Genetic algorithm-based optimal guidance method with geometric constraint impact angle control
Through the geometric constraint impact angle control method based on genetic algorithm, the problem that traditional guidance law is difficult to achieve precise control of missile drop angles is solved, and the precise constraints of missile drop angles and the reduction of control energy consumption is achieved.
Patent Information
- Application Number
- CN202411003396.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-07-25
- Publication Date
- 2024-12-31
AI Technical Summary
The traditional proportional guidance and bias proportional guidance laws are difficult to achieve precise control of missile drop angles, and the control is complex, making it difficult to take into account the simplicity of the control method and the drop angle constraints.
Using the geometric constraint impact angle control method based on genetic algorithm, the geometric mathematical model of the missile's proportional guided law is established to construct the relationship between the switching of variable gain guided law coefficients and the target perspective, and randomly select parameters, and use the genetic algorithm. The optimal guiding coefficient is selected for proportional guidance control.
The precise constraints on the drop angle of the missile are achieved, the missile is less overloaded and the control energy consumption is less, which simplifies the guidance law control method.
Smart Images
Figure CN119225385A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the field of missile and guidance technology, and relates to an optimal guidance method with geometrically constrained impact angle control based on a genetic algorithm. Background Art
[0002] Helicopter-mounted anti-tank missiles have always played an important role in anti-tank operations. Increasing the missile's landing angle and controlling the accuracy of the landing angle to attack the weakly protected parts of the tank (such as the top of the turret, etc.) is an ideal way to damage the tank. Although the proportional guidance law is simple to control, it is difficult to accurately determine the landing angle. Although the offset proportional guidance law can accurately control the landing angle, it has problems such as complex control. Summary of the invention
[0003] The present invention aims to provide an optimal guidance control method with geometrically constrained impact angle control based on a genetic algorithm, which can not only realize a simple control mode but also accurately constrain the terminal landing angle, thereby solving the contradictory relationship between the guidance law control mode and the landing angle constraint which is difficult to solve with traditional proportional guidance and offset proportional guidance.
[0004] In order to achieve the above tasks, the present invention adopts the following technical solutions:
[0005] An optimal guidance method with geometrically constrained impact angle control based on genetic algorithm, comprising:
[0006] Establish the missile's proportional guidance law and target geometry mathematical model;
[0007] The missile adopts a two-stage variable gain guidance law guidance scheme; the proportional guidance coefficient of the first stage is recorded as N1, and the second stage is recorded as N2; under the constraint of the expected missile landing angle, the relationship between the switching of the variable gain guidance law coefficient and the target viewing angle is constructed;
[0008] Multiple groups of N1 and N2 satisfying the relationship are randomly selected, and the optimal individuals N1 and N2 are selected through genetic algorithm to serve as the proportional guidance coefficients of the two-stage variable gain guidance law. The missile is proportionally guided and controlled according to the guidance coefficients.
[0009] Furthermore, the missile's proportional guidance law and target geometry mathematical model is as follows:
[0010]
[0011] Among them, R represents the distance between the projectile and the target, υ m is the missile speed, ε is the target viewing angle, q is the missile-target line of sight angle, and θ is the missile speed inclination angle. The dot above the parameter indicates the derivative of the parameter, and the number of dots indicates the order.
[0012] Furthermore, the construction of the relationship between the switching of the variable gain steering law coefficient and the target viewing angle includes:
[0013] a) Construct the relationship between the missile-target perspective q and the target perspective:
[0014] q=q0-(ε-ε0) / (N1-1) (3)
[0015] Among them, q0 represents the initial sight angle of the projectile and target, and ε0 represents the initial target viewing angle;
[0016] b) Constructing two-stage proportional guidance coefficients N1, N2 and target viewing angle ε under the constraint of landing angle Π s The relationship between them is:
[0017]
[0018] ε s represents the target viewing angle at the switching point of the steering coefficient, q s Indicates the missile-target viewing angle at the guidance coefficient switching point.
[0019] Furthermore, N1 and N2 satisfy N1<1, N2≥2.
[0020] Further, the variable gain guidance law guidance is expressed as:
[0021]
[0022] Where N represents the proportional guidance law coefficient, which can be N1 or N2; q is the missile-target line-of-sight angle, and θ is the missile velocity inclination angle.
