An attack time and angle control guidance method, device, equipment and medium

Abstract

The application discloses an attack time and angle control guidance method and device, equipment and medium, and relates to the field of missile control guidance. The method comprises the following steps: a dynamic model is established based on the scene of a single missile intercepting a stationary target in a two-dimensional plane; the expected trajectory of the missile is generated by adopting a cubic Bezier curve based on the dynamic model, with the attack time, attack angle and maximum normal acceleration as constraints; the trajectory tracking error is calculated according to the current position of the missile and the expected trajectory; the expected heading angle is calculated according to the tracking error and the heading angle of the expected trajectory; the heading angle tracking error is calculated according to the actual heading angle of the missile and the expected heading angle; and the normal overload instruction required by the missile is determined according to the heading angle tracking error and a preset time tracking guidance law. The application realizes accurate tracking of the expected trajectory.

Description

Technical Field

[0001] This application relates to the field of missile control and guidance, and in particular to a method, apparatus, equipment and medium for attack time and angle control guidance based on cubic Bézier curves. Background Technology

[0002] As enemy defenses become increasingly sophisticated, higher demands are placed on missile capabilities and guidance systems to effectively damage them. Modern guidance missions not only require missiles to accurately hit their targets but also to strike them at a specified time or angle. However, in certain combat scenarios, both desired time and desired angle are required simultaneously, thus placing even greater demands on the design of guidance laws. Attack time-angle guidance laws allow missiles to strike targets at a specific angle at a designated attack time, possessing significant application value in actual combat and attracting extensive research from scholars.

[0003] Currently, there are two main methods to achieve guidance at a specified attack time and angle. The first method uses optimal control theory or sliding mode control theory to directly design the guidance law to satisfy the specified attack angle and attack time constraints. The second method to achieve attack time and angle guidance is polynomial guidance or trajectory shaping guidance. This method indirectly designs the state profile that satisfies the attack time and angle constraints, and further designs the guidance law to track the proposed state profile.

[0004] However, existing attack time and attack angle guidance methods have low guidance accuracy. Summary of the Invention

[0005] The purpose of this application is to provide an attack time and angle control guidance method, device, equipment and medium that can achieve accurate tracking of the desired trajectory.

[0006] To achieve the above objectives, this application provides the following solution:

[0007] Firstly, this application provides an attack time and angle control guidance method, including:

[0008] A dynamic model is established based on the scenario of a single missile intercepting a stationary target in a two-dimensional plane.

[0009] Based on the aforementioned dynamic model, the desired trajectory of the missile is generated using cubic Bézier curves, with constraints on attack time, attack angle, and maximum normal acceleration.

[0010] Calculate the trajectory tracking error based on the missile's current position and desired trajectory;

[0011] The desired heading angle is calculated based on the tracking error and the heading angle of the desired trajectory;

[0012] Calculate the heading angle tracking error based on the missile's actual heading angle and desired heading angle;

[0013] The required normal overload command for the missile is determined based on the heading angle tracking error and the preset time tracking guidance law.

[0014] Secondly, this application provides an attack time and angle control guidance device, comprising:

[0015] The dynamics model building module is used to: build a dynamics model based on the scenario of a single missile intercepting a stationary target in a two-dimensional plane;

[0016] The missile's desired trajectory generation module is used to: generate the missile's desired trajectory using a cubic Bézier curve, based on the aforementioned dynamic model and constrained by attack time, attack angle, and maximum normal acceleration.

[0017] The trajectory tracking error calculation module is used to calculate the trajectory tracking error based on the missile's current position and desired trajectory.

[0018] The desired heading angle calculation module is used to: calculate the desired heading angle based on the tracking error and the heading angle of the desired trajectory;

[0019] The heading angle tracking error calculation module is used to calculate the heading angle tracking error based on the missile's actual heading angle and desired heading angle.

[0020] The normal overload command determination module is used to determine the normal overload command required by the missile based on the heading angle tracking error and the preset time tracking guidance law.

[0021] Thirdly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described attack time and angle control guidance method.

[0022] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described attack time and angle control guidance method.

