A proportional guidance law for cooperative attack of stationary targets by asynchronous launch of multiple projectiles

Abstract

The application discloses a proportional guidance law suitable for asynchronous launching of multiple missiles for cooperative attack on a static target. In the design of the guidance law, a same predetermined attack time is set, normal and tangential accelerations of the missiles are adjusted, motion parameters of the missiles are adjusted, a real-time residual flight time is calculated, and the attack time consistency is achieved before the predetermined attack time. The guidance law is launched at different times and is independent of communication of the missile group in the later period, and has strong anti-interference performance.

Description

Technical Field

[0001] The present invention belongs to the field of automated coordinated control, and in particular relates to a proportional guidance law suitable for asynchronously launching multiple missiles to coordinately attack stationary targets. Background Art

[0002] With the advancement of modern military defense technology, single-missile attacks are becoming less effective in certain attack scenarios. To address the drawbacks of single-missile missiles, such as insufficient destructive power and susceptibility to interception, coordinated multi-missile attacks can address these issues. Simultaneously shooting down missiles approaching from different directions is extremely challenging for defense systems. In other words, if two or more missiles in a coordinated attack group can penetrate an enemy's defenses, they can effectively destroy its core combat capabilities. To achieve this goal, a representative attack method is the design of coordinated guidance laws.

[0003] Under the control of a coordinated guidance law, missiles adjust their motion parameters by acquiring spatial distance, angle, and other parameters, ensuring that each missile in the swarm arrives at the target at the same time and detonates to cause damage. Currently, there are two main attack strategies for designing guidance laws. One involves the swarm exchanging information in real time through an inter-missile communication network during flight, adjusting its relative motion parameters with neighboring missiles to achieve attack timing consistency. The other eliminates the need for real-time inter-missile communication and instead establishes a pre-determined attack time at launch. This synchronizes the attack by ensuring that each missile reaches the target at the preset time, treating the simultaneous attack as a time-of-attack attack. Compared to the second coordinated attack method without a communication network, the first method, which involves swarms operating with real-time communication, offers greater adjustability. However, it places higher demands on the timeliness of inter-missile communication. Furthermore, if one missile is intercepted and communication data is lost, whether the remaining missiles can continue to form a new communication topology is a question designers must consider. The second coordinated swarm without a communication network offers a significant advantage in this regard. Even if a missile is intercepted and shot down, it does not affect the effective coordinated attack of the remaining missiles, resulting in a more robust system.

[0004] Previous literature has explored impact time guidance, proposing two general categories of guidance laws: those based on optimal control and those based on Lyapunov stability. The first approach formulates the attack problem as an optimal control problem with impact time as a boundary condition. This approach takes into account the minimization of control energy and produces suboptimal control inputs. The second approach uses Lyapunov stability theory to design a guidance law that minimizes the error between the impact time and the preset impact time. The estimated impact time is the sum of the elapsed flight time and the estimated remaining flight time.

[0005] In light of the above, a fixed impact time guidance method is adopted. This method uses the deviation between the sum of the flight time and the estimated remaining flight time and the impact time. When the deviation between the sum of the flight time and the estimated remaining flight time for all missiles and the preset fixed time approaches zero before the endpoint, the attack time consistency of the missile group is achieved. This method eliminates the need for inter-missile information cross-linking after all missiles are launched; only in-flight state adjustments based on the preset fixed time are required. Based on the above description, the present invention proposes a proportional guidance law for coordinated multi-missile attacks on stationary targets. Summary of the Invention

[0006] The present invention provides a distributed cooperative guidance law for attacking a stationary target based on the line of sight, so as to accurately control multiple missiles to attack the target simultaneously.

[0007] The technical solution to achieve the purpose of the present invention is: a proportional guidance law suitable for asynchronously launching multiple missiles to coordinately attack a stationary target, the steps of which are as follows:

[0008] Step 1: Set When multiple missiles attack a stationary target simultaneously, the time of launching the first missile is taken as the standard time. , the remaining missiles are launched after the first missile, and the launch time interval between the second missile and the first missile is , and so on, The time interval between the launch of the first missile and the launch of the second missile is , No. The distance between the first missile and the second missile is , =1, 2, 3,…, n.

[0009] Step 2: The distance at which the sensor on the missile detects the target , own movement speed The angle between the missile's flight speed and the missile-target sight line ;according to 、 、 , and obtain the Estimated remaining flight time of the missile , go to step 3.

[0010] Step 3: Set the same preset attack time , combined with the time interval , Standard Time , estimated remaining flight time , get the attack time deviation of the missile ;

[0011] Step 4: Based on the missile's attack time deviation Design the proportional guidance law, i.e. the normal acceleration and tangential acceleration , combined with the missile dynamics model, the missile dynamics model updates the next moment , return to step 2.

[0012] Compared with the prior art, the present invention has the following significant advantages:

[0013] (1) Controlling the velocity normal and tangential acceleration inputs when designing the guidance law greatly improves the efficiency of collaborative guidance;

[0014] (2) It only needs to calculate the missile launch time difference at launch, and no real-time communication between missiles is required during the subsequent flight. Even if an individual missile is intercepted mid-flight, it will not affect the coordinated attack of other missiles;

[0015] (3) The guidance law has a simple structure and is easy to implement algorithmically. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a planar schematic diagram of multiple missiles of the present invention attacking a static target simultaneously.

[0017] Figure 2 This invention Schematic diagram of the missile's dynamic plane.

[0018] Figure 3 It is a missile flight trajectory simulation diagram of the present invention.

[0019] Figure 4 It is a graph showing the deviation change of the estimated remaining flight time of the missile of the present invention.

[0020] Figure 5 It is a diagram showing the change in tangential acceleration of the missile of the present invention.

[0021] Figure 6 It is a diagram showing the change in normal acceleration of the missile of the present invention.

[0022] Figure 7 It is a speed variation diagram of the missile of the present invention.

[0023] Figure 8 It is a schematic diagram of the workflow of the present invention. DETAILED DESCRIPTION

[0024] Combine Figure 8 A proportional guidance law suitable for asynchronously launching multiple missiles to coordinately attack a stationary target is proposed. The steps are as follows:

[0025] Step 1: Set When multiple missiles attack a stationary target simultaneously, the time of launching the first missile is taken as the standard time. , the remaining missiles are launched after the first missile, and the launch time interval between the second missile and the first missile is , and so on, The time interval between the launch of the first missile and the launch of the second missile is , No. The distance between the first missile and the second missile is , =1, 2, 3,…, n.

[0026] At the beginning of the launch, the first The time of launching the first missile is compared with the time of launching the first missile, and the interval of the obtained standard time is As an input value, adjust the attack time of the missile to achieve the same attack time as the first missile;

[0027] ,

[0028] in, represents the launch time of the i-th missile.

[0029] Step 2: In order to study the flight status of each missile, select missiles are the research objects. The distance at which the sensor on the missile detects the target , own movement speed The angle between the missile's flight speed and the missile-target sight line ;according to , , , get the estimated remaining flight time of n missiles , =1, 2, 3, …, n; Since the missile is affected by the environment, target and itself during flight, it is difficult to express the estimated remaining flight time using a mathematical formula. Therefore, in order to facilitate research, the estimated remaining flight time is used as the actual estimated remaining flight time.

[0030] according to , , Get the first Estimated remaining flight time of missiles :

[0031] ,

[0032] Since the launch time of missiles will not be completely synchronized in actual combat scenarios, it is assumed here that the difference between the launch time of each missile and the standard launch time is To ensure the consistency of attack time, it is necessary to Taking this into account, the estimated remaining time deviation can be expressed as :

[0033] ,

[0034] During launch, the time when the first missile is launched is used as the standard time. , the remaining missiles are launched after the first missile, and the launch time interval between the second missile and the first missile is , and so on, The time interval between the launch of the first missile and the launch of the second missile is , No. The distance between the first missile and the second missile is , =1, 2, 3, ..., n; it is not difficult to find that when the If a missile is launched after the standard time, Is positive, merge the constant term, in other words, set the attack time shortened to achieve synchronization with other missiles. Is positive, it means the The sum of the missile's flight time and the estimated remaining flight time must be greater than the set attack time, which means it needs to be accelerated; otherwise, it needs to be decelerated.

[0035] Step 3: Set the same preset attack time , combined with the time interval , Standard Time , estimated remaining flight time , get the attack time deviation of the missile The details are as follows:

[0036] ,

[0037] Step 4: Build a missile dynamics model (e.g., Distributed cooperative guidance law for multiple missiles with input delay and topology switching) and control the input normal acceleration according to the multi-missile system. and tangential acceleration , calculate the next moment according to the missile dynamics model , , :

[0038] ,

[0039] ,

[0040] Among them, the coefficient 、 are all normal numbers, Indicates the estimated remaining time deviation index, , Take 1-3, For the The angle between the missile's velocity direction and the missile-target line of sight; For the Missile speed, For the The distance from the missile to the target, For the The missile's sight angle, is the derivative of the sight angle with respect to time, For the The attack time deviation of the missiles.

[0041] To get the next moment , , , the multi-missile system needs to adjust the system state through control input. Therefore, the obtained , which is input as acceleration 、 In the middle, you can go to the control input.

[0042] The first missiles 、 Input into the missile dynamics model to obtain the next moment 、 、 :

[0043] ,

[0044] ,

[0045] ,

[0046] ,

[0047] ,

[0048] In the above formula, For the The result of the time derivative of the missile's target distance is: For the Missile speed, For the The derivative of the missile's velocity with respect to time is: For the The angle between the missile's velocity direction and the missile-target line of sight, also known as the yaw angle, For the The missile heading angle, For the The result of the time derivative of the missile's heading angle is: For the The missile's sight angle, 、 Respectively The tangential acceleration and normal acceleration of the missile.

[0049] Return to step 2 until , the remaining time for each missile to reach the target tends to be consistent, maintain its current flight state, and exit the cycle.

[0050] The present invention designs a proportional guidance law suitable for asynchronously launching multiple missiles to coordinately attack stationary targets. Based on the design concept of a traditional proportional guidance law with a single input, it adopts dual inputs of tangential and normal accelerations to obtain a higher convergence rate. By calculating the deviation between the remaining time and the expected attack time, the multiple missiles are driven to adjust their own motion parameters during flight to achieve consistency in attack time before the destination. Even if one or two missiles are intercepted by the defense system during flight, the remaining missiles can still complete the coordinated attack. Local interference does not affect the global control, and the law has strong robustness.

[0051] The following is the proof of the convergence time and stability of the control system:

[0052] First, find the estimated remaining time deviation, and we get:

[0053] ,

[0054] Derivative of the estimated remaining time deviation is :

[0055] ,

[0056] Among them, the estimated remaining flight time is derived as , as follows:

[0057] ,

[0058] Combining the tangential and normal acceleration expressions and the dynamic model, we can reorganize the above formula and get:

[0059] ,

[0060] Constructing Lyapunov functions , and we can get :

[0061] ,

[0062] The derivative of the estimated remaining time deviation is:

[0063] ,

[0064] Substituting the designed tangential and normal accelerations into the above formula, we get:

[0065] ,

[0066] Continue to sort out:

[0067] ,

[0068] Lemma 1: If the function Satisfies the following inequality

[0069] ,

[0070] In the formula is the independent variable, 、 、 All are normal numbers.