[0023] Furthermore, N1 and N2 selected by the genetic algorithm are used as different individuals of the genetic algorithm, and the individuals are iteratively selected to obtain the optimal individual, including:
[0024] Determine the fitness function of the genetic algorithm; initialize the genetic algorithm population size, crossover probability, mutation probability, maximum iteration steps and chromosome length parameters, and randomly initialize the individual coding sequence;
[0025] The fitness value is calculated according to the individual coding sequence obtained by initialization, and the roulette wheel selection method is used to select the parent individuals with the size of the fitness value as the probability of selecting the individual; the selected population individuals are randomly paired with probability, and the crossover points are randomly determined for crossover exchange; the mutation points of the individuals after crossover are randomly selected with the mutation probability for mutation, and finally the offspring population is obtained;
[0026] Decode the obtained offspring population individuals, and randomly expand the number of offspring individuals to make their total number equal to that of the parent generation. Calculate the fitness value of the decoding results, and record the average fitness value and the optimal fitness value.
[0027] Repeat the above steps until the maximum number of iterations is reached and then stop the calculation.
[0028] Furthermore, the crossover probability is set to 0.8, and the mutation probability is set to 0.1.
[0029] A guidance device comprises a processor, a memory and a computer program stored in the memory; when the processor executes the computer program, the optimal guidance control method with geometrically constrained impact angle control based on a genetic algorithm is implemented.
[0030] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the optimal guidance control method with geometrically constrained impact angle control based on a genetic algorithm is implemented.
[0031] Compared with the prior art, the present invention has the following technical features:
[0032] The method provided by the present invention has a simple guidance law control mode and can accurately realize the angle of impact constraint while having a small overload of the missile and a small control energy consumption. BRIEF DESCRIPTION OF THE DRAWINGS
[0033] Figure 1 It is a schematic diagram of variable gain proportional guidance trajectory;
[0034] In the figure, N1 and N2 represent the two-stage variable gain proportional guidance law coefficients, R0 and R s , ε0 and ε s , q0 and q s They represent the missile-target distance, target viewing angle, and missile-target sight angle at the initial moment and the guidance law switching moment respectively; the shaded area A represents the angle range when a single fixed guidance law coefficient is used, and B represents the angle range corresponding to the guidance law switching point;
[0035] Figure 2 It is a flow chart of the optimal guidance law control scheme with geometrically constrained impact angle control based on genetic algorithm;
[0036] Figure 3 It is a graph of the relationship between energy consumption and genetic algebra;
[0037] Figure 4 It is a comparison chart of missile overload curves based on the optimal guidance law selected by genetic algorithm and other combinations of guidance law coefficients;
[0038] Figure 5 It is a comparison chart of missile control energy consumption curves based on the optimal guidance law selected by genetic algorithm and the combination of other guidance law coefficients;
[0039] Figure 6It is a comparison chart of missile trajectory curves based on the optimal guidance law selected by genetic algorithm and other combinations of guidance law coefficients;
[0040] Figure 7 It is a comparison chart of missile inclination curves based on the optimal guidance law selected by genetic algorithm and other combinations of guidance law coefficients. DETAILED DESCRIPTION
[0041] Referring to the accompanying drawings, the present invention provides an optimal guidance method with geometrically constrained impact angle control based on a genetic algorithm, comprising the following steps:
[0042] Step 1: Establish the missile's proportional guidance law and target geometry mathematical model, as follows:
[0043]
[0044] Among them, R represents the distance between the projectile and the target, υ m is the missile speed, ε is the target viewing angle, q is the missile-target line of sight angle, and θ is the missile speed inclination angle. In this scheme, the dot above the parameter represents the derivative of the parameter, and the number of dots represents the order.
[0045] When the target is stationary, the proportional guidance can be simplified as:
[0046]
[0047] Where N represents the proportional guidance law coefficient.
[0048] Step 2: The missile adopts a two-stage variable gain guidance law guidance scheme; the proportional guidance coefficient of the first stage is recorded as N1, and the second stage is recorded as N2;
[0049] Under the constraint of the expected missile landing angle, the relationship between the switching of the variable gain guidance law coefficient and the target viewing angle is constructed based on the missile's proportional guidance law and target geometry mathematical model, including:
[0050] a) Construct the relationship between the missile-target perspective q and the target perspective:
[0051] q=q0-(ε-ε0) / (N1-1) (3)
[0052] Among them, q0 represents the initial sight angle of the projectile and target, and ε0 represents the initial target viewing angle.
[0053] b) Constructing two-stage proportional guidance coefficients N1, N2 and target viewing angle ε under the constraint of landing angle Π s The relationship between them is:
[0054]
[0055] ε sIndicates the target viewing angle at the switching point of the guidance coefficient. When the N1 and N2 values are determined, ε s That is, q s Indicates the missile-target viewing angle at the guidance coefficient switching point.
