CN115993772A

CN115993772A - Four-stage two-dimensional guidance method based on Bezier curve

Info

Publication number: CN115993772A
Application number: CN202211465454.7A
Authority: CN
Inventors: 程志强; 庞云福; 刘磊; 马超; 向崇文; 熊传梁; 王亮
Original assignee: Chinese People's Liberation Army 91776
Current assignee: Chinese People's Liberation Army 91776
Priority date: 2022-11-22
Filing date: 2022-11-22
Publication date: 2023-04-21

Abstract

The invention provides a four-stage two-dimensional guidance method based on a Bezier curve, which is characterized by comprising the steps of judging whether an expected impact angle meets constraint conditions under a sight line coordinate system, adjusting the expected impact angle under the sight line coordinate system, judging whether the length of the Bezier curve is matched with the rest flight distance, adjusting the track angle in the sight line coordinate system, judging whether the Bezier track in a fixed sight line coordinate system is completely tracked, generating lateral acceleration for tracking the Bezier track in the sight line coordinate system, attacking a target by using a proportional guidance control method and the like. The four-stage guidance control method based on the Bezier curve is designed based on the monotonicity rule of the two-stage track length, and the high-precision control of the attack time and the attack angle under the condition of the aircraft speed is realized. The method has wide application range, and changes the situation that the related guidance law of the prior Bezier curve is not suitable for the conditions of too small emission angle and expected impact angle.

Description

Four-stage two-dimensional guidance method based on Bezier curve

Technical Field

The invention belongs to the technical field of guidance, and particularly relates to a four-stage two-dimensional guidance method based on Bezier curves.

Background

The (ITACG) guidance law controlling the attack angle and time can control the aircraft to strike targets at different angles at the same time, and has high actual combat value. Especially for the sea assault, the ITACG guidance law can be simultaneously emptied, so that the interception effect of an air defense system at the tail end of the opposite side is reduced, and the accident prevention probability is improved. The current ITACG guidance law rarely considers the speed change condition, and the ITACG guidance law based on the Bezier curve can be well adapted to the speed change condition. However, the current ITACG guidance law based on bezier curves has a large usage limit and cannot be used in cases where the initial emission angle is too small or where the desired impingement angle is too small.

Specifically, other ITACG guidance laws mainly include a variable guidance parameter method, a sliding mode control method, a centralized decision method in a flight process, a decentralized decision method in a flight process and the like. These control methods are generally difficult to accommodate for variable speed conditions.

Disclosure of Invention

In order to solve the problems in the prior art, the invention provides a two-dimensional collaborative guidance law with good robustness, small calculated amount and wide application range. The invention first generates a two-segment guidance track based on Bezier curves, as shown in FIG. 2. The first segment of the track is Bezier curve

The second section is straight line section->

Wherein E is ₃ The point is a line segment->

Is defined by a central point of the lens. The two-segment track can be expressed as +.>

Corresponding toLength of->

The track has a length with θ ₀ The characteristic of monotonic change of the size of the track, and the binary method is used for searching the binary track with specific length and PI adjusting theta ₀ Thereby adjusting the accuracy of the track length.

In the first stage of the invention, the missile needs to adjust the value theta of the expected impact angle in the line-of-sight coordinate system _f,LOS . When theta is as _f,LOS When too small, the curvature of the bezier curve is too large, and it is difficult to form an effective striking. To solve this problem, θ is adjusted _f,LOS To a reasonable extent theta _s ≤|θ _f,LOS |≤θ _b . When 0 is less than or equal to theta _f,LOS ＜θ _s Or-pi < theta _f,LOS ＜-θ _b When the expected speed is the y direction of the sight line coordinate system, the acceleration of the sight line coordinate system is as follows:

a _LOS ＝k _p,1 ×(θ _LOS -π/2)+k _i,1 ×∫(θ _LOS -π/2)dt

when-theta _s ＜θ _f,LOS < 0 or theta _b ＜θ _f,LOS When pi is less, the expected speed is the sight line coordinate system-y direction, then the sight line coordinate system acceleration is:

a _LOS ＝k _p,1 ×(θ _LOS +π/2)+k _i,1 ×∫(θ _LOS +π/2)dt

when theta is as _f,LOS Satisfy theta _s ≤|θ _f,LOS |≤θ _b And when the process is completed, the second stage is carried out. The second stage is aimed at adjusting the track angle so that the two-stage track length formed by the speed direction and the impact direction is equal to the expected flight length. This stage goal is equivalent to