[0023] According to the specific embodiments provided in this application, the following technical effects are disclosed:

[0024] To address the aforementioned issues, this application provides an attack time and angle control guidance method, apparatus, device, and medium. It employs cubic Bézier curves to generate the desired missile trajectory, satisfying constraints on attack time, angle, and maximum normal acceleration. The trajectory tracking error is calculated based on the missile's current position and the desired trajectory. The desired heading angle is calculated based on the tracking error and the heading angle of the desired trajectory. The heading angle tracking error is calculated based on the missile's actual heading angle and the desired heading angle. The required normal overload command for the missile is determined based on the heading angle tracking error and a preset time tracking guidance law. This achieves precise tracking of the desired trajectory and solves the ballistic shaping guidance problem under multiple constraints. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 A flowchart illustrating an attack time and angle control guidance method provided in an embodiment of this application;

[0027] Figure 2 A schematic diagram illustrating the specific implementation process of an attack time and angle control guidance method provided in an embodiment of this application;

[0028] Figure 3 A schematic diagram of a two-dimensional missile intercepting a stationary target, provided as an embodiment of this application;

[0029] Figure 4 A schematic diagram of a Bézier curve provided in an embodiment of this application;

[0030] Figure 5 This is a schematic diagram of a path tracking scenario provided in an embodiment of this application;

[0031] Figure 6 A schematic diagram of the desired heading angle vector field under different parameters provided in an embodiment of this application;

[0032] Figure 7 A schematic diagram illustrating the iterative process of distance control parameters provided in an embodiment of this application;

[0033] Figure 8 A schematic diagram illustrating the iterative process of the cost function provided in an embodiment of this application;

[0034] Figure 9 A schematic diagram of the normal acceleration curve of a missile provided in an embodiment of this application;

[0035] Figure 10 A schematic diagram of the heading angle curve of a missile provided in an embodiment of this application;

[0036] Figure 11 A schematic diagram of the desired trajectory and the actual trajectory of the missile provided for an embodiment of this application;

[0037] Figure 12 This is a schematic diagram of a tracking error curve provided in an embodiment of this application;

[0038] Figure 13 A functional module diagram of an attack time and angle control guidance device provided in an embodiment of this application;

[0039] Figure 14 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0040] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0041] Existing guidance laws designed directly for attack time angles based on optimal control theory or sliding mode control theory mostly require estimation of the remaining flight time. When the initial heading angle or attack angle is large, significant estimation errors often occur, affecting guidance accuracy. Research based on polynomial state profiles largely fails to consider overload constraints during guidance. Furthermore, state profiles with relative distance as the independent variable struggle to handle large initial heading angles or attack angles because the relative distance is not monotonic. Trajectory shaping guidance designs guidance trajectories based on geometry to meet corresponding guidance tasks. However, most trajectory shaping guidance methods fail to consider overload constraints or cannot handle excessively large or small initial heading angles or attack angles, making it difficult to meet multi-mission requirements.

[0042] To address the aforementioned issues, this application provides a ballistic shaping guidance strategy. On one hand, it considers attack time, attack angle, and overload constraints to design a guidance trajectory based on Bézier curves that satisfies the guidance mission. On the other hand, it designs a desired heading angle vector field and a path-following guidance law to achieve precise tracking of the designed trajectory.

[0043] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0044] In one exemplary embodiment, such as Figure 1As shown, an attack time and angle control guidance method is provided, which includes the following steps 201 to 206.

[0045] Step 201: Establish a dynamic model based on the scenario of a single missile intercepting a stationary target in a two-dimensional plane.

[0046] Step 202: Based on the aforementioned dynamic model, and constrained by attack time, attack angle, and maximum normal acceleration, the desired trajectory of the missile is generated using cubic Bézier curves.

[0047] Step 203: Calculate the trajectory tracking error based on the missile's current position and desired trajectory.

[0048] Step 204: Calculate the desired heading angle based on the tracking error and the heading angle of the desired trajectory.

[0049] Step 205: Calculate the heading angle tracking error based on the missile's actual heading angle and desired heading angle.

[0050] Step 206: Determine the normal overload command required for the missile based on the heading angle tracking error and the preset time tracking guidance law.

[0051] By implementing steps 201 to 206 above, the guidance trajectory is designed using a cubic Bézier curve to meet the constraints of attack time, angle, and maximum normal acceleration. An optimization algorithm is introduced to solve the cost function to determine the control parameters of the trajectory, resulting in a unique ballistic trajectory that satisfies the guidance mission. Based on this, a hyperbolic sinusoidal vector field path tracking guidance algorithm is developed, which achieves accurate tracking of the desired trajectory and solves the ballistic shaping guidance problem under multiple constraints.