[0056] Initially, randomly select M groups (20-30 groups) of N1 and N2 that satisfy equation (4). Solve through the genetic algorithm in step 3 to obtain the optimal individual N1 and N2 as the proportional guidance coefficients of the two-stage variable gain guidance law. The missile is controlled by proportional guidance according to the guidance coefficients.
[0057] Step three, based on the traditional genetic algorithm, the selected N1 and N2 are used as different individuals of the genetic algorithm, and the individuals are iteratively selected to obtain the optimal individual.
[0058] Determine the fitness function of the genetic algorithm; initialize the genetic algorithm population size, crossover probability, mutation probability, maximum iteration steps and chromosome length parameters, and randomly initialize the individual coding sequence.
[0059] The fitness value is calculated according to the initialized individual coding sequence, and the roulette wheel selection method is used to select the parent individual with the size of the fitness value as the probability of selecting the individual; the selected population individuals are randomly paired with probability, and the crossover point is randomly determined for crossover exchange; the mutation point is randomly selected for the individuals after the crossover with the mutation probability to mutate, and finally the offspring population is obtained.
[0060] The obtained offspring population individuals are decoded, and the number of offspring individuals is randomly expanded to make their total amount equal to that of the parent generation. The fitness value of the decoding results is calculated, and the average fitness value and the optimal fitness value are recorded.
[0061] Repeat the above steps until the maximum number of iterations is reached and then stop the calculation.
[0062] In step three, the crossover probability is set to 0.8, and the mutation probability is set to 0.1.
[0063] In step 3, N1 and N2 generated by formula (4) satisfy N1<1, N2>2, and the specific derivation is as follows:
[0064] a. Definition and solution of dimensionless distance and dimensionless target perspective:
[0065] By combining equations (1) and (2), we can obtain:
[0066]
[0067] Dividing equation (5) by equation (1) and integrating it, we get:
[0068]
[0069] Among them, ε0 and R0 represent the initial target viewing angle value and the projectile-target distance value respectively.
[0070] Let ρ = R / R0 represent the dimensionless distance and substitute it into equation (6):
[0071]
[0072] Let sinε / sinε0 be the dimensionless target perspective, and substitute (7) into (5) to obtain:
[0073]
[0074] Analyzing equations (7) and (8), we can see that when the proportional guidance coefficient N>1, the target viewing angle decreases as the missile-target distance decreases; when N<1, the target viewing angle increases as the missile-target distance decreases; when N=1, the target viewing angle remains constant. It can be seen that from the perspective of the seeker field of view constraint, the proportional guidance coefficient should be N≥1.
[0075] b. Dimensionless overload definition and solution:
[0076] Formula (8) combines formula (2) and formula (5) to get:
[0077]
[0078] Ballistic overload is defined as:
[0079]
[0080] Define dimensionless overload as:
[0081]
[0082] Among them, a m Represents the missile's acceleration.
[0083] Dimensionless Overload The law of change with dimensionless distance ρ is:
[0084]
[0085] When N>2, the trajectory overload decreases as the missile-target distance decreases, and the overload converges at the end of the trajectory; when N=2, the overload remains constant as the missile-target distance changes; and when N<2, it gradually increases and diverges, making it difficult for the missile to hit the target. Therefore, considering the convergence of the missile terminal overload and the convergence of the target viewing angle, the effective navigation ratio of the proportional guidance law should be taken as N>2.
[0086] c. Criteria for the step-by-step variable gain proportional guidance law
[0087] The trajectory angle that can be achieved when the guidance law switches to terminal guidance at the current moment in the mid-guidance segment is called the current angle A, and its value depends on the initial conditions of the trajectory in the terminal guidance segment and the proportional guidance coefficient N2 in the terminal guidance segment:
[0088]
[0089] Taking the derivative of equation (11) and combining equation (3) and equation (6) in parallel, we can obtain:
[0090]
[0091] In summary, the prerequisites for the implementation of the proportional guidance law with segmented variable gain are:
[0092] Before the missile enters the terminal guidance, a proportional guidance law with a relatively small navigation coefficient (N < 1) is added as the mid-range guidance. The task of the mid-range guidance is to provide the initial conditions of the trajectory that meet the large angle of attack requirements for the terminal guidance. The guidance law is switched at point S (the switching point of the guidance coefficient). When the proportional guidance law with a relatively large navigation coefficient (N ≥ 2) is switched as the terminal guidance, the terminal overload of the missile converges and the target viewing angle converges, and the trajectory angle of attack of the terminal guidance is improved. When N1 < N2, It shows that the current landing angle becomes larger and larger as the mid-stage guidance phase progresses, and it is expected that the landing angle may reach the desired landing angle, thus meeting the landing angle constraint requirements of the segmented variable gain proportional guidance scheme.
