A relative distance-based hyperbolic-like lead angle reshaping terminal guidance strategy

Abstract

The application discloses a kind of hyperbolic-like front angle remodeling terminal guidance strategy based on relative distance, including the following steps: establishing the kinematic model of missile in two-dimensional plane intercepts stationary target;Design guidance strategy based on hyperbolic equation, solve the geometric parameters of hyperbolic according to the initial conditions of missile and target, obtain the analytical equation of guidance strategy about design parameter;According to the kinematic relationship inverse solution specified angle of different launch angle parameters.The guidance strategy in the application uses equation constraint to front angle information, meets the attack angle constraint under the condition of zero miss distance strike, and end view angle rate converges to 0, and guidance parameters are obtained by numerical integration calculation, without linearization to model, simplify the design of guidance system.The application improves the applicability of guidance system, and the design method is simple and applicable.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of missile guidance system design, and particularly relates to a terminal guidance strategy of hyperbolic-like lead angle remodeling based on relative distance. BACKGROUND

[0002] The guidance control technology has wide application in the military and aerospace fields, such as missile guidance, unmanned aerial vehicle navigation and satellite attitude control. The traditional guidance control method mainly focuses on the realization of zero miss distance, for example, the famous proportional guidance method. However, for the missile with zero miss distance as the guidance task, it is difficult to effectively attack the target as the target defense capability upgrades. At this moment, it is a key requirement to attack the target at a specified angle to achieve the enhancement of penetration capability. In addition, the view angle of the sensor for detecting the target of the missile in the real combat scene cannot be detected without dead angle. Therefore, it is necessary to design a guidance strategy with terminal attack angle constraint and limited view angle.

[0003] In recent years, the guidance law with attack angle constraint is a research hotspot at home and abroad, including the terminal attack angle constraint guidance law based on the proportional guidance method considering the bias quantity, the attack angle constraint guidance law based on the optimal theory considering the cost weighting of the remaining flight time, and the terminal attack angle constraint guidance law designed by the non-singular sliding mode control which can be controlled from any lead angle. These methods solve the problem of impact angle to some extent, but there are still many challenges in practical application, such as complex design, large amount of detection information, and some still need to linearize the missile kinematics, which is extremely inconvenient for practical application in real engineering.

[0004] Obviously, it is very important to design a guidance strategy with fall angle constraint and view angle constraint based on analytical equation, which overcomes the existing conservatism, simplifies the design method, reduces the view angle change, and improves the applicability of the guidance system. SUMMARY

[0005] The technical problem to be solved by the application is that with the substantial improvement of the defense capability of the target, the missile needs to attack the target at a certain specified angle, that is, a guidance strategy with attack angle constraint needs to be designed. And due to the influence of the field of view angle constraint, the lead angle of the missile under this guidance strategy cannot always exceed the maximum field of view angle. The application designs a terminal guidance strategy of hyperbolic-like lead angle remodeling based on relative distance, which realizes the specified attack angle according to the initial condition information. Unlike the existing methods, the method adopted by the application simplifies the design method while meeting the field of view angle constraint of the missile and improving the applicability of the guidance system, and does not need to linearize the model.

[0006] To achieve the above technical purposes, the technical scheme of the application is as follows:

[0007] A kind of end guidance strategy based on relative distance's hyperbolic-like pre-angle remodeling, comprising the following steps:

[0008] S1: considering the two-dimensional plane where missile and stationary target are located as attack plane, the kinematic model of missile intercepting stationary target in attack plane is established;

[0009] S2: the pre-angle equation is designed as the guidance strategy of hyperbolic-like expression about time variation;

[0010] S3: the formula of the related parameters of hyperbolic-like expression is solved according to the initial conditions of missile and target, including the distance of hyperbolic-like lower displacement to origin And the distance of hyperbolic-like vertex to origin , the analytical guidance strategy with parameters Is obtained, wherein parameter It is the parameter ratio of hyperbolic asymptote slope and real half axis length;

[0011] S4: based on the kinematic equation of S1, the analytical guidance strategy with parameters Obtained by S3, the parameter Value is inversely solved according to numerical integration method with the change of initial launch angle under the specified impact angle constraint.

[0012] The beneficial effects of the present application are:

[0013] (1) the pre-angle equation designed in the present application is the attack angle constraint guidance strategy of hyperbolic-like expression about time variation, which is the analytical equation design for missile pre-angle information, involves less information and is simple in method.

[0014] (2) the present application uses analytical method, and according to the initial conditions of missile and target, the analytical form of guidance parameters about parameter Can be obtained, without linearization of the model, simple in design and strong in applicability.

[0015] (3) since the field of view angle constraint is considered in design, it has strong practicability, and can realize zero miss distance constraint, end line-of-sight angle rate convergence to 0 and specified attack angle requirement, thereby achieving better attack effect. BRIEF DESCRIPTION OF DRAWINGS

[0016] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced below, and obviously, the drawings in the following description are only some embodiments of the present application, and those skilled in the art can obtain other drawings according to these drawings without creative labor.

[0017] Figure 1Flow chart of the missile terminal guidance strategy based on relative distance hyperbolic-like pre-angle remodeling of the present application;

[0018] Figure 2 Schematic diagram of two-dimensional attack plane for missile intercepting stationary target of the present application;

[0019] Figure 3 Schematic diagram of hyperbolic equation curve of the present application;

[0020] Figure 4 Schematic diagram of simulation of the guidance strategy of the present application under different attack angle constraints, wherein (a) represents the flight trajectory of the missile, (b) represents the pre-angle curve of the missile about the missile-target distance, (c) represents the variation curve of the missile angle of view, and (d) represents the variation curve of the missile guidance command. DETAILED DESCRIPTION

[0021] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art belong to the scope of protection of the present application.

[0022] The present application discloses a missile terminal guidance strategy based on relative distance hyperbolic-like pre-angle remodeling, comprising the following steps: establishing a kinematic model of a missile intercepting a stationary target in a two-dimensional plane; designing a guidance strategy based on a hyperbolic equation, solving the geometric parameters of the hyperbolic equation according to the initial conditions of the missile and the target, and obtaining an analytical equation of the guidance strategy about the design parameters; and inversely solving the parameters of different launch angles under a specified impact angle according to the kinematic relationship. The guidance strategy in the present application adopts equation constraint on the pre-angle information, meets the zero-missile impact under the attack angle constraint, and converges the terminal line-of-sight angle rate to 0. The guidance parameters are obtained by numerical integration calculation, without linearization of the model, which simplifies the design of the guidance system. The present application improves the applicability of the guidance system, and the design method is simple and has strong applicability.

[0023] Figure 1 Flow chart of the missile terminal guidance strategy based on relative distance hyperbolic-like pre-angle remodeling of the present application. The specific process of the strategy will be described below with reference to Figure 1 As shown in Figure 1 , the specific implementation steps of the strategy are as follows:

[0024] S1: considering the two-dimensional plane where the missile and the stationary target are located as an attack plane, a kinematic model of the missile intercepting the stationary target in the attack plane is established.

[0025] As shown in Figure 2 , and Denote the missile and the target respectively. The kinematic model of the missile intercepting a stationary target in the attack plane is:

[0026] (1)

[0027] in, is the missile's flight speed, is the missile's lead angle, is the distance between the missile and the target, is the ballistic inclination angle of the missile, From the missile's perspective, is the missile velocity tangential acceleration.

[0028] S2: A guidance strategy to design the lead angle equation as a hyperbolic-like expression with respect to time variation.

[0029] Leading angle based on hyperbolic expression The contour equation is:

[0030] (2)

[0031] in, are the parameters to be solved, which are the distance from the vertex of the hyperbola to the origin, the slope of the asymptote, and the distance from the lower displacement of the hyperbola to the origin, and they are all positive real numbers. is the initial missile-target distance, that is, the distance from the initial missile position to the stationary target.

[0032] To facilitate the solution, further transformation can be obtained:

[0033] ,

[0034] Among them, the parameters .

[0035] The initial conditions of the missile and target are as follows: The initial position of the missile is , the target position is , the missile's initial ballistic inclination is , the initial viewing angle is determined by the following equation:

[0036] .

[0037] S3: Solve the formula for the relevant parameters of the hyperbolic expression based on the initial conditions of the missile and the target, including the distance from the hyperbolic displacement to the origin and the distance from the hyperbola vertex to the origin , get the parameter The analytical guidance strategy of It is the ratio of the slope of the hyperbola asymptote to the length parameter of the real semi-axis. The detailed implementation steps are as follows:

[0038] Since the terminal lead angle needs to satisfy:

[0039] ,

[0040] And since the initial lead angle is known, we can get:

[0041] ,

[0042] where, is the initial launch angle of the missile, is the lead angle at the initial missile distance.

[0043] From the above formula, we can get two equations about :

[0044] (3)

[0045] In addition, the positive and negative signs in front of the lead angle profile equation are determined by the sign of the launch angle. Here we consider the case when the launch angle is positive, as shown in Figure 3 .

[0046] The guidance strategy obtained in this way is an analytical guidance law about the parameter , and needs to be solved by S4.

[0047] S4: Based on the kinematics equation S1, the analytical guidance strategy with parameter obtained in S3, according to the numerical integration method, the value of under the specified impact angle constraint changes with the initial launch angle is solved.

[0048] According to the transformation and integration of the first two equations of the kinematics equation (1), the following equation is obtained:

[0049] ,

[0050] where, is the specified impact angle of the missile, is the initial line of sight angle, which can be calculated according to the initial conditions.