[0052] This application considers a scenario where a missile M intercepts a stationary target T in a two-dimensional plane, such as... Figure 3 As shown, xoy represents the inertial coordinate system. Assuming the missile's velocity is constant, let V... m Indicated by γ; the direction of velocity is represented by γ. m It means that γ m ∈(-π,π); γ m0 This represents the initial heading angle. The missile's initial position is (x0, y0), and the target's initial position is (x0, y0). f ,y f ).

[0053] The following establishes a dynamic model of a single missile intercepting a single stationary target. This dynamic model includes the equations of relative motion between the missile and the target, as well as the equations of motion of the missile.

[0054] The equation of relative motion between the missile and the target is shown in formula (1).

[0055]

[0056] Among them, R m This indicates the line-of-sight distance between the missile and the target; q is the first derivative of the line-of-sight distance; m This indicates the line-of-sight angle between the missile and the target; η is the first derivative of the line-of-sight angle of the bullet; m Indicates the missile's leading angle; a m and γ m These represent the missile's normal acceleration and heading angle, respectively. Let represent the first derivative of the missile's heading angle. Considering the target is stationary, this application studies the missile's guidance problem in an inertial Cartesian coordinate system. The missile's equation of motion is shown in formula (2) below.

[0057]

[0058] In the formula, x is the x-coordinate of the missile's current position. Let y be the first derivative of the missile's current x-coordinate, and y be the missile's current y-coordinate. Let be the first derivative of the ordinate of the missile's current position.

[0059] In another exemplary embodiment of this application, step 202 is replaced by steps 301 to 305.

[0060] Step 301: Design the trajectory of a single missile intercepting a stationary target based on a cubic Bézier curve, and determine the Bézier curve expression; the Bézier curve expression includes the first included angle control parameter, the second included angle control parameter, the first distance control parameter, and the second distance control parameter;

[0061] Step 302: Establish a cost function with attack time and maximum normal acceleration as constraints;

[0062] Step 303: Determine the first included angle control parameter and the second included angle control parameter based on the missile's initial heading angle and initial attack angle;

[0063] Step 304: Solve the cost function to obtain the first distance control parameter and the second distance control parameter;

[0064] Step 305: Based on the first included angle control parameter, the second included angle control parameter, the first distance control parameter, the second distance control parameter, and the missile's initial position and target position, determine the missile's desired position coordinates and the first and second derivatives of each desired position coordinate; the missile's desired position coordinates constitute the desired trajectory.

[0065] This application employs a cubic Bezier trajectory combined with constraints on the initial launch angle, attack angle, and attack time to ensure precise attack on a stationary target with ideal attack time and angle, while minimizing the maximum normal acceleration during guidance. Therefore, the guidance mission of this application is summarized as follows:

[0066]

[0067] Where t represents time T d and γ f These represent the expected attack time and the expected attack angle, respectively. The maximum normal acceleration of the missile during guidance is denoted by f. max (a m Let Ja represent the desired normal acceleration.

[0068] A Bézier curve is a parametric curve, such as... Figure 4 As shown, it takes the form of a polynomial for the trajectory parameter ε, the order of which is determined by the number of control points, and the relative positions of the control points determine the shape of the curve.

[0069] This application uses cubic Bézier curves to design the trajectory, with four control points P. i (i = 0, 1, 2, 3), where control point P i The coordinates are (x i ,y i The expression for a cubic Bézier curve is as follows:

[0070]

[0071] In the formula, P(ε) represents the coordinates of a point on the cubic Bézier curve.

[0072] Cubic Bézier curves offer a high degree of control flexibility. The shape of the curve can be easily adjusted by moving control points to meet specific design requirements. Furthermore, cubic Bézier curves generate smooth trajectories, where the missile's normal acceleration at each point can be analytically calculated. Therefore, this application employs cubic Bézier curves to obtain the optimal trajectory for the guidance mission.

[0073] As can be seen from formula (4), when ε=0, P(0)=P0, corresponding to the first control point; when ε=1, P(1)=P3, corresponding to the last control point. Next, three properties of Bézier curves are given.

[0074] Property 1: The starting point and ending point of a cubic Bézier curve correspond to the first control point and the last control point, respectively.

