Low-altitude aircraft dynamic safety interval control method

Abstract

The invention discloses a dynamic safety interval control method for a low-altitude aircraft, relates to the technical field of low-altitude flight control, and solves the technical problem that the aircraft cannot be effectively controlled in the prior art. The method comprises the following steps: 1, selecting a certain aircraft as a target aircraft, calculating a potential field force FAB generated by a front aircraft on the target aircraft, and defining a state-space equation of the target aircraft in combination with an acceleration requirement of the target aircraft; if the target aircraft is an unmanned aerial vehicle, skipping to the step 2, and if the rear aircraft is a manned aircraft, skipping to the step 3; 2, eliminating a state estimation error caused by the operation time delay of the target aircraft by using an operation time delay compensation method, and obtaining a state-space equation of the target aircraft under the time delay tau; 3, solving the state-space equation by a genetic optimization algorithm to obtain an optimal interval control parameter; the dynamic interval control model provided by the invention greatly improves the operation efficiency of the complex low-altitude fusion airspace on the premise of conforming to the aircraft interval standard.

Description

Technical Field

[0001] The present invention relates to the technical field of low-altitude flight control, and in particular to a dynamic safety interval control method for low-altitude aircraft. Background Art

[0002] A prominent challenge facing the global aviation industry is how to efficiently utilize low-altitude airspace. Separation standards and control management are key barriers to the integration of manned and unmanned aircraft. As demand for low-altitude airspace increases, the inadequacy of traditional separation control standards and models becomes increasingly apparent, making technological innovation crucial for improving operational efficiency. This pressing need is increasingly recognized as a key area of ​​research and development worldwide.

[0003] Given the significant challenges associated with integrating drones with manned aircraft for air traffic control in low-altitude airspace, it is necessary to develop and apply sophisticated separation control and conflict resolution mechanisms. Simultaneously managing these two types of aircraft is significantly more complex than traditional air traffic control strategies. The constrained airspace and complex environments common in these integrated scenarios have the potential to trigger conflicts and produce severe ripple effects. Therefore, developing robust separation control models and algorithms is crucial for the integrated operation of manned and unmanned aircraft. Existing separation control strategies primarily focus on conflict time and routes, such as spatial closing rates based on conflict duration or distance. However, these strategies only provide ad hoc solutions, fail to capture the dynamic motion patterns of aircraft, and fail to fully reflect interactions and their associated risks. Consequently, defining these interactions and developing corresponding control behaviors remains challenging. Summary of the Invention

[0004] In order to solve the problems existing in the above-mentioned prior art, the present invention provides a dynamic safety interval control method for low-altitude aircraft, which solves the technical problem that the prior art cannot effectively control the aircraft in combination with the dynamic motion mode of the aircraft.

[0005] A method for dynamic safety separation control of low-altitude aircraft, comprising:

[0006] Step 1: Select an aircraft as the target aircraft and calculate the potential force F generated by the aircraft in front on the target aircraft AB , calculate the acceleration of the target aircraft under the action of the potential field force, and define the state space equation of the target aircraft based on the acceleration requirements of the target aircraft; if the target aircraft is a UAV, jump to step 2; if the target aircraft is a manned aircraft, jump to step 3;

[0007] Step 2: Use the operation delay compensation method to eliminate the state estimation error caused by the operation delay of the target aircraft and obtain the state space equation of the target aircraft under the time delay τ;

[0008] Step 3: Use genetic optimization algorithm to solve the state space equation to obtain the optimal interval control parameters.

[0009] Furthermore, the step 1 includes:

[0010] Step 1.1: Calculate the acceleration of the target aircraft under the action of the potential field force:

[0011]

[0012] m B is the mass of the target aircraft;

[0013] Step 1.2: Determine the state space equation of the target aircraft:

[0014]

[0015] X B (t) is the state vector of the target aircraft:

[0016] X B (t)=(x B (t),y B (t),z B (t),v B (t)) T ,

[0017] In the formula, (x B (t),y B (t),z B (t)) is the spatial coordinate of the target aircraft at time t, v B (t) is the speed of the target aircraft at time t;

[0018] u B (t) is the state input vector, which represents the acceleration components in the x-axis, y-axis and z-axis directions respectively:

[0019]

[0020] A and B represent the state matrix and input matrix respectively:

[0021]

[0022] In the state matrix, θ x ,θ y ,θ z Represents the angle between the velocity vector and the coordinate axis.

[0023] Furthermore, the step 2 includes: assuming that the target aircraft B will maintain the control input of the previous time delay [t-τ, t-2τ,] within the time delay [t, t-τ] Operation, the state space of the target aircraft B under time delay τ is expressed as:

[0024]

[0025] Among them, τ is the operation delay size. Through statistical analysis in actual scenarios, K is the linear state feedback controller gain, which is used to compensate for the control difference caused by the operation delay.

[0026] Furthermore, the genetic optimization algorithm in step 3 is a dung beetle optimization algorithm.

[0027] Furthermore, in step 1, the potential force F generated by the front aircraft on the target aircraft is calculated. AB include:

[0028] Step A: Establish a protected area model based on the types of preceding and target aircraft and their flight separation requirements;

[0029] Step B: Define the potential field strength function in the repulsive and attractive regions of the protected area model;

[0030] Step C: A Monte Carlo algorithm based on dynamic interaction weights is used to calculate the interaction potential field value and the potential field center position of the overlapping area between the protection zones of the preceding aircraft and the target aircraft.

[0031] Step D: Based on the solution of step C, further calculate the potential field force acting on the target aircraft.

[0032] Furthermore, the step A includes: considering that the risk in the direction of the aircraft speed is higher than the risk on both sides, designing an ellipsoidal protection zone model:

[0033]

[0034] Where h is the limit height, a, b, and c are the semi-axis lengths of the ellipsoid along the x, y, and z axes, respectively. The x-axis is the direction of the aircraft's velocity, and the y and z axes are orthogonal to the x-axis. a, b, c, and h are set according to the aircraft type.

