Energy optimal guidance method for intercepting average maneuvering target

Abstract

The invention discloses an energy optimal guidance method for intercepting a uniform maneuvering target, and the method comprises the steps: obtaining the sight angular speed # imgabs0 # of an aircraft relative to the target, the speed Vc of the aircraft approaching the target, and the acceleration # imgabs1 # of the target through a photoelectric pod and other sensors carried on the aircraft in real time, and taking # imgabs2 # and # imgabs3 # as two input quantities; and inputting the output quantity # imgabs4 # into a pre-trained full-connection neural network to obtain a corresponding output quantity # imgabs4 # as an optimal control instruction, and controlling the unmanned aerial vehicle to intercept the average maneuvering target through the optimal control instruction.

Description

Technical Field

[0001] The present invention relates to the field of aircraft guidance and control, and particularly to an energy-optimal guidance method for intercepting an equipotential maneuvering target. Background Art

[0002] "Low, slow, and small" unmanned aerial vehicles (UAVs) have characteristics such as low cost and high combat flexibility. Currently, they have been widely applied in practice and have become a new force in various industries. Traditional countermeasures against UAVs (missile interception, lasers, microwaves) have disadvantages such as high cost-effectiveness ratio and large omissions. Using an aircraft to counter an aircraft has become a research hotspot in various countries due to its low cost-effectiveness ratio and flexibility.

[0003] The difficulty of using an aircraft to counter an aircraft is that the maneuvering capabilities of both the enemy and our side are comparable, and the endurance of UAVs is limited. This places higher requirements on the overload ratio and energy consumption of the guidance law. Proportional navigation (PN) is the most widely used guidance law and has been proven to be energy-optimal for intercepting non-maneuvering targets when its navigation ratio is equal to 3. However, when the target maneuvers, the available overload of the PN guidance law needs to be designed to be more than three times the target maneuver. To solve this problem, people designed the Augmented Proportional Navigation (APN) guidance law by introducing the normal acceleration information of the target under the assumption of constant target maneuver. APN can achieve zero terminal acceleration convergence when dealing with a maneuvering target with a constant lateral acceleration. However, in practice, due to overcompensation, the overload ratio of APN may increase or even be higher than that of PN during the guidance process. In addition, some people derived the optimal guidance law for the virtual control quantity using a relative virtual frame, and its form is similar to the two-dimensional Augmented Ideal Proportional Navigation (AIPN), which ensures that the required overload of the interceptor is lower than the target overload at the end of the guidance, but does not constrain the overload ratio during the entire guidance process.

[0004] Based on the above problems, the inventor of the present invention focuses on considering the guidance scheme for intercepting equipotential maneuvering targets, aiming to solve the problem that it is difficult to analytically solve the energy-optimal guidance model under the constraint of equipotential maneuvering ability by setting reasonable neural network input and output and neural network structure, and to give a guidance and control method that can control the aircraft to successfully intercept a maneuvering target under the constraint of equipotential maneuvering ability. Summary of the Invention

[0005] To overcome the above problems, the present inventor has conducted intensive research and designed an energy-optimal guidance method for intercepting an equal-strength maneuvering target. In this method, an energy-optimal guidance model under the constraint of the equal-strength maneuvering capabilities of both sides is derived. Aiming at the problem that it is difficult to analytically solve the energy-optimal guidance model under the constraint of equal-strength maneuvering capabilities, a parameterized system with the same solution space as the original guidance problem and opposite motion is designed. The initial state of the parameterized system is designed according to the terminal constraints of the original guidance problem, and numerical integration is performed to obtain the Hamiltonian guidance trajectory that satisfies optimality. The mapping relationship between the flight state and the optimal control command is fitted by using the function approximation ability of the fully connected neural network to obtain the energy-optimal neural network guidance model. Then, the input quantities of the model are obtained. After training the fully connected neural network model with simulation data, the trained fully connected neural network is installed in the aircraft, and then the optimal control command is output in real time by using this neural network model. The UAV is controlled by this optimal control command to intercept the equal-strength maneuvering target, thus completing the present invention.

[0006] Specifically, the object of the present invention is to provide an energy-optimal guidance method for intercepting an equal-strength maneuvering target. In this method, the line-of-sight angular velocity of the aircraft relative to the target is obtained in real time The velocity V of the aircraft approaching the target c and the acceleration of the target

[0007] and and are used as two input quantities and input into a pre-trained fully connected neural network to obtain the corresponding output quantity as the optimal control command, and the aircraft is controlled to fly towards the target based on this optimal control command, and finally the aircraft intercepts the target.