[0075] Property 2: The direction of the tangent to a cubic Bézier curve at its starting point is determined by the straight line connecting the first two control points. Similarly, the direction of the tangent at its ending point is determined by the straight line connecting the last two control points.

[0076] Property 3: The shape of a cubic Bézier curve depends entirely on the relative positions of the control points and is independent of the choice of coordinate system.

[0077] According to property 1, if we choose the missile's initial position as the first control point P0 and the target position as the last control point P3, then the coordinate representation of the cubic Bézier curve is:

[0078]

[0079] In the formula, x(ε) and y(ε) are the abscissa and ordinate of a point on the cubic Bézier curve, respectively; the distance from the first control point P0 to the second control point P1 is denoted as the first distance control parameter R1, and the vector... The first angle control parameter γ1 is the angle between the vector and the x-axis. The distance is defined by the first control point P0 to the second control point P1. Similarly, the distance between the third control point P2 and the fourth control point P3 is denoted as the second distance control parameter R2, and the vector... The angle between the vector and the x-axis is the second angle control parameter γ2. It consists of the third control point P2 to the fourth control point P3. The coordinates (x1, y1) of the second control point P1 and the coordinates (x2, y2) of the third control point P2 can generally be expressed as:

[0080]

[0081] Substituting equation (6) into equation (5), we get:

[0082]

[0083] Where x0 and y0 are the x and y coordinates of the first control point, respectively; f1, f2, f3, and f4 are intermediate parameters; f1 = (1-ε) 3 +3ε(1-ε) 2 f2 = ε(1-ε) 2 f3 = ε 2 (1-ε), f4=ε 3 +3ε 2 (1-ε).

[0084] R1, R2, γ1, and γ2 are selected as control parameters to determine the trajectory shape. Property 3 indicates that once the positions of the first control point P1 and the second control point P2 are determined, the desired trajectory of the designed missile is unique. Therefore, trajectory design is transformed into determining the control parameters R1, R2, γ1, and γ2 based on the guidance mission (3) and the initial state of the missile.

[0085] The following analysis examines the guidance trajectory constraints, including initial heading angle and attack angle constraints, attack time constraints, and maximum normal acceleration constraints.

[0086] (1) Initial heading angle and attack angle constraints

[0087] Assuming initial time t = 0, the initial heading angle and attack angle constraints are as follows:

[0088]

[0089] contrast Figure 3 and Figure 4 From property 2, we can obtain the first included angle control parameter and the second included angle control parameter:

[0090] γ1=γ m0 ,γ2=π+γ f (9).

[0091] (2) Attack time constraints

[0092] The attack time constraint refers to the time limit for the missile to attack from t=0 to t=T. d The target is located at the attack point. From a trajectory design perspective, the entire trajectory lasts for T seconds. d .

[0093] definition Taking the derivative of equation (7) with respect to the parameter ε, we can obtain the first derivative of the missile's desired position coordinates, namely the first derivative of the missile's desired position x' (broad axis) and the first derivative of the missile's desired position y' (vertical axis):

[0094]

[0095] Where f1', f2', f3', and f4' are the first derivatives of f1, f2, f3, and f4, respectively.

[0096] The desired trajectory length l is:

[0097]

[0098] Considering the missile speed V m Constant, expected attack time t = T d Then attack time The normalization equation is:

[0099]

[0100] Note that the above equation is difficult to solve analytically. Therefore, a numerical calculation method is used to obtain the normalized attack time:

[0101]

[0102] Therefore, the attack time constraint in the guidance mission (3) can be restated as:

[0103]

[0104] (3) Maximum normal acceleration constraint

[0105] Given the limited overload of missiles, it is usually necessary to impose a normal acceleration constraint to minimize its maximum value. The normal acceleration of a missile during guidance along a Bezier trajectory will be analyzed below.

[0106] Define the second derivative of the x-coordinate of the missile's desired position. The second derivative of the ordinate of the missile's desired position Taking the second derivative of parameter ε in equation (7) yields:

[0107]

[0108] Where f1”, f2”, f3”, and f4” are the second derivatives of f1, f2, f3, and f4, respectively.

[0109] missile's normal acceleration a m The following formula can be used for calculation:

[0110]

[0111] The maximum normal acceleration directly reflects the missile's maximum turning rate. Observing formula (16), its form is quite complex and cannot be solved analytically. Therefore, the missile's maximum normal overload can be obtained through numerical calculation:

[0112] f max (a m )=max|a m (iΔε)|,i=0,1,...,n (17).

