Cluster target-oriented multi-unmanned aerial vehicle guidance probability optimal allocation method

Abstract

The invention discloses a cluster target-oriented multi-unmanned aerial vehicle guidance probability optimal allocation method, which comprises the following steps of: re-expressing a system utilizing a PN guidance law as a linear time-varying system dynamically formed by an unmanned aerial vehicle autopilot and a seeker by utilizing zero-control miss distance; according to a control theory, the system can be established in a block diagram form, target maneuvering and initial course errors are taken as input, and zero-control miss distance is taken as output; secondly, introducing a covariance analysis method to accurately calculate an average value and a variance of zero-control miss distance under target random maneuvering and course error interference; by combining the effective action radius of the airborne load of the unmanned aerial vehicle, the guidance probability of a single unmanned aerial vehicle to a single target can be accurately obtained, an optimal distribution result is obtained by combining a marginal income column enumeration method, and on this basis, the unmanned aerial vehicle is controlled to fly to the target by a proportional guidance law.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-target cluster guidance, and in particular to a method for optimally allocating guidance probabilities of multiple unmanned aerial vehicles (UAVs) facing cluster targets. Background Art

[0002] With the development of information technology and low-altitude economy, the application of drones has become more and more extensive. However, the widespread use of drone swarms in urban environments poses a serious threat to low-altitude safety. Therefore, it is necessary to control drone swarms and capture them safely and effectively when necessary. In order to solve this problem, various research institutions are actively studying effective countermeasures against drone swarms. Among them, using drone swarms to guide target swarms has been considered an effective means. In the cluster confrontation problem, accurately assigning multiple pursuers to multiple targets (MPMTA) is crucial to achieve high-probability guidance. However, the current MPMTA method mainly relies on empirical fitting to establish the allocation model, which may lead to inaccurate results. In addition, the probability calculation method based on the typical Monte Carlo method requires a lot of time and experimental costs, which is not very applicable 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 TY, He SM, et al. "Evaluation Model and exact optimization algorithm min mis sile-target assignment." JOURNAL OF GUIDANCE, CONTRO L. AND DYNAMIC S, 2023, 46(9), (16Apr 2023). However, the scheme is based on the estimated probability, so the accuracy of the data basis of the scheme needs to be improved.

[0004] Based on the above problems, the inventors have conducted in-depth research on the guidance probability of each aircraft, hoping to design a multi-UAV precise allocation method with optimal cluster target guidance probability that can solve the above problems. Summary of the invention

[0005] In order to overcome the above problems, the inventors have conducted intensive research and designed an optimal allocation method for the guidance probability of multiple UAVs facing cluster targets. In this method, by utilizing the zero-control miss amount, the system using the PN guidance law is re-expressed as a linear time-varying system composed of the UAV autopilot and the dynamics of the seeker; according to control theory, the system can be established in the form of a block diagram, with the target maneuver and the initial heading error as input, and the zero-control miss amount as output; then, the covariance analysis method is introduced to accurately calculate the average value and variance of the zero-control miss amount under the interference of the target random maneuver and heading error; by combining the effective action radius of the UAV's onboard payload, the guidance probability of a single UAV to a single target can be accurately obtained, and then combined with the column enumeration method of marginal benefits to obtain the optimal allocation result, on this basis, the UAV is controlled by the proportional guidance law to track the target, thereby completing the present invention.

[0006] Specifically, the purpose of the present invention is to provide an optimal allocation method for the guidance probability of multiple UAVs facing cluster targets. In this method, a covariance analysis method is introduced to obtain the mean and variance of the terminal miss amount under the interference of target random maneuvering and heading error, and the guidance probability of a single UAV to a single target is obtained by combining the effective action radius of the UAV airborne payload;

[0007] All guidance probabilities and target threat values ​​corresponding to each allocation scheme are used together as input values ​​of the column enumeration method based on marginal benefits to obtain the optimal allocation result.

