CN117742161A - Terminal guidance stage trajectory planning method and system based on view angle constraint - Google Patents
Terminal guidance stage trajectory planning method and system based on view angle constraint Download PDFInfo
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Abstract
The invention provides a terminal guidance stage trajectory planning method and system based on view angle constraint, and relates to the technical field of trajectory planning, wherein the method comprises the following steps: taking the minimum off-target quantity and the minimum control energy as objective functions, comprehensively considering the falling angle constraint, the dynamic constraint and the path constraint, constructing a ballistic planning control model of a terminal guidance stage time interval, and carrying out optimization solution on the ballistic planning control model based on initial attitude information of the missile, initial physical parameters of the missile and a missile constraint data set to obtain an optimal state vector of the missile at each moment and an optimal control vector of the missile at each moment from the starting moment of the terminal guidance stage to the ending moment of the terminal guidance stage, thereby completing ballistic planning of the terminal guidance stage. Compared with the existing missile guidance means with only falling angle constraint, the missile guidance method combines the view angle constraint, so that the influence of the falling angle constraint on the missile flight track is reduced to a certain extent, and the target hitting accuracy is improved.
Description
Technical Field
The invention relates to the technical field of ballistic planning, in particular to a terminal guidance stage ballistic planning method and system based on view angle constraint.
Background
In order to reduce the cost of tactical missiles and reduce the volume of missiles, tactical missiles widely use strapdown seekers. Compared with a platform type seeker with a detector arranged on a top-stabilized platform, the detector of the strapdown seeker is rigidly and fixedly connected with the projectile body, and the detector must rotate along with the angle of the projectile body, so that the detection range is relatively small, and the amplitude of the angle of view of the projectile in the process of making and guiding is limited to a certain extent. Meanwhile, in order to improve the damage effect on ground targets or ship targets, a falling angle constraint is generally added to terminal guidance of the missile. When the guidance law of the missile has a falling angle constraint, the flight track of the missile may generate a large bending, and for the missile provided with the strapdown seeker, the target may be out of the field of view of the seeker. Therefore, a guidance planning method capable of reducing the influence of the falling angle constraint on the missile flight trajectory and improving the target hitting accuracy is needed.
Disclosure of Invention
The invention aims to provide a terminal guidance stage trajectory planning method and system based on view angle constraint, which lighten the influence of falling angle constraint on the missile flight track and improve the target hitting accuracy.
In order to achieve the above object, the present invention provides the following.
In one aspect, the invention provides a terminal guidance stage trajectory planning method based on view angle constraint, which comprises the following steps.
And constructing a ballistic planning control model of the terminal guidance stage time interval. The two endpoints of the terminal guidance stage time interval are terminal guidance stage starting time and terminal guidance stage ending time; the trajectory planning control model is a model taking the minimum off-target quantity and control energy as an objective function and comprehensively considering falling angle constraint, dynamic constraint and path constraint; the falling angle constraint is that the speed inclination angle of the missile at the end time of the terminal guidance stage is equal to the falling angle constraint value; the path constraints include angle of attack constraints, sideslip angle constraints, and view angle constraints; the attack angle constraint is that the attack angle of the missile is smaller than the attack angle threshold value; the sideslip angle constraint is that the missile sideslip angle is smaller than a sideslip angle threshold value; the view angle constraint is that the missile view angle is smaller than a view angle threshold; the dynamic constraint is an integrated control model of the missile in the terminal guidance stage time interval; the integrated control model includes a state vector, a control vector, and a state vector rate of change.
And solving the trajectory planning control model based on the acquired missile initial attitude information, the missile initial physical parameters and the missile constraint data set to obtain an optimal state vector data set and an optimal control vector data set. The missile initial attitude information is missile attitude information at the moment before the initial moment of the terminal guidance stage time interval; the initial physical parameters of the missile are missile fixing physical parameters; the missile constraint data set comprises a falling angle constraint value, an attack angle threshold value, a sideslip angle threshold value and a view angle threshold value; the optimal state vector data set comprises an optimal state vector of the missile at each moment between the starting moment of the terminal guidance stage and the ending moment of the terminal guidance stage; the optimal control vector data set includes an optimal control vector for the missile at each time between a terminal guidance phase start time and a terminal guidance phase end time.
Optionally, the ballistic planning control model is solved using gaussian pseudo-spectroscopy.
Optionally, solving the trajectory planning control model by using a Gaussian pseudo-spectrum method based on the acquired missile initial attitude information, the missile initial physical parameters and the missile constraint data set, and specifically comprising the following steps.
Converting the ballistic planning control model of the terminal guidance stage time interval into a ballistic planning control model of a virtual time interval; the terminal guidance stage time interval is [ t ] 0 ,t f ]The virtual time interval is [ -1,1]；t 0 Indicating the starting time of the terminal guidance stage, t f Indicating the end time of the end guidance phase.
Discretizing the trajectory planning control model of the virtual time interval to obtain a trajectory planning control model in a discrete form.
Based on the missile initial attitude information, the missile initial physical parameters and the missile constraint data set, solving a discrete form trajectory planning control model to obtain an optimal state vector data set and an optimal control vector data set.
Optionally, discretizing the trajectory planning control model of the virtual time interval to obtain a trajectory planning control model in a discrete form, which specifically comprises the following steps.
Discretizing the state vector to obtain a state vector in a discrete form.
Discretizing the control vector to obtain a discrete form control vector.
Based on the control vector in the discrete form and the state vector in the discrete form, discretizing the dynamic constraint to obtain the dynamic constraint in the discrete form.
Discretizing the falling angle constraint to obtain the falling angle constraint in a discrete form.
Discretizing the objective function to obtain the objective function in a discrete form.
And constructing and obtaining a discrete ballistic planning control model based on the path constraint, the discrete dynamic constraint, the discrete falling angle constraint and the discrete objective function.
Optionally, constructing a ballistic planning control model of the terminal guidance stage time interval, and specifically comprising the following steps.
And establishing a view angle model according to the conversion relation between the projectile body coordinate system and the sight line coordinate system determined by analysis.
And establishing a guidance engagement model according to the motion relation of the guided missile and the hit target in the pitching plane, which is determined through analysis.
And building a flight control model according to the relation between the state vector and the control vector determined by analysis.
And establishing an integrated control model based on the guidance engagement model and the flight control model.
And establishing an objective function by taking minimum off-target quantity and minimum control energy as targets, and establishing a ballistic planning control model of the terminal guidance stage time interval based on the view angle model, the integrated control model, the falling angle constraint and the objective function.
The invention also provides a terminal guidance stage trajectory planning system based on the view angle constraint, which executes the terminal guidance stage trajectory planning method based on the view angle constraint when being operated by a computer.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a terminal guidance stage trajectory planning method and a terminal guidance stage trajectory planning system based on view angle constraint, wherein the method comprises the following steps: taking the minimum off-target quantity and the minimum control energy as objective functions, comprehensively considering the falling angle constraint, the dynamic constraint and the path constraint, constructing a ballistic planning control model of a terminal guidance stage time interval, and solving the ballistic planning control model based on the acquired initial missile attitude information, initial missile physical parameters and a missile constraint data set to obtain an optimal state vector of the missile at each moment and an optimal control vector of the missile at each moment from the starting moment of the terminal guidance stage to the ending moment of the terminal guidance stage, thereby completing ballistic planning of the terminal guidance stage. Compared with the existing missile with the falling angle constraint, the missile launching device combines the view angle constraint, so that the influence of the falling angle constraint on the missile flight track is reduced to a certain extent, and the target hitting accuracy is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flowchart of a terminal guidance stage trajectory planning method based on view angle constraint provided in embodiment 1 of the present invention.
Fig. 2 is a flowchart of step A1 in the method provided in embodiment 1 of the present invention.
Fig. 3 is a schematic diagram of the interaction between a missile and a target in the method provided in embodiment 1 of the present invention.
Fig. 4 is a diagram of a transformation relationship between coordinate systems commonly used in missile motion in the method provided in embodiment 1 of the present invention.
FIG. 5 is a schematic representation of the transformation matrix between the projectile coordinate system and the line-of-sight coordinate system in the method of example 1 of the present invention.
Fig. 6 is a flowchart of step A2 in the method provided in embodiment 1 of the present invention.
Fig. 7 is a flowchart of step a22 in the method provided in embodiment 1 of the present invention.
Fig. 8 is a diagram showing the change of the relative distance between the missile and the target in the missile during the missile preparation process in the method provided by the embodiment 1 of the present invention.
Fig. 9 is a graph showing the change of the velocity and inclination angle in case 1 in the method according to embodiment 1 of the present invention.
Fig. 10 is a view angle change chart in case 1 in the method provided in embodiment 1 of the present invention.
Fig. 11 is a diagram showing the change of the relative distance between the missile and the target in the missile during the missile preparation process in the method of embodiment 1 of the present invention.
Fig. 12 is a graph showing the change of the velocity and inclination angle in case 2 in the method provided in example 1 of the present invention.
Fig. 13 is a view angle change chart in case 2 in the method provided in embodiment 1 of the present invention.
Fig. 14 is a graph showing the change of the relative distance between the missile and the missile during the guidance in case 3 in the method provided by the embodiment 1 of the present invention.
Fig. 15 is a graph showing the change of the velocity and inclination angle in case 3 in the method provided in example 1 of the present invention.
Fig. 16 is a view angle change chart in case 3 in the method provided in embodiment 1 of the present invention.
Fig. 17 is a schematic structural diagram of an end guidance stage trajectory planning system based on view angle constraint according to embodiment 2 of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a terminal guidance stage trajectory planning method and system based on view angle constraint, which lighten the influence of falling angle constraint on the missile flight track and improve the target hitting accuracy.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Example 1.
The embodiment provides a terminal guidance stage trajectory planning method based on view angle constraint, as shown in a flowchart in fig. 1, and the terminal guidance stage trajectory planning method based on view angle constraint provided by the embodiment comprises the following steps.
A1, constructing a ballistic planning control model of the terminal guidance stage time interval. The two endpoints of the terminal guidance stage time interval are terminal guidance stage starting time and terminal guidance stage ending time; the trajectory planning control model is a model taking the minimum off-target quantity and control energy as an objective function and comprehensively considering falling angle constraint, dynamic constraint and path constraint; the falling angle constraint is that the speed inclination angle of the missile at the end time of the terminal guidance stage is equal to the falling angle constraint value; the path constraints include angle of attack constraints, sideslip angle constraints, and view angle constraints; the attack angle constraint is that the attack angle of the missile is smaller than the attack angle threshold value; the sideslip angle constraint is that the missile sideslip angle is smaller than a sideslip angle threshold value; the view angle constraint is that the missile view angle is smaller than a view angle threshold; the dynamic constraint is an integrated control model of the missile in the terminal guidance stage time interval; the integrated control model includes a state vector, a control vector, and a state vector rate of change. As shown in the flowchart of fig. 2, the step A1 specifically includes the following steps.
A11, establishing a view angle model according to the conversion relation between the projectile body coordinate system and the sight line coordinate system determined by analysis. Considering a three-dimensional combat scene, a schematic diagram of the engagement of a missile with a target is shown in fig. 3. Wherein O represents the origin of a ground coordinate system, M represents the mass center of the missile, T represents the mass center of the target, r represents the relative distance between the missile and the hit target, namely the distance between the missile and the hit target, and theta v Indicating the inclination of the speed of the missile, i.e. the angle phi between the direction of the speed of the missile and the horizontal plane v Is the missile velocity deflection angle, namely the included angle between the missile velocity direction and the vertical plane, theta L Representing inclination angle of sight of missile, i.e. included angle of sight of missile and horizontal plane L The angle of sight of the missile, namely the included angle between the sight of the missile and a vertical plane, eta represents the angle of sight of the missile, namely the included angle between the sight of the missile and a speed direction, V m Indicating the missile speed.
Fig. 4 shows the conversion relationship between 5 coordinate systems commonly used in missile motion. Wherein Oxyz represents a ground coordinate system or a transmitting coordinate system, O is a missile transmitting point, the Ox axis is in a horizontal plane, the direction north is positive, the Oy axis is in a vertical plane, the upward direction is positive, and the Oz axis is determined according to a right-hand rule; mx 1 y 1 z 1 Representing a projectile coordinate system, M being the mass center of the missile, mx 1 The axis coincides with the longitudinal axis of the projectile and points to the head as positive, my 1 The axis being in the longitudinal symmetry plane of the projectile, perpendicular to Mx 1 The axis is positive upwards, mz 1 The axis being perpendicular to x 1 My 1 The plane, the direction is determined according to the right hand rule, and the upward direction is positive; mx 2 y 2 z 2 Representing a ballistic coordinate system, M is the mass center of the missile, and Mx 2 Velocity vector V of axis and passing through missile centroid m Coincidence, my 2 The axis being located to contain the missile velocity vector V m Is perpendicular to Mx and is in the vertical plane of 2 The axis is positive upwards, mz 2 The shaft is determined according to the right hand rule; mx 3 y 3 z 3 Representing a speed coordinate system, M being the mass center of the missile, mx 3 Axle and missile velocity vector V m Coincidence, my 3 The shaft being located longitudinally of the projectile bodyIn the plane of symmetry and Mx 3 The axis is vertical and positive upwards, mz 3 The axis being perpendicular to x 3 My 3 A plane whose direction is determined according to the right hand rule; mx 4 y 4 z 4 Represents a sight line coordinate system, M is a missile mass center, and Mx 4 The axis coincides with the missile vision MT, the pointing target is positive, my 4 The axis is located in a vertical plane containing the line of sight MT, and is perpendicular to Mx 4 The axis is positive upwards, mz 4 The axis being perpendicular to x 4 My 4 Plane whose direction is determined according to the right hand rule.
From FIG. 4, a transformation matrix between the projectile coordinate system and the line of sight coordinate system can be derived, as shown in FIG. 5, using matrix L Δ Represents the coordinate transformation matrix L (α, β). L (γ) in FIG. 5 v )·L(φ v ,θ v )·L -1 (φ L ,θ L ) Wherein alpha represents missile attack angle, beta represents missile sideslip angle and gamma v The missile velocity tilting angle is represented, and the available formula (1) is formed according to a three-dimensional rotation transformation matrix of an missile body coordinate system and a sight line coordinate system.
cosη=L Δ (1,1) （1）。
In the formula (1), eta represents the missile field angle and L Δ (1, 1) represents a coordinate transformation matrix L Δ Is located in the first column of the first row. Matrix L Δ The first element of (1, 1) is written out, and the view angle expression of the missile can be obtained as shown in the formula (2).
（2）。
In formula (2), δ=Φ v -φ L The front angle of the missile on the yaw plane is represented, alpha represents the attack angle of the missile, beta represents the sideslip angle of the missile, and gamma v Indicating the missile velocity pitch angle.
To simplify the calculation of the missile field angle, the following assumptions are introduced.
Suppose 1: δ=0, i.e. Φ v =φ L It is assumed that the movements of the missile with respect to the target all occur in a vertical plane.
Suppose 2: gamma ray v =0, i.e. the model is only for sideslip Turn (STT) missiles, the velocity tilt angle of which remains around 0 °.
Suppose 3: cos β≡1, i.e. the slip angle is relatively small during the boot process.
The view angle expression can be simplified to be shown in expression (3).
cosη=cos(α+θ v -θ L ) （3）。
The specific simplification process is as follows: from hypothesis 1, hypothesis 2 and hypothesis 3, sin δ=0, cos δ=1, sin γ can be derived v =0、cosγ v =1, cos β=1, and this is taken into formula (3) to obtain formula (4).
（4）。
It can thus be derived that the missile field angle consists mainly of the missile attack angle, the missile velocity tilt angle and the missile line of sight tilt angle when the guided movement of the missile satisfies the above-mentioned assumptions 1, 2 and 3. The view angle model is shown in the formula (5).
|η|=|α+θ v -θ L | （5）。
A12, establishing a guidance engagement model according to the motion relation of the guided missile and the hit target in the pitching plane, which is determined through analysis.
In the design process of guidance laws, a three-dimensional guidance model is generally decomposed into two guidance planes, one is a pitching plane, namely a plumb plane containing a projectile body; one is the yaw plane, i.e. the horizontal plane. For the guided missile at the yaw plane, in order to ensure that δ=0 in the above assumption 1 holds, it is necessary to ensure that the missile satisfies Φ during the guided missile v =φ L 。
And (3) enabling the guided movement of the missile on the yaw plane to select a tracking method, and enabling the initial moment of terminal guidance to meet the equality of the sight deflection angle and the speed deflection angle, thereby obtaining the formula (6).
（6）。
In formula (6), t 0 Represents the initial moment phi of terminal guidance v (t) shows the missile velocity deflection angle phi at the time t L (t) represents the missile line of sight deflection angle at the time t,represent phi v (t) deriving time and adding to the time>Represent phi L (t) deriving time. From the above, phi can be deduced v =φ L It is ensured that hypothesis 1 holds. Therefore, only the movement of the missile in the pitching plane needs to be subjected to ballistic planning, and the guidance engagement model of the missile in the pitching plane is represented by the formula (7).
（7）。
In the formula (7), V m Representing missile velocity, cos representing cosine function, θ v Indicating the velocity dip angle of the missile, theta L Representing the inclination angle of the sight of the missile, V t Representing the speed, sigma, of the hit object t Representing yaw rake angle of hit target, taking V when hit target is stationary t =0，σ t =0, sin denotes a sine function, r denotes the distance between the missile and the hit target,indicating r is derived over time, and is added to>Represents θ L And (5) deriving time.
A13, establishing a flight control model according to the relation between the state vector and the control vector determined by analysis. The flight control model is shown in formula (8).
（8）。
In the formula (8), m represents missile mass, X represents aerodynamic resistance applied during missile flight, g represents gravitational acceleration, sin represents sine function, cos represents cosine function, and theta v Representing the inclination angle of the missile speed, vm representing the missile speed, Y representing the lift force applied during the missile flight, omega z The angular velocity of the missile at the yaw axis is represented, tan represents a tangent function, beta represents the sideslip angle of the missile, omega x The angular velocity of the missile on the rolling shaft is represented, alpha represents the attack angle of the missile, and omega y The angular velocity of the missile at the pitching axis is represented, Z represents the lateral force applied to the missile during the flying process, Q represents the dynamic pressure applied to the missile warhead, S represents the reference area of the missile warhead,representing the average aerodynamic chord length of the missile, C l Representing roll direction aerodynamic moment coefficient function, C m Representing pitch aerodynamic moment coefficient function, C n Representing the aerodynamic moment coefficient function in yaw direction, I xx The moment of inertia representing the rolling direction of the missile, I yy Indicating moment of inertia in pitch direction of missile, I zz Representing moment of inertia, delta, of the yaw direction of the missile x Indicating the steering deflection angle control quantity delta of the missile rolling rudder y Indicating the steering deflection angle control quantity delta of the pitching rudder of the missile z Indicating the steering angle control of the yaw rudder of the missile, < +.>Meaning Vm is derived over time and is added to>Represents θ v Time derivative, add to>Indicating alpha as a derivative of time,>representing beta as a derivative of time, the following is added>Represents ω x Time derivative, add to>Represents ω y Time derivative, add to>Represents ω z And (5) deriving time.
A14, establishing an integrated control model based on the guidance fight model and the flight control model. The integrated control model is shown in formula (9).
（9）。
In the formula (9), x (t) represents a state vector at time t, and the state vector x= [ r, V m ,θ v ,θ L ,α,β,ω x ,ω y ,ω z ] T The superscript T denotes the transpose of the vector, r denotes the distance between the missile and the hit target, V m Indicating missile speed, theta v Indicating the velocity dip angle of the missile, theta L The angle of inclination of the sight of the missile is represented by alpha, the attack angle of the missile is represented by beta, the sideslip angle of the missile is represented by omega x Indicating angular velocity, ω, of the projectile at the axis of rotation y Representing angular velocity, ω, of the missile at the pitch axis z The angular velocity of the missile on the yaw axis is represented, u (t) is represented by a control vector at time t, and the control vector u= [ delta ] x ,δ y ,δ z ] T ，δ x Indicating the steering deflection angle control quantity delta of the missile rolling rudder y Indicating the steering deflection angle control quantity delta of the pitching rudder of the missile z The control quantity of the yaw rudder deflection angle of the missile is represented, t represents the moment t,and x (t) is the derivative of time.
And A15, taking the minimum off-target quantity and the minimum control energy as targets, establishing an objective function, and establishing a ballistic planning control model of the terminal guidance stage time interval based on the view angle model, the integrated control model, the falling angle constraint and the objective function. The ballistic planning control model of the obtained terminal guidance stage time interval is shown in a formula (10).
（10）。
In the formula (10), the term before the plus sign indicates the miss distance, i.e. the bullet distance should be as small as possible at the end of the final guidance phase, the term after the plus sign indicates the control capability, i.e. the minimum control work performed by the control vector is performed in the final guidance phase time interval, min indicates the minimization, J indicates the objective function value, x indicates the state vector, x 1 The first term of the state vector, superscript 2, to the power of 2, t 0 Indicating the starting time of the terminal guidance stage, t f The end time of the terminal guidance stage is represented by u, the control vector is represented by u, the superscript T represents the transposition of the vector, R represents the Redberg constant, dt represents differentiation of the time T, f (·) represents the integrated control model, and x 3 Third term of representing state vector, θ d Representing the falling angle constraint value.
Wherein the path constraint C (x (t), u (t), t.ltoreq.0 is specifically represented by three constraints shown in the formula (11).
（11）。
In the formula (11), the attack angle constraint, the sideslip angle constraint and the view angle constraint are respectively from top to bottom, delta is the sideslip angle threshold value meeting the assumption 3, and alpha max For angle of attack threshold, η max Is the view angle threshold. Through the process, the final ballistic planning problem based on the view angle constraint is converted into the solution of the ballistic planning control model.
And A2, solving the trajectory planning control model to obtain an optimal state vector data set and an optimal control vector data set. In this embodiment, the ballistic planning control model is solved based on the acquired missile initial attitude information, the missile initial physical parameters and the missile constraint data set. The acquired missile initial attitude information is missile attitude information at the moment before the initial moment of the terminal guidance stage time interval; the initial physical parameters of the missile are missile fixing physical parameters; the missile constraint data set comprises a falling angle constraint value, an attack angle threshold value, a sideslip angle threshold value and a view angle threshold value; the optimal state vector data set comprises an optimal state vector of the missile at each moment between the starting moment of the terminal guidance stage and the ending moment of the terminal guidance stage; the optimal control vector data set includes an optimal control vector for the missile at each time between a terminal guidance phase start time and a terminal guidance phase end time.
Because the problem has strong nonlinearity, the ballistic planning control model constructed in the step A1 can be solved by utilizing an optimization solving algorithm such as a Gaussian pseudo-spectrum method. In the embodiment, a Gaussian pseudo-spectrum method is adopted to solve a ballistic planning control model. Specifically, as shown in the flowchart of fig. 6, the solution of the ballistic planning control model by using the gaussian pseudo-spectrum method specifically includes the following steps.
A21, converting the ballistic planning control model of the terminal guidance stage time interval into a ballistic planning control model of the virtual time interval. The terminal guidance stage time interval is [ t ] 0 ,t f ]The virtual time interval is [ -1,1]；t 0 Indicating the starting time of the terminal guidance stage, t f Indicating the end time of the end guidance phase. Integrating interval t in objective function by element conversion method 0 ,t f ]Transition to interval [ -1,1]As shown in formula (12).
（12）。
In the formula (12), the amino acid sequence of the compound,the method comprises the steps of carrying out a first treatment on the surface of the Since the time interval is limited to [ -1,1]The dynamic change of the variable then occurs at a series of Legendre-Gauss (LG) points τ i (i=1, …, K), τ i Is the root of the Legendre polynomial, and is easy to obtain tau i ∈[-1,1]The Legendre polynomial function is shown in equation (13).
（13）。
In the formula (13), P k (τ) is a Legendre polynomial function, τ is an unknown variable, K represents the number of Legendre Gaussian points, K represents K τroots, the superscript K is the power of the square, k| represents the factorization of K, and d is the differential sign.
A22, discretizing the trajectory planning control model of the virtual time interval to obtain a discrete trajectory planning control model. As shown in the flowchart of fig. 7, step a22 specifically includes the following steps.
And A221, discretizing the state vector to obtain a discrete form state vector. In this embodiment, the state vector is approximated by using k+1 lagrangian lagranger interpolation polynomials, and the approximation process is shown in equation (14).
（14）。
In formula (14), τ i =-1，，/>Representing the product.
And A222, discretizing the control vector to obtain a discrete form control vector. In this embodiment, the approximation is performed using K lagrangian lagranger interpolation polynomials, and the approximation process is shown in equation (15).
（15）。
In the formula (15), the amino acid sequence of the compound,。
a223, discretizing the dynamic constraint based on the control vector in the discrete form and the state vector in the discrete form to obtain the dynamic constraint in the discrete form. The dynamic constraint may be converted to equation (16) based on the discrete form of the state vector and the discrete form of the control vector.
（16）。
The term to the left of the equation sign is further discretized to obtain equation (17).
（17）。
In the formula (17), the amino acid sequence of the compound,。
this translates the dynamic constraint into a set of algebraic constraints as shown in equation (18).
（18）。
And A224, discretizing the falling angle constraint to obtain the falling angle constraint in a discrete form. It should be noted that the above discrete form of dynamic constraint is only at LG point and does not include boundary points, so that it is also necessary to add two matching points at two boundary points, and the two boundary points of the end guidance stage time interval are shown in the formulas (19) and (20), respectively.
（19）。
（20）。
In the formulas (19) to (20), X 0 State vector, X, representing the start time of the terminal guidance phase in discrete form 0 Should be identical to the state at the end of the previous phase, X f A state vector representing a discrete form of the end guidance phase,the discrete form of the state vector representing the constant equal to the end time of the end guidance phase includes the discretized falling angle constraint, and therefore, the equation (20) can be used as the discrete form of the falling angle constraint.
And A225, discretizing the objective function to obtain the objective function in a discrete form. In this embodiment, the integration function in the objective function after the element conversion can be converted into the one shown in the formula (22) by using the Gao Sile let de-product formula (21).
（21）。
（22）。
In the formula (22), ω i Weighted gaussian.
The discretized objective function can be obtained as shown in equation (23).
（23）。
A226, constructing a discrete form trajectory planning control model based on the constraint. In this embodiment, a discrete ballistic planning control model may be constructed based on the path constraint formula (11), the discrete dynamic constraint formula (18), the discrete falling angle constraint formula (20), and the discrete objective function formula (23).
A23, solving a discrete form trajectory planning control model to obtain an optimal state vector data set and an optimal control vector data set. The optimal control problem is discretized through the steps, and is converted into a general nonlinear programming problem which can be solved by a Gaussian pseudo-spectrum method, and the optimal state vector data set and the optimal control vector data set which meet a dynamic constraint formula (18), a falling angle constraint formula (20) and a path constraint formula (11) are solved by taking a formula (23) as an objective function based on the acquired initial attitude information of the missile, initial physical parameters of the missile and the missile constraint data set.
The following specific examples are provided in this embodiment to demonstrate the advantages of the terminal guidance stage trajectory planning method based on the view angle constraint provided by the present invention, and considering the terminal guidance process of the guided missile equipped with the strapdown seeker, the main physical parameters and initial states of the missile are shown in table 1.
TABLE 1 Main physical parameters of missile
Aiming at a static hit target, selecting an initial missile-borne distance of 55km and a missile flying speed V m Mach 3, delta=5 °, alpha max =60° is an initial simulation parameter, and the following three cases are solved using GPOPS-ii in MATLAB toolbox, and simulation results are shown in fig. 8 to 16.
Case 1: η (eta) max =90°, corresponding to no field angle constraint and no falling angle constraint.
Case 2: η (eta) max =90° corresponding to no field angle constraint, θ d =90°。
Case 3: η (eta) max =60°，θ d =90°。
Fig. 8, 11 and 14 show the change of the relative distances of the missile during the guidance in case 1, case 2 and case 3, respectively, and it can be seen that the missile finally hits the target in all three cases.
Fig. 9 to 10 show the velocity tilt and angle of view of the missile of case 1 during the course of the lead, and it can be seen that the angle of view of the missile remains substantially small without the falling angle constraint, only reaching 55 ° at the final hit.
Fig. 12 to 13 show velocity inclination change diagrams and view angle change diagrams of the missile in the process of manufacturing guidance in case 2, from which it can be seen that the view angle amplitude of the missile gradually increases in the rear end of the final guidance, the absolute value before collision reaches 90 ° before collision with a target, and for the missile equipped with the strapdown leader, the missile is highly likely to exceed the view limit in the rear end of the final guidance, thereby losing the target and causing guidance failure.
Fig. 15 to 16 show the change of the velocity tilt angle and the view angle of the missile during the guidance in case 3, from which it can be seen that the change of the view angle of the missile is limited to 60 ° with the addition of the view angle constraint, the amplitude of which is reduced. By comparing fig. 8 to 13, it can be found that by adding the falling angle constraint, a trajectory satisfying the falling angle constraint can be obtained, and it can be found that the flight time of the missile will be longer in order to satisfy the falling angle constraint. By comparing fig. 11 to 16, it can be found that by adjusting η max And (3) the value can be used for drawing a terminal guidance track which meets the falling angle constraint and does not violate the view angle constraint by utilizing Gaussian pseudo-spectrum regulation.
According to the terminal guidance stage trajectory planning method based on the view angle constraint, the off-target quantity and the minimum control energy are taken as target functions, the falling angle constraint, the dynamic constraint and the path constraint are comprehensively considered, a trajectory planning control model of a terminal guidance stage time interval is constructed, and the trajectory planning control model is solved based on the acquired initial attitude information of the missile, the initial physical parameters of the missile and the missile constraint data set to obtain an optimal state vector data set and an optimal control vector data set. Compared with the existing missile with only falling angle constraint, the embodiment combines the view angle constraint, so that the influence of the falling angle constraint on the missile flight track is reduced to a certain extent, and the accuracy of target hitting is improved; in addition, a real expression of the missile field angle in the three-dimensional fight scene is given by utilizing the conversion relation between coordinates, and simplification is carried out by reasonable assumption; the three-dimensional view angle constraint problem is converted into the two-dimensional view angle constraint problem by performing dimension reduction treatment on the view angle on the yaw plane by using a tracking method.
Example 2.
Furthermore, the method of embodiment 1 of the present invention can also be implemented by means of the architecture of the end guidance stage trajectory planning system based on the view angle constraints shown in fig. 17. As shown in fig. 17, the hybrid reinforcement learning-based on-vehicle task offloading scheduling system may include a ballistic planning control model construction module and a ballistic planning control model solution module; some modules can also have sub-modules and units for realizing the functions, for example, the sub-modules or sub-units of the ballistic planning control model building module, including a view angle model building unit, a guidance engagement model building unit, a flight control model building unit, an integrated control model building unit, an objective function building unit, a ballistic planning control model building unit and the like; the ballistic planning control model solving module comprises an integral interval converting unit, a model discretizing unit and a Gaussian pseudo-spectrum solving unit. Of course, the architecture shown in fig. 17 is merely exemplary, and one or at least two components of the system shown in fig. 17 may be omitted as actually needed when different functions are implemented.
Specific examples are employed herein, but the above description is merely illustrative of the principles and embodiments of the present invention, which are presented solely to aid in the understanding of the method of the present invention and its core ideas; it will be appreciated by those skilled in the art that the modules or steps of the invention described above may be implemented by general-purpose computer means, alternatively they may be implemented by program code executable by computing means, whereby they may be stored in storage means for execution by computing means, or they may be made into individual integrated circuit modules separately, or a plurality of modules or steps in them may be made into a single integrated circuit module. The present invention is not limited to any specific combination of hardware and software.
Also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (10)
1. The terminal guidance stage trajectory planning method based on the view angle constraint is characterized by comprising the following steps of:
constructing a ballistic planning control model of a terminal guidance stage time interval; the two endpoints of the terminal guidance stage time interval are terminal guidance stage starting time and terminal guidance stage ending time; the trajectory planning control model is a model taking the minimum off-target quantity and control energy as an objective function and comprehensively considering falling angle constraint, dynamic constraint and path constraint; the falling angle constraint is that the speed inclination angle of the missile at the end time of the terminal guidance stage is equal to the falling angle constraint value; the path constraints include angle of attack constraints, sideslip angle constraints, and view angle constraints; the attack angle constraint is that the attack angle of the missile is smaller than an attack angle threshold value; the sideslip angle constraint is that the missile sideslip angle is smaller than a sideslip angle threshold value; the view angle constraint is that the missile view angle is smaller than a view angle threshold; the dynamic constraint is an integrated control model of the missile in a terminal guidance stage time interval; the integrated control model comprises a state vector, a control vector and a state vector change rate;
solving the trajectory planning control model based on the acquired missile initial attitude information, the missile initial physical parameters and the missile constraint data set to obtain an optimal state vector data set and an optimal control vector data set; the missile initial attitude information is missile attitude information at a moment before the initial moment of a terminal guidance stage time interval; the initial physical parameters of the missile are missile fixing physical parameters; the missile constraint data set comprises a falling angle constraint value, an attack angle threshold value, a sideslip angle threshold value and a view angle threshold value; the optimal state vector data set comprises an optimal state vector of the missile at each moment between the starting moment of the terminal guidance stage and the ending moment of the terminal guidance stage; the optimal control vector data set comprises optimal control vectors of missiles at each time between the starting time of the terminal guidance stage and the ending time of the terminal guidance stage.
2. The terminal guidance phase trajectory planning method based on view angle constraints of claim 1, wherein the trajectory planning control model is solved using gaussian pseudo-spectroscopy.
3. The terminal guidance stage trajectory planning method based on view angle constraint according to claim 2, wherein the trajectory planning control model is solved by using a gaussian pseudo-spectrum method based on the acquired missile initial attitude information, missile initial physical parameters and missile constraint data set, and specifically comprising the following steps:
converting the ballistic planning control model of the terminal guidance stage time interval into a ballistic planning control model of a virtual time interval; the terminal guidance stage time interval is [ t ] 0 ,t f ]The virtual time interval is [ -1,1]；t 0 Indicating the starting time of the terminal guidance stage, t f Indicating the end time of the terminal guidance stage;
discretizing a trajectory planning control model of the virtual time interval to obtain a trajectory planning control model in a discrete form;
and solving a discrete ballistic planning control model based on the missile initial attitude information, the missile initial physical parameters and the missile constraint data set to obtain an optimal state vector data set and an optimal control vector data set.
4. The terminal guidance stage trajectory planning method based on view angle constraint of claim 3, wherein the discretizing of the trajectory planning control model of the virtual time interval to obtain the trajectory planning control model of a discrete form specifically comprises:
discretizing the state vector to obtain a state vector in a discrete form;
discretizing the control vector to obtain a discrete form control vector;
discretizing the dynamic constraint based on a control vector in a discrete form and a state vector in a discrete form to obtain the dynamic constraint in the discrete form;
discretizing the falling angle constraint to obtain a discrete falling angle constraint;
discretizing the objective function to obtain a discrete form objective function;
and constructing and obtaining a discrete ballistic planning control model based on the path constraint, the discrete dynamic constraint, the discrete falling angle constraint and the discrete objective function.
5. The terminal guidance phase trajectory planning method based on view angle constraint of claim 1, wherein constructing a trajectory planning control model of a terminal guidance phase time interval specifically comprises:
establishing a view angle model according to the conversion relation between the projectile body coordinate system and the sight line coordinate system determined by analysis;
establishing a guidance engagement model according to the motion relation of the guided missile and the hit target in the pitching plane;
establishing a flight control model according to the relation between the state vector and the control vector determined by analysis;
establishing an integrated control model based on the guidance engagement model and the flight control model;
and establishing an objective function by taking minimum off-target quantity and minimum control energy as targets, and establishing a ballistic planning control model of a terminal guidance stage time interval based on the view angle model, the integrated control model, the falling angle constraint and the objective function.
6. The terminal guidance phase trajectory planning method based on view angle constraint of claim 5, wherein the terminal guidance phase time interval trajectory planning control model is as follows:
；
wherein min represents minimization, J represents an objective function value, x represents a state vector, x= [ r, V m ,θ v ,θ L ,α,β,ω x ,ω y ,ω z ] T ，x 1 The first term representing the state vector, superscript 2 representing the power of 2, r representing the distance between the missile and the hit target, V m Indicating missile speed, theta v Indicating the velocity dip angle of the missile, theta L The angle of inclination of the sight of the missile is represented by alpha, the attack angle of the missile is represented by beta, the sideslip angle of the missile is represented by omega x Indicating angular velocity, ω, of the projectile at the axis of rotation y Indicating missilesAngular velocity at pitch axis, ω z Indicating angular velocity of missile at yaw axis, t 0 Indicating the starting time of the terminal guidance stage, t f Represents the end time of the terminal guidance phase, u represents the control vector, u= [ delta ] x ,δ y ,δ z ] T The superscript T denotes the transpose of the vector, delta x Indicