A high-speed aircraft cluster cooperative guidance method based on space-time synchronous attractor domain

Abstract

The application designs a high-speed aircraft cluster cooperative guidance method based on space-time synchronous attraction domain. An artificial potential field is designed to keep a proper distance between aircrafts, avoid collision while gathering; a speed matching item is designed based on consistency theory to realize dynamic consistency of aircraft speed; a guidance law based on resistance acceleration-speed profile is designed to meet the cooperative requirements of terminal range, height, speed and other aircrafts, and the combination of the three realizes efficient autonomous clustering and guidance of the aircraft. The application can make the aircraft cluster reach the target point with high precision under the conditions of meeting complex constraints such as heat flow, overload, dynamic pressure, collision avoidance, clustering, dynamic consistency of speed and the like through the design of attraction domain, angle of attack and roll angle control.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of aircraft guidance and control, and relates to a high-speed aircraft cooperative guidance method based on a space-time synchronous attractive domain, which is used for realizing cooperative flight and high-precision arrival at a target point of a high-speed aircraft cluster. BACKGROUND

[0002] The high-speed aircraft refers to an aircraft with a flight speed of more than 5 Mach, and the high-speed aircraft can control the aircraft by relying on aerodynamic lift and drag without the thrust of its own engine, so as to realize non-ballistic flight with long distance and large range.

[0003] The high-speed aircraft cluster flight refers to that multiple aircrafts replace the traditional single individual in a cluster cooperative manner, and utilize the group advantage to more effectively complete the scheduled task, for example, in the military field, the cooperative flight of the high-speed aircraft cluster can realize saturation attack on enemy targets and improve the damage efficiency on high-value and high-protection targets.

[0004] However, compared with low-speed aircrafts such as unmanned aerial vehicles, the cooperative flight of the high-speed aircraft cluster has the following difficulties: 1. The flight airspace and speed span are large, and the aerodynamic drag is dynamically time-varying; 2. The aircraft does not have power, and it is difficult to realize acceleration and constant speed flight, so the relative position and speed cooperation are difficult; 3. The complex constraints such as heat flow, overload, dynamic pressure, collision avoidance, cluster, speed dynamic consistency need to be considered. Therefore, the research on the cooperative guidance method of the high-speed aircraft in the complex environment has important significance and research value for supporting the saturation attack of the high-speed aircraft and improving the guidance precision and cooperative ability of the cluster in the complex environment. SUMMARY

[0005] The technical problem solved by the application is to overcome the shortcomings of the prior art, and a high-speed aircraft cooperative guidance method based on a space-time synchronous attractive domain is provided, which can enable the aircraft cluster to arrive at a target point with high precision under the condition of meeting complex constraints such as heat flow, overload, dynamic pressure, collision avoidance, cluster, and speed dynamic consistency through attractive domain design, attack angle and roll angle control.

[0006] The technical scheme of the application is: a high-speed aircraft cluster cooperative guidance method based on a space-time synchronous attractive domain, characterized by comprising:

[0007] The upper limit and the lower limit of the distance between the aircraft clusters are set, and the relative position between the high-speed aircraft clusters is controlled in real time;

[0008] The average speed and average acceleration of the aircraft cluster are calculated as the expected speed and expected acceleration of the aircraft cluster; the difference between the speed and acceleration of the aircraft cluster and the expected speed and acceleration of the corresponding aircraft cluster is calculated, and the weighted sum of the difference vectors is taken as the speed matching term, which is applied to the high-speed aircraft to achieve the predetermined speed and acceleration;

[0009] The expected flight distance between the aircraft cluster and the target point is calculated; the heat flow, overload, dynamic pressure constraints and quasi-equilibrium gliding conditions during the flight of the aircraft cluster are converted into flight resistance constraints; the resistance acceleration-speed profile of the aircraft cluster is designed according to the remaining flight distance, the expected flight distance and the flight resistance constraints; a closed-loop guidance law is designed to make the aircraft cluster fly according to the designed resistance acceleration-speed profile, and the size of the aircraft cluster's roll angle is calculated; the heading angle error corridor is designed, and the sign of the aircraft cluster's roll angle is calculated; the flight guidance term is designed according to the size of the roll angle and the sign of the roll angle, so that the aircraft cluster reaches the target point.

