Remaining flight trajectory inversion cooperative guidance law design method for strike maneuvering target

Abstract

The invention relates to the field of anti-ship missile collaborative guidance laws, and discloses a method for designing a residual flight trajectory inversion collaborative guidance law of a striking maneuvering target, and the method comprises the steps: 1, giving a missile and maneuvering target motion relation under a relative coordinate system according to a missile-maneuvering target kinematics equation in a vector form; step 2, giving a missile-target kinematical equation of the motion model under the relative system based on the motion relation in the step 1; 3, according to the kinematics equation in the step 2, rearranging the missile-target motion relation when the target is static; 4, based on the missile-target motion relation in the step 3, under the given vector guidance model, designing a residual flight path analytical solution; and 5, deducing a guidance law according to the analysis of the residual flight path in the step 4, the guidance law realizes the high-precision prediction of the residual flight time through an inversion guidance strategy, and provides a reliable theoretical support for time cooperative guidance.

Description

Technical Field

[0001] This invention relates to the field of cooperative guidance laws for anti-ship missiles, specifically a design method for cooperative guidance laws that invert the remaining flight trajectory when striking a maneuvering target. Background Technology

[0002] Missile swarms employing time-coordinated guidance laws to launch saturation attacks on maneuvering targets, significantly improving missile penetration probability and strike effectiveness, which is of great significance for anti-ship warfare. Although existing guidance laws have made some progress in time-coordinated guidance, guidance methods for striking maneuvering targets still face numerous engineering challenges. Most existing research assumes that the missile can freely control its flight speed during the terminal guidance phase, using the missile's acceleration along its velocity axis as the control input, and then designing guidance commands using a consensus protocol. However, most cruise missiles cannot freely control their flight speed during the terminal guidance phase, making such methods difficult to implement effectively in engineering. Therefore, designing multi-missile time-coordinated guidance strategies without relying on velocity axis control has become a key and challenging problem in the current missile guidance field. To address this, this invention proposes a method for designing a cooperative guidance law based on the residual flight trajectory inversion for striking maneuvering targets. Summary of the Invention

[0003] The purpose of this invention is to provide a method for designing a cooperative guidance law for retrieving the residual flight trajectory of a maneuvering target, so as to solve the problems mentioned in the background art.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a method for designing a cooperative guidance law for retrieving the residual flight trajectory of a maneuvering target, comprising the following steps:

[0005] Step 1: Based on the missile-maneuvering target kinematic equations in vector form, give the motion relationship between the missile and the maneuvering target in the relative coordinate system;

[0006] Step 2: Based on the motion relationship in Step 1, give the missile-target kinematic equations for the motion model in the relative frame.

[0007] Step 3: Based on the kinematic equations from Step 2, reorganize the relationship between the projectile and the target motion when the target is stationary;

[0008] Step 4: Based on the missile-target motion relationship in Step 3, design the analytical solution for the remaining flight trajectory under the given vector guidance model;

[0009] Step 5: Based on the analysis of the remaining flight trajectory in Step 4, derive the guidance law.

[0010] Preferably: In step 1, the missile velocity vector and the target velocity vector are respectively represented by... and Indicates; line-of-sight vector This indicates the target's position relative to the missile; the projections of the line-of-sight angle in the vertical and horizontal directions are respectively... and In three-dimensional space, the missile's forward angle Defined as missile velocity vector and line-of-sight vector The angle between them, symbol , and They represent , and The unit vector, that is:

[0011]

[0012] in It is a relative distance; and These are the speeds of the missile and the target, respectively; missile speed. and target speed If the value remains constant throughout the guidance process, then the missile-maneuvering target kinematic equations in vector form are:

[0013]

[0014]

[0015]

[0016] in as well as The control acceleration vectors for the missile and the target are given respectively. Then, the motion relationship between the missile and the maneuvering target in the relative coordinate system is given, and the relative velocity vector is defined as:

[0017]

[0018] The relative velocity unit vector is defined as ,in For the relative velocity magnitude, the relative velocity vector Differentiating, we get:

[0019]

[0020] in Indicates tangential relative acceleration. This is the normal relative acceleration.