[0008] Among them, the fully connected neural network includes 1 input layer, 3 hidden layers and 1 output layer;

[0009] The input layer includes neurons for receiving the input state tuple and neurons for receiving the input state tuple ;

[0010] Each hidden layer contains 20 neurons;

[0011] The output layer contains 1 neuron, which outputs the optimal control command

[0012] Among them, the tansig function is set as the activation function in the hidden layer;

[0013] The purelin function is set as the activation function in the output layer.

[0014] Among them, during the training process of the fully connected neural network, multiple groups of data are extracted from the optimal trajectory obtained by simulation as the basic data. After standardizing the basic data, it is divided into a training set, a validation set, and a test set;

[0015] Each group of data includes input quantities and output quantities

[0016] Among them, the input quantity is standardized by the following formula (1):

[0017]

[0018] Among them, represents the input quantity after standardization

[0019] represents the input quantity to be standardized in the basic data;

[0020] represents the mean value of all input quantities in the basic data;

[0021] represents the variance of all input quantities in the basic data.

[0022] Among them, the input quantity is standardized by the following formula (2):

[0023]

[0024] Among them, represents the input quantity after standardization

[0025] represents the input quantity to be standardized in the basic data;

[0026] represents the mean value of all input quantities in the basic data;

[0027] represents the variance of all input quantities in the basic data.

[0028] Among them, the output quantity is standardized by the following formula (3):

[0029]

[0030] Among them, Represents the output quantity after standardization processing

[0031] Represents the output quantity to be standardized in the basic data;

[0032] Represents the average value of all output quantities in the basic data ;

[0033] Represents the variance of all output quantities in the basic data ;

[0034] Among them, the stopping condition for the training of the fully connected neural network is that the loss function drops to 5×10 -8 or less or the number of training rounds reaches 3000 rounds.

[0035] Among them, the loss function is the mean square error between the output value of the fully connected neural network and the true value.

[0036] The beneficial effects of the present invention include:

[0037] According to the energy-optimal guidance method for intercepting an equal-strength maneuvering target provided by the present invention, this method can successfully intercept the target under the equal-strength maneuvering capabilities of both sides, providing a new solution for the low-cost interception of low, slow, and small targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Shows a schematic diagram of the change trend of MSE of the training set, validation set, and test set during the training process of the embodiment of the present application;

[0039] Figure 2 Shows a schematic diagram of the flight trajectories in the embodiment of the present application and the comparative example;

[0040] Figure 3 Shows a schematic diagram of the change of the distance between the aircraft and the target over time in the embodiment of the present application and the comparative example;

[0041] Figure 4 Shows a schematic diagram of the change of the aircraft acceleration over time in the embodiment of the present application and the comparative example;

[0042] Figure 5 Shows a schematic diagram of the change of the energy consumption of the aircraft over time in the embodiment of the present application and the comparative example. DETAILED DESCRIPTION OF THE INVENTION

[0043] The present invention will be further described in detail below through the drawings and embodiments. Through these descriptions, the features and advantages of the present invention will become more clearly defined.

[0044] As used herein, the term "exemplary" means "serving as an example, instance, or illustration". Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or better than other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise specified.

[0045] The present invention provides an energy-optimal guidance method for intercepting an equal-potential maneuvering target. In this method, the line-of-sight angular velocity of the aircraft relative to the target is obtained in real time. The velocity V of the aircraft approaching the target c and the acceleration of the target An optoelectronic pod is provided on the aircraft. The target is captured by the optoelectronic pod, and after the target is captured, the V c and

[0046] And and are used as two input quantities and input into a pre-trained fully connected neural network to obtain corresponding output quantities As the optimal control command, and based on this optimal control command, the aircraft is controlled to fly towards the target, and finally the aircraft intercepts the target.

[0047] In this application, by deriving the energy-optimal guidance model under the constraint of the equal-potential maneuvering ability of the enemy and ourselves, aiming at the problem that it is difficult to analytically solve the energy-optimal guidance model under the constraint of the equal-potential maneuvering ability, a parameterized system with the same solution space as the original guidance problem and opposite motion is designed; according to the terminal constraint of the original guidance problem, the initial state of the parameterized system is designed, and numerical integration is performed to obtain the Hamiltonian guidance trajectory that satisfies the optimality; the function approximation ability of the fully connected neural network is used to fit the mapping relationship between the flight state and the optimal control command, and an energy-optimal fully connected neural network is obtained. Among them, the mapping relationship between the flight state and the optimal guidance command is: Based on this, in this application, the above and are set as two input quantities of the fully connected neural network, which can enable the fully connected neural network to output the optimal control command in real time.

[0048] In a preferred embodiment, in order to achieve a balance between accuracy and efficiency, the fully connected neural network includes 1 input layer, 3 hidden layers and 1 output layer;

[0049] The input layer includes neurons for receiving the input state tuple and neurons for receiving the input state tuple ;

[0050] Each hidden layer contains 20 neurons;

[0051] The output layer includes 1 neuron, and outputs the optimal control instruction.

[0052] Preferably, the tansig function is set as the activation function in the hidden layer;

[0053] The purelin function is set as the activation function in the output layer.

[0054] In a preferred embodiment, during the training process of the fully connected neural network, multiple groups of data are extracted from the optimal trajectory obtained by simulation as the basic data, and after standardizing the basic data, it is divided into a training set, a validation set, and a test set; preferably, the training set, the validation set, and the test set are split according to the ratio of 70:15:15;

[0055] Each group of data includes an input quantity and an output quantity

[0056] Preferably, the input quantity is standardized by the following formula (I):

[0057]

[0058] where, represents the input quantity after standardization

[0059] represents the input quantity to be standardized in the basic data;

[0060] represents the mean value of all input quantities in the basic data ;

[0061] represents all input quantities in the basic data ;

[0062] Preferably, the input quantity is standardized by the following formula (II):

[0063]

[0064] where, represents the input quantity after standardization

[0065] represents the input quantity to be standardized in the basic data;

[0066] Represents the mean value of all input quantities in the basic data ;

[0067] Represents the mean value of all input quantities in the basic data of the variance.

[0068] Preferably, the output quantity is standardized by the following formula (III):

[0069]

[0070] wherein, represents the output quantity after standardization

[0071] represents the output quantity to be standardized in the basic data;

[0072] represents the mean value of all output quantities in the basic data ;

[0073] represents the mean value of all output quantities in the basic data of the variance.

[0074] Preferably, the stopping condition for the training of the fully connected neural network is that the loss function drops below 5×10 -8 or the number of training rounds reaches 3000 rounds.

[0075] Preferably, the loss function is the mean square error between the output value and the true value of the fully connected neural network.

[0076] Embodiment

[0077] Simulate the process of the aircraft intercepting the target. Set the flight speeds of the aircraft and the target to be 50m / s and 40m / s respectively. Then the approaching speed V c (0) ∈ [-90m / s, -10m / s] and takes values uniformly at intervals of 10; The overload capabilities of the target and the aircraft are in equilibrium. Take the maximum acceleration a m = 15m / s 2 , then the target acceleration is within [-15m / s 2 , 15m / s 2 and takes values uniformly at intervals of 3. The maximum jerk of the aircraft takes within [-10m / s 3 , 10m / s 3 and takes values uniformly at intervals of 0.5.

[0078] Let the maximum terminal guidance time \(t\) during the guidance process f = 20 s, that is, the numerical integration stops when it reaches 20 s. Set the integration step size to 0.001 s, and perform numerical integration by combining different initial values of state variables, obtaining a total of 4059 optimal trajectories. Uniformly discretize the dataset \(\Delta\) from each optimal trajectory at intervals of 0.05 s.

[0079] Split \(\Delta\) into a training set, a validation set, and a test set in the ratio of 70:15:15.

[0080] Train a fully connected neural network with this dataset \(\Delta\). This fully connected neural network includes 1 input layer, 3 hidden layers, and 1 output layer;

[0081] The input layer includes neurons for receiving the input state tuple and neurons for receiving the input state tuple ;

[0082] Each hidden layer contains 20 neurons;

[0083] The output layer contains 1 neuron, outputting the optimal control instruction

[0084] Before training, perform normalization processing on the input quantity using the following formula (1):

[0085]

[0086] where, represents the input quantity after normalization processing

[0087] represents the input quantity to be normalized in the basic data;

[0088] represents the mean value of all input quantities in the basic data ;

[0089] represents the mean value of all input quantities in the basic data ;

[0090] Before training, perform normalization processing on the input quantity using the following formula (2):

[0091]

[0092] where, represents the input quantity after normalization processing

[0093] Represents the input quantity to be normalized in the basic data;

[0094] Represents all input quantities in the basic data mean value;

[0095] Represents all input quantities in the basic data variance.