[0035] Furthermore, the potential field strength function expressions in the repulsive region and the attractive region in step B are as follows:

[0036]

[0037] E i Represents the potential field of any point in space affected by the aircraft, and defines E i <0 is a repulsive field, E i>0 is the gravitational field; α is the acceleration of the aircraft; η1, η2, η3, η4 are the field strength coefficients; θ is the velocity direction and the angle between the line connecting any point i and the aircraft; σ is the parameter that controls the rate of change of the electric field intensity with distance, pl i For pseudo distance, by setting the standard distance parameter L in different directions x-y and L x-z , and calculate the angle between the aircraft's direction and speed to correct the distance in real space:

[0038]

[0039] in, is the speed of the aircraft; θ represents the angle between the speed and the direction of the aircraft's position; κ is the correction parameter; L x-y and L x-z Take the corresponding a and c values ​​according to the aircraft type;

[0040] pL balance is the pseudo-equilibrium distance:

[0041]

[0042] Among them L balance Balance distance for states related to acceleration

[0043] L balance =L0·exp(-λ·α)

[0044] L0 is L balance The basic distance, λ is a parameter.

[0045] Furthermore, in order to prevent the potential field value from being affected by the extremely small pseudo-distance pl i This causes a numerical explosion and ensures that under any circumstances, the repulsive force in the opposite direction of the velocity does not exceed the maximum value in the positive direction. The potential field value at 5 km in the positive direction is set to the global maximum value E. max .

[0046] E max ={E i |l i =5km,θ=0 0}

[0047]

[0048] If the calculation result E i ≥E max , then let E i =E max :

[0049] E i =min(Ei ,E max )

[0050] Furthermore, the step C comprises:

[0051] Step C.1: Generate N random points in the minimum circumscribed cuboid of the ellipsoid, denoted as where x i ~U(xmax min ), y i ~U(ymax min ), z i ~U(zmax min ), where U represents the Ellip A ∪Ellip B Evenly distributed in the middle;

[0052] Step C.2: Calculate the number of random points N that satisfy both ellipsoid equations. inside :

[0053]

[0054] Where I is the indicator function, when the point (x i ,y i ) takes the value 1 when it is within the intersection of the two ellipsoids, otherwise it takes the value 0;

[0055]

[0056] Where S AB is the intersection area of ​​the two ellipsoids;

[0057] Step C.3: The interaction potential field strength in the overlapping area needs to be determined based on the interaction state between the aircraft to determine the dynamic interaction weight; record point (x i ,y i ,z i ) is subjected to the potential field strength E i , the dynamic interaction weight of aircraft A and B is μ A (v A ),μ B (v A ,v B ):

[0058]

[0059] in, is the maximum speed of the aircraft, tanh is the hyperbolic tangent function, and the strength of the interactive potential field can be modified by the different relative motion trends of the two aircraft to meet the control requirements in special cases. ψ1 and ψ2 are control parameters to meet the requirements of the potential field extreme value.

[0060] Step C.4: Total potential field strength in the interaction region The mean value of the potential field in the region:

[0061]

[0062] Step C.5: Center of the interaction area:

[0063]

[0064] Determine the potential field center and the average potential field value in the interaction region.

[0065] Furthermore, the step D comprises:

[0066] Identify the target aircraft and determine the number of aircraft ahead that will affect the target aircraft;

[0067] If there is only one aircraft ahead, calculate the potential field force generated by the aircraft ahead A on the target aircraft B:

[0068]

[0069] Where, is the mean value of the total potential field intensity in the interaction area between the front aircraft A and the target aircraft B, ζ is the type parameter, δ is the speed parameter, is the speed of target aircraft B, is the speed of the leading aircraft A, The line connecting the target aircraft B and the center of the interaction area is The angle between

[0070] The direction of the potential force is determined according to the position of the target aircraft and the center of the interaction area, thereby obtaining the potential force F on the target aircraft. AB ;

[0071] If there are two or more aircraft ahead, calculate the potential force F generated by each aircraft ahead A1, A2, A3, ... on the target aircraft B in turn. A1B 、F A2B 、F A3B , ..., and then perform orthogonal decomposition of the potential field force according to the velocity direction of the target aircraft B. During the orthogonal decomposition, the force in the direction perpendicular to the velocity does not change the motion state and is therefore uniformly set to 0. The minimum value of the force in the positive velocity direction and the maximum value in the negative velocity direction are taken as the base force in that direction. The base forces in each direction are vector-synthesized to obtain the potential field force F that the target aircraft B is subjected to in the multi-aircraft interaction scenario. AB .

[0072] The beneficial effects of the present invention include:

[0073] (1) This paper analyzes the flight performance and control risks of manned and unmanned aircraft in a low-altitude fusion scenario, establishes a multi-classification protection zone model, and introduces a potential field generation function within the protection zone framework to characterize the comprehensive risk posed by aircraft. Numerical analysis demonstrates that the proposed aircraft protection zone and potential field generation model can effectively characterize the impact range and state changes of aircraft during actual operation.

[0074] (2) This paper proposes a set of interactive potential field theories to characterize the interaction relationship between aircraft and introduces operation time delay to establish a dynamic separation control model for manned and unmanned aircraft. The DBO algorithm is used and combined with actual operation data to calibrate the model parameters. This improves the matching degree between the dynamic separation control model and the actual performance of the aircraft.

[0075] (3) The proposed model was verified through multiple simulation scenarios and actual operation scenarios. The results show that the dynamic separation control model proposed in this invention significantly improves the operational efficiency of complex low-altitude fusion airspace while meeting aircraft separation standards. Compared with the actual operation scenario, the average separation between manned and unmanned aircraft using the model control law was reduced by 34.5%, and the fusion operation separation between unmanned aircraft and manned aircraft was reduced by 20.4%. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 This is a schematic diagram of the protection zone model involved in the embodiment of this application.

[0077] Figure 2 is a cross section of the aircraft protection zone along the speed direction involved in the embodiment of the present application, wherein: Figure 2 (a) is the cross section of the large UAV in the velocity direction, Figure 2 (b) is the cross section of the small UAV in the velocity direction, Figure 2 (c) is the cross section of the speed direction of the Category B manned aircraft.

[0078] Figure 3 The embodiment of the present application involves generating potential field intensity contour maps on the XY horizontal plane and the XZ vertical plane using different aircraft potential field influence areas, wherein: Figure 3 (a) is the equipotential line diagram of a large UAV in different motion states. Figure 3 (b) is the equipotential line diagram of type B manned aircraft in different motion states.

[0079] Figure 4 It is the projection of the aircraft interaction area involved in the embodiment of the present application in the XY and XZ directions.