[0021] Preferably, in step 2, for the motion model in the relative frame, the missile-target kinematic equations are characterized as:

[0022]

[0023]

[0024]

[0025] in Line of sight vector The rotational angular velocity vector, Relative velocity vector The angular velocity vectors of rotation are expressed as follows:

[0026]

[0027] Furthermore, define the relative leading angle. Relative velocity vector With line of sight vector The included angle between them, relative to the leading angle, satisfies:

[0028]

[0029] in For a unit vector, the derivative of the above equation with respect to the relative leading angle is:

[0030]

[0031] Line-of-sight angular velocity vector The derivative is:

[0032]

[0033] in This refers to interference caused by the target's maneuver.

[0034] Preferably, in step 3, the bullet-target motion relationship when the target is stationary is reorganized as follows:

[0035]

[0036]

[0037] in velocity vector The rotational angular velocity, defined according to the missile lead angle. The pre-angular derivative in vector form is:

[0038]

[0039] Where the unit vector Defined as The expression for the line-of-sight angular velocity vector is:

[0040] .

[0041] Preferably, in step 4, under the given vector guidance model, an analytical solution for the remaining flight trajectory is designed in the following form:

[0042]

[0043] in To match the missile's forward angle Related auxiliary functions, Designed as:

[0044]

[0045] in Let these be the guidance parameters, denoted as... For the design Differentiation yields:

[0046]

[0047] According to the definition of residual flight trajectory, when striking a stationary target, the residual flight trajectory satisfies... We obtain the derivative of the preceding angle:

[0048] .

[0049] Preferably, in step 5, the guidance law can be derived based on the relationship between control acceleration and lead angle:

[0050]

[0051] in .

[0052] Compared with the prior art, the beneficial effects of this invention are as follows:

[0053] This invention, based on the missile-maneuvering target kinematic equations in vector form, gives the motion relationship between the missile and the maneuvering target in a relative coordinate system. Based on this motion relationship, it then gives the missile-target kinematic equations for a motion model in a relative system. Next, based on these kinematic equations, the missile-target motion relationship when the target is stationary is reorganized. Based on this missile-target motion relationship, under the given vector guidance model, an analytical solution for the remaining flight trajectory is designed. Then, based on the obtained analytical solution for the remaining flight trajectory, the guidance law is derived. The guidance law of this invention achieves high-precision prediction of the remaining flight time through an inversion guidance strategy, providing reliable theoretical support for time-coordinated guidance. Attached Figure Description

[0054] Figure 1 This is a kinematic model in an inertial frame.

[0055] Figure 2 Different parameters of the present invention Simulation results of the lower baseline guidance law;

[0056] Figure 3 The simulation results of the baseline guidance law under different initial lead angles of this invention are shown below.

[0057] Figure 4 For inter-missile communication topology;

[0058] Figure 5 for Simulation results of time-coordinated guidance law;

[0059] Figure 6 for Simulation results of time-coordinated guidance law. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] Example

[0062] Please see Figure 1-6 The diagram illustrates a method for designing a cooperative guidance law for retrieving the residual flight trajectory of a maneuvering target, comprising the following steps:

[0063] Step 1: Based on the missile-maneuvering target kinematic equations in vector form, give the motion relationship between the missile and the maneuvering target in the relative coordinate system;

[0064] Step 2: Based on the motion relationship in Step 1, give the missile-target kinematic equations for the motion model in the relative frame.

[0065] Step 3: Based on the kinematic equations from Step 2, reorganize the relationship between the projectile and the target motion when the target is stationary;

[0066] Step 4: Based on the missile-target motion relationship in Step 3, design the analytical solution for the remaining flight trajectory under the given vector guidance model;

[0067] Step 5: Based on the analysis of the remaining flight trajectory in Step 4, derive the guidance law.