[0071] So It will converge to the origin in a finite time, and the finite time settlement time satisfies

[0072] ,

[0073] According to the above arrangement of Lyapunov function and Lemma 1, it can be concluded that the fixed convergence time T of the multi-missile cooperative control system satisfies:

[0074] ,

[0075] in, , as well as Parameters and estimated remaining time deviation at the initial moment The design will affect the convergence speed of the control system, so it is only necessary to adjust the control parameters to make , you can estimate the remaining time deviation At the preset time It converges to zero before, thus completing the consistency convergence of the multi-bullet attack time.

[0076] Example 1

[0077] Combine Figures 1 to 8A proportional guidance law suitable for asynchronously launching multiple missiles to coordinately attack a stationary target is proposed. The steps are as follows:

[0078] Step 1: Assume that three missiles attack a stationary target at the same time. The attack diagram is as follows: Figure 1 When launching, the launch time of the first missile is taken as the standard time, and the second missile is launched 3s later than the first missile, which is the launch time interval between the second and first missiles. , and so on for the other missiles;

[0079] Step 2: Substitute the missile-target distance, speed and other motion information detected by the three missiles into

[0080] In the missile estimated remaining flight time expression, the attack target is a stationary target, the number of missile groups is set to 3, and the plane attack model is shown in Figure 2 , in the figure Indicates the target of attack. Indicates the Missile positions, For the The angle between the missile's velocity direction and the missile-target line of sight, also known as the yaw angle. For the The missile speed, the initial state of the launch is random, and the estimated remaining flight time is expressed as follows:

[0081] ,

[0082] In order to achieve the consistency of the missile group, the launch time difference of each missile is shared through the weapon platform, so that To add to the control input, for example, the second missile is 3 seconds late from the standard launch time, and the standard attack time is set to 50 seconds, then the actual flight time of the second missile must be controlled within 47 seconds, and so on for other missiles.

[0083] Step 3: Determine the deviation of the estimated remaining time =0, , =1, 2, 3, 4, 5. If true, it means that the current estimated remaining flight time is consistent with the fixed attack time, and the current flight state can be maintained. If not, the current deviation is input into the guidance law of the missile-target line of sight direction to obtain the control input 、 , go to step 3

[0084] Step 4: Establish a missile dynamics model based on the existing literature and control input of the multi-missile system 、 , according to the missile dynamics model, the current moment is obtained , , , return to step 2.

[0085] ,

[0086] ,

[0087] in , , , Usually take a constant of 1-3, For the The angle between the missile's velocity direction and the missile-target line of sight, also known as the yaw angle. For the Missile speed, For the The distance from the missile to the target, For the The missile's sight angle, is the derivative of the sight angle with respect to time, For the The attack time deviation of the missiles.

[0088] To get the next moment , , , the multi-missile system needs to adjust the system state through control input. Therefore, the obtained , can be controlled by input 、 .

[0089] The first missile 、 , input into the missile dynamics model, and get the next moment , , .

[0090] ,

[0091] ,

[0092] ,

[0093] ,

[0094] ,

[0095] In the above formula, For the The derivative of the missile's target distance with respect to time is: For the Missile speed, For the The derivative of the missile's velocity with respect to time is: For the The angle between the missile's velocity direction and the missile-target line of sight, also known as the yaw angle, For the The missile heading angle, For the The result of the time derivative of the missile's heading angle is: For the The missile's sight angle, 、 Respectively The tangential acceleration and normal acceleration of the missile.

[0096] Return to step 2 until =0, the time for each missile to reach the target tends to be consistent, the current flight status of each missile is maintained, and the loop exits.

[0097] The flight trajectory of each missile in the swarm is shown in the figure below: Figure 3 , the end point coordinates are (15000.15000), Figure 4-Figure 7 They represent the estimated remaining time deviation, tangential acceleration, normal acceleration and speed of the missile respectively. It is not difficult to find that in the coordinated attack process, the acceleration of the missiles can be executed within the effective range. When the state of the missile group is stable, the speed of each missile tends to be stable. The convergence process is fast and stable, which has engineering significance and simplifies the design process. Figure 8 .

[0098] Simulation results show that the guidance law has the characteristics of fast system convergence and high stability.

Claims

1. A proportional guidance law suitable for asynchronously launching multiple missiles to coordinately attack stationary targets, characterized in that: Here are the steps: Step 1: Set When multiple missiles attack a stationary target simultaneously, the time of launching the first missile is taken as the standard time. , the remaining missiles are launched after the first missile, and the launch time interval between the second missile and the first missile is , and so on, The time interval between the launch of the first missile and the launch of the second missile is , No. The distance between the first missile and the second missile is , =1, 2, 3, ..., n; Step 2: The distance at which the sensor on the missile detects the target , own movement speed The angle between the missile's flight speed and the missile-target sight line ;according to 、 、 , and obtain the Estimated remaining flight time of the missile , go to step 3; Step 3: Set the same preset attack time , combined with the time interval , Standard Time , estimated remaining flight time , get the attack time deviation of the missile ; Step 4: Based on the missile's attack time deviation Design the proportional guidance law, i.e. the normal acceleration and tangential acceleration , combined with the missile dynamics model, the missile dynamics model updates the next moment , return to step 2; Among them, combined with the missile dynamics model, the missile dynamics model updates the next moment , as follows: The first missiles 、 Input into the missile dynamics model to update the next moment : ， ， ， ， ， Return to step 1 until =0, the remaining time of each missile tends to be consistent, the current flight status of each missile is maintained, and the loop exits; In the above formula, For the The distance at which the sensor on the missile detects the target The result of the time derivative is, For the Missile speed, For the The derivative of the missile's velocity with respect to time is: For the The angle between the missile's velocity direction and the missile-target line of sight, For the The missile heading angle, For the The result of the time derivative of the missile's heading angle is: For the The missile's sight angle, is the derivative of the sight angle with respect to time, For the The tangential acceleration of the missile, For the Normal acceleration of the missile.

2. The proportional guidance law applicable to asynchronously launching multiple missiles to coordinately attack stationary targets according to claim 1 is characterized in that: In step 1, at the initial stage of launch, the first The time when the missile is launched is compared with the time when the first missile is launched, and the interval between the obtained standard times is As an input value, adjust the attack time of the missile to achieve the same attack time as the first missile; ， in, represents the launch time of the i-th missile.

3. The proportional guidance law for asynchronously launching multiple missiles to coordinately attack stationary targets according to claim 2 is characterized by: In step 2, The distance at which the sensor on the missile detects the target , own movement speed The angle between the missile's flight speed and the missile-target sight line ;according to 、 、 , and obtain the Estimated remaining flight time of the missile , as follows: according to 、 、 , calculate the Estimated remaining flight time of the missile : ， in, Indicates the navigation ratio, which is set to a constant 1 to 3 when attacking a stationary target.

4. The proportional guidance law for asynchronously launching multiple missiles to coordinately attack stationary targets according to claim 3 is characterized by: In step 3, set the same preset attack time , combined with the time interval , Standard Time , estimated remaining flight time , get the attack time deviation of the missile at time t , as follows: 。 5. According to the proportional guidance law for asynchronously launching multiple missiles to coordinately attack a stationary target according to claim 4, in step 4, the attack time deviation of the missile is calculated based on the target's Design the proportional guidance law, i.e. the normal acceleration and tangential acceleration , as follows: ， ， If the estimated remaining time deviates , then the current estimated remaining time deviation is input into the proportional guidance law and the calculation continues; in, coefficient 、 are all normal numbers, Indicates the estimated remaining time deviation index, , Take 1-3, For the The angle between the missile's velocity direction and the missile-target line of sight; For the Missile speed, For the The distance from the missile to the target, For the The missile's sight angle, is the derivative of the sight angle with respect to time, For the The attack time deviation of the missiles.

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