[0080] Figure 5 Schematic diagram of aircraft interaction potential field force calculation involved in an embodiment of the present application.

[0081] Figure 6 A schematic diagram of the synthesis of multiple potential field forces involved in the embodiments of the present application.

[0082] Figure 7 A schematic diagram of the airspace structure of 14 days of ADSB data of a certain low-altitude approach airspace in China in 2024 involved in the embodiments of the present application.

[0083] Figure 8 A part of the data of the car-following of a manned aircraft of Class A involved in the embodiments of the present application, wherein, Figure 8 (a) is the car-following trajectory of the manned aircraft of Class A at a time interval, Figure 8 (b) is the speed distribution of the car-following of the manned aircraft of Class A.

[0084] Figure 9 The dynamic separation control effect of the leading aircraft at different motion stages in the dynamic separation control scenario of two manned aircrafts of Class A involved in the embodiments of the present application, wherein, Figure 9 (a) is the leading aircraft in the deceleration stage, Figure 9 (b) is the leading aircraft in the equilibrium stage.

[0085] Figure 10 The manned-unmanned hybrid operation scenario involved in the embodiments of the present application, wherein, Figure 10 (a) is the hybrid operation scenario with an initial separation of 35 km and the leading aircraft in the acceleration state, Figure 10 (b) is the hybrid operation scenario with an initial separation of 15 km and the leading aircraft in the deceleration state.

[0086] Figure 11 The motion trajectories of aircrafts A, B, C and D when separation control is performed in the first manned-unmanned hybrid operation scenario involved in the embodiments of the present application, wherein, 13(a) is the complete motion trajectory of the aircrafts A, B, C and D, 13(b) is the control separation change of aircraft B to aircraft A, 13(c) is the control separation change of aircraft D to aircraft A, 13(d) is the control separation change of aircraft D to aircraft B, and 13(e) is the control separation change of aircraft C to aircraft D. DETAILED DESCRIPTION

[0087] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the application for protection, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of this application.

[0088] Example 1

[0089] The specific embodiments of the present invention are described in detail below;

[0090] A method for dynamic safety separation control of low-altitude aircraft, comprising:

[0091] Step 1: Select an aircraft as the target aircraft and calculate the potential force F generated by the aircraft in front on the target aircraft AB , define the state space equation of the target aircraft in combination with the acceleration requirements of the target aircraft; if the target aircraft is a UAV, jump to step 2; if the target aircraft is a manned aircraft, jump to step 3;

[0092] Step 2: Use the operation delay compensation method to eliminate the state estimation error caused by the operation delay of the target aircraft and obtain the state space equation of the target aircraft under the time delay τ;

[0093] Step 3: Use genetic optimization algorithm to solve the state space equation to obtain the optimal interval control parameters.

[0094] In another embodiment, step 1 includes:

[0095] Step 1.1: Calculate the acceleration of the target aircraft under the action of the potential field force:

[0096]

[0097] m B is the mass of the target aircraft;

[0098] Step 1.2: Determine the state space equation of the target aircraft:

[0099]

[0100] X B (t) is the state vector of the target aircraft:

[0101] X B (t)=(x B (t),yB (t),z B (t),v B (t)) T ,

[0102] In the formula, (x B (t),y B (t),z B (t)) is the spatial coordinate of the target aircraft at time t, v B (t) is the speed of the target aircraft at time t;

[0103] u B (t) is the state input vector, which represents the acceleration components in the x-axis, y-axis and z-axis directions respectively:

[0104]

[0105] A and B represent the state matrix and input matrix respectively:

[0106]

[0107] In the state matrix, θ x ,θ y ,θ z Represents the angle between the velocity vector and the coordinate axis.

[0108] In another embodiment, step 2 includes: assuming that the target aircraft B will maintain the control input of the previous time delay [t-τ, t-2τ,] within the time delay [t, t-τ] Operation, the state space of target aircraft B under time delay τ is expressed as

[0109]

[0110] Among them, τ is the operation delay size. Through statistical analysis in actual scenarios, K is the linear state feedback controller gain, which is used to compensate for the control difference caused by the operation delay.

[0111] In another embodiment, the genetic optimization algorithm in step 3 adopts the Dung Beetle Optimization Algorithm (DBO) algorithm.

[0112] The DBO algorithm optimizes position updates by simulating four dung beetle behaviors: ball rolling, reproduction, foraging, and stealing. The ball rolling behavior enhances the algorithm's global search capabilities. Reproduction and foraging behaviors enable dung beetles to explore around themselves and the optimal individual, gradually narrowing the search boundary and range with each iteration. Stealing behavior performs a dynamic local search near the optimal individual. The entire process involves initializing the dung beetle swarm and parameters, calculating fitness, updating positions, checking boundaries, and updating the optimal solution until a termination criterion is met. Finally, the global optimal solution and its fitness are output.

[0113] In another embodiment, in step 1, the potential force F generated by the preceding aircraft on the target aircraft is calculated. AB include:

[0114] Step A: Establish a protected area model based on the types of preceding and target aircraft and their flight separation requirements;

[0115] Step B: Define the potential field strength function in the repulsive and attractive regions of the protected area model;

[0116] Step C: A Monte Carlo algorithm based on dynamic interaction weights is used to calculate the interaction potential field value and the potential field center position of the overlapping area between the protection zones of the preceding aircraft and the target aircraft.

[0117] Step D: Based on the solution of step C, further calculate the potential field force acting on the target aircraft.

[0118] In another embodiment, the step A includes: considering that the risk in the direction of the aircraft speed is higher than the risk on both sides, designing an ellipsoidal protection zone model:

[0119]

[0120] Where h is the limit height, a, b, and c are the semi-axis lengths of the ellipsoid along the x, y, and z axes, respectively. The x-axis is the direction of the aircraft's velocity, and the y and z axes are orthogonal to the x-axis. a, b, c, and h are set according to the aircraft type.

[0121] Specifically, it is necessary to first define the potential field generation range of the aircraft, that is, the protection zone model. From the perspective of aircraft operation risk, the risk in the aircraft speed direction is significantly higher than the risk on both sides. Therefore, the embodiment proposes an ellipsoid protection zone model such as Figure 1 Its expression is as follows:

[0122]

[0123] (x0, y0, z0) are the aircraft coordinates. To achieve three-dimensional modeling of different aircraft protection zones in the same space-time dimension, this embodiment establishes a new coordinate system with the aircraft speed direction as the x-axis. At the same time, the unit vector of the speed is defined. The orthogonal unit vectors are (y-axis), (z-axis). In order to ensure that the y-axis is parallel to the horizontal plane, yes and The normal vector of the plane formed by yes and The normal vector of the plane.