[0068] In this embodiment, in step 1, the missile velocity vector and the target velocity vector are respectively used as and Indicates; line-of-sight vector This indicates the target's position relative to the missile; the projections of the line-of-sight angle in the vertical and horizontal directions are respectively... and In three-dimensional space, the missile's forward angle Defined as missile velocity vector and line-of-sight vector The angle between them, symbol , and They represent , and The unit vector, that is:

[0069]

[0070] in It is a relative distance; and These are the speeds of the missile and the target, respectively; missile speed. and target speed If the value remains constant throughout the guidance process, then the missile-maneuvering target kinematic equations in vector form are:

[0071]

[0072]

[0073]

[0074] in as well as The control acceleration vectors for the missile and the target are given respectively. Then, the motion relationship between the missile and the maneuvering target in the relative coordinate system is given, and the relative velocity vector is defined as:

[0075]

[0076] The relative velocity unit vector is defined as ,in For the relative velocity magnitude, the relative velocity vector Differentiating, we get:

[0077]

[0078] in Indicates tangential relative acceleration. This is the normal relative acceleration.

[0079] Furthermore, in step 2, for the motion model in the relative frame, the missile-target kinematic equations are characterized as:

[0080]

[0081]

[0082]

[0083] in Line of sight vector The rotational angular velocity vector, Relative velocity vector The angular velocity vectors of rotation are expressed as follows:

[0084]

[0085] Furthermore, define the relative leading angle. Relative velocity vector With line of sight vector The included angle between them, relative to the leading angle, satisfies:

[0086]

[0087] in For a unit vector, the derivative of the above equation with respect to the relative leading angle is:

[0088]

[0089] Line-of-sight angular velocity vector The derivative is:

[0090]

[0091] in This refers to interference caused by the target's maneuver.

[0092] Preferred: In step 3, the bullet-target motion relationship when the target is stationary is reorganized as follows:

[0093]

[0094]

[0095] in velocity vector The rotational angular velocity, defined according to the missile lead angle. The pre-angular derivative in vector form is:

[0096]

[0097] Where the unit vector Defined as The expression for the line-of-sight angular velocity vector is:

[0098] .

[0099] Furthermore, in step 4, under the given vector guidance model, an analytical solution for the remaining flight trajectory is designed in the following form:

[0100]

[0101] in To match the missile's forward angle Related auxiliary functions, Designed as:

[0102]

[0103] in Let these be the guidance parameters, denoted as... For the design Differentiation yields:

[0104]

[0105] According to the definition of residual flight trajectory, when striking a stationary target, the residual flight trajectory satisfies... We obtain the derivative of the preceding angle:

[0106] .

[0107] In this embodiment, in step 5, the guidance law can be derived based on the relationship between control acceleration and lead angle:

[0108]

[0109] in .

[0110] Furthermore, considering the kinematic model of the missile-stationary target in three-dimensional space, a baseline guidance law is designed. Then the closed-loop system can achieve zero miss distance, zero terminal lead angle, and zero terminal acceleration constraint, and the missile's remaining flight trajectory can be determined by... Precise calculations.

[0111] The proof process is divided into three parts, which provide detailed derivations of the zero miss distance, zero terminal lead angle, and zero terminal acceleration constraints.

[0112] (1) Zero miss constraint, firstly, the auxiliary function Applying L'Hospital's rule:

[0113]

[0114]

[0115] This indicates that for ,function Continuous and bounded and satisfying The relative distance can be obtained as:

[0116]

[0117] The above has already been given That is, the remaining flight trajectory will decrease strictly monotonically from the initial value to zero, and due to the auxiliary function And it is bounded, therefore when From time to time This clearly satisfies the zero miss distance constraint.