[0010] The upper and lower limits of the distance between the aircraft clusters are set to control the relative positions of the high-speed aircraft clusters in real time, which includes:

[0011] The relative distance between the aircraft clusters is determined, and the upper and lower limits of the distance between the aircraft clusters are set to keep the aircraft clusters from colliding with each other while keeping them within the communication range and gathering;

[0012] An artificial potential function is designed; the artificial potential function is a non-negative continuous derivable function with respect to the distance between adjacent aircraft, which behaves as a repulsive force when the distance between adjacent aircraft is less than the lower limit, and behaves as an attractive force when the distance between adjacent aircraft is greater than the upper limit;

[0013] The artificial potential field force is solved according to the artificial potential function and the determined relative distance between adjacent aircraft, and the superposition of the artificial potential field forces between multiple aircraft in the aircraft cluster is considered, so that the artificial potential field force acting on any aircraft in the cluster is the resultant force of the artificial potential field forces generated by all other adjacent aircraft; the artificial potential field force is used to control the position of the aircraft in real time.

[0014] The upper limit of the distance between the aircraft is set to 20 km, and the lower limit of the distance between the aircraft is set to 0.5 km.

[0015] The calculation formula of the artificial potential function is:

[0016]

[0017] In the formula, r is the relative distance between two adjacent aircraft, r0 is the action distance when the artificial potential field force is 0, and f(r) is the artificial potential field force, is the artificial potential function.

[0018] The calculation formula of the artificial potential force is:

[0019]

[0020] In the formula, f0 is the amplitude of the artificial potential force when the relative distance of two adjacent aircrafts is 0, and s3(r) is the artificial potential force base function, and the calculation formula thereof is

[0021]

[0022] s3(r)=s2(r)r+(r a +r b )s1(r) / 2

[0023] wherein r a is the left boundary of the step interval, r b is the right boundary of the step interval, k1 is a variable for adjusting the steepness of the step interval, s1(r) and s2(r) are intermediate variables, the superposition of the artificial potential forces of multiple aircrafts in the cluster is considered, and the calculation formula of the artificial potential force received by the i-th aircraft is:

[0024]

[0025] wherein f i1 is the total artificial potential force received by the i-th aircraft, f ij is the artificial potential force received by the i-th aircraft by the j-th aircraft, ||x i -x j || is the distance between the i-th aircraft and the j-th aircraft, and N is the number of aircrafts in the cluster.

[0026] The calculation formula of the speed matching term is:

[0027]

[0028] wherein f i2 is the speed matching term of the i-th aircraft, a ij is the weighted coefficient of the speed matching term of the i-th aircraft and the j-th aircraft, which can be adjusted according to the speed matching effect, V i is the speed of the i-th aircraft, V j is the speed of the j-th aircraft, D i is the resistance acceleration of the i-th aircraft, and D j is the resistance acceleration of the j-th aircraft.

[0029] The calculation formula of the expected flight distance is:

[0030]

[0031] wherein, is the current latitude of the aircraft fleet, λ is the current longitude of the aircraft fleet, is the target latitude of the aircraft fleet, λ f is the target longitude of the aircraft fleet, R earth is the Earth radius.

[0032] The conversion of the heat flux, overload, dynamic pressure constraints and quasi- equilibrium glide conditions into flight resistance constraints:

[0033]

[0034] wherein, D qmax is the heat flux constraint of the aircraft, Q is the maximum dynamic pressure allowed by the aircraft, ρ0 is the atmospheric density, V is the speed of the aircraft, S is the reference area of the aircraft, C D is the drag coefficient of the aircraft, R n is the radius of curvature of the aircraft stagnation point, k q is the heat flux rate coefficient;

[0035] D nymax = n ymax gC D / C L

[0036] wherein, D nymax is the maximum overload constraint of the aircraft, g is the gravitational acceleration, C D ,C L are the lift and drag coefficients of the aircraft;

[0037] D cpmax = cp max SC D / m

[0038] wherein, D cpmax is the maximum dynamic pressure constraint of the aircraft, m is the mass of the aircraft;

[0039] D eg = (g-V 2 / r)C D / C L

[0040] wherein, D eg is the maximum quasi-equilibrium glide constraint of the aircraft, r is the distance of the aircraft to the Earth center.