[0096] Before training, the output quantity is normalized by the following formula (III):

[0097]

[0098] where, Represents the output quantity after normalization

[0099] Represents the output quantity to be normalized in the basic data;

[0100] Represents all output quantities in the basic data mean value;

[0101] Represents all output quantities in the basic data variance.

[0102] The tansig function is set as the activation function in the hidden layer;

[0103] The purelin function is set as the activation function in the output layer.

[0104] The loss function of training is set to the mean square error (MSE) between the neural network output value and the true value; the change trends of MSE of the training set, validation set, and test set during the training process are as Figure 1 shown. It can be seen that after 3000 rounds of training, the MSEs of the latter three all drop to 5×10 -8 or less.

[0105] The above-trained fully connected neural network is installed in the aircraft, and the aircraft is used to intercept the target. The initial position of the aircraft is set to (0m, 0m), the initial track angle of the aircraft is 60°, the speed of the aircraft is 50m / s, and during the guidance process, the constraint |a M | ≤ a m ; the initial position of the target is set to (800m, 50m), the initial track angle of the target is 180°, the speed of the target is 40m / s, the target moves at a constant speed in the initial stage, and when the relative distance r is less than 350, it escapes with the maximum maneuvering ability, that is, take aT = 15 m / s 2 。The final flight path of the aircraft is as shown by the red line in Figure 2 ; the changing trend of the distance between the aircraft and the target is as shown by the red line in Figure 3 ; Figure 4 the changing trend of the aircraft's acceleration during the interception process is shown by the red line in Figure 5 ; the changing trend of the aircraft's energy consumption during the interception process is shown by the red line in

[0106] Comparative example

[0107] Set the initial position of the aircraft to (0 m, 0 m), the initial flight path angle of the aircraft to 60°, the aircraft speed to 50 m / s, and during the guidance process, constrain |a M | ≤ a m ; set the initial position of the target to (800 m, 50 m), the initial flight path angle of the target to 180°, the target speed to 40 m / s, the target moves at a constant speed in the initial stage, and when the relative distance r is less than 350, it escapes with the maximum maneuverability, that is, take a T = 15 m / s 2 .

[0108] When the guidance command in the aircraft is obtained through the proportional navigation guidance law (PN) recorded in Kreindler, E., “Optimality of Proportional Navigation,” AIAA Journal, Vol. 11, No. 6, 1973, pp. 878 - 880., the final flight path of the aircraft is as shown by the black line in Figure 2 ; the changing trend of the distance between the aircraft and the target is as shown by the black line in Figure 3 ; the changing trend of the aircraft's acceleration is as shown by the black line in Figure 4 ; the changing trend of the aircraft's energy consumption is as shown by the black line in Figure 5 .

[0109] When the guidance command in the aircraft is obtained through the augmented proportional navigation guidance law (APN) recorded in Ghosh, S., Ghose, D., and Raha, S., “Capturability of Augmented Pure Proportional Navigation Guidance Against Time - Varying Target Maneuvers,” Journal of Guidance, Control, and Dynamics, Vol. 37, No. 5, 2014, pp. 1446–1461., the final flight path of the aircraft is as shown by the black line in Figure 2As shown by the medium pink line, the changing trend of the distance between the aircraft and the target is as follows Figure 3 As shown by the medium pink line, the changing trend of the acceleration of the aircraft is as follows Figure 4 As shown by the medium pink line, the changing trend of the energy consumption of the aircraft is as follows Figure 5 As shown by the medium pink line.

[0110] When the guidance command in the aircraft is obtained through the Augmented Ideal Proportional Navigation (AIPN) guidance law recorded in [6] Jeon I S, Cho H, Lee J I. Exact guidance solution for maneuvering target on relative virtual frame formulation[J]. Journal of Guidance, Control, and Dynamics, 2015, 38(7):1330 - 1340., the final trajectory of the aircraft is as follows Figure 2 As shown by the medium blue line, the changing trend of the distance between the aircraft and the target is as follows Figure 3 As shown by the medium blue line, the changing trend of the acceleration of the aircraft is as follows Figure 4 As shown by the medium blue line, the changing trend of the energy consumption of the aircraft is as follows Figure 5 As shown by the medium blue line.