[0118] (2) Zero terminal lead angle constraint: To analyze the characteristics of the missile's lead angle terminal, an auxiliary function is introduced as follows:

[0119]

[0120] Substituting the derivative of the preceding angle into the above equation, we get:

[0121]

[0122] It can be verified that when the guidance parameters meet the requirements... At that time, for have According to the properties of continuous functions, there exists a constant. and This makes the following equation true:

[0123]

[0124] The above formula can be rearranged as follows:

[0125]

[0126] Integrating the above differential inequality from the initial time to the current time:

[0127]

[0128] in The initial value for the remaining flight trajectory, Equivalent to:

[0129]

[0130] Therefore, at the guidance terminal moment:

[0131]

[0132] in as well as Therefore, since both sides of the inequality are zero, we know that... This indicates that the missile's lead angle will converge to zero at the guidance terminal.

[0133] (3) Zero terminal acceleration constraint: According to the above formula, we can obtain

[0134]

[0135] Therefore, the vector form of control acceleration for:

[0136]

[0137] The missile velocity vector rotation angular velocity can be further simplified as follows:

[0138]

[0139] It has been proven that the guidance terminal always meets the requirements. ,right Applying L'Hospital's rule:

[0140]

[0141] because It can be known that when have Known for A continuous function, according to the properties of continuous functions, exists on an interval. Within this interval, the following relationship holds:

[0142]

[0143] in , It is a sufficiently small constant. Further, we can obtain:

[0144]

[0145] In the interval Solve the above differential inequality internally:

[0146]

[0147] in Entering the interval for the front angle The remaining flight path at that time was further processed:

[0148]

[0149] when When the above expression is used, it is equivalent to:

[0150]

[0151] because as well as The above formula shows Substitute this result into It can be known that:

[0152]

[0153] Mode Equivalent to ,as well as Therefore, the missile's terminal control acceleration converges to zero.

[0154] Furthermore, the guidance law proposed in this invention is derived in reverse from the analytical solution of the remaining flight trajectory, wherein... This holds true throughout, representing the missile's remaining flight trajectory. It is globally accurate; proof complete.

[0155] The above describes the design and analysis process of the remaining flight trajectory, and the corresponding remaining flight time can be obtained by the following formula:

[0156]

[0157] Easy to verify Therefore, the remaining flight time obtained It is also globally accurate.

[0158] Guidance laws have been designed using inversion guidance strategies. And the corresponding precise remaining flight time was obtained. Next, based on the above theoretical results, the consistency error will be calculated and a feedback guidance law will be designed to complete the time-coordinated guidance for striking stationary targets in three-dimensional space.

[0159] For missile assemblies Define the remaining flight time consistency error as The remaining flight time From exact analytical solution Calculations were performed, and the time-coordinated guidance law was designed as follows:

[0160]

[0161] in To ensure the convergence of consistency error, the feedback term, A scalar function is defined as follows:

[0162]

[0163] in For constant parameters, The preset convergence time is determined by the specified convergence distance. Decision. To facilitate subsequent guidance law design, three scalar functions are given here. , ,in (Right now ).

[0164] Furthermore, considering the kinematic model of the missile-stationary target in three-dimensional space, a cooperative guidance law is designed. And the remaining flight time is determined by Analytical calculations show that the closed-loop system can achieve time-coordinated guidance for multiple missiles.

[0165] Substituting the designed cooperative guidance law into the lead angle dynamics, we can obtain:

[0166]

[0167] The corresponding derivative of the remaining flight trajectory is:

[0168]

[0169] For the remaining flight time Differentiate, and Substituting the values, we get:

[0170]

[0171] Choosing Lyapunov functions This verifies the stability of the closed-loop system, completing the proof.

[0172] In this embodiment, the final form of the obtained feedback guidance law will be analyzed, and the equation will be... The following is a revised version:

[0173]

[0174] in It can be considered as a time-varying proportional coefficient, and its specific expression is:

[0175]

[0176] The proportional coefficient in the obtained guidance law It is the missile's forward angle. The function can be further obtained , combined The proportionality coefficient is known. Always greater than The above results explain the terminal convergence characteristics of the lead angle and control acceleration from the perspective of proportional guidance. It can be seen that although the guidance law designed in this invention adopts the inverse guidance strategy, the final guidance command has the same mathematical form as the traditional forward design method.

