阅读说明：本技术 一种针对初始航迹角自由的控制时间的二维协同制导方法 (Two-dimensional cooperative guidance method for control time of initial track angle freedom ) 是由 程志强 李涛 夏青峰 刘梦觉 王吉心 马超 向崇文 刘磊 彭耿 张帆 庞云福 于 2021-09-08 设计创作，主要内容包括：本发明提出了一种针对初始航迹角自由的控制时间的二维协同制导方法,其特征在于计算期望飞行距离、确定轨迹搜索初始值、确定期望攻击角度、计算贝塞尔曲线的控制点、计算贝塞尔轨迹长度、视贝塞尔轨迹长度调整初始航迹角大小、使用自适应网格直接搜索算法调整参数、在飞行过程中根据真实飞行速度实时调整初始航迹角、实时跟踪轨迹等计算步骤。本发明基于贝塞尔曲线长度单调性变化规律,设计了使用二分法和自适应网格直接搜索算法确定初始航迹角和期望攻击角度以及轨迹动态调整控制器,实现了飞行器变速度条件下的攻击时间和攻击角度的高精度控制。该算法的复杂度低,工程实现简单,具有收敛速度快、适于机载弹载计算机实时计算的优点。(The invention provides a two-dimensional cooperative guidance method aiming at the free control time of an initial track angle, which is characterized by comprising the calculation steps of calculating an expected flight distance, determining a track search initial value, determining an expected attack angle, calculating a control point of a Bezier curve, calculating the length of the Bezier track, adjusting the size of the initial track angle according to the length of the Bezier track, adjusting parameters by using an adaptive grid direct search algorithm, adjusting the initial track angle in real time according to the real flight speed in the flight process, tracking the track in real time and the like. The invention designs a dynamic track adjustment controller which determines an initial track angle and an expected attack angle by using a dichotomy and a self-adaptive grid direct search algorithm and realizes the high-precision control of attack time and attack angle under the condition of variable speed of an aircraft based on the monotonous change rule of the Bezier curve length. The algorithm is low in complexity, simple in engineering realization and high in convergence speed, and is suitable for real-time calculation of the airborne missile-borne computer.)

1. A two-dimensional cooperative guidance method aiming at control time of initial flight path angle freedom is characterized by comprising the following steps:

s1 according to the expected striking time t_DDetermining the expected flight distance L of the aircraft according to the speed profile of the aircraft_D；

S2, determining an initial track search value, specifically comprising: initial track angle θ₀Initial ratio parameterk, lower limit of search angle θ_sUpper limit of search angle θ_bSearching precision epsilon;

s3: determining an expected attack angle θ_fWherein theta_f＝kθ₀；

S4: determining a control point P of the Bezier curve according to the initial track angle and the expected attack angle_c(x_c,y_c) The method specifically comprises the following steps:

recording the initial position of the aircraft as E₁(x₁,y₁) Target position is E₂(x₂,y₂) Initial track angle of theta₀The desired attack angle is theta_f. The position of the control point can be calculated as:

y_c＝y₁+tan(θ_f)(x_c-x_l)

s5: calculating the Bessel track length, specifically:

notation E₁、P_c、E₃The Bessel curve of point composition isNoting its length as

S6: adjusting the size of the initial track angle according to the Bessel track length specifically comprises the following steps:

if it is notThen theta_s＝θ₀，Returning to the step (2),

if it is notThen theta_b＝θ₀，Returning to the step (2),

if it is notThen proceed to S7;

s7: using the adaptive grid direct search algorithm to adjust the parameter k, specifically:

let κ (τ) be the curvature of each point on the Bessel locus, letUsing an adaptive grid direct search algorithm such that κ_int+κ_maxMinimum, if the algorithm converges, proceed to S8; otherwise, adjusting the parameter k, and returning to S2;

s8: real-time theta adjustment during flight₀The position of (a) is specifically:

recording the residual length of the track in the flying process as L_realThe future t can be estimated from the aircraft speed profile during flight_DDistance of flight L within time t_estThen the feedback theta can be dynamically fed back according to the current flight speed₀To control the arrival time, wherein:

Δθ₀＝k_p(L_real-L_est)+k_i∫(L_real-L_est)dt

k_pand k is_iProportional and integral gains, respectively, determined according to aircraft performance; tracking the current trajectory is performed using a trajectory tracking algorithm.

Technical Field

The invention belongs to the technical field of guidance, and particularly relates to a two-dimensional cooperative guidance method for control time of initial track angle freedom

Background

The (ITCG) guidance law for controlling attack time can control an aircraft to strike a target at the same time, and has wide application prospect in military affairs. Particularly for the cooperative sea assault, the ITCG guidance law can reduce the interception effect of an opposite air defense system and improve the assault defense probability, and as part of ships have omnidirectional detection and protection capability, the tail end impact angle is not limited at the moment. For a naval vessel equipped with a vertical launching system, because the missile launched by the system has omnidirectional attack capability, the system is equivalent to an opportunity of selecting a proper initial course angle. The optimization and selection of the initial course angle are rarely considered in the current ITCG guidance law, and the guidance law has the defects of high calculation complexity and inconvenience for real-time calculation under the condition of missile speed.