[0041] The form of the resistance acceleration-velocity profile is a piecewise linear function, and its calculation formula is:

[0042]

[0043] Wherein, D is the aircraft drag acceleration-velocity profile, C1-C5 are constant parameters of the drag acceleration-velocity profile.

[0044] The lift-drag ratio calculation formula of the aircraft tracking drag acceleration-velocity profile is:

[0045]

[0046] In the formula (L / D) C is the lift-drag ratio required by the longitudinal guidance, (L / D)0 is the lift-drag ratio required by the planned standard drag acceleration-velocity profile, D and D0 are the drag accelerations of the actual flight and the standard orbit respectively, are the height change rates of the actual flight and the standard orbit respectively; f1, f2, f3 and f4 are variable gain coefficients calculated from the standard orbit.

[0047] The lift-drag ratio (L / D)0 required by the planned standard drag acceleration-velocity profile is specifically:

[0048]

[0049] The height change rate of the standard orbit is:

[0050]

[0051] Wherein, D, are the drag acceleration and its first and second order derivatives respectively, C D , are the drag coefficient and its first and second order derivatives respectively, h s =-7110 represents a constant related to atmospheric parameters;

[0052] The calculation formula of the roll angle is:

[0053] σ=arccos((L / D) C / (L / D))).

[0054] When the error between the heading angle of the high-speed aircraft and the heading angle of the line connecting the high-speed aircraft and the missile exceeds the heading angle error corridor, the sign of the roll angle of the high-speed aircraft is reversed, and the method for calculating the sign of the aircraft cluster roll angle is:

[0055]

[0056] In the formula: Δψ corridor is the width of the heading angle error corridor; Δψ out >Δψ in >0 are the outer boundary and inner boundary widths of the heading angle error corridor respectively; V a and V bis a parameter to be set; when the aircraft heading angle error exceeds the boundary of the aircraft heading angle error corridor, the aircraft roll angle is reversed, i.e. the sign is changed;

[0057] The sign of the aircraft cluster roll angle is determined by the heading angle error corridor as follows:

[0058]

[0059] wherein T hor is a lateral guidance period, and the heading angle error Δψ is defined as the deviation of the aircraft heading angle ψ and the aircraft line-of-sight angle Φ:

[0060] Δψ = ψ - Φ

[0061] The aircraft heading angle ψ is obtained by spherical triangle:

[0062]

[0063] The calculation formula of the flight guidance term is as follows:

[0064] f i3 = L i cos(σ i )

[0065] wherein f i3 is the flight guidance term of the i-th aircraft, L i is the lift of the i-th aircraft.

[0066] Compared with the prior art, the present application has the following advantages:

[0067] The present application designs a high-speed aircraft cluster cooperative guidance method based on space-time synchronous attractive domain. By designing an artificial potential field, the aircrafts maintain a proper distance and avoid collision while gathering; based on the consistency theory, a speed matching term is designed to realize the dynamic consistency of the aircraft speed; a guidance law based on the resistance acceleration-speed profile is designed to meet the cooperative requirements of the terminal range, height and speed of the aircraft, and the combination of the three effectively solves the cooperative guidance problem of the high-speed aircraft cluster under the cooperative conditions of considering aerodynamic resistance, collision avoidance and cluster constraints, and dynamic consistency of speed. BRIEF DESCRIPTION OF DRAWINGS

[0068] Figure 1 is a flow chart of the method of the present application. DETAILED DESCRIPTION

[0069] The high-speed vehicle cluster needs to meet three index requirements during flight, one is that the distance between the clusters needs to be kept in a suitable interval, two is that the speed of the cluster needs to be kept dynamic consistent during flight, three is that the cluster needs to accurately arrive at the target position. Therefore, the high-speed vehicle cluster cooperative guidance is to adjust the attack angle and the roll angle of the vehicle to adjust the size and direction of the aerodynamic force, so that the vehicle cluster cooperatively flies under the condition of meeting the index requirements.