[0113] Note that x', y', x”, y” are all functions of the control parameters R1, R2, γ1, γ2, and the trajectory parameter ε. Therefore, the missile's normal acceleration a mIt is also a function of control parameters R1, R2, γ1, γ2, and trajectory parameter ε. For a pre-designed guidance trajectory, its control parameters are determined, and the missile's normal acceleration a... m It is only a function of the trajectory parameter ε. Therefore, the maximum normal acceleration on the trajectory can be calculated using formula (17).

[0114] Similar to the attack time constraint, the normalization formula (17) yields the maximum normal acceleration:

[0115]

[0116] Among them, a n It is a positive constant representing the missile's available overload, which is determined by the missile's physical structure.

[0117] The guidance mission (3) and trajectory design under missile initial state constraints are reformulated as a problem of solving control parameters R1, R2, γ1, and γ2, where γ1 and γ2 can be obtained from equation (9). To satisfy constraint (14) and minimize minf... max (a m Given the constraints, the first distance control parameter R1 and the second distance control parameter R2 are determined by minimizing the following cost function, which is expressed as follows:

[0118]

[0119] Where J(R) represents the cost function, and R = [R1, R2] T R1 is the first distance control parameter, R2 is the second distance control parameter, ω1 and ω2 are two positive constants. Considering that equation (14) is a hard constraint, we choose ω1 > ω2. This refers to the attack time.

[0120] Next, the zero-order Adam algorithm is given to solve the cost function (19). Step 304 specifically includes: using the zero-order Adam algorithm to solve the cost function, obtaining the first distance control parameter and the second distance control parameter. The form of the zero-order Adam algorithm is as follows:

[0121]

[0122] Where the subscript k represents the current iteration step, and k-1 represents the previous iteration step; This represents the zeroth gradient of the cost function J. express The square of each element; m k and v kThese are the first-order and second-order moment estimates, respectively; β1 and β2 are the exponential decay rates controlling these moment estimates, typically set to 0.9 and 0.999, respectively; σ is a very small positive constant (e.g., 10). -8 ), where η represents the learning rate, μ is a small positive constant, and u is a random vector following a Gaussian distribution.

[0123] Based on the zero-order Adam algorithm to minimize the cost function, the relative distances R1 and R2 are obtained, and all control parameters are calculated using equation (9). Therefore, the guided trajectory that satisfies the guidance mission and the initial state of the missile is uniquely defined. Using the first included angle control parameter γ1, the second included angle control parameter γ2, the first distance control parameter R1, and the second distance control parameter R2, combined with equations (7), (10), and (15), the position coordinates of the desired trajectory of the designed missile and its first and second derivatives can be obtained.

[0124] The following design uses a hyperbolic sinusoidal vector field path tracking guidance algorithm to track the designed guidance trajectory:

[0125] Path tracking scenarios such as Figure 5 As shown, the curve represents the designed desired trajectory. The missile's initial position deviates from the predetermined path. γ p γ represents the heading angle on the desired trajectory. m This represents the missile's actual heading angle. Assume the desired path can be represented as y. p =h(x p (t)), x p (t) represents the x-coordinate of the desired trajectory, y p (t) represents the ordinate of the desired trajectory, and h() is the fitting function for the desired trajectory. The trajectory tracking error is expressed as follows:

[0126] e y =h(x)-y(21).

[0127] Note that after the trajectory design is completed, x p and y p They are all merely functions of the trajectory parameter ε. When x p and y p There exists a functional relationship, which means that every x p Corresponding to a unique y p Based on the current position's x-coordinate, a unique trajectory parameter ε and y-coordinate can be obtained. If x p and y p The functional relationship between them does not hold (as shown in the figure). Figure 5 ), or when the current position coordinate x is outside the projection range of the desired trajectory x-axis (as shown in the figure). Figure 5 Point P in l), select the point on the desired trajectory that is closest to the current position (point P l corresponding point P0), and take its ε and y values.

