A multi-unmanned aerial vehicle guidance probability optimal allocation method for cluster targets

Abstract

The application discloses a multi-unmanned aerial vehicle guidance probability optimal distribution method for cluster targets. In the method, a system using a PN guidance law is re-expressed as a linear time-varying system composed of an unmanned aerial vehicle autopilot and a seeker dynamics by using a zero control miss distance. According to a control theory, the system can be established as a block diagram form, with a target maneuver and an initial heading error as inputs and the zero control miss distance as output. Then, a covariance analysis method is introduced to accurately calculate the average value and variance of the zero control miss distance under the interference of the target random maneuver and the heading error. By combining the effective action radius of the unmanned aerial vehicle on-board load, the guidance probability of a single unmanned aerial vehicle to a single target can be accurately obtained, and the optimal distribution result is obtained by combining a marginal revenue enumeration method, and on this basis, the unmanned aerial vehicle is controlled to fly to the target by a proportional guidance guidance law.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of multi-target swarm guidance, and particularly relates to a multi-unmanned aerial vehicle guidance probability optimal allocation method for swarm targets. BACKGROUND

[0002] With the development of information technology and low-altitude economy, the application of unmanned aerial vehicles (UAVs) is becoming more and more widespread, but the widespread application of UAV swarms in urban environments poses a serious threat to low-altitude safety, so it is necessary to control the UAV swarm and, if necessary, to safely and effectively capture it. In order to solve this problem, various research institutions are actively researching effective countermeasures against UAV swarms. Among them, using a UAV swarm to guide a target swarm has been considered an effective means. In the problem of swarm confrontation, accurately allocating multiple pursuers to multiple targets (MPMTA) is crucial to achieving a high probability of guidance. However, current MPMTA methods mainly rely on empirical fitting to establish an allocation model, which can lead to inaccurate results. In addition, the probability calculation method based on the typical Monte Carlo method requires a large amount of time and experimental cost, which is not very suitable in practice. Therefore, there is an urgent need for a fast and accurate evaluator to improve the allocation effect.

[0003] A more scientific and effective allocation scheme is given in Jin T Y, He SM, et al.“Evaluation Model and exact optimization algorithm in missile-target assignment.”JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICS, 2023, 46(9), (16 Apr 2023). However, this scheme is based on estimated probabilities, so the accuracy of the data basis of this scheme needs to be improved.

[0004] Based on the above problems, the present inventors have conducted in-depth research on the guidance probability of each aircraft in the hope of designing a multi-unmanned aerial vehicle precise allocation method for swarm target guidance probability optimization that can solve the above problems. SUMMARY

[0005] In order to overcome the above problems, the present inventors have made intensive research and designed a multi-unmanned aerial vehicle guidance probability optimal allocation method for cluster targets, in which, by using zero control miss distance, the system using PN guidance law is re-expressed as a linear time-varying system composed of an unmanned aerial vehicle autopilot and a seeker dynamic; according to control theory, the system can be established in a block diagram form, taking target maneuvering and initial heading error as input and zero control miss distance as output; then, a covariance analysis method is introduced to accurately calculate the mean value and variance of the zero control miss distance under the interference of target random maneuvering and heading error; by combining the effective action radius of the unmanned aerial vehicle on-board load, the guidance probability of a single unmanned aerial vehicle to a single target can be accurately obtained, and the optimal allocation result is obtained by combining the marginal enumeration method, and on this basis, the unmanned aerial vehicle is controlled by the proportional guidance guidance law to track the target, so that the present application is completed.

[0006] Specifically, the present application aims to provide a multi-unmanned aerial vehicle guidance probability optimal allocation method for cluster targets, in which, a covariance analysis method is introduced to obtain the mean value and variance of the terminal miss distance under the interference of target random maneuvering and heading error, and the guidance probability of a single unmanned aerial vehicle to a single target is obtained by combining the effective action radius of the unmanned aerial vehicle on-board load.

[0007] The total guidance probability corresponding to each allocation scheme and the threat value of the target are jointly taken as the input value of the marginal enumeration method, so as to obtain the optimal allocation result.

