each high-speed aircraft are shown in Table 1, and the structural and aerodynamic parameters are m i =200kg, S i =0.4m 2 , C D0,i =0.04 and K D,i =0.1, The atmospheric density and local gravity acceleration are actual models that vary with flight altitude. The guidance parameters in the designed collaborative guidance method are selected as N = 4, κ = 6, σ m =5°, μ=2 and K=200, the pitch and yaw channel guidance command limit is 100m / s 2 .

[0134] In the experimental example, the following results are obtained through simulation:

[0135] (1) The flight trajectory curves of the four aircraft in three-dimensional space, such as Figure 4 As shown in;

[0136] (2) The flight speed of the four aircraft changes with time, such as Figure 5 As shown in;

[0137] (3) The remaining flight time variation curves of the four aircraft, such as Figure 6 As shown in;

[0138] (4) Curves of the field of view angles of the four aircraft changing with time, such as Figure 7 As shown in;

[0139] (5) The time-varying curves of the coordinated guidance commands of the four aircraft in the pitch and yaw channels, such as Figure 8 as shown in .

[0140] Depend on Figure 4 It can be seen that, although the initial conditions are very different, after utilizing the method provided in the present invention, multiple aircraft can accurately and simultaneously reach the designated target position in three-dimensional space.

[0141] Depend on Figure 5 It can be seen that under the influence of aerodynamic drag and gravity, the flight speed of each aircraft varies in a large range, especially for the fourth aircraft, the flight speed variation range exceeds 150m / s. Therefore, the existing collaborative guidance law based on the constant speed assumption is not suitable for the actual scenario considered.

[0142] Depend on Figure 6 It can be seen that under the action of the provided collaborative precision guidance method, multiple aircraft can overcome the adverse effects brought about by the large-scale changes in flight speed and achieve consistent convergence of the remaining flight time in a relatively short time. After the error converges, the collaborative guidance law degenerates into a variable gain proportional guidance law.

[0143] Depend on Figure 7 It can be seen that the field of view angle of each aircraft finally converges to zero, that is, the speed direction of the aircraft will eventually point to the target. This result is beneficial to improving the terminal position accuracy and reducing the terminal energy consumption.

[0144] Depend on Figure 8 It can be seen that the initial guidance instructions of each aircraft are large to achieve rapid convergence of the remaining flight time error. Then the guidance instructions decrease rapidly and remain in a small range until reaching the target position. Finally, the guidance instructions converge to zero, and the energy consumption is reasonably distributed, which is conducive to engineering applications.

[0145] The experimental example verifies the effectiveness of the high-speed aircraft coordinated precision guidance method under the condition of uncontrollable flight speed provided in the present invention.

[0146] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0147] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for cooperative guidance of high-speed aircraft under the condition of uncontrollable flight speed, characterized in that: include: Construct the velocity dynamics equation of the aircraft; Design a variable gain proportional guidance law for three-dimensional guidance scenarios; Determining a dynamic equation of a guidance state relative to a remaining flight trajectory length based on the variable gain proportional guidance law and the velocity dynamic equation; Based on the dynamic equation of the guidance state relative to the remaining flight trajectory length, the remaining flight time is predicted and corrected using the modified Euler method; determining a coordinated guidance instruction based on the remaining flight time; controlling a plurality of aircraft based on the collaborative guidance instructions; Among them, the expression of the aircraft cooperative guidance instruction is as follows: Among them, a i is the coordinated guidance instruction of the i-th aircraft, is the field of view angle σ with the i-th aircraft i The related function, V i is the velocity vector of the ith aircraft, Ω i is the line of sight rotation velocity vector of the i-th aircraft, a t,i To adjust the bias command size of the remaining flight time, ν i is the unit vector of the bias instruction; The direction of the bias command should be consistent with the direction of the variable gain proportional guidance command, that is: Among them, U i is the speed of the ith aircraft, R i =||R i || is the relative distance between aircraft i and the target position; Design bias instruction a t,i for: Where N is the guidance parameter, t go,i is the predicted value of the remaining flight time of the ith aircraft, and the predicted value of the remaining flight time of the ith aircraft t go,i The derivative of is: For the i-th aircraft, define the local error e of the remaining flight time i for: Among them, t go,j is the predicted value of the remaining flight time of the jth aircraft, a ij is the adjacency matrix, κ>3 is the guidance parameter, ψ(σ i ) is about σ i The function is of the form: Among them, μ>1, σ m >0 is a normal number.

2. The method for high-speed aircraft cooperative guidance under uncontrollable flight speed conditions according to claim 1, characterized in that: The expression of the velocity dynamics equation is as follows: in, is the speed U of the i-th aircraft i The derivative of S i is the aerodynamic reference area of ​​the ith aircraft, C D0,i is the zero-lift drag coefficient of the ith aircraft, q i is the dynamic pressure of the ith aircraft, m i is the mass of the ith aircraft, K D,i is the lift-induced drag coefficient of the ith aircraft at the aerodynamic drag D, a i is the acceleration vector of the ith aircraft, g i is the local gravitational acceleration of the ith aircraft, g i =[0,0,-g i ] T is the corresponding local gravity acceleration vector, θ i is the velocity height angle of the ith aircraft.