[0070] As shown in Figure 1 The application designs a high-speed vehicle cluster cooperative guidance method based on space-time synchronous attractive domain. The artificial potential field is designed to keep the appropriate distance between the vehicles, avoid collision while gathering; the speed matching term is designed based on the consensus theory to realize the dynamic consistency of the speed of the vehicles; the guidance law based on the resistance acceleration-speed profile is designed to meet the cooperative requirements of the terminal range, height and speed of the vehicles. The specific method is as follows:

[0071] (1) Control the relative position between the high-speed vehicle clusters

[0072] The motion environment of the high-speed vehicle cluster is designed as an artificial potential field, and various constraints during flight (such as keeping a certain distance between the vehicles, avoiding collision; the distance between the vehicles should not be too far, the whole group should be kept together, and the communication range should be avoided) are converted into attractive and repulsive positions designed according to certain rules. The high-speed vehicle cluster keeps the appropriate distance under the action of the combined force of attraction and repulsion. The specific steps are as follows:

[0073] (a) In order to avoid the aerodynamic flow field of the high-speed vehicle cluster interfering with each other, the lower limit of the distance between the vehicles is set to 0.5km, and in order to avoid the communication interruption between the high-speed vehicle clusters, the upper limit of the distance between the vehicles is set to 20km.

[0074] (b) The design of the artificial potential function usually imitates the real gravitational field or electromagnetic field in physics, or can be constructed into any form that meets the conditions according to actual needs. In order to keep the appropriate distance between the high-speed vehicle clusters, the construction of the artificial potential function needs to meet the following requirements: the potential function V(r) is a non-negative continuous derivable function about the distance r between adjacent vehicles; when r→0, the potential function V(r)→∞, the potential field force between the vehicles behaves as a repulsive force to avoid collision; when r=r0, that is, the distance between the vehicles is equal to the expected distance, the potential function V(r) is at the minimum point, and the potential field force f1=0; when r>r0, within a small range, the potential field force between the vehicles should behave as an attractive force to keep the high-speed vehicle cluster gathered; when r→∞, the potential field force f1 should converge to a small constant c2 to ensure that the vehicles with a relatively long distance maintain a certain attractive force while reducing the influence of mutual interference.

[0075] (c) Design the artificial potential force function based on hyperbolic tangent function.

[0076] Artificial potential force base function s1(r)

[0077]

[0078] Artificial potential force base function s2(r)

[0079]

[0080] wherein, r a , r b are the left and right boundaries of the step interval, s1(r), s2(r) are intermediate variables, and k1 is a variable for adjusting the steepness of the step interval, which can be taken as k1 = 3.5 in general cases.

[0081] Artificial potential force base function s3(r)

[0082] s3(r) = s2(r) r + (r a + r b ) s1(r) / 2

[0083] The artificial potential force function designed for the spring-like force is as follows

[0084]

[0085] wherein, r is the distance between two adjacent aircrafts, r0 is the action distance when the artificial potential force is 0, and f0 is the amplitude of the artificial potential force when the relative distance between two adjacent aircrafts is 0.

[0086] Considering the superposition of artificial potential forces of multiple aircrafts in the cluster, the i-th aircraft is in the cluster and receives the resultant force of the artificial potential forces generated by all other adjacent aircrafts.

[0087]

[0088] wherein, f i1 is the total artificial potential force received by the i-th aircraft, f ij is the artificial potential force received by the i-th aircraft from the j-th aircraft, ||x i -x j || is the distance between the i-th aircraft and the j-th aircraft, and N is the number of aircrafts in the cluster.

[0089] (2) High-speed aircraft cluster relative velocity and acceleration control strategy

[0090] The velocity matching is used to make the vehicles have the same motion tendency. The velocity and acceleration of the vehicles are adjusted according to the velocity and acceleration of the neighbors, so that the velocity of the vehicles is dynamically consistent.