[0128] The goal of path tracking is to guide the missile to reach the predetermined path and ensure its accurate tracking. When the missile starts on the desired trajectory, it can track the path by aligning with the heading angle on the desired trajectory. If the initial position of the missile deviates from the expected path, its heading angle should include an additional component outside the heading angle on the expected path. This adjustment ensures that the missile moves along the direction of the desired trajectory while gradually reducing the distance from the desired trajectory until it reaches the desired trajectory. Therefore, the desired heading angle γ d has the following expression:

[0129]

[0130] where k1 is a positive constant, γ p is the heading angle on the desired trajectory, and it is defined that Due to the boundedness of the hyperbolic tangent function, it can be known that when |e y | >> 0, Δγ p the sign of is determined jointly by cos(γ p ) and e y . The parameter k1 reflects the change in the heading angle of the missile near the desired trajectory. The larger the value of k1, the steeper the change in the heading angle. Figure 6 shows the desired heading angle vector fields under different parameters. Figure 6 In (a) of, the desired heading angle vector field is when k1 = 1. Figure 6 In (b) of, the desired heading angle vector field is when k1 = 5.

[0131] Next, design a preset-time tracking guidance law to track the proposed desired heading angle. Define the heading angle tracking error as:

[0132]

[0133] The preset-time tracking guidance law is as follows:

[0134]

[0135] where T s is the preset time, k a is a positive constant that satisfies k a > 1, is the first derivative of the desired heading angle of the missile.

[0136] Since a trajectory with attack time constraints is introduced, and the path tracking guidance law cannot directly handle attack time constraints, time errors are minimized by timely tracking of the required heading angle command. Considering the conservatism of convergence time in the application of finite and fixed time theories, this application chooses a pre-set time theory to design the tracking guidance law, i.e., formula (24).

[0137] Therefore, the guidance mission (3) achieved using the ballistic shaping guidance strategy proposed in this application can be described in the following steps:

[0138] First, based on the initial heading angle γ m0 and attack angle γ f The control parameters γ1 and γ2 are calculated based on equation (9), and the control parameters R1 and R2 are obtained by solving the cost function (19) based on the zero-order Adam algorithm.

[0139] Next, the control parameters γ1, γ2, R1 and R2, as well as the initial position and target position of the missile, are substituted into equations (7), (10) and (15) to obtain the position coordinates of the designed trajectory and its first and second derivatives.

[0140] Then, based on equation (21), the tracking error e is calculated according to the missile's current position and desired trajectory. y Combined with the heading angle γ of the desired trajectory p Further, the desired heading angle γ is obtained. d .

[0141] Finally, based on equation (21), the actual heading angle γ of the missile is calculated. m and desired heading angle γ d Calculate the heading angle tracking error The required normal overload command a for the missile is obtained by combining the preset time-tracking guidance law. m .

[0142] In one exemplary embodiment, such as Figure 2 As shown, an attack time and angle control guidance method is provided, which includes the following steps 101 to 106.

[0143] Step 101: Establish a dynamic model for a single missile intercepting a single stationary target.

[0144] Step 102: Parametricize the Bézier curve expression.

[0145] Step 103: Analyze guidance trajectory constraints.

[0146] Step 104: Establish the cost function and solve for the control parameters.

[0147] Step 105: Design a hyperbolic sinusoidal vector field path tracking guidance algorithm to track the designed guidance trajectory.

[0148] Step 106: The guidance process of the missile system is realized through the ballistic shaping guidance strategy described above.

[0149] The effectiveness of the proposed method is verified below through a specific example of a single missile attacking a single stationary target. The specific implementation steps are as follows:

[0150] (1) Missile simulation system settings: Consider the scenario of a single missile intercepting a stationary target in a two-dimensional plane. The initial position of the missile is located at the origin (0, 0), its speed is 300 m / s, its initial heading angle is -120°, and the available overload is set to 200 m / s. 2 The target's location is (12000m, 0m). The desired attack angle is γ. f = -30°, expected attack time T d =55s.

[0151] (2) Solving for control parameters: The initial values ​​of the control parameters are set as R1 = 5000m and R2 = 2500m. The obtained control parameters are shown in Table 1.

[0152] Table 1 Control Parameters

[0153] <![CDATA[γ1]]> <![CDATA[γ2]]> <![CDATA[R1]]> <![CDATA[R2]]> -120° 150° 9120m 2458m

[0154] (3) Path tracking: The path tracking error is set to Δx = -20m, Δy = 10m, Δγ = 10m. m =10°, representing the difference from the desired trajectory. The path tracking algorithm parameters are set as follows: k1 = 0.01, k2 = 30, k a =3.2, T s =8s. g = 9.8m / s 2 When the line-of-sight distance of the projectile meets R... m The simulation terminates when the value is less than 1m.