[0093] That is, the condition must be met: N1<1, N2≥2 to proceed to step 3, otherwise return to step 1.
[0094] Example:
[0095] Take the anti-tank missiles carried by armed helicopters as an example. Figure 1 Shown is a typical schematic diagram of a two-stage variable gain proportional guidance trajectory; this example is used to further illustrate the solution of the present invention.
[0096] Step 1, set the value range of N1 and N2: N1∈(0,1), N2∈[2,5];
[0097] Based on the above area, set the expected landing angle Π and input the initial target viewing angle value; then use formula (4) to randomly select 20 groups of initial N1 and N2 values, and use the values of N1 and N2 to calculate the 20 groups of target viewing angles ε corresponding to the switching point s , denoted as ε s0 , and perform binary encoding on each group of N1 and N2.
[0098] Step 2: Substitute [N1, N2, ε s0] is substituted into equation (1) and equation (2), where the value of ε in equation (1) is ε s0 .
[0099] Step 2.1, select the proportional guidance coefficient N = N1, calculate the corresponding target angle ε and record it as ε s .
[0100] Step 2.2, if ε s ≥ε s0 , then switch the guidance command and set the proportional guidance coefficient N = N2; otherwise, do not switch the guidance command, N = N1;
[0101] Step 2.3, after switching the guidance command, N=N2, calculate the missile-target distance R and the target viewing angle ε s Whether the expected landing angle constraint is met.
[0102] Step 2.4: If the expected angle constraint is met, the calculation ends and the control energy consumption n of the missile during the entire guidance process is calculated and output. e If not satisfied, proceed to step 3:
[0103] where n e The value is calculated as:
[0104]
[0105] a m (t) represents the acceleration at a certain moment t during the entire flight of the missile, and dt represents the integration time step.
[0106] Step 3: for [N1, N2, ε s0 ]Use genetic algorithm to make the best selection:
[0107] Step 3.1, for [N1, N2, ε s0 ] Perform fitness evaluation to select the best individual;
[0108]
[0109] Among them, F(X) is the fitness value, f(X) is the fitness evaluation function, X represents the individual, C min Represents the fitness coefficient.
[0110] Step 3.2, for [N1, N2, ε s0 ] to perform selection operation:
[0111]
[0112] Among them, M is the population size, and the fitness of individual i is F i , the probability of an individual being selected is p is .
[0113] Step 3.3, for [N1, N2, ε s0 ] to perform crossover operation:
[0114] Uniform crossover is selected, and the genes at each locus of the two paired individuals are exchanged with the same crossover probability to form two new individuals.
[0115] Step 3.3. For [N1, N2, ε s0 ] to perform mutation operation:
[0116]
[0117] Assume that the binary code of an individual is X = x1x2…x k …x l , x k is the mutation point, r represents the decoding coefficient, and its value range is After uniform mutation operation is performed on individual X at this point, a new individual X = x1x2…x k ′…x l .
[0118] Step 4: Form the offspring individual X = x1x2…x k ′…x l , and expand the number of offspring individuals to the number of parent individuals.
[0119] Step 5: Re-enter the ballistic equations (1) and (2), and combine them with equation (15) to calculate the missile's control energy consumption n e :
[0120] Step 6: Repeat steps 3-5 above to reach the iterative number and select the energy consumption n e The smallest group is regarded as the best individual.
[0121] Matlab / Simulink is used for verification calculation, missile coordinates (0, 0), target coordinates (5000, 0), missile initial inclination angle is 30°, speed is 300m / s. For the optimal result (Scn.1), 5 groups of results are randomly selected for comparison. The calculation results are shown in Table 1. The relationship between the control energy consumption and the number of iterations is shown in Table 1. Figure 3 As shown, the missile overload curve is as follows Figure 4 As shown, the control energy consumption curve is as follows Figure 5 As shown, the missile trajectory curve and missile inclination curve are as follows Figure 6 and Figure 7 As shown in the figure, by comparing the curves, it is not difficult to find that the optimal guidance law with geometric constraint impact angle control based on genetic algorithm has a greater guidance advantage, which is specifically manifested in the minimum missile overload and the minimum control energy consumption.