[0008] The guidance probability of a single unmanned aerial vehicle to a single target is obtained by the following formula (I):

[0009]

[0010] In the formula, p ij represents the guidance probability of the i th unmanned aerial vehicle to the j th target;

[0011] ρ represents the effective action radius of the unmanned aerial vehicle on-board load;

[0012] represents the mean value of the terminal miss distance when the i th unmanned aerial vehicle guides the j th target;

[0013] represents the variance of the terminal miss distance when the i th unmanned aerial vehicle guides the j th target;

[0014] z represents the zero control miss distance.

[0015] In the formula, the is the first element of the M(t) matrix at the terminal time,

[0016] The The first element on the diagonal of the P(t) matrix at the end time;

[0017] The M(t) matrix and the P(t) matrix are obtained through the following formula (II):

[0018]

[0019] wherein, denotes the derivative of M(t);

[0020] denotes the derivative of P(t);

[0021] F(t) denotes a dynamic matrix;

[0022] G(t) denotes a control matrix;

[0023] Q(t) denotes a spectral density matrix;

[0024] M(t)' denotes M(t) obtained at the previous time;

[0025] P(t)' denotes P(t) obtained at the previous time;

[0026] M(t) and P(t) obtained at the previous time are substituted into formula (II) at the current time to obtain and M(t) is obtained by integrating and P(t) is obtained by integrating .

[0027] wherein, formula (II) is iterated to the final time T F The M(t) matrix obtained at the final time is the M(t) matrix at the end time, and the P(t) matrix obtained is the P(t) matrix at the end time.

[0028] wherein, the dynamic matrix F(t) is shown in the following formula (III):

[0029]

[0030] wherein, w n denotes the natural oscillation frequency of the second-order system of the unmanned aerial vehicle autopilot;

[0031] ξ n denotes the damping ratio of the second-order system of the unmanned aerial vehicle autopilot;

[0032] N denotes a proportional guidance coefficient;

[0033] V c denotes the relative speed between the unmanned aerial vehicle and the target in the line-of-sight direction;

[0034] Ks represents a system gain;

[0035] T go represents a remaining flight time.

[0036] wherein the control matrix G(t) is shown in the following formula (four) :

[0037]

[0038] wherein V P represents a speed of the UAV.

[0039] wherein the spectral density matrix Q(t) is shown in the following formula (five) :

[0040]

[0041] wherein μ σ represents an initial pointing angle of the UAV,

[0042] μ T represents an initial acceleration of the target,

[0043] T F represents an estimated flight time.

[0044] wherein the remaining flight time is obtained by the following formula (six) :

[0045] T gp = T F -t (six)

[0046] wherein t represents a current time point starting from the UAV taking off.

[0047] The present application has the beneficial effects including:

[0048] (1) The cluster target guidance probability optimal multi-UAV precise distribution method provided by the present application introduces the covariance analysis method, can accurately and quickly calculate the mean and variance of the guidance end miss distance under the influence of target maneuvering and pointing error, and further obtain the normal distribution function of the miss distance, and more accurately solve the guidance probability of a single UAV to a single target.

[0049] (2) The cluster target guidance probability optimal multi-UAV distribution method provided by the present application obtains the optimal distribution result through the marginal enumeration method on the basis of the accurate guidance probability of a single UAV to a single target, so that each target has a corresponding UAV for tracking, and the overall guidance success possibility is maximum. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1A trajectory diagram of a target tracked by a UAV in an embodiment of the present application is shown.

[0051] Figure 2 A curve showing the overload of a UAV over time in an embodiment of the present application is shown. DETAILED DESCRIPTION

[0052] The present application is further described in detail by the accompanying drawings and embodiments. The features and advantages of the present application will become more apparent from the detailed description, when taken in conjunction with the accompanying drawings.

[0053] The term "exemplary" is used herein to mean "serving as an example, instance, or illustration." Any implementation described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other implementations. Unless specifically indicated otherwise, the drawings are not necessarily to scale.