[0008] The guidance probability of a single UAV to a single target is obtained by the following formula (1):

[0009]

[0010] Among them, p ij represents the guidance probability of the i-th UAV to the j-th target;

[0011] ρ represents the effective action radius of the UAV's airborne payload;

[0012] It represents the mean value of the terminal miss distance when the i-th UAV guides the j-th target;

[0013] represents the variance of the terminal miss distance when the i-th UAV guides the j-th target;

[0014] z represents the zero control miss distance.

[0015] Among them, the The value is the first element of the matrix M(t) at the end time.

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

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

[0018]

[0019] in, represents the derivative of M(t);

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

[0021] F(t) represents the dynamics matrix;

[0022] G(t) represents the control matrix;

[0023] Q(t) represents the spectral density matrix;

[0024] M(t)′ represents the M(t) obtained at the previous moment;

[0025] P(t)′ represents P(t) obtained at the previous moment;

[0026] By substituting the M(t) and P(t) obtained at the previous moment into the current moment's formula (2), we can obtain and Again Integrate to get M(t), Integrate to get P(t).

[0027] Wherein, the formula (II) is iterated to the estimated flight time 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.

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

[0029]

[0030] Among them, w n represents the natural oscillation frequency of the second-order system of the UAV autopilot;

[0031] ξ n represents the damping ratio of the second-order system of the UAV autopilot;

[0032] N represents the proportional guidance coefficient;

[0033] V c Indicates the relative speed between the UAV and the target along the line of sight;

[0034] Ks represents the system gain;

[0035] T go Indicates the remaining flight time.

[0036] Wherein, the control matrix G(t) is shown in the following formula (IV):

[0037]

[0038] Among them, V P Indicates the speed of the drone.

[0039] Wherein, the spectrum density matrix Q(t) is shown in the following formula (V):

[0040]

[0041] Among them, μ σ represents the initial pointing angle of the drone,

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

[0043] T F Indicates the estimated flight time.

[0044] Wherein, the remaining flight time is obtained by the following formula (VI):

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

[0046] Among them, t represents the current time starting from the time when the drone takes off.

[0047] The beneficial effects of the present invention include:

[0048] (1) According to the multi-UAV precise allocation method with optimal cluster target guidance probability provided by the present invention, the covariance analysis method is introduced in the method, which can accurately and quickly calculate the mean and variance of the guidance terminal miss amount under the influence of target maneuver and pointing error, and then obtain the normal distribution function of the miss amount, and more accurately solve the guidance probability of a single UAV to a single target;

[0049] (2) According to the optimal allocation method of multi-UAV guidance probability for cluster targets provided by the present invention, on the basis of the precise guidance probability of a single UAV to a single target, the optimal allocation result is obtained by the column enumeration method of marginal benefits, so that each target has a corresponding UAV to track, and the overall guidance success probability is maximized. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1A schematic diagram showing the trajectory of a target tracked by a drone in an embodiment of the present application is shown;

[0051] Figure 2 The graph of the UAV overload changing over time in the embodiment of the present application is shown. DETAILED DESCRIPTION

[0052] The present invention will be further described in detail below through the accompanying drawings and embodiments. Through these descriptions, the characteristics and advantages of the present invention will become more clear and distinct.

[0053] The word "exemplary" is used exclusively herein to mean "serving as an example, embodiment, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise noted.

[0054] The present invention provides a method for optimal allocation of guidance probabilities of multiple UAVs facing cluster targets. In the method, a covariance analysis method is introduced to obtain the mean and variance of the terminal miss distance under the interference of random maneuvering of the target and heading error, and the guidance probability of a single UAV to a single target is obtained by combining the effective action radius of the UAV airborne payload.

[0055] All guidance probabilities and target threat values ​​corresponding to each allocation scheme are used together as input values ​​of the column enumeration method based on marginal benefits to obtain the optimal allocation result.

[0056] Preferably, the guidance probability of a single UAV to a single target is obtained by the following formula (1):

[0057]

[0058] Among them, p ij represents the guidance probability of the i-th UAV to the j-th target;

[0059] ρ represents the effective action radius of the UAV's airborne payload, which is determined by specific factors such as the type and material of the payload;

[0060] It represents the mean value 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 amount, that is, the terminal miss amount of each guidance.