[0155] (4) Results Analysis: The iterative processes of the distance control parameters and cost function are as follows: Figure 7 and Figure 8 As shown. Among them, Figure 7 In the diagram, (a) represents the iterative process of the first distance control parameter R1. Figure 7 (b) in the diagram represents the iterative process of the second distance control parameter R2. Figure 7 In the diagram, (a) represents the iterative process of the first distance control parameter R1. Figure 7 (b) in the diagram represents the iterative process of the second distance control parameter R2. From... Figure 7 and Figure 8 It can be seen that the optimization algorithm drives the iterative process from the initial value to the optimal solution, resulting in a gradual decrease in the cost function. Furthermore, the total number of iterations required is relatively small.

[0156] Path tracking simulation results are as follows Figures 9-12 As shown. The actual attack time was 55.089 seconds. The time error of the attack time was within 0.1 seconds. Figure 9 and Figure 10 The missile's normal acceleration curve and heading angle curve are displayed. Figure 11 The designed expected trajectory and the missile's actual trajectory are presented. Figure 12 The tracking error curve is given. From... Figure 10 It can be seen that the missile's actual heading angle can track the desired heading angle within a preset time, and then the missile's state aligns with the desired trajectory. From Figure 12 As can be seen, the tracking error in the later stages of the missile's trajectory is essentially zero, meaning that the missile's trajectory in the later stages completely overlaps with the desired trajectory, thus fulfilling the guidance mission requirements. Therefore, the simulation results above fully verify the effectiveness of the guidance strategy proposed in this application.

[0157] This application also provides an application scenario in which the attack time and angle control guidance method described above is applied. Specifically, the attack time and angle control guidance method provided in this embodiment can be applied in a missile interception scenario. A missile interception scenario includes an information acquisition stage, a control and guidance link, and an interception stage. The initial parameters of the missile enter the control and guidance link from the information acquisition stage, obtaining the required normal overload command for the missile, and then enter the downstream interception stage. The attack time and angle control guidance method provided in this embodiment belongs to the control and guidance link. Specifically, in the control and guidance link process targeting a missile interception target, a dynamic model can be established based on the scenario of a single missile intercepting a stationary target in a two-dimensional plane. Based on the dynamic model, with attack time, attack angle, and maximum normal acceleration as constraints, a cubic Bézier curve is used to generate the desired trajectory of the missile. The trajectory tracking error is calculated based on the missile's current position and the desired trajectory. The desired heading angle is calculated based on the tracking error and the heading angle of the desired trajectory. The heading angle tracking error is calculated based on the missile's actual heading angle and the desired heading angle. The required normal overload command for the missile is determined based on the heading angle tracking error and a preset time tracking guidance law.

[0158] Based on the same inventive concept, this application also provides an attack time and angle control guidance device for implementing the attack time and angle control guidance method described above. The solution provided by this device is similar to the solution described in the above method; therefore, the specific limitations in one or more attack time and angle control guidance device embodiments provided below can be found in the limitations of the attack time and angle control guidance method described above, and will not be repeated here.

[0159] In one exemplary embodiment, such as Figure 13As shown, an attack time and angle control guidance device is provided, comprising:

[0160] The dynamic model building module T1 is used to: build a dynamic model based on the scenario of a single missile intercepting a stationary target in a two-dimensional plane;

[0161] The missile's desired trajectory generation module T2 is used to: generate the missile's desired trajectory using a cubic Bézier curve, based on the aforementioned dynamic model and constrained by attack time, attack angle, and maximum normal acceleration.

[0162] The trajectory tracking error calculation module T3 is used to calculate the trajectory tracking error based on the missile's current position and desired trajectory.

[0163] The desired heading angle calculation module T4 is used to: calculate the desired heading angle based on the tracking error and the heading angle of the desired trajectory;

[0164] The heading angle tracking error calculation module T5 is used to calculate the heading angle tracking error based on the missile's actual heading angle and desired heading angle.

[0165] The normal overload command determination module T6 is used to determine the normal overload command required by the missile based on the heading angle tracking error and the preset time tracking guidance law.