[0124]

[0125] The new coordinate system can be expressed as:

[0126]

[0127] At the same time, v x 、v y 、v z is the velocity component in each direction. In order to better simulate the influence of the altitude layer, the top and bottom of the ellipsoid are truncated after exceeding a certain altitude range (see Figure 1 ). Referring to the aircraft separation standard, aircraft must establish an altitude separation of more than 300m when they are more than 10km away, so the cutoff parameter h = 300m is set. At the same time, if the spatial point is outside the influence zone, the distance is infinite. The aircraft protection zone expression is as follows:

[0128]

[0129] Because the scenario set in this embodiment is a low-altitude approach zone, the establishment of a protected area must take into account the different types of aircraft, including manned and unmanned aircraft, and their specific flight separation requirements. UAVs are typically remotely controlled by a ground control station or autonomously flown according to a pre-set flight plan. UAV control may include both an autoflight system and commands from a remote pilot. This results in the control response of the UAV often relying on pre-set programs or remote commands from a ground controller, which can increase response time and complexity, necessitating a protected area model with greater safety margins.

[0130] In low-altitude fusion operation scenarios, manned aircraft are usually only small and medium-sized aircraft. Therefore, this embodiment models the manned aircraft protection zone based on Class A (e.g., Cessna 172, SR20) and Class B (e.g., Modern Ark 60, Cessna525) in the aircraft approach performance classification. The specific parameters of the protection zone model are set according to the classification standards for manned and unmanned aircraft (see Table 1). For unmanned aircraft, referring to the standard classification of actual scenarios, this article stipulates that unmanned aircraft with a maximum take-off weight of more than 150kg are large unmanned aircraft, and unmanned aircraft with a maximum take-off weight of less than 150kg are small and medium-sized unmanned aircraft. See Table 1 for specific parameters.

[0131] Table 1 Aircraft parameter a, b, h settings

[0132]

[0133] According to the cross section of the aircraft protection zone along the speed direction (such as Figure 1 As shown), the altitude coefficient c of different types of aircraft can also be determined, such as Figure 2 , as shown in Table 2,Figure 2 middle, Figure 2 (a) is the cross section of the large UAV in the velocity direction, Figure 2 (b) is the cross section of the small UAV in the speed direction (the same as that of Category A manned aircraft), Figure 2 (c) is the cross section of the speed direction of the Category B manned aircraft.

[0134] Table 2 Aircraft parameter c settings

[0135]

[0136]

[0137] In another embodiment, the aircraft protection zone is divided into a repulsive zone and an attractive zone. The front half of the protection zone contains only the repulsive zone, as aircraft do not exert gravitational forces on opposing aircraft to reduce the distance between them. The back half of the protection zone contains both attractive and repulsive zones, with the state equilibrium distance used as the critical value for dividing the repulsive and attractive zones.

[0138] Furthermore, the aircraft's acceleration also affects the potential field distribution. Specifically, when the aircraft is accelerating (α > 0), the space in the positive direction of the velocity (the front half of the protected area) will intensify its repulsive field due to increased safety risks. Conversely, the space in the opposite direction of the velocity (the back half of the protected area) will amplify the attractive field and shrink the repulsive field due to decreased safety risks. Conversely, when the aircraft is decelerating (α < 0), the repulsive field in the front half of the protected area decreases, while the repulsive field in the back half of the protected area increases and shrinks the attractive field.

[0139] The potential field strength function expressions in the repulsive region and the attractive region in step B are as follows:

[0140]

[0141] E i Represents the potential field of any point in space affected by the aircraft, and defines E i <0 is a repulsive field, E i >0 is the gravitational field; α is the acceleration of the aircraft; η1, η2, η3, η4 are the field strength coefficients; θ is the velocity direction and the angle between the line connecting any point i and the aircraft; σ is the parameter that controls the rate of change of the electric field intensity with distance, pl i For pseudo distance, by setting the standard distance parameter L in different directions x-y and L x-z , and calculate the angle between the aircraft's direction and speed to correct the distance in real space:

[0142]

[0143] in, is the speed of the aircraft; θ represents the angle between the speed and the direction of the aircraft's position; κ is the correction parameter; L x-y and L x-z Take the corresponding a and c values ​​according to the aircraft type;

[0144] pL balance is the pseudo-equilibrium distance:

[0145]

[0146] Among them L balance Balance distance for states related to acceleration

[0147] L balance =L0·exp(-λ·α)

[0148] L0 is L balance The basic distance, λ is a parameter.

[0149] In another embodiment, in order to prevent the potential field value from being affected by the extremely small pseudo distance pl i This causes a numerical explosion and ensures that under any circumstances, the repulsive force in the opposite direction of the velocity does not exceed the maximum value in the positive direction. The potential field value at 5 km in the positive direction is set to the global maximum value E. max .

[0150] E max ={E i |l i =5km,θ=0 0}

[0151]

[0152] If the calculation result E i ≥E max , then let E i =E max :

[0153] E i =min(E i ,E max )

[0154] In this embodiment, the state equilibrium distance L is established by the critical condition balance Parameter solution, critical condition (1): the limit acceleration of the aircraft is α max =6000km / h 2 , critical condition (2): The aircraft is in the extreme acceleration state L balance =5km, the aircraft is in the extreme deceleration state L balance =L x-yBased on the parameter solution settings, the parameters of the equilibrium distance can be obtained as shown in Table 3.

[0155] Table 3 Parameters of equilibrium distance

[0156]

[0157] The potential field intensity contour maps on the XY horizontal plane and the XZ vertical plane are generated using the potential field influence areas of different aircraft, such as Figure 3 At the same time, this embodiment performs dimensionless processing on the potential field strength, where the red area represents the repulsive field and the blue area represents the attractive field. Figure 3 (a) and (b) show the potential contours of large UAV and Class B manned aircraft in different motion states, respectively. The potential field distribution in the ellipsoidal protection zone shows a compression trend along the vertical direction of motion. balance This reveals the critical value between the gravitational field and the repulsive field.

[0158] Figure 3 (a) shows a large drone at different locations. The acceleration is α1 = 0, α2 = -α max , α3=α max The potential field distribution generated by the motion along the velocity vector (1,1,0) is shown. When the aircraft is in a uniform velocity state (α1 = 0), the area in the positive velocity direction presents a higher safety risk, manifesting as a larger repulsive field. The area in the negative velocity direction within the equilibrium distance exhibits a smaller repulsive field, while the area beyond the equilibrium distance, lacking the risk of collision with the aircraft, exhibits an attractive field, allowing the following aircraft to accelerate and shorten the distance.

[0159] The aircraft acceleration is α2 = -6000 km / h 2 When the aircraft decelerates at a significant rate, it experiences significant deceleration. Compared to the uniform velocity scenario, the potential field in the positive direction of velocity exhibits a repulsive force, but the intensity of the field decreases. Furthermore, due to the rearward shift in the equilibrium distance, the potential field in the opposite direction of velocity exhibits only repulsive force. This indicates that when an aircraft decelerates at a significant rate, the repulsive field in the airspace behind it increases significantly in both intensity and range. In this case, the aircraft behind it requires a larger deceleration area to avoid flight collisions.

[0160] The acceleration of the aircraft is α3 = 6000 km / h 2 When the aircraft is in a significantly accelerated state, the repulsive field in the positive direction of velocity is significantly enhanced. However, in the negative direction of velocity, the forward shift in equilibrium distance causes the repulsive field area to shrink significantly, and the potential field strength to decrease. Simultaneously, both the gravitational field area and potential field strength increase. Therefore, at the same speed, the forward shift in equilibrium distance during acceleration provides greater acceleration space for the following aircraft, shortening the flight interval.

[0161] Figure 3 (b) shows the potential field distribution of a Class B manned aircraft under different acceleration states. The protected area and potential field generation area of ​​the manned aircraft are significantly smaller than those of the UAV, revealing the difference in risk and complexity between manned and UAV aircraft. Furthermore, under the same motion state, the more aggressive repulsive force zone ratio is shown, reflecting the higher safety requirements for manned aircraft.

[0162] In another embodiment, the step C comprises:

[0163] There is a potential field influence area around each aircraft during operation. When the potential field influence areas of different aircraft intersect, this interaction area will interact due to the interaction of their respective potential fields. When the potential field influence areas of multiple aircraft intersect in the airspace, this interaction will affect the motion state of the aircraft and avoid potential conflicts. In the absence of physical contact, the motion state of the aircraft may still be adjusted due to changes in the state of the surrounding aircraft. This phenomenon can be understood as an object in a potential field being able to exert a virtual "external force" on other non-contact objects. This embodiment defines this force that can affect the motion state of the aircraft as the potential field force generated by the aircraft interaction field. Therefore, this embodiment proposes a potential field force framework based on the interactive potential field to characterize this interaction relationship.

[0164] According to aircraft potential field theory, aircraft A and B can determine the strength and range of their potential fields based on their own motion states. Therefore, when the potential field influence areas of two aircraft interact, they can be represented by the overlapping area of ​​two ellipsoids:

[0165] S AB =Ellip A ∩Ellip B

[0166] Ellip A is the potential field influence area of ​​aircraft A, Ellip B The potential field influence zone of aircraft B. The interaction between aircraft is affected by the strength of the interaction potential field in the overlapping region and is generated by the potential field center. Because the interaction potential field strength in the overlapping region is unevenly distributed and irregularly shaped, this embodiment uses a Monte Carlo algorithm based on dynamic interaction weights to determine the interaction potential field value and the potential field center position in the overlapping region to characterize the influence of the potential field force. The algorithm steps are as follows:

[0167] Step C.1: Generate N random points in the minimum circumscribed cuboid of the ellipsoid, denoted as where x i :U(xmax min ), y i :U(ymax min ), zi :U(zmax min ), where U represents the Ellip A ∪Ellip B Evenly distributed in the middle;

[0168] Step C.2: Calculate the number of random points N that satisfy both ellipsoid equations. inside :

[0169]

[0170] Where I is the indicator function, when the point (x i ,y i ) takes the value 1 when it is within the intersection of the two ellipsoids, otherwise it takes the value 0;

[0171]

[0172] Where S AB is the intersection area of ​​the two ellipsoids;

[0173] Step C.3: The interaction potential field strength in the overlapping area needs to be determined based on the interaction state between the aircraft to determine the dynamic interaction weight; record point (x i ,y i ,z i ) is subjected to the potential field strength E i , the dynamic interaction weight of aircraft A and B is μ A (v A ),μ B (v A ,v B ):

[0174]

[0175] in, is the maximum speed of the aircraft, and tanh is the hyperbolic tangent function. The strength of the interaction potential field can be modified by the different relative motion trends of the two aircraft to meet the control requirements in special situations. ψ1 and ψ2 are control parameters to meet the extreme value requirements of the potential field;

[0176] Specifically, it is generally believed that when two aircraft (the leading aircraft and the trailing aircraft (in this embodiment, the target aircraft is the trailing aircraft)) are in an interactive state, the leading aircraft only calculates the trailing potential field influence space and the trailing aircraft only calculates the leading potential field influence space. The expression of the rear potential field affecting the space is:

[0177]

[0178] The target aircraft B should be in a uniform speed state when it is not affected by the intersection area. The expression of the potential field influence space in front of the target aircraft B under the car-following behavior is:

[0179]

[0180] Step C.4: Total potential field strength in the interaction region The mean value of the potential field in the region:

[0181]

[0182] Step C.5: Center of the interaction area:

[0183]

[0184] The projections of the interaction area between aircraft A and B in the XY and XZ directions are as follows: Figure 4 According to the Monte Carlo algorithm, the potential field center and average potential field value of the interaction area can be determined.

[0185] In another embodiment, the step D comprises:

[0186] Identify the target aircraft and determine the number of aircraft ahead that will affect the target aircraft;

[0187] If there is only one aircraft ahead, calculate the potential force generated by the aircraft ahead A on the target aircraft B:

[0188]

[0189] Where, is the mean value of the total potential field strength in the interaction area between the front aircraft A and the target aircraft B, ζ is the type parameter, δ is the speed parameter, is the speed of target aircraft B, is the speed of the leading aircraft A, The line connecting the target aircraft B and the center of the interaction area is The angle between

[0190] The direction of the potential force is determined according to the position of the target aircraft and the center of the interaction area, thereby obtaining the potential force F on the target aircraft. AB ;

[0191] Specifically, in the theory of aircraft interaction potential fields, the diverse interactions between aircraft form interaction potential fields with varying strengths, properties, and shapes. When an aircraft is in an interaction potential field, changes in its position and parameters will trigger interactions between the potential field and the aircraft. This phenomenon reflects the concept of short-range forces in classical physics. These potential field forces will affect the target aircraft and cause changes in its state of motion. The main factors affecting the magnitude of the potential field force F include: the strength and center position of the interaction potential field, the speed difference, and the type of aircraft. The following is a detailed summary of these influencing factors:

[0192] (1) Interaction potential field strength and center

[0193] The magnitude of the field force is mainly affected by the strength of the potential field and is proportional to the strength of the potential field; the closer the aircraft is to the center of the potential field, the greater the field force it is subjected to.

[0194] (2) Speed

[0195] The impact of speed on the field forces acting on an aircraft is primarily reflected in the speed difference and direction. A larger speed difference indicates a more pronounced tendency to approach surrounding aircraft, increasing the repulsive force and reducing the gravitational force. The direction of speed also directly reflects the tendency of two aircraft to approach.

[0196] (3) Aircraft type

[0197] Aircraft are primarily categorized into manned and unmanned aircraft, as well as by size. This significantly limits the safe separation between them. In air traffic control operations, aircraft weight and wingspan are the most common methods for distinguishing aircraft size.

[0198] The potential force on the aircraft is defined using equations from electric field force theory:

[0199] F=E·q

[0200] The charge q can be compared to the flight state of an aircraft (speed ), its distance from the source, and its type.

[0201] Specifically, the greater the alignment of the aircraft's velocity with the field source direction, the more significant the field force, e.g. Figure 5 shown.

[0202]

[0203] Where, is the speed parameter; ζ is the type parameter, δ is the speed parameter; The line connecting the target aircraft B and the center of the interaction area is Angle.

[0204] In another embodiment, if there are two or more leading aircraft, the potential field force F generated by each leading aircraft A1, A2, A3, ... on the target aircraft B is calculated in sequence. A1B 、F A2B 、F A3B , ..., and then perform orthogonal decomposition of the potential field force according to the velocity direction of the target aircraft B. During the orthogonal decomposition, the force in the direction perpendicular to the velocity does not change the motion state and is therefore uniformly set to 0. The minimum value of the force in the positive velocity direction and the maximum value in the negative velocity direction are taken as the base force in that direction. The base forces in each direction are vector-synthesized to obtain the potential field force F that the target aircraft B is subjected to in the multi-aircraft interaction scenario. AB .

[0205] Specifically, analyzing the combined effects of multiple aircraft acting on a single aircraft can be viewed as a combined force acting on the target aircraft. This requires considering the status of all preceding aircraft to ensure safe spacing between them. Therefore, the traditional vector superposition method cannot be used to analyze the gravitational or repulsive forces acting on the target aircraft. To effectively analyze the superposition of these multi-aircraft interaction forces, this embodiment proposes a velocity-direction-based interaction force synthesis algorithm.

[0206] (1) Vector decomposition

[0207] The vector interaction forces of multiple aircraft on the target aircraft are calculated and orthogonally decomposed according to the velocity direction of the target aircraft.

[0208] (2) Composite superposition

[0209] During orthogonal decomposition, the force in the direction perpendicular to the velocity does not change the state of motion and is therefore uniformly set to 0; the minimum value of the force in the positive direction of the velocity and the maximum value in the negative direction of the velocity are taken as the base force in that direction.

[0210] (3) Vector synthesis, such as Figure 6 As shown: the reference forces in each direction are vector synthesized.

[0211] Using this multi-stage interaction force synthesis algorithm, the target aircraft can generate vector-synthesized interaction forces in multi-aircraft interaction scenarios and perform safety interval control according to the acceleration generated by the resultant force.

[0212] Specifically, in order to verify the effectiveness of the method proposed in the present invention, this embodiment uses 14 days of ADSB data of a low-altitude approach airspace in China in 2024. The airspace structure is as follows: Figure 7As shown in the figure, the purple solid line is the sector boundary, the dashed lines are the two runways used to distinguish manned aircraft from unmanned aircraft, and the black solid line is the airway. The data within this area includes flight data for four types of aircraft: Class A manned aircraft, large unmanned aircraft, Class B manned aircraft, and small unmanned aircraft, all within an altitude of 2.4 km.

[0213] Parameter Solution of Dynamic Interval Control Model

[0214] This embodiment conducts spatiotemporal feature mining based on ADS-B data, and selects data sets that meet the characteristics of car-following behavior through a track association mechanism under a unified spatiotemporal dimension. After screening, a total of 32 sets of Class A manned aircraft and 27 sets of Class B manned aircraft tracking data were obtained, totaling 12,640 records. Figure 8 The following are some examples of Class A manned-machine following data, where: Figure 8 (a) is the tracking trajectory of a Class A manned aircraft at a time interval. Figure 8 (b) shows the velocity distribution of a Class A manned-aircraft following pair. The figure shows the trajectory and velocity data for some following pairs. It can be seen that the trajectories of these aircraft closely overlap, with only temporal differences. The speed variations also demonstrate clear following characteristics. These phenomena are highly consistent with observed following behavior in practice.

[0215] The model was calibrated using trajectory data from a pair of aircraft following a target and the Dung Beetle optimization algorithm. The mean absolute percentage error (MAPE) was chosen as the metric for evaluating and validating the calibration results. The specific expression of MAPE is as follows:

[0216]

[0217] in, It represents the true value of the i-th time. represents the estimated value from the i-th simulation of the selected car-following model, and N is the sample size for model parameter calibration. The number of iterations in the dung beetle optimization algorithm was set to 50. The calibration results for the parameters in the dynamic interval control model are shown in Table 4.

[0218] Table 4 Calibration results of parameters in dynamic interval control model

[0219]

[0220] In the table, κ is the correction parameter, η1, η2, η3, and η4 are the field strength coefficients, σ ​​is the parameter that controls the rate of change of the electric field intensity with distance, ζ is the type parameter, δ is the speed parameter, and K is the gain of the linear state feedback controller, which is used to compensate for the control difference caused by the operation delay.

[0221] Simulation Scenario 1

[0222] This scenario simulates two Class A manned aircraft (a LM =20km) dynamic interval control scenario. In the accelerated simulation setting, the intervals between the front and rear vehicles are assumed to be 35km and 20km respectively. α A =1000km / h 2 ; For the deceleration simulation scenario, the distances between the two are set to 35km and 15km. α A =-1000km / h 2 According to the potential field model proposed in this paper, the motion state of the rear machine is simulated and the motion state of the rear machine is divided into four stages: free acceleration stage (stage 1), restricted acceleration stage (stage 2), deceleration stage (stage 3) and equilibrium stage (stage 4). Figure 9 As shown, Figure 9 This is the dynamic interval control effect of the leading aircraft at different motion stages in the dynamic interval control scenario of two Class A manned aircraft involved in the embodiment of the present application, wherein: Figure 9 (a) The leading aircraft is in the deceleration phase. Figure 9 (b) The leading machine is in the balance stage.

[0223] Figure 9 (a) and (b) show the situation when the leading aircraft is decelerating. When the initial separation is 35 km ( Figure 9 In (a), the gravity effect on the following aircraft is significantly reduced compared to the acceleration scenario, which is attributed to the deceleration of the leading aircraft. Furthermore, when the following aircraft are separated by 15 km, the state transitions to the deceleration phase, and the initial repulsive force effect is significantly enhanced due to the larger speed difference between the two aircraft. Figure 9 (b) shows the dynamic separation control process when the initial separation (15 km) is even smaller. Due to the close proximity of the two aircraft, the following aircraft immediately enters a deceleration state. Based on verification in both scenarios, the aircraft can achieve dynamic equilibrium at approximately 10 km, demonstrating that the model's control law can meet the aircraft's safe separation standards at various separations and states, including acceleration and deceleration.

[0224] Simulation Scenario 2

[0225] This scenario sets up a manned and unmanned fusion operation scenario, in which the rear aircraft is a large UAV (a LU = 25km), the preceding aircraft is a Class B manned aircraft (a SM =15km). In the acceleration simulation setting, it is assumed that the distance between the front and rear vehicles is 35km, α A =1000km / h 2; the deceleration simulation scenario sets the interval between them as 15km, α A = -1000km / h 2 . Specifically as Figure 10 shown.

[0226] Figure 10 (a) shows the fusion operation scenario with an initial interval of 35km and the leading aircraft in the acceleration state. The UAV has obvious control lag due to the existence of operation time-space delay, that is, the trailing aircraft cannot respond to the acceleration control in the first time. In addition, since the protection area of the large UAV is larger, the state transition distance will be significantly forward, so the deceleration stage start time will also be significantly forward. It can be found that when the interval between the two aircrafts is 23km, the trailing aircraft triggers the state transition. This also directly leads to the final equilibrium distance of the two aircrafts being 14km, which reflects the need for more generous interval to meet the safety needs under the fusion operation scenario.

[0227] Figure 10 (b) shows the fusion operation scenario with an initial interval of 15km and the leading aircraft in the deceleration state. Given the large speed difference between the leading and trailing aircrafts and the small interval, the model directly triggers the deceleration state. The final equilibrium interval stabilizes at about 11km.

[0228] Actual fusion operation scenario verification.

[0229] In order to verify that the proposed dynamic interval control model is applicable to the interval control under the manned-unmanned fusion operation scenario, this paper will select the actual operation scenario of the low-altitude approach airspace in Sichuan to verify and analyze.

[0230] Actual scenario 1

[0231] In actual operation scenario 1, Table 5 shows the types, initial positions and motion states of the aircrafts in this scenario. Figure 11 (a) shows the complete motion trajectory of the aircrafts in the scenario, and the interaction relationship between the four aircrafts in the scenario is as follows: (1) aircraft B→aircraft A; (2) aircraft D→aircraft B→aircraft A; (3) aircraft C→aircraft D→aircraft B→aircraft A;

[0232] Table 5 Initial information of aircrafts in actual scenario 1

[0233]

[0234] Figure 11 (a) shows the interval control between aircrafts under different interaction relationships. In Figure 11 (b), aircraft B triggers the gravity effect through model control, and its interval with aircraft A is constantly reduced. Compared with the actual trajectory, its interval is reduced by 56.3%. Figure 11(c) also demonstrates the model’s ability to improve the efficiency of separation control. The control separation between aircraft D and aircraft A is improved by 41.7% compared to the actual separation. Figure 11 (d) demonstrates interval control in more complex situations. Compared with the actual operation scenario, a more refined interval control strategy is implemented, achieving a 28.1% improvement in interval performance. Figure 11 (e) Demonstrates the interval control effect in a manned-unmanned fusion operation scenario, where the UAV achieves a 19.5% improvement in interval performance under operation delay.

[0235] The above-described embodiments merely represent specific implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of protection of the present application. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the technical concept of the present application, and all such variations and improvements fall within the scope of protection of the present application.

Claims

1. A method for dynamic safety interval control of low-altitude aircraft, characterized in that: include: Step 1: Select an aircraft as the target aircraft and calculate the potential force F generated by the aircraft in front on the target aircraft. AB , calculate the acceleration of the target aircraft under the action of the potential field force, and define the state space equation of the target aircraft based on the acceleration requirements of the target aircraft; if the target aircraft is a UAV, jump to step 2; if the target aircraft is a manned aircraft, jump to step 3; Step 2: Use the operation delay compensation method to eliminate the state estimation error caused by the operation delay of the target aircraft and obtain the state space equation of the target aircraft under the time delay τ; Step 3: Use genetic optimization algorithm to solve the state space equation to obtain the optimal interval control parameters.

2. A low-altitude aircraft dynamic safety interval control method according to claim 1, characterized in that: The step 1 comprises: Step 1.1: Calculate the acceleration of the target aircraft under the action of the potential field force: m B is the mass of the target aircraft; Step 1.2: Determine the state space equation of the target aircraft: X B (t) is the state vector of the target aircraft: X B (t)=(x B (t),y B (t),z B (t),v B (t)) T , In the formula, (x B (t),y B (t),z B (t)) is the spatial coordinate of the target aircraft at time t, v B (t) is the speed of the target aircraft at time t; u B (t) is the state input vector, which represents the acceleration components in the x-axis, y-axis and z-axis directions respectively: A and B represent the state matrix and input matrix respectively: In the state matrix, θ x ,θ y ,θ z Represents the angle between the velocity vector and the coordinate axis.