[0177] Furthermore, numerical simulations under different operating conditions were used to verify the effectiveness of the inversion guidance strategy, specifically including the remaining flight trajectory. Baseline guidance law and cooperative guidance law The simulation analysis shows that the stationary target is located at the origin, the initial missile-target distance is 10 km, and the missile's flight speed is 300 m / s.

[0178] (1) Simulation verification of baseline guidance law

[0179] The simulations were divided into two groups, each using different guidance parameters and initial conditions to fully verify the performance of the proposed baseline guidance law and to focus on analyzing the accuracy of the remaining flight time prediction. The first group of simulations fixed the missile's initial lead angle at [value missing]. Guidance parameters The values ​​were selected as 0.3, 0.35, 0.4, and 0.45 respectively, and the simulation results are as follows: Figure 2 As shown.

[0180] Figure 2 The simulation results show the changes in the missile's flight trajectory, relative distance and remaining flight time, lead angle, and control acceleration. The simulation results also demonstrate that the guidance parameters... The smaller the value, the closer the missile's flight trajectory is to a straight line. The smaller the lead angle during guidance, the greater the corresponding control acceleration amplitude. It is worth noting that although the missile flies with a large lead angle in the initial stage, the remaining flight time still maintains a high prediction accuracy.

[0181] To further verify the adaptability of the baseline guidance law to the initial guidance conditions, the initial lead angle of the missile was set as follows: , , and Guidance parameters Fixed as The simulation results are as follows Figure 3 As shown in the simulation curves, the baseline guidance law ensures accurate target hits for the missile under different initial lead angles. However, as the initial lead angle increases, the missile's flight trajectory gradually curves, particularly... Figure 3The slope of the remaining flight time curve in -b is strictly maintained at -1. The above simulation results verify the effectiveness of the baseline guidance law in striking stationary targets. This guidance law achieves high-precision prediction of the remaining flight time through the inversion guidance strategy, providing reliable theoretical support for time-coordinated guidance.

[0182] (2) Simulation verification of cooperative guidance law

[0183] Two sets of simulations were set up to verify the effectiveness of the guidance law for achieving multi-missile coordination. The missile adopts... Figure 4 The communication topology shown.

[0184] Selecting guidance parameters The corresponding simulation results of cooperative guidance are as follows: Figure 5 As shown, the missile's flight trajectory, relative distance and remaining flight time, lead angle and consistency error, and control acceleration curve under the guidance law are respectively derived from... Figure 5 -a to Figure 5 -d indicates that due to the different relative distances between the missile and the target and the different missile lead angles, the consistency error of the remaining flight time at the initial moment is relatively large. Under the action of the designed cooperative guidance law, the remaining flight time of each missile tends to be consistent, and finally the cooperative strike on the target is achieved. In addition, after the consistency error is eliminated, the missile lead angle and control acceleration converge to zero at the terminal moment.

[0185] Secondly, the guidance parameters Adjusted to With the initial missile operating conditions and other simulation conditions unchanged, the corresponding cooperative guidance simulation results are given as follows: Figure 6 As shown in Table 1, the missile miss distance and impact time are compared under two sets of parameters.

[0186] It can be seen that when the guidance parameters After the initial acceleration, the amplitude of the missile's control acceleration decreases accordingly. Therefore, the convergence of the consistency error between the missile's lead angle and remaining flight time is relatively slow, and ultimately the missile... The target was hit at time s. Combining the above results with those in Table 1, the guidance parameters... Increasing the value will lead to a decrease in the proportional coefficient, resulting in a larger flight time for a smaller proportional coefficient. This is consistent with the flight time control characteristics of the traditional proportional guidance law. Both sets of simulation results above demonstrate the effectiveness of the multi-missile time-coordinated guidance law based on the inversion guidance strategy.