Wherein L is _est Representing the distance travelled by the missile during the expected time. The dichotomy can be used to find

Then look atThe expected acceleration of the linear coordinate system is:

/>

when (when)

And L is equal to _est The size is close enough, and the third stage is entered. The stage objective is to track and adjust the trajectory generated in the second stage. Selecting a point B closest to the missile on a two-section track under a sight line coordinate system _LOS (τ ₀ ) Assuming that the tangential distance from the missile to the point is d, the desired acceleration is:

wherein q is ₁ And q ₂ As a function of the parameters,

θ _d is the desired direction. During the flight, the correction can be carried out>

To adjust the track length. The specific calculation method comprises the following steps:

wherein L is _real The specific calculation method of (a) is as follows:

L _real ＝|J|(N(1+D)-N(τ ₀ +D))+||E ₃ E ₂ ||

wherein N (u) is:

j, K, U, D can be calculated as follows:

J＝E ₁ -2P _c +E ₂

K＝P _c -E ₁

U＝|K| ² /|J| ² -(J·K)/|J| ²

D＝(J·K)/|J| ²

and when the missile enters a two-section track straight line section or the residual time is insufficient, the fourth stage is shifted.

The fourth stage is a proportional guidance method, which comprises the following steps:

a＝Nω×v

where N is a proportional guidance parameter, ω is the line of sight angular rate, and v is the missile flight speed.

The invention has the advantages that:

(1) The first stage only needs to judge how to increase the impact angle in the sight line coordinate system; the second and third stages use dichotomy, with the computational complexity being logarithmic; the fourth stage is the proportional navigational method. The calculated amount of the algorithm in each stage is small, and the requirement of real-time calculation can be met;

(2) Real-time adjustment of sight coordinate system by PI control algorithm

The size has good robustness to the resistance possibly encountered in the flight process of the aircraft, and can realize high-precision striking time control;

(3) The guidance law is suitable for the condition that the initial emission angle and the expected impact angle are smaller, has a wide application range, and effectively expands the range based on Bezier curve striking.

Drawings

FIG. 1 is a flow chart of the calculation of the guidance law of the present invention;

FIG. 2 is a two-segment guidance trajectory based on Bezier curves.

Detailed Description

For the purposes of making the objects, technical solutions and some of the details of the present application more clear, the technical solutions of the present application will be clearly and completely described below with reference to specific embodiments of the present application and corresponding drawings. It will be apparent that the described embodiments are only some, but not all, of the embodiments of the present application. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present disclosure.

The specific steps of this embodiment are shown in fig. 1. A four-stage two-dimensional guidance method based on Bezier curves comprises the following steps: a flight trajectory generator, a dynamic trajectory adjuster, and a trajectory tracker. Taking a missile striking fixed target as an example, the launching point is E ₁ = (0, 0), strike target position is E ₂ = (10000,0) initial emission angle θ ₀ = -60 °, desired striking angle θ _f =0°, desired striking time t _D =60 s. Since the initial desired attack angle is too small, the missile will fly in the negative direction of the Y-axis in the first stage until the desired attack angle in the line of sight coordinate system meets the conditions. After entering the second stage, the missile can quickly adjust the track angle to form a Bezier curve with proper length. After entering the third stage, the missile will track the track formed in the previous stage and fly to the hit target. In the fourth stage, the final striking is achieved using a proportional guidance method. Parameters of the first to fourth stages need to be designed for different missiles. In tracking the track, the track tracker may be selected to track a tangent to the closest point of the missile. Let d be the distance from missile to tangent, θ _d Is the angle between the tangent line and the X axis. The heading acceleration may be as follows:

wherein q is ₁ And q ₂ As a function of the parameters,

q ₁ and q ₂ Typical values of (2) and (3.74).

While the foregoing description of the embodiments of the present invention has been presented in conjunction with the drawings, it should be understood that the invention is not limited to the particular embodiments, but is capable of numerous modifications and variations within the spirit and scope of the invention.