[0091] (a) According to the vector superposition principle, the average velocity and acceleration of the neighbors are calculated and used as the expected velocity and acceleration of the cluster;

[0092] (b) In the actual calculation, the velocity matching item of the i-th vehicle is calculated as the weighted sum of the velocity vector difference between the i-th vehicle and the j-th vehicle, as shown in the following formula:

[0093]

[0094] wherein f i2 is the velocity matching item of the i-th vehicle, a ij is the weighted coefficient of the velocity matching item of the i-th vehicle and the j-th vehicle, which can be adjusted according to the velocity matching effect, V i is the velocity of the i-th vehicle, V j is the velocity of the j-th vehicle, D i is the drag acceleration of the i-th vehicle, and D j is the drag acceleration of the j-th vehicle. In the process of motion of the high-speed vehicle cluster, the relative position changes, and the neighbor relationship between the vehicles changes. When a vehicle enters or exits the neighbor of another vehicle, the effect of the velocity matching item will appear or disappear. Through the second-order smooth step function, the change process can be smooth, avoiding the sudden change of force, which is beneficial to the stable formation keeping.

[0095] (3) Guidance strategy of high-speed vehicle cluster

[0096] The high-speed vehicles not only need to keep the relative state coordination, but also need to accurately reach the target point under the flight constraint conditions such as heat flow, dynamic pressure, and overload. Therefore, it can be assumed that the high-speed vehicles track a virtual leader on the basis of collision avoidance, cluster, and dynamic consistency of velocity. The state quantity and control quantity of the virtual leader are solved through the guidance law based on the drag acceleration-velocity profile. The guidance of the virtual leader is divided into longitudinal guidance and lateral guidance. The longitudinal guidance mainly generates the reference drag acceleration profile through the range prediction, and obtains the control quantity by tracking the reference drag acceleration profile based on the feedback linearization theory, so as to meet the requirements of the range, height, and velocity at the handover point. The lateral guidance is to ensure that the virtual leader flies to the target point by designing the lateral heading error corridor. In the flight process, the virtual leader broadcasts its position and velocity information in real time, and the high-speed vehicle cluster tracks the virtual leader through the design of the flight guidance item.

[0097] (a) First, the expected flight distance between the virtual leader and the target point is calculated, denoted as follows:

[0098]

[0099] wherein, is the current latitude of the fleet of aircraft, and λ is the current longitude of the fleet of aircraft, is the latitude of the target point of the fleet of aircraft, and λ f is the longitude of the target point of the fleet of aircraft, and R earth is the radius of the Earth.

[0100] (b) Considering the stability and reliability of the internal structure of the aircraft, the heat flow, overload, and dynamic pressure constraints are converted into flight resistance constraints with quasi-equilibrium glide conditions:

[0101]

[0102] wherein, D qmax is the heat flow constraint of the aircraft, Q is the maximum dynamic pressure allowed by the aircraft, p0 is the atmospheric density, V is the speed of the aircraft, S is the reference area of the aircraft, C D is the drag coefficient of the aircraft, R n is the radius of the aircraft stagnation point, k q is the heat flow rate coefficient.

[0103] D nymax = n ymax gC D / C L

[0104] wherein, D nymax is the maximum overload constraint of the aircraft, g is the gravitational acceleration, C D , and C L are the lift coefficient and the drag coefficient of the aircraft.

[0105] D cpmax = cp max SC D / m

[0106] wherein, D cpmax is the maximum dynamic pressure constraint of the aircraft, and m is the mass of the aircraft.

[0107] D eg = (g - V 2 / r)C D / C L

[0108] wherein, D eg is the maximum quasi-equilibrium glide constraint of the aircraft, and r is the distance from the aircraft to the center of the Earth.

[0109] (c) The rate of change of ground distance and speed during the virtual navigator's flight is:

[0110]

[0111] During the flight of the high-speed aircraft, due to the high speed of the virtual navigator and the small trajectory angle, γ can be considered a small angle, with cosγ = 1 and sinγ = 0. Integrating, the remaining flight distance can be obtained:

[0112]

[0113] The mathematical expression for the drag acceleration-velocity profile is shown below:

[0114]

[0115] Where C1 to C5 are constant parameters of the drag acceleration profile, which can be obtained through (V0,D0) and (V1,D5). e (V2,D) e ), (V f D f The nominal profile is determined by four points: (V0, D0), (V...). f D f The drag acceleration profile can be calculated based on the speed and altitude of the high-speed aircraft's starting and target points. The shape of the drag acceleration profile is only related to the entry velocity V1, exit velocity V2, and drag acceleration D of the constant drag segment. e The value of D depends on the distance. If the remaining flight distance is greater than the expected flight distance, then D needs to be increased. e Conversely, D decreases. e .