[0166] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 14 As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores missile control and guidance data. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements an attack time and angle control guidance method.

[0167] Those skilled in the art will understand that Figure 14The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0168] In one exemplary embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0169] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0170] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0171] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0172] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0173] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0174] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. An attack time and angle control guidance method, characterized by, The attack time and angle control guidance method includes: A dynamic model is established based on the scenario of a single missile intercepting a stationary target in a two-dimensional plane. Based on the aforementioned dynamic model, and constrained by attack time, attack angle, and maximum normal acceleration, the desired trajectory of the missile is generated using cubic Bézier curves, specifically including: The trajectory of a single missile intercepting a stationary target is designed based on cubic Bézier curves, and the expression of the Bézier curve is determined. The expression of the Bézier curve includes the first included angle control parameter, the second included angle control parameter, the first distance control parameter, and the second distance control parameter. A cost function is established with attack time and maximum normal acceleration as constraints; The first included angle control parameter and the second included angle control parameter are determined based on the missile's initial heading angle and initial attack angle; The cost function is solved to obtain the first distance control parameter and the second distance control parameter; Based on the first included angle control parameter, the second included angle control parameter, the first distance control parameter, the second distance control parameter, and the missile's initial position and target position, the desired position coordinates of the missile and the first and second derivatives of each desired position coordinate are determined; the desired position coordinates of the missile constitute the desired trajectory. Calculate the trajectory tracking error based on the missile's current position and desired trajectory; The desired heading angle is calculated based on the tracking error and the heading angle of the desired trajectory; Calculate the heading angle tracking error based on the missile's actual heading angle and desired heading angle; The required normal overload command for the missile is determined based on the heading angle tracking error and the preset time tracking guidance law; the preset time tracking guidance law is expressed as follows: ； in, For the missile's normal acceleration, For missile speed, For preset time, For positive integers, Indicates time, For heading angle tracking error, The desired heading angle of the missile. Let be the first derivative of the missile's desired heading angle.

2. The time-to-attack and angle control guidance method of claim 1, wherein, The expression for the Bézier curve is as follows: ； in, These are trajectory parameters; These are the x and y coordinates of a point on a cubic Bézier curve, respectively. These are the x and y coordinates of the first control point, respectively. For intermediate parameters; This is the first distance control parameter. This is the second distance control parameter. This is the first included angle control parameter. This is the second included angle control parameter.

3. The time-to-attack and angle control guidance method of claim 1, wherein, The cost function is expressed as follows: ； in, Represents the cost function, , This is the first distance control parameter. This is the second distance control parameter. and They are two positive numbers. For the attack time, This represents the maximum normal acceleration.

4. The time-to-attack and angle control guidance method of claim 1, wherein, Solving the cost function yields the first distance control parameter and the second distance control parameter, specifically including: The zero-order Adam algorithm is used to solve the cost function to obtain the first distance control parameter and the second distance control parameter.

5. The time-to-attack and angle control guidance method of claim 1, wherein, The tracking error is expressed as follows: ； wherein, is a trajectory tracking error, is a fitting function of the desired trajectory, is a lateral coordinate of the current position of the missile, is a longitudinal coordinate of the current position of the missile.

6. An attack time and angle control guidance device based on the attack time and angle control guidance method according to claim 1, characterized by The attack time and angle control guidance device includes: The dynamics model building module is used to: build a dynamics model based on the scenario of a single missile intercepting a stationary target in a two-dimensional plane; The missile's desired trajectory generation module is used to: generate the missile's desired trajectory using a cubic Bézier curve, based on the aforementioned dynamic model and constrained by attack time, attack angle, and maximum normal acceleration. The trajectory tracking error calculation module is used to calculate the trajectory tracking error based on the missile's current position and desired trajectory. The desired heading angle calculation module is used to: calculate the desired heading angle based on the tracking error and the heading angle of the desired trajectory; The heading angle tracking error calculation module is used to calculate the heading angle tracking error based on the missile's actual heading angle and desired heading angle. The normal overload command determination module is used to determine the normal overload command required by the missile based on the heading angle tracking error and the preset time tracking guidance law.

7. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the attack time and angle control guidance method according to any one of claims 1-5.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that, When the computer program is executed by the processor, it implements the attack time and angle control guidance method as described in any one of claims 1-5.

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