Claims

1. A four-stage two-dimensional guidance method based on Bezier curves is characterized by comprising the following steps:

s1, judging the expected impact angle theta _f Whether the constraint condition is satisfied under the sight line coordinate system or not, the step and the step S2 are the first stage of the guidance law, specifically:

the initial position is recorded as E ₁ (x ₁ ,y ₁ ) The striking target position is E ₂ (x ₂ ,y ₂ )，θ _f The value in the line of sight coordinate system is theta _f,LOS If the constraint condition theta is satisfied _s ≤|θ _f,LOS |≤θ _b Go to S3, otherwise execute S2, where

Is a parameter set before the algorithm is run;

s2, adjusting the expected impact angle theta under the sight line coordinate system _f,LOS The method specifically comprises the following steps:

if 0.ltoreq.θ _f,LOS ＜θ _s Or-pi < theta _f,LOS ＜-θ _b Tangential acceleration a in the line-of-sight coordinate system _LOS The method comprises the following steps:

a _LOS ＝k _p,1 ×(θ _LOS -π/2)+k _i,1 ×∫(θ _LOS -π/2)dt

if-theta _s ＜θ _f,LOS < 0 or theta _b ＜θ _f,LOS < pi, tangential acceleration a in line-of-sight coordinate system _LOS The method comprises the following steps:

a _LOS ＝k _p,1 ×(θ _LOS +π/2)+k _i,1 ×∫(θ _LOS +π/2)dt

wherein θ is _LOS Representing the value of the track angle in the line of sight coordinate system, k _p,1 And k is equal to _i,1 Proportional and integral parameters, acceleration a, respectively _LOS Returning to the step S1 for execution after the execution is finished；

S3, judging whether the two-section track length is matched with the remaining flight distance, wherein the step and the step S4 are the second stage of the guidance law, and specifically comprise the following steps:

the two-section track is a striking track with a Bezier curve at the first half section and a straight line at the second half section, and if the length of the Bezier curve is matched with the rest flight distance, the step S5 is executed, otherwise, the step S4 is executed;

s4, adjusting a track angle in a sight line coordinate system, wherein the track angle specifically comprises the following steps:

calculating the remaining flight distance L under the sight line coordinate system by a dichotomy _est Corresponding two-section track angle

The calculation method is that for the appointed +.>

P _c The point coordinates are:

for the following

Let j=e ₁ -2P _c +E ₂ ，K＝P _c -E ₁ Wherein->

The calculation method of (1) is as follows:

wherein τ ₀ ＝0，D＝(J·K)/|J ² The calculation method of N (u) is as follows:

the calculation method of U is as follows:

U＝|K| ² /|J| ² -(J·K)/|J| ²

tangential acceleration in the line of sight coordinate system is:

wherein k is _p,2 And k is equal to _i,2 Proportional and integral parameters, acceleration a, respectively _LOS Returning to the step S3 after the execution is finished;

s5, judging whether the Bezier track in the fixed line-of-sight coordinate system is completely tracked, wherein the fixed line-of-sight coordinate system refers to the line-of-sight coordinate system LOS when the step S3 exits ⁰ The third stage of the guidance law is the steps of the step and the step S6, specifically:

recording the position of the missile at the moment of exiting in the step S3 as

Judging by->

E ₂ 、/>

Constitutive Bessel track B _Los If the tracking is finished, turning to the step S7 if the Bezier curve tracking is finished, otherwise turning to the step S6;

and S6, generating lateral acceleration for tracking Bezier tracks in a sight line coordinate system, wherein the method specifically comprises the following steps:

the closest point of the missile distance tracking track is recorded as B _LOS (τ ₀ ) Tangential acceleration in the line-of-sight coordinate system at this step is:

wherein q is ₁ And q ₂ Is the parameter, d is the missile reaching the point B _LOS (τ ₀ ) The distance of tangent line, the missile speed is variable, the trajectory track should be changed in real time, and the length of the remaining track is recorded as L _real Then

The amount of change of (c) is:

wherein k is _p And k is equal to _i Is a proportional and integral parameter;

s7, attacking the target by using a proportional pilot control method, wherein the method specifically comprises the following steps:

tangential acceleration at this stage is:

a＝Nω×v

where N is the proportional steering gain, ω is the line of sight rate, and v is the missile velocity vector.