[0187] Table 1 Simulation results under different parameters

[0188]

[0189] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0190] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for designing a cooperative guidance law for inverting the residual flight trajectory of an attack on a maneuvering target, characterized in that, Includes the following steps: Step 1: Based on the missile-maneuvering target kinematic equations in vector form, give the motion relationship between the missile and the maneuvering target in the relative coordinate system; Step 2: Based on the motion relationship in Step 1, give the missile-target kinematic equations for the motion model in the relative frame. Step 3: Based on the kinematic equations from Step 2, reorganize the relationship between the projectile and the target motion when the target is stationary; Step 4: Based on the missile-target motion relationship in Step 3, design the analytical solution for the remaining flight trajectory under the given vector guidance model; Step 5: Based on the analysis of the remaining flight trajectory in Step 4, derive the guidance law.

2. The method for designing a cooperative guidance law for retrieving the residual flight trajectory of a maneuvering target according to claim 1, characterized in that: In step 1, the missile velocity vector and the target velocity vector are respectively used as... and express; Line of sight vector Indicates the target's position relative to the missile; The projections of the viewing angle in the vertical and horizontal directions are respectively and In three-dimensional space, the missile's forward angle Defined as missile velocity vector and line-of-sight vector The angle between them, symbol , and They represent , and The unit vector, that is: ， in It is a relative distance; and These are the speeds of the missile and the target, respectively; missile speed. and target speed If the value remains constant throughout the guidance process, then the missile-maneuvering target kinematic equations in vector form are: ， ， ， in as well as The control acceleration vectors for the missile and the target are given respectively. Then, the motion relationship between the missile and the maneuvering target in the relative coordinate system is given, and the relative velocity vector is defined as: ， The relative velocity unit vector is defined as ,in For the relative velocity magnitude, the relative velocity vector Differentiating, we get: ， in Indicates tangential relative acceleration. This is the normal relative acceleration.

3. The method for designing a cooperative guidance law for inverting the residual flight trajectory of a maneuvering target according to claim 2, characterized in that: In step 2, for the motion model in the relative frame, the missile-target kinematic equations are characterized as follows: ， ， ， in Line of sight vector The rotational angular velocity vector, Relative velocity vector The angular velocity vectors of rotation are expressed as follows: ， Furthermore, define the relative leading angle. Relative velocity vector With line of sight vector The included angle between them, relative to the leading angle, satisfies: ， in For a unit vector, the derivative of the above equation with respect to the relative leading angle is: ， Line-of-sight angular velocity vector The derivative is: ， in This refers to interference caused by the target's maneuver.

4. The method for designing a cooperative guidance law for retrieving the residual flight trajectory of a maneuvering target according to claim 3, characterized in that: In step 3, the relationship between projectile and target motion when the target is stationary is reorganized as follows: ， ， in velocity vector The rotational angular velocity, defined according to the missile lead angle. The pre-angular derivative in vector form is: ， Where the unit vector Defined as The expression for the line-of-sight angular velocity vector is: 。 5. The method for designing a cooperative guidance law for retrieving the residual flight trajectory of a maneuvering target according to claim 4, characterized in that: In step 4, under the given vector guidance model, the analytical solution for the remaining flight trajectory is designed in the following form: ， in To match the missile's forward angle Related auxiliary functions, Designed as: ， in Let these be the guidance parameters, denoted as... For the design Differentiation yields: ， According to the definition of residual flight trajectory, when striking a stationary target, the residual flight trajectory satisfies... We obtain the derivative of the preceding angle: 。 6. The method for designing a cooperative guidance law for inverting the residual flight trajectory of a maneuvering target according to claim 5, characterized in that: In step 5, the guidance law can be derived based on the relationship between control acceleration and lead angle: ， in .

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