[0054] The present application provides a multi-UAV guidance probability optimal allocation method for cluster targets. In the method, a covariance analysis method is introduced to obtain the mean and variance of the terminal miss distance under target random maneuver and heading error interference. The guidance probability of a single UAV for a single target is obtained by combining the effective action radius of the UAV on-board load.

[0055] The total guidance probability corresponding to each allocation scheme and the threat value of the target are collectively used as the input value of the marginal benefit-based column enumeration method, so as to obtain the optimal allocation result.

[0056] Preferably, the guidance probability of a single UAV for a single target is obtained by the following formula (I):

[0057]

[0058] wherein, p ij represents the guidance probability of the i-th UAV for the j-th target;

[0059] represents the effective action radius of the UAV on-board load, which is determined by specific factors such as the type and material of the load;

[0060] represents the mean of the terminal miss distance when the i-th UAV guides the j-th target;

[0061] represents the variance of the terminal miss distance when the i-th UAV guides the j-th target;

[0062] z represents the zero-control miss distance, i.e., the terminal miss distance of each guidance.

[0063] In the present application, after the acceleration is calculated by the PN, it is integrated to obtain the position information of the UAV of our side, and the zero-control miss distance z is obtained by subtracting the position information of the target UAV.

[0064] Preferably, the The value is taken as the first element of the M(t) matrix at the final time.

[0065] The The value is taken as the first element on the diagonal of the P(t) matrix at the final time.

[0066] Both the M(t) matrix and the P(t) matrix are obtained by the following equation (ii):

[0067]

[0068] in, The derivative of M(t) is represented;

[0069] The derivative of P(t) is represented by .

[0070] F(t) represents the dynamic matrix;

[0071] G(t) represents the control matrix;

[0072] Q(t) represents the spectral density matrix;

[0073] M(t)′ represents M(t) obtained at the previous time step;

[0074] P(t)′ represents P(t) obtained at the previous time step;

[0075] That is, by substituting M(t) and P(t) obtained at the previous time step into equation (ii) at the current time step, we can obtain... and Again Integrating gives M(t), for Integrate to obtain P(t).

[0076] Preferably, equation (ii) is iterated to the estimated flight time T. F The M(t) matrix obtained at the final moment is the M(t) matrix at the end time, and the P(t) matrix obtained is the P(t) matrix at the end time. The iteration time is preferably 0.01 seconds. The estimated flight time T... F The value is 10 seconds. The estimated flight time T described in this application... F This is based on a time constant greater than 10 times, where the time constant is 1; that is, during guidance, it must be ensured that the time between the UAV and the target meeting at maximum speed is greater than 10 seconds. Therefore, before guidance, a preliminary judgment must be made on the distance and speed between the UAV and the target to ensure that the guidance time is greater than 10 seconds before the UAV can be arranged to track and enter the guidance phase; otherwise, the UAV cannot be arranged to perform guidance.

[0077] Preferably, the dynamic matrix F(t) is shown as formula (three) below:

[0078]

[0079] wherein w n represents the natural oscillation frequency of the second-order system of the unmanned aerial vehicle autopilot; the value thereof is preferably 16;

[0080] ξ n represents the damping ratio of the second-order system of the unmanned aerial vehicle autopilot; the value thereof is preferably 0.7;

[0081] N represents the proportional guidance coefficient; the value thereof is 3-5, preferably 4;

[0082] V c represents the relative speed between the unmanned aerial vehicle and the target in the line-of-sight direction; the target speed is obtained by detecting the target speed through a sensor such as a radar;

[0083] w s represents the natural oscillation frequency of the second-order system of the seeker, preferably 17;

[0084] K s represents the system gain; the value thereof is preferably 0.95*w s 2 ;

[0085] T go represents the remaining flight time;

[0086] The remaining flight time is obtained by formula (six) below:

[0087] T go = T F -t (six)

[0088] wherein t represents the current time since the takeoff of the unmanned aerial vehicle.

[0089] Preferably, the control matrix G(t) is shown as formula (four) below:

[0090]

[0091] wherein V P represents the initial speed of the unmanned aerial vehicle.