3. The method for high-speed aircraft cooperative guidance under uncontrollable flight speed conditions according to claim 1, characterized in that: The expression of the variable gain proportional guidance law in the three-dimensional guidance scenario is as follows: in, For variable gain proportional guidance instructions, is the field of view angle σ with the i-th aircraft i The related function, Ω i is the line of sight rotation velocity vector of the i-th aircraft, V i is the velocity vector of the ith aircraft.

4. The method for cooperative guidance of high-speed aircraft under uncontrollable flight speed conditions according to claim 1, characterized in that: The expression of the dynamic equation of the guidance state relative to the remaining flight trajectory length is as follows: Among them, x i In the guidance state, D go,i is the remaining flight trajectory length, f(x i ) represents the value of x i The function of is the tangential acceleration of the flight speed of the ith aircraft under the action of drag and gravity, U i is the speed of the ith aircraft, V i is the velocity vector of the ith aircraft, It is a variable gain proportional guidance instruction.

5. A high-speed aircraft cooperative guidance system under the condition of uncontrollable flight speed, characterized in that: include: The first dynamic equation building module is used to build the velocity dynamic equation of the aircraft; Design module, used to design variable gain proportional guidance law in three-dimensional guidance scenario; A second dynamic equation building module is used to determine the dynamic equation of the guidance state relative to the remaining flight trajectory length based on the variable gain proportional guidance law and the speed dynamic equation; A remaining flight time prediction and correction module, used to predict and correct the remaining flight time using a modified Euler method based on a dynamic equation of the guidance state relative to the remaining flight trajectory length; A collaborative guidance instruction determination module, configured to determine a collaborative guidance instruction based on the remaining flight time; A control module, configured to control a plurality of aircraft based on the collaborative guidance instructions; Among them, the expression of the aircraft cooperative guidance instruction is as follows: Among them, a i is the coordinated guidance instruction of the i-th aircraft, is the field of view angle σ with the i-th aircraft i The related function, V i is the velocity vector of the ith aircraft, Ω i is the line of sight rotation velocity vector of the i-th aircraft, a t,i To adjust the bias command size of the remaining flight time, ν i is the unit vector of the bias instruction; The direction of the bias command should be consistent with the direction of the variable gain proportional guidance command, that is: Among them, U i is the speed of the ith aircraft, R i =||R i || is the relative distance between aircraft i and the target position; Design bias instruction a t,i for: Where N is the guidance parameter, t go,i is the predicted value of the remaining flight time of the ith aircraft, and the predicted value of the remaining flight time of the ith aircraft t go,i The derivative of is: For the i-th aircraft, define the local error e of the remaining flight time i for: Among them, t go,j is the predicted value of the remaining flight time of the jth aircraft, a ij is the adjacency matrix, κ>3 is the guidance parameter, ψ(σ i ) is about σ i The function is of the form: Among them, μ>1, σ m >0 is a normal number.

6. The high-speed aircraft cooperative guidance system under the condition of uncontrollable flight speed according to claim 5, characterized in that: The expression of the velocity dynamics equation is as follows: in, is the speed U of the i-th aircraft i The derivative of S i is the aerodynamic reference area of ​​the ith aircraft, C D0,i is the zero-lift drag coefficient of the ith aircraft, q i is the dynamic pressure of the ith aircraft, m i is the mass of the ith aircraft, K D,i is the lift-induced drag coefficient of the ith aircraft at the aerodynamic drag D, a i is the acceleration vector of the ith aircraft, g i is the local gravitational acceleration of the ith aircraft, g i =[0,0,-g i ] T is the corresponding local gravity acceleration vector, θ i is the velocity height angle of the ith aircraft.

7. The high-speed aircraft cooperative guidance system under the condition of uncontrollable flight speed according to claim 5, characterized in that: The expression of the variable gain proportional guidance law in the three-dimensional guidance scenario is as follows: in, For variable gain proportional guidance instructions, is the field of view angle σ with the i-th aircraft i The related function, Ω i is the line of sight rotation velocity vector of the i-th aircraft, V i is the velocity vector of the ith aircraft.

8. The high-speed aircraft cooperative guidance system under uncontrollable flight speed conditions according to claim 5, characterized in that: The expression of the dynamic equation of the guidance state relative to the remaining flight trajectory length is as follows: Among them, x i In the guidance state, D go,i is the remaining flight trajectory length, f(x i ) represents the value of x i The function of is the tangential acceleration of the flight speed of the ith aircraft under the action of drag and gravity, U i is the speed of the ith aircraft, V i is the velocity vector of the ith aircraft, It is a variable gain proportional guidance instruction.

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