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

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

[0065] Said The value is the first element on the diagonal of the matrix P(t) at the end time;

[0066] The M(t) matrix and the P(t) matrix are both obtained by the following formula (II):

[0067]

[0068] in, represents the derivative of M(t);

[0069] represents the derivative of P(t);

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

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

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

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

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

[0075] That is, by substituting the M(t) and P(t) obtained at the previous moment into the current moment's formula (2), we can obtain and Again Integrate to get M(t), Integrate to get P(t).

[0076] Preferably, the formula (II) is iterated to the estimated flight time 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. The time of each iteration is not long, preferably 0.01 seconds. The estimated flight time T F The value of is 10 seconds. The estimated flight time T in this application F It is obtained based on a time constant greater than 10 times, where the time constant is 1; that is, during guidance, at least the time when the UAV and the target meet at the maximum speed is greater than 10s. 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 10s before arranging the UAV for tracking and entering guidance, otherwise the UAV cannot be arranged for guidance.

[0077] Preferably, the dynamics matrix F(t) is as shown in the following formula (III):

[0078]

[0079] Among them, w n Represents the natural oscillation frequency of the second-order system of the UAV autopilot; its value is preferably 16;

[0080] ξ n It represents the damping ratio of the second-order system of the UAV autopilot; its value is preferably 0.7;

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

[0082] V c Indicates the relative speed between the drone and the target along the line of sight. It is obtained by detecting the target speed through sensors such as 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; its value is preferably 0.95*w s 2 ;

[0085] T go Indicates the remaining flight time;

[0086] The remaining flight time is obtained by the following formula (VI):

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

[0088] Among them, t represents the current time starting from the time when the drone takes off.

[0089] Preferably, the control matrix G(t) is shown in the following formula (iv):

[0090]

[0091] Among them, V P Indicates the initial speed of the drone.

[0092] Preferably, the spectrum density matrix Q(t) is as shown in the following formula (V):

[0093]

[0094] Among them, μ σ Indicates the initial pointing angle of the drone, and its value is determined by the relative position of our drone and the target;

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

[0096] T F Indicates the estimated flight time.

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

[0098] The marginal benefit-based column enumeration method described in the present application can specifically select the method described in Jin TY, He SM, et al. "Evaluation Model and exact optimization algorithm in missile-target assignment." JOURNAL OF GUIDANCE, CONTRO L. AND DYNAMICS, 2023, 46(9), (16Apr2023).

[0099] Example

[0100] Set to control 6 drones to track 4 targets;

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

[0102]

[0103] The mobility of the four targets is: a. T =[1.5, 0.6, 0, 0.9] m / s 2 ;

[0104] The threat values ​​of the four targets are: W = [0.6, 0.1, 0.2, 0.4];

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

[0106]

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

[0108] ρ represents the effective action radius of the UAV's airborne payload;

[0109] It represents the mean value of the terminal miss distance when the i-th UAV tracks the j-th target;

[0110] represents the variance of the terminal miss distance when the i-th UAV tracks the j-th target;

[0111] z represents the zero-control miss amount;

[0112] Said The value is the first element of the matrix M(t) at the end time.

[0113] Said The value is the first element on the diagonal of the matrix P(t) at the end time;

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

[0115]

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

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

[0118] F(t) represents the dynamics matrix;

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

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

[0121] M(t)′ represents the M(t) obtained at the previous moment;

[0122] P(t)′ represents P(t) obtained at the previous moment;

[0123] By substituting the M(t) and P(t) obtained at the previous moment into the current moment's formula (2), we can obtain and Again Integrate to get M(t), Integrate to get P(t).

[0124] The formula (II) is iterated to estimate the flight time 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; T F The value of is 10 seconds;

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

[0126]

[0127] Among them, w n It represents the natural oscillation frequency of the second-order system of the UAV autopilot, and its value is 16;

[0128] ξ n It represents the damping ratio of the second-order system of the UAV autopilot, and its value is 0.7;

[0129] N represents the proportional guidance coefficient; its value is 4;

[0130] V c Indicates the relative speed between the UAV and the target along the line of sight;

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

[0132] K s Indicates the system gain, the value is 0.95*w s 2 ;

[0133] T go Indicates the remaining flight time;

[0134] T go =T F -t

[0135] Among them, t represents the current time starting from the time when the drone takes off.