[0116] (d) Once the drag acceleration profile is determined, the virtual navigator needs to adjust its angle of attack and roll angle in real time during flight to track the drag acceleration profile. To simplify the design and reduce control complexity, during the virtual navigator's flight, the angle of attack α only needs to track the pre-planned angle of attack profile; the only actual control variable is the roll angle σ. Longitudinal guidance determines the absolute value of the roll angle σ, thereby determining the virtual navigator's descent speed to control the range. Lateral guidance only determines the direction of the roll angle σ, controlling the virtual navigator's lateral range by adjusting the sign of the roll angle. Once the angle of attack and drag acceleration profile are determined, the corresponding control rates are:

[0117]

[0118] α c =α0 + f4(D - D0)

[0119] In the formula (L / D) Cis the required lift-drag ratio for longitudinal guidance, (L / D)0 is the planned standard drag acceleration

[0120] is the required lift-drag ratio for the profile, D, D0 are the drag accelerations for the actual flight and the standard trajectory, respectively, are the altitude rates of change for the actual flight and the standard trajectory, respectively, f1, f2, f3, f4 are the variable gain coefficients calculated from the standard trajectory.

[0121] where the reference altitude rate and the reference longitudinal lift-drag ratio can be expressed in terms of the drag acceleration as follows:

[0122]

[0123] where D, are the drag acceleration and its first and second derivatives, respectively, C D , are the drag coefficient and its first and second derivatives, respectively, h s = -7110 are constants related to atmospheric parameters.

[0124] (e) When the error between the heading angle of the high-speed vehicle and the heading angle of the line connecting the high-speed vehicle and the target exceeds the heading angle error corridor, the sign of the high-speed vehicle's roll angle is reversed, and the method for calculating the sign of the roll angle of the vehicle cluster is:

[0125]

[0126] where Δψ corridor is the width of the heading angle error corridor; Δψ out > Δψ in > 0 are the outer boundary and the inner boundary width of the heading angle error corridor, respectively; V a and V b are parameters to be set. When the error of the vehicle's heading angle exceeds the boundary of the vehicle's heading angle error corridor, the roll angle of the vehicle is reversed, i.e., the sign is changed. Therefore, the sign of the roll angle of the vehicle can be determined using the heading angle error corridor:

[0127]

[0128] where T hor is the lateral guidance period, and the heading angle error Δψ is defined as the deviation between the heading angle ψ of the vehicle and the line-of-sight angle Φ of the vehicle:

[0129] Δψ = ψ - Φ

[0130] The heading angle ψ of the vehicle can be obtained by spherical trigonometry:

[0131]

[0132] (f) The formula of flight guidance term is:

[0133] f i3 = L i cos(σ i )

[0134] Where f i3 is the flight guidance term of the i-th aircraft, L i is the lift of the i-th aircraft.

[0135] (4) High-speed aircraft cluster cooperative guidance based on space-time synchronous attractive domain

[0136] The high-speed aircraft cluster relative position control strategy, relative velocity and acceleration control strategy, and guidance strategy are integrated to form the high-speed aircraft cluster cooperative guidance law based on space-time synchronous attractive domain, and its expression is:

[0137] U i = f i1 + f i2 + f i3

[0138] Where U i is the total guidance term of the i-th aircraft, f i1 is the artificial potential field term of the i-th aircraft, which is used to realize the aggregation and collision avoidance of the aircraft cluster; f i2 is the velocity matching term of the i-th aircraft, which is used to realize the velocity matching of the aircraft cluster; f i3 is the flight guidance term of the i-th aircraft, which is used to ensure the accurate arrival of the cluster at the target point.