Specifically, the ITCG guidance law mainly includes a variable guidance parameter method, a sliding mode control method, a centralized decision method in the flight process, a distributed decision method in the flight process, and the like. The control methods rarely consider the optimization problem of the initial course angle, are difficult to adapt to the condition of variable speed, mostly depend on communication coordination in the flight process, and can not complete cooperative attack once being interfered. Finally, the guidance law partially based on geometry is complex in calculation process and not beneficial to real-time calculation of an airborne computer.

Disclosure of Invention

In order to solve the problems in the prior art, the invention provides a two-dimensional cooperative guidance method aiming at the free control time of an initial track angle, which comprises the following steps:

s1 according to the expected striking time t_DDetermining the expected flight distance L of the aircraft according to the speed profile of the aircraft_D；

S2, determining an initial track search value, specifically comprising: initial track angle θ₀Initial proportional parameter k, search angle lower limit θ_sUpper limit of search angle θ_bSearching precision epsilon;

s3: determining an expected attack angle θ_fWherein theta_f＝kθ₀；

S4: determining a control point P of the Bezier curve according to the initial track angle and the expected attack angle_c(x_c,y_c) The method specifically comprises the following steps:

recording the initial position of the aircraft as E₁(x₁,y₁) Target position is E₂(x₂,y₂) Initial track angle of theta₀The desired attack angle is theta_f. The position of the control point can be calculated as:

s5: calculating the Bessel track length, specifically:

notation E₁、P_c、E₃The Bessel curve of point composition isNoting its length as

S6: adjusting the size of the initial track angle according to the Bessel track length specifically comprises the following steps:

if it is notThen theta_s＝θ₀，Returning to the step (2),

if it is notThenReturning to the step (2),

if it is notThen proceed to S7;

s7: using the adaptive grid direct search algorithm to adjust the parameter k, specifically:

let κ (τ) be the curvature of each point on the Bessel locus, letUsing adaptive mesh directThe search algorithm makes k_int+κ_maxMinimum, if the algorithm converges, proceed to S8; otherwise, adjusting the parameter k, and returning to S2;

s8: real-time theta adjustment during flight₀The position of (a) is specifically:

recording the residual length of the track in the flying process as L_realThe future t can be estimated from the aircraft speed profile during flight_DDistance of flight L within time t_estThen the feedback theta can be dynamically fed back according to the current flight speed₀To control the arrival time, wherein:

Δθ₀＝k_p(L_real-L_est)+k_i∫(L_real-L_est)dt

k_pand k is_iProportional and integral gains, respectively, determined according to aircraft performance;

and S9, adjusting the flight track in real time by using the calculation parameters.

The two-dimensional collaborative guidance method aiming at the control time of the initial track angle freedom provided by the invention uses the dichotomy search to determine the Bezier curve end point range and the specific position, the calculation complexity is logarithmic, the convergence speed is high, the calculation amount is small, and the requirement of real-time calculation can be met. The invention also designs a PI control algorithm to adjust the position of the Bezier curve end point in real time, has good robustness to the resistance possibly encountered in the flight process of the aircraft, and can realize high-precision attack time control. The method is suitable for the condition of speed change of the aircraft, does not need communication guarantee in the attack process, and has high robustness and strong anti-interference capability.

Drawings

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

FIG. 2 is a two-stage guidance track based on Bezier curves;

FIG. 3 velocity profile without lateral maneuver.

Detailed Description

In order to make the objects, technical solutions and advantages of the present application more apparent, the technical solutions of the present application will be described in detail and completely with reference to the following specific embodiments of the present application and the accompanying drawings. It should be apparent that the described embodiments are only some of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.

The specific steps of this embodiment are shown in fig. 1, and the present invention first calculates an initial heading angle and an expected attack angle, as shown in fig. 2. The Bezier curve corresponding to the track can be expressed asThis trajectory has two characteristics:

(1) for 90 ° > θ₀＞0°，90°＞θ_f＞0°，With theta₀Becomes larger and becomes larger.

(2) For 90 ° > θ₀＞0°，90°＞θ_f＞0°，With theta_fBecomes larger and becomes larger.

Based on the characteristics of the two monotonicity, the method theoretically ensures the theta_f＝kθ₀The correctness of the trajectory length is controlled using bisection and PI. Therefore, the focus of this patent is to make k if k is determined_int+κ_maxAnd minimum. To calculate the trajectory, first the expected impact time t is determined_DDetermining a desired flight distance L from an aircraft velocity profile_D. Secondly, setting initial parameters, such as initial track angle theta₀45 degrees, initial proportion parameter k 1.0, angle searching upper limit theta_s0.1 °, lower limit of angle search θ_bThe search precision ∈ is 0.01, 89.9 °. Then according to the initial track angle theta₀And a desired attack angle theta_f＝kθ₀Determining a control point P of a Bezier curve_c(x_c,y_c). Note E₁As a starting point, E₂The initial straight line and the incident straight line are expressed as formula (1).