[0051] Taylor expand the equation in the integral to N terms, and then use the numerical integration method to calculate the value of the parameter under different launch angles for the specified impact angle , and its expansion form is as follows:

[0052] ,

[0053] where, is the corresponding term order in the summation, Specifies the number of expansion items. is the first Bernoulli number, as shown below:

[0054] ,

[0055] in, is the nth derivative of x, The dependent variable corresponding to this limit is found.

[0056] According to the numerical integration method, the inverse solution is obtained as the initial launch angle changes under the specified landing angle constraint. The process is as follows: Substitute all parameters into the above formula, here we take N=5. Since the expanded integral is difficult to solve, the gradient method is used here to find the integral from 0 to k. Due to monotonicity, the result of k from 0 to 1000 (when it is greater than this number, the angle change is not obvious) is in one-to-one correspondence with the k value. From this, we can calculate the result when the result of the equation on the right is at the specified falling angle. The corresponding k value is near .

[0057] It should be understood that all variables in this article with a dot on them are the derivatives of the variables, unless the derivatives of the variables have actual physical meanings.

[0058] The following example illustrates the effectiveness of the proposed method using a missile intercepting a stationary target. The missile's speed is 250 m / s, its initial position is (0, 0) km, and its target position is (5, 0) km. The missile's maximum overload is limited to 10 g, where g is the acceleration due to gravity. The missile's maximum viewing angle is constrained to 60 degrees. Given a 60° initial viewing angle, the attack angles chosen are: -60 degrees, -45 degrees, and -35 degrees. Numerical integration can be used to determine the parameters to be solved.

[0059] The interception simulation diagram for the stationary target is as follows: Figure 4 As shown, Figure 4 (a), (b), (c) and (d) in the figure respectively represent the missile's flight trajectory, the missile's lead angle change curve with respect to the missile-target distance, the missile's visual angle change curve, and the missile's guidance instruction change curve. Figure 4 As can be seen from (a), the proposed method can effectively intercept stationary targets under the desired attack angle constraint.

[0060] According to the above analysis and description, it can be seen that the guidance strategy proposed in the present invention effectively realizes the requirements of attack angle constraint and viewing angle constraint. It does not require linearization of the model and has the characteristics of simple design method, high adaptability and flexibility, and low computational complexity.

[0061] The above merely provides the preferred embodiment of the present application, and is not used to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A relative distance based hyperbolic-like pre-angle reshaping terminal guidance method, characterized in that, The method comprises the following steps: S1: considering a two-dimensional plane where the missile and the stationary target are located as an attack plane, a kinematics model of the missile intercepting the stationary target in the attack plane is established; S2: a lead angle equation is designed as a guidance strategy of a hyperbolic curve expression about time variation; S3: Solve the formula of the related parameters of the hyperbolic-like curve expression according to the initial conditions of the missile and the target, including the distance from the lower displacement of the hyperbolic-like curve to the origin And the distance from the vertex of the hyperbolic-like curve to the origin , get the analytical guidance strategy with parameters , where the parameter is the ratio of the slope of the hyperbolic asymptote to the parameter of the real semi-axis length; S4: Based on the kinematic equation of S1, the parameters obtained in S3 The analytical guidance strategy is obtained according to the numerical integration method, and the parameters changing with the initial launch angle under the specified impact angle constraint are inversely solved values; In step S1, the kinematics model of the missile intercepting the stationary target in the attack plane is: （1） wherein, is the flight speed of the missile, is the lead angle of the missile, is the missile-target distance of the missile, is the trajectory angle of the missile, is the line-of-sight angle of the missile, is the tangential acceleration of the missile speed; Step S2 comprises: Pre-angles based on hyperbolic expressions The profile equation is: （2） wherein, are positive real numbers, respectively the distance from the hyperbolic vertex to the origin, the asymptote slope, the distance from the hyperbolic vertex to the origin, and is the initial missile-target distance, i.e. the distance from the initial missile position to the stationary target. Further transformation is performed on formula (2) to obtain: ， wherein the parameters ; Step S3 comprises: The distance of the hypocycloid from the origin and the distance of the hypocycloid vertex from the origin The formula is: （3） wherein, is the initial launch angle of the missile, is the lead angle at the initial missile-target distance; In step S4, the following equation is obtained according to the deformation and integration of the first two equations of the kinematics equation (1): ， wherein, is the initial line-of-sight angle, is the specified impact angle of the missile; The integral is Taylor expanded to N terms and the specified impact angle is calculated by numerical integration method through iteration The parameters of the different launch angles The value of its expansion form is as follows: ， wherein, is the order of the corresponding term in the summation, is the specified number of expansion terms, is the first Bernoulli number, as shown in the following equation: ， wherein is the n-th derivative of x with respect to t, is the dependent variable corresponding to the limit. According to the numerical integration method, the parameter varying with the initial launching angle under the specified landing angle constraint is solved inversely The process of the value is as follows: all parameters are substituted into the above formula, N=5 is taken, the integral from 0 to k is solved by using the gradient method, and thus the corresponding k value is calculated when the right side of the equation is close to the specified landing angle .

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