Claims

1. A high-speed aircraft cluster cooperative guidance method based on space-time synchronous attractor domain, characterized in that, The application relates to a method for controlling a high-speed aircraft cluster. The method comprises the following steps: setting an upper limit and a lower limit of the distance between the aircraft cluster, and controlling the relative position between the high-speed aircraft cluster in real time; calculating the average speed and the average acceleration of the aircraft cluster as the expected speed and the expected acceleration of the aircraft cluster; calculating the difference between the speed and the acceleration of the aircraft cluster and the expected speed and the expected acceleration of the corresponding aircraft cluster, taking the weighted sum of the difference as a speed matching item, and applying the speed matching item to the high-speed aircraft to make the high-speed aircraft reach the predetermined speed and acceleration; calculating the expected flight distance between the aircraft cluster and a target point; converting the heat flow, the overload and the dynamic pressure constraints and the quasi-equilibrium gliding condition into the flight resistance constraint during the flight of the aircraft cluster; designing a resistance acceleration-speed profile of the aircraft cluster according to the remaining flight distance, the expected flight distance and the flight resistance constraint; designing a closed-loop guidance law to make the aircraft cluster fly according to the designed resistance acceleration-speed profile, and calculating the size of the roll angle of the aircraft cluster; designing a flight guidance item according to the size of the roll angle and the sign of the roll angle to make the aircraft cluster reach the target point. The method for controlling the relative position between the high-speed aircraft cluster in real time comprises the following steps: determining the relative distance between the aircraft cluster, setting the upper limit and the lower limit of the distance between the aircraft cluster, and making the aircraft cluster keep gathering and not exceed the communication range and not collide with each other; designing an artificial potential function; the artificial potential function is a non-negative continuous derivable function about the distance between adjacent aircraft, and shows repulsive force when the distance between adjacent aircraft is less than the lower limit, and shows attractive force when the distance between adjacent aircraft is greater than the upper limit; solving the artificial potential field force according to the artificial potential function and the determined relative distance between adjacent aircraft, considering the superposition of the artificial potential field forces between multiple aircraft in the aircraft cluster, and making the artificial potential field force received by any aircraft in the cluster be the resultant force of the artificial potential field forces generated by all adjacent aircraft; and controlling the position of the aircraft in real time by using the artificial potential field force. The upper limit of the distance between the aircraft is set as 20km, and the lower limit of the distance between the aircraft is set as 0.5km. The calculation formula of the artificial potential function is as follows:

2. The method of claim 1, wherein: The calculation formula of the artificial potential field force is as follows: In the formula, f0 is the amplitude of the artificial potential field force when the relative distance between two adjacent aircraft is 0, and s3(r) is the artificial potential field force base function, and the calculation formula of s3(r) is as follows: The calculation formula of the speed matching item is as follows: The calculation formula of the expected flight distance is as follows:

3. The method of claim 2, wherein: ​ 4. The method of claim 2, wherein: ​ In the formula, r is the relative distance between two adjacent aircrafts, r0 is the action distance when the artificial potential field force is 0, f(r) is the artificial potential field force, is the artificial potential function.

5. The method of claim 4, wherein: ​ ​ s3(r) = s2(r) r + (r a + b )s1(r) / 2 where r a is the right boundary of the step interval, r b is the left boundary of the step interval, k1 is a variable for adjusting the steepness of the step interval, s1(r), s2(r) are intermediate variables, and the artificial potential force formula for the ith aircraft is considered in view of the superposition of artificial potential forces of multiple aircrafts in the cluster. where f i1 is the total artificial potential force on the ith UAV, f ij is the artificial potential force on the ith UAV from the jth UAV, ||x i -x j || is the distance between the ith UAV and the jth UAV, and N is the number of UAVs in the swarm.

6. The method of claim 5, wherein: ​ wherein f i2 is the speed matching term of the i-th aircraft, a ij is the weighting coefficient of the speed matching term of the i-th aircraft and the j-th aircraft, which can be adjusted according to the speed matching effect, V i is the speed of the i-th aircraft, V j is the speed of the j-th aircraft, D i is the drag acceleration of the i-th aircraft, D j is the drag acceleration of the j-th aircraft.

7. The method of claim 1, wherein: ​ wherein, is the current latitude of the cluster of aircraft, λ is the current longitude of the cluster of aircraft, is the latitude of the target point of the cluster of aircraft, λ f is the longitude of the target point of the cluster of aircraft, R earth is the radius of the earth.

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