[0122] Table 16 Calculation results under group 16 working conditions
[0123] Scn. <![CDATA[N1]]> <![CDATA[N2]]> Es(°) <![CDATA[n e (m 2 / s 3 )]]> <![CDATA[a m (m / s 2 )]]> ∏(°) <![CDATA[1 (最优) ]]> 0.022 2.0 59.99 <![CDATA[3.39*10 4 ]]> -54.3 -89.8 2 0.022 3.0 79.26 <![CDATA[4.85*10 4 ]]> -105.8 -90.0 3 0.022 4.0 89.00 <![CDATA[6.45*10 4 ]]> -146.2 -89.9 4 0.50 3.0 60.00 <![CDATA[4.86*10 4 ]]> -140.3 -89.9 5 0.80 3.0 43.64 <![CDATA[5.06*10 4 ]]> -185.9 -90.0
[0124] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the protection scope of the present application.
Claims
1. An optimal guidance method with geometrically constrained impact angle control based on genetic algorithm, characterized in that: include: Establish the missile's proportional guidance law and target geometry mathematical model; The missile adopts a two-stage variable gain guidance law guidance scheme; in The proportional guidance coefficient of the first section is recorded as N1, and the proportional guidance coefficient of the second section is recorded as N2. Under the constraint of the expected missile landing angle, the relationship between the switching of the variable gain guidance law coefficient and the target viewing angle is constructed; Multiple groups of N1 and N2 satisfying the relationship are randomly selected, and the optimal individuals N1 and N2 are selected through genetic algorithm to serve as the proportional guidance coefficients of the two-stage variable gain guidance law. The missile is proportionally guided and controlled according to the guidance coefficients.
2. The optimal guidance method with geometrically constrained impact angle control based on genetic algorithm according to claim 1, characterized in that: The proportional guidance law and target geometry mathematical model of the missile is as follows: Where R represents the distance between the projectile and the target, v m is the missile speed, ε is the target viewing angle, q is the missile-target line of sight angle, and θ is the missile speed inclination angle. The dot above the parameter indicates the derivative of the parameter, and the number of dots indicates the order.
3. The optimal guidance method with geometrically constrained impact angle control based on genetic algorithm according to claim 1, characterized in that: The step of constructing the relationship between the switching of the variable gain steering law coefficient and the target viewing angle includes: a) Construct the relationship between the missile-target perspective q and the target perspective: q=q0-(ε-ε0) / (N1-1) (3) Among them, q0 represents the initial sight angle of the projectile and target, and ε0 represents the initial target viewing angle; b) Constructing two-stage proportional guidance coefficients N1, N2 and target viewing angle ε under the constraint of landing angle Π s The relationship between them is: ε s represents the target viewing angle at the switching point of the steering coefficient, q s Indicates the missile-target viewing angle at the guidance coefficient switching point.
4. The optimal guidance method with geometrically constrained impact angle control based on genetic algorithm according to claim 1, characterized in that: The N1 and N2 satisfy N1<1 and N2≥2.
5. The optimal guidance method with geometrically constrained impact angle control based on genetic algorithm according to claim 1, characterized in that: The variable gain guidance law is expressed as: Where N represents the proportional guidance law coefficient, which can be N1 or N2; q is the missile-target line of sight angle, which is the missile velocity inclination angle.
6. The optimal guidance method with geometrically constrained impact angle control based on genetic algorithm according to claim 1, characterized in that: The genetic algorithm selects N1 and N2 as different individuals of the genetic algorithm, and iteratively selects the individuals to obtain the optimal individual, including: Determine the fitness function of the genetic algorithm; initialize the genetic algorithm population size, crossover probability, mutation probability, maximum iteration steps and chromosome length parameters, and randomly initialize the individual coding sequence; The fitness value is calculated according to the individual coding sequence obtained by initialization, and the roulette wheel selection method is used to select the parent individuals with the size of the fitness value as the probability of selecting the individual; the selected population individuals are randomly paired with probability, and the crossover points are randomly determined for crossover exchange; the mutation points of the individuals after crossover are randomly selected with the mutation probability for mutation, and finally the offspring population is obtained; Decode the obtained offspring population individuals, and randomly expand the number of offspring individuals to make their total number equal to that of the parent generation. Calculate the fitness value of the decoding results, and record the average fitness value and the optimal fitness value. Repeat the above steps until the maximum number of iterations is reached and then stop the calculation.
7. The optimal guidance method with geometrically constrained impact angle control based on genetic algorithm according to claim 6, characterized in that: The crossover probability is set to 0.8, and the mutation probability is set to 0.
1.
8. A guidance device, comprising a processor, a memory and a computer program stored in the memory; when the processor executes the computer program, it implements the optimal guidance control method with geometrically constrained impact angle control based on genetic algorithm according to any one of claims 1-7.
9. A computer-readable storage medium, wherein a computer program is stored in the medium; characterized in that: When the computer program is executed by a processor, the optimal guidance control method with geometrically constrained impact angle control based on a genetic algorithm according to any one of claims 1 to 7 is implemented.