3. The method for dynamic safety interval control of low-altitude aircraft according to claim 1, characterized in that: The step 2 includes: assuming that the target aircraft B will maintain the control input of the previous time delay [t-τ, t-2τ,] within the time delay [t, t-τ]. Operation, the state space of target aircraft B under time delay τ is expressed as Among them, τ is the operation delay size. Through statistical analysis in actual scenarios, K is the linear state feedback controller gain, which is used to compensate for the control difference caused by the operation delay.

4. The method for dynamic safety interval control of low-altitude aircraft according to claim 1, characterized in that: The genetic optimization algorithm described in step 3 is a dung beetle optimization algorithm.

5. The method for dynamic safety interval control of low-altitude aircraft according to claim 1, characterized in that: In step 1, calculate the potential force F generated by the front aircraft on the target aircraft AB include: Step A: Establish a protected area model based on the types of preceding and target aircraft and their flight separation requirements; Step B: Define the potential field strength function in the repulsive and attractive regions of the protected area model; Step C: A Monte Carlo algorithm based on dynamic interaction weights is used to calculate the interaction potential field value and the potential field center position of the overlapping area between the protection zones of the preceding aircraft and the target aircraft. Step D: Based on the solution of step C, further calculate the potential field force acting on the target aircraft.

6. A low-altitude aircraft dynamic safety interval control method according to claim 5, characterized in that: Step A includes: considering that the risk in the direction of aircraft speed is higher than the risk on both sides, designing an ellipsoidal protection zone model: Where h is the limit height, a, b, and c are the semi-axis lengths of the ellipsoid along the x, y, and z axes, respectively. The x-axis is the direction of the aircraft's velocity, and the y and z axes are orthogonal to the x-axis. a, b, c, and h are set according to the aircraft type.

7. A low-altitude aircraft dynamic safety interval control method according to claim 5, characterized in that: The potential field strength function expressions in the repulsive region and the attractive region in step B are as follows: E i Represents the potential field of any point in space affected by the aircraft, and defines E i <0 is a repulsive field, E i >0 is the gravitational field; α is the acceleration of the aircraft; η1, η2, η3, η4 are the field strength coefficients; θ is the velocity direction and the angle between the line connecting any point i and the aircraft; σ is the parameter that controls the rate of change of the electric field intensity with distance, pl i For pseudo distance, by setting the standard distance parameter L in different directions x-y and L x-z , and calculate the angle between the aircraft's direction and speed to correct the distance in real space: in, is the speed of the aircraft; θ represents the angle between the speed and the direction of the aircraft's position; k is the correction parameter; L x-y and L x-z Take the corresponding a and c values ​​according to the aircraft type; pL balance is the pseudo-equilibrium distance: Among them L balance Balance distance for states related to acceleration L balance =L0·exp(-λ·a) L0 is L balance The basic distance, λ is a parameter.

8. A low-altitude aircraft dynamic safety interval control method according to claim 5, characterized in that: In order to prevent the potential field value from being affected by the extremely small pseudo-distance pl i This causes a numerical explosion and ensures that under any circumstances, the repulsive force in the opposite direction of the velocity does not exceed the maximum value in the positive direction. The potential field value at 5 km in the positive direction is set to the global maximum value E. max ; E max ={E i |l i =5km,θ=0 0 } If the calculation result E i ≥E max , then let E i =E max : The i =min(E i ,E max )。 9. A low-altitude aircraft dynamic safety interval control method according to claim 5, characterized in that: The step C comprises: Step C.1: Generate N random points in the minimum circumscribed cuboid of the ellipsoid, denoted as where x i ~U(xmax min ), y i ~U(ymax min ), z i ~U(zmax min ), where U represents the Ellip A ∪Ellip B Evenly distributed in the middle; Step C.2: Calculate the number of random points N that satisfy both ellipsoid equations. inside : Where I is the indicator function, when the point (x i ,y i ) takes the value 1 when it is within the intersection of the two ellipsoids, and 0 otherwise; Where S AB is the intersection area of ​​the two ellipsoids; Step C.3: The interaction potential field strength in the overlapping area needs to be determined based on the interaction state between the aircraft to determine the dynamic interaction weight; record point (x i ,y i ,z i ) is subjected to the potential field strength E i , the dynamic interaction weight of aircraft A and B is μ A (v A ),μ B (v A ,v B ): in, is the maximum speed of the aircraft, and tanh is the hyperbolic tangent function. The strength of the interaction potential field can be modified by the different relative motion trends of the two aircraft to meet the control requirements in special situations. ψ1 and ψ2 are control parameters to meet the extreme value requirements of the potential field; Step C.4: Total potential field strength in the interaction region The mean value of the potential field in the region: Step C.5: Center of the interaction area: Determine the potential field center and the average potential field value in the interaction region.

10. A low-altitude aircraft dynamic safety interval control method according to claim 1, characterized in that: The step D comprises: Identify the target aircraft and determine the number of aircraft ahead that will affect the target aircraft; If there is only one aircraft ahead, calculate the potential field force generated by the aircraft ahead A on the target aircraft B: Where, is the mean value of the total potential field intensity in the interaction area between the front aircraft A and the target aircraft B, ζ is the type parameter, δ is the speed parameter, is the speed of target aircraft B, is the speed of the leading aircraft A, The line connecting the target aircraft B and the center of the interaction area is Angle; The direction of the potential force is determined according to the position of the target aircraft and the center of the interaction area, thereby obtaining the potential force F on the target aircraft. AB ; If there are two or more aircraft ahead, calculate the potential force F generated by each aircraft ahead A1, A2, A3, ... on the target aircraft B in turn. A1B 、F A2B 、F A3B , ..., and then perform orthogonal decomposition of the potential field force according to the velocity direction of the target aircraft B. During the orthogonal decomposition, the force in the direction perpendicular to the velocity does not change the motion state and is therefore uniformly set to 0. The minimum value of the force in the positive velocity direction and the maximum value in the negative velocity direction are taken as the base force in that direction. The base forces in each direction are vector-synthesized to obtain the potential field force F that the target aircraft B is subjected to in the multi-aircraft interaction scenario. AB .

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