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

[0137]

[0138] Among them, V P Indicates the initial speed of the drone, which is 30m / s.

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

[0140]

[0141] Among them, μ σ represents the initial pointing angle of the drone,

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

[0143] The total guidance probability and target threat value corresponding to each allocation scheme are used as the input value of the column enumeration method based on marginal benefits in Jin TY, He SM, et al. "Evaluation Model and exact optimization algorithm in missile-target assignment." JOURNAL OF GUIDANCE, CONTROL. AND DYNAMICS, 2023, 46(9), (16Apr 2023). The optimal allocation result is obtained after 0.05s 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 drone attacks the assigned target. After 17.84 seconds, all drones track the corresponding target. The movement trajectory is as follows: Figure 1 As shown in the figure, the final guidance miss distance is less than 0.5m, which is within the effective action radius of the airborne payload. Figure 2 It can be seen that at the end of the guidance, the overloads of all pursuers tend to converge, and the overload of each pursuer is controlled within a small range, ensuring that the system can stably and safely catch up with the maneuvering target during the guidance process.

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

[0148] The present invention has been described above in conjunction with preferred embodiments, but these embodiments are only exemplary and serve only as an illustration. On this basis, the present invention may be subjected to a variety of substitutions and improvements, all of which fall within the scope of protection of the present invention.

Claims

1. A method for optimal allocation of guidance probabilities of multiple UAVs for cluster targets, characterized in that: In this method, the covariance analysis method is introduced to obtain the mean and variance of the terminal miss distance under the interference of target random maneuver and heading error, and combined with the effective action radius of the UAV's airborne payload, the guidance success probability of a single UAV to a single target is obtained; All guidance probabilities and target threat values ​​corresponding to each allocation scheme are used together as input values ​​of the column enumeration method based on marginal benefits to obtain the optimal allocation result.

2. The optimal allocation method for multi-UAV guidance probability for cluster targets according to claim 1 is characterized in that: The guidance probability of a single UAV to a single target is obtained by the following formula (1): Among them, p ij represents the guidance probability of the i-th UAV to the j-th target; ρ represents the effective action radius of the UAV's airborne payload; It represents the mean value of the terminal miss distance when the i-th UAV guides the j-th target; represents the variance of the terminal miss distance when the ith UAV guides the ith target; z represents the zero control miss distance.

3. The optimal allocation method of multi-UAV guidance probability for cluster targets according to claim 2 is characterized in that: Said The value is the first element of the matrix M(t) at the end time. Said The value is the first element on the diagonal of the matrix P(t) at the end time; The M(t) matrix and the P(t) matrix are both obtained by the following formula (II): in, represents the derivative of M(t); represents the derivative of P(t); F(t) represents the dynamics 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 P(t) obtained at the previous moment; By substituting the M(t) and P(t) obtained at the previous moment into the current moment's formula (2), we can obtain and Again Integrate to get M(t), Integrate to get P(t).

4. The optimal allocation method for multi-UAV guidance probability for cluster targets according to claim 3 is characterized in that: The formula (II) is iterated to estimate the flight time 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.

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

6. The optimal allocation method for multi-UAV guidance probability for cluster targets according to claim 3 is characterized in that: The control matrix G(t) is shown in the following formula (IV): Among them, V P Indicates the initial speed of the drone.

7. The optimal allocation method of multi-UAV guidance probability for cluster targets according to claim 3 is characterized in that: The spectrum density matrix Q(t) is shown in the following formula (V): Among them, μ σ represents the initial pointing angle of the drone, μ T represents the initial acceleration of the target, T F Indicates the estimated flight time.

8. The optimal allocation method of multi-UAV guidance probability for cluster targets according to claim 5 is characterized in that: The remaining flight time is obtained by the following formula (VI): T go =T F -t (six) Among them, t represents the current time starting from the time when the drone takes off.

Images