[0111] From Figure 2 and Figure 3 it can be known that the miss distances of PN and APN are 20.1637m and 70.0321m respectively, and the target cannot be successfully intercepted. While the miss distances of AIPN and the embodiment are both less than 0.1m, and the target can be successfully intercepted. From Figure 4 it can be seen that at the end of guidance, the acceleration value of AIPN tends to the target acceleration, while the acceleration of the embodiment tends to be around 0, which will ensure that the aircraft has a greater maneuver margin at the end of guidance to cope with the additional maneuvers of the target. From Figure 5 it can be seen that the energy consumption of the embodiment is lower than that of AIPN when the guidance is completed.

[0112] From the embodiment and the comparative example, it can be known that the energy - optimal guidance method for intercepting an equipotential maneuvering target provided by the present application can not only successfully intercept the target, but also has a greater maneuver margin and lower energy consumption, and can still successfully intercept the target when the target has a greater speed and acceleration.

[0113] The present invention has been described above in combination with preferred embodiments. However, these embodiments are merely exemplary and only serve an illustrative purpose. On this basis, various substitutions and improvements can be made to the present invention, and these all fall within the protection scope of the present invention.

Claims

1. An energy-optimal guidance method for intercepting a balanced maneuvering target, characterized in that, In this method, the line-of-sight angular velocity of the aircraft relative to the target is obtained in real time The velocity V of the aircraft approaching the target c and the acceleration of the target And take and as two input quantities, input them into a pre-trained fully connected neural network to obtain the corresponding output quantity as the optimal control command, and control the aircraft to fly towards the target based on this optimal control command, finally enabling the aircraft to intercept the target.

2. The energy-optimal guidance method for intercepting an equal-potential maneuvering target according to claim 1, characterized in that the fully connected neural network includes 1 input layer, 3 hidden layers and 1 output layer; The input layer includes neurons for receiving an input state tuple and neurons for receiving an input state tuple ; each hidden layer contains 20 neurons; The output layer contains one neuron, which outputs the optimal control command 3. The energy-optimal guidance method for intercepting an equal-potential maneuvering target according to claim 2, characterized in that the tansig function is set as the activation function in the hidden layer; the purelin function is set as the activation function in the output layer.

4. The energy-optimal guidance method for intercepting an equal-potential maneuvering target according to claim 1, characterized in that during the training process of the fully connected neural network, multiple groups of data are extracted from the optimal trajectory obtained by simulation as basic data, and after standardizing the basic data, they are divided into a training set, a validation set and a test set; Each set of data includes an input quantity and an output quantity 5. The energy-optimal guidance method for intercepting an equal-potential maneuvering target according to claim 4, characterized in that Normalize the input quantity by the following formula (1): The specific operation is as follows: Among them, represents the input quantity after standardization processing Indicates the input quantity to be standardized in the basic data; Represents the mean of all input quantities in the basic data ; Represents the variance of all input quantities in the basic data .

6. The energy-optimal guidance method for intercepting an equal-potential maneuvering target according to claim 4, characterized in that The input quantity is normalized by the following formula (II): Do normalization processing: Among them, represents the input quantity after standardization processing Indicates the input quantity to be standardized in the basic data; represents the mean value of all input quantities in the basic data ; represents the variance of all input quantities in the basic data .

7. The energy-optimal guidance method for intercepting an equal-potential maneuvering target according to claim 4, characterized in that The output quantity is normalized by the following formula (III): The processing is as follows: Among them, represents the output quantity after standardization processing Indicates the output quantity to be standardized in the basic data; Represents the mean of all output quantities in the basic data ; Represents the variance of all output quantities in the basic data .

8. The energy-optimal guidance method for intercepting an equal-potential maneuvering target according to claim 4, characterized in that The stopping condition for the training of the fully connected neural network is that the loss function drops to 5×10 -8 or less or the number of training epochs reaches 3000 epochs.

9. The energy-optimal guidance method for intercepting an equal-potential maneuvering target according to claim 8, characterized in that the loss function is the mean square error between the output value and the true value of the fully connected neural network.

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