[0092] Preferably, the spectral density matrix Q(t) is shown as formula (five) below:

[0093]

[0094] wherein μ σ represents the initial pointing angle of the unmanned aerial vehicle, the value of which is determined by the relative position of the unmanned aerial vehicle and the target.

[0095] μ T denotes the initial acceleration of the target;

[0096] T F denotes the estimated time of flight.

[0097] In a preferred embodiment, in the method, based on the number of targets and the number of UAVs, all possible allocation schemes are obtained, and for the tracking relationship in all schemes, the guidance probability of each UAV tracking each target is obtained respectively; on this basis, the threat value of the target is combined together as the input value of the marginal revenue-based column enumeration method, so as to obtain the optimal allocation result.

[0098] The marginal revenue-based column enumeration method described in the present application can specifically select the method described in Jin T Y, He SM, et al. "Evaluation Model and exact optimization algorithm in missile-target assignment." JOURNAL OF GUIDANCE, CONTROL. AND DYNAMICS, 2023, 46(9), (16 Apr 2023).

[0099] Embodiment

[0100] 6 UAVs are set to track 4 targets;

[0101] The initial position coordinates of the 6 UAVs and the 4 targets are shown in the following table:

[0102]

[0103] The maneuvering situation of the 4 targets is: a T = [1.5, 0.6, 0, 0.9] m / s 2 ;

[0104] The threat value of the 4 targets is: W = [0.6, 0.1, 0.2, 0.4];

[0105] Based on the initial situation of the 6 UAVs and the 4 targets, the guidance probability of a single UAV to a single target for each combination situation is obtained by the following formula (I);

[0106]

[0107] p ij denotes the guidance probability of the i-th UAV to the j-th target;

[0108] ρ denotes the effective action radius of the UAV on-board payload;

[0109] represents the mean value of the terminal miss distance when the ith unmanned aerial vehicle tracks the jth target;

[0110] represents the variance of the terminal miss distance when the ith unmanned aerial vehicle tracks the jth target;

[0111] z represents the zero control miss distance;

[0112] the is the first element of the M(t) matrix at the terminal time,

[0113] the is the first element on the diagonal of the P(t) matrix at the terminal time;

[0114] The M(t) matrix and the P(t) matrix are obtained by the following formula (two):

[0115]

[0116] wherein, represents the derivative of M(t);

[0117] represents the derivative of P(t);

[0118] F(t) represents a dynamic matrix;

[0119] G(t) represents a control matrix;

[0120] Q(t) represents a spectral density matrix;

[0121] M(t)' represents the M(t) obtained at the previous time;

[0122] P(t)' represents the P(t) obtained at the previous time;

[0123] M(t) and P(t) obtained at the previous time are substituted into formula (two) at the current time to obtain and M(t) is obtained by integrating and P(t) is obtained by integrating .

[0124] The formula (two) is iterated to the final time of the estimated flight time T F The M(t) matrix obtained at the final time is the M(t) matrix at the terminal time, and the P(t) matrix obtained is the P(t) matrix at the terminal time; F The value of T

[0125] The dynamic matrix F(t) is shown in the following formula (three):

[0126]

[0127] wherein w n represents the natural oscillation frequency of the second order system of the autopilot of the UAV, and is equal to 16;

[0128] ξ n represents the damping ratio of the second order system of the autopilot of the UAV, and is equal to 0.7;

[0129] N represents the proportional guidance coefficient, and is equal to 4;

[0130] V c represents the relative speed between the UAV and the target in the line-of-sight direction;

[0131] w s represents the natural oscillation frequency of the second order system of the seeker, and is equal to 17;

[0132] K s represents the system gain, and is equal to 0.95*w s 2 ;

[0133] T go represents the remaining flight time;

[0134] T go =T F -t

[0135] wherein t represents the current time since the UAV took off.

[0136] The control matrix G(t) is shown in the following formula (four):

[0137]

[0138] wherein V P represents the initial speed of the UAV, and is equal to 30 m / s.

[0139] The spectral density matrix Q(t) is shown in the following formula (five):

[0140]

[0141] wherein μ σ represents the initial pointing angle of the UAV,

[0142] μ T represents the initial acceleration of the target.

[0143] The optimal assignment result is obtained after 0.05 s as follows:

[0144]

[0145] That is, U1 and U2 jointly track T1, U3 tracks T2, U4 tracks T3, and U5 and U6 jointly track T4.

[0146] Each UAV attacks the assigned target, and after 17.84 s, all UAVs track the corresponding target, and the motion trajectory is as shown in Figure 1 The final guidance miss distance is less than 0.5 m, and the effective action radius of the airborne load is within the effective action radius of the airborne load. Figure 2 It can be seen from

[0147] The above embodiment results show that the multi-UAV guidance probability optimal assignment method for cluster targets can accurately solve the multi-target assignment problem, and provides a reliable solution for solving similar problems.

[0148] The above describes the present application in combination with preferred embodiments, but these embodiments are only exemplary and serve only to illustrate. On this basis, various substitutions and improvements can be made to the present application, and these all fall within the protection scope of the present application.

Claims

1. A method for multi-UAV guidance probability optimal allocation aiming at a cluster target, characterized in that, In the method, the covariance analysis method is introduced to obtain the mean and variance of the terminal miss distance under the target random maneuver and heading error interference, and the guidance success probability of a single UAV to a single target is obtained by combining the effective action radius of the UAV-borne load. The whole guidance probability corresponding to each allocation scheme and the threat value of the target are taken as the input values of the marginal benefit-based column enumeration method, so as to obtain the optimal allocation result. The guidance probability of a single UAV to a single target is obtained by the following formula (I): wherein p ij represents the guidance probability of the ith UAV to the jth target; ρ represents the effective action radius of the UAV-borne load; represents the mean of the end miss distance of the ith UAV when guiding the jth target; σ2ijdenotes the variance of the end-point miss distance of the ith UAV guiding the jth target; z represents the zero-control miss distance; The The first element of the matrix of end moments M(t) when the value is taken, The The first element on the diagonal of the matrix of end times P(t) when the value is taken; The M(t) matrix and the P(t) matrix are obtained by the following formula (II): wherein denotes the derivative of M(t); denotes the derivative of P(t); F(t) represents the dynamic matrix; G(t) represents the control matrix; Q(t) represents the spectral density matrix; M(t)' represents the M(t) obtained at the previous moment; P(t)' represents the P(t) obtained at the previous moment; M(t) and P(t) obtained at the previous time are substituted into the equation (2) at the current time to obtain and M(t) is obtained by integrating M(t) is obtained by integrating P(t) is obtained by integrating 2. The multi-UAV guidance probability optimal allocation method for cluster targets according to claim 1, characterized in that, said formula (two) iteration to the estimated time of flight T F The M(t) matrix obtained at the final moment is the terminal moment M(t) matrix, and the P(t) matrix obtained is the terminal moment P(t) matrix.

3. The multi-UAV guidance probability optimal allocation method for cluster targets according to claim 1, characterized in that, The dynamic matrix F(t) is shown in the following formula (III): wherein w n represents the natural oscillation frequency of the second order system of the autopilot of the drone; ξ n represents the damping ratio of the autopilot second order system of the drone; w s ω denotes the natural oscillation frequency of the second order system of the probe head; N represents the proportional guidance coefficient; V c represents the relative speed between the UAV and the target in the line-of-sight direction; K s represents the system gain; T go represents the remaining flight time.

4. The multi-UAV guidance probability optimal allocation method for cluster targets according to claim 1, characterized in that, The control matrix G(t) is shown in the following formula (IV): V P represents the initial speed of the UAV.

5. The multi-UAV guidance probability optimal allocation method for cluster targets according to claim 1, characterized in that, The spectral density matrix Q(t) is shown in the following formula (V): wherein μ σ denotes the initial pointing angle of the drone, μ T the initial acceleration of the target, T F represents an estimated time of flight.

6. The multi-UAV guidance probability optimal allocation method for cluster targets according to claim 3, characterized in that, The remaining flight time is obtained by the following formula (VI): T go = T F -t (six) Wherein, t represents the current time from the take-off of the UAV.

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