The focal points of the two straight lines are the control points P of the Bezier curve_c. The bezier curve equation can be expressed as shown in equation (2).

P(τ)＝(1-τ)²E₁+2(1-τ)τP_c+τ²E₂,τ∈[0,1] (2)

Because the invention adopts the second-order Bezier curve, the curve length has an analytic solution, and the calculation mode is as follows:

wherein J ═ E₁-2P_c+E₃，K＝P_c-E₁，D＝(J·K)/|J|²，E＝|K|²/|J|²，U＝E-D²，If it is notIt is said that the initial track angle and the desired attack angle have been calculated accurately, with the second order bezier curve length equal to the desired length. If it is notThenIf it is notThenThe track can be adjusted by repeatedly calculating formulas of Bessel control points and lengths.

As can be seen from the above algorithm, different k correspond to different curves. Therefore, multiple sets of bezier curves may correspond to the same curve length. The problem now is how to determine the value of k and thus a unique set of bezier curves. Since each missile is required to dissipate kinetic energy during lateral maneuvers, it is desirable to design the maximum and cumulative curvatures of the resulting curves to be as small as possible. For a bezier curve, the curvature calculation method is as follows:

wherein the molecular product uses the outer product. dB (tau)/d tau and dB (tau)/d tau²The calculation methods are respectively as follows:

dB(τ)/dτ＝-2(1-τ)E₁+(2-4τ)P_c+2τE₂ (5)

dB(τ)/dτ²＝2E₁-4P_c+2E₂ (6)

we expect the curvature of the curve for k to satisfy the following two equations as small as possible:

further, the present invention contemplates finding the appropriate k such that k is_int+κ_maxThe value of (c) is minimal. The adaptive grid direct search algorithm is adopted to adjust and calculate k, and when the algorithm converges, a length L is found_DAnd a second order bezier trajectory with a smaller overall curvature.

For the purpose of controlling the impact time with high precision, the impact time can be controlled according to the actual flying speed during the flying processAnd (4) dynamically adjusting the track. The future t can be estimated during flight from the aircraft velocity profile_DDistance of flight L within time t_estAnd can calculate L_realIf the distance to be flown of the current track is the current flight speed, the theta can be dynamically fed back according to the current flight speed₀To control the time of arrival. The calculation method is as follows:

Δθ₀＝k_p(L_real-L_est)+k_i∫(L_real-L_est)dt (9)

wherein k is_pAnd k is_iProportional and integral gains, respectively, need to be designed according to aircraft performance.

The following is further explained by combining with a specific calculation example, and the two-dimensional cooperative guidance method for the control time of the initial track angle freedom provided by the invention comprises the following steps: a flight trajectory generator, a dynamic trajectory adjuster and a trajectory tracker. Taking the case of a fixed target hit by a missile, the launch point is E₁When the target position is (0,0), the striking target position is E₂(10000,0), expected striking time t_D53s, k 1, and an initial emission angle θ₀At 41.53 °, the desired striking angle is θ_f-41.53 °. The flight path generator calculates the expected flight distance to be 11.2 km and the control point to be P according to the flight profile_c= (5000,4429). The maximum transverse side overload of the missile is assumed to be 200m/s²A typical flight velocity profile is shown in fig. 3. Further, designing a position feedback parameter k of the dynamic trajectory adjuster_p＝1.0e^-4，k_i＝2.0e^-4. The trajectory tracker may be chosen to track a tangent to the nearest point to the missile. Let d be the distance from the missile to the tangent, θ_dIs the angle between the tangent and the X axis. The heading acceleration may be as follows:

wherein q is₁And q is₂As the parameter(s) is (are),q₁and q is₂Typical values of (a) are 2 and 3.74.

The guidance law operation is roughly divided into two phases. The first phase is the flight path generator operation, calculating the initial theta₀And theta_fThe size of (2). After the calculation is finished, the dynamic track adjuster dynamically corrects the track according to the current state, and meanwhile, the track tracker tracks the current generated track by providing lateral overload. The two run synchronously. The calculation steps of the dynamic trajectory adjuster and the trajectory tracker at each time step are as follows:

(1) firstly, a dynamic track adjuster estimates a flight distance L according to a flight profile, a current flight speed and a residual flight time_est。

(2) Secondly, the dynamic track adjuster calculates the actual residual distance L of the track according to the formula (4)_real。

(3) Adjusting the Bezier curve end point position theta by the dynamic trajectory adjuster according to the formula (5)₀。

(4) The trajectory tracking controller again selects the point on the curve closest to the current position.

(5) Finally, the trajectory tracking controller calculates the required lateral acceleration according to equation (10).

Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive faculty, based on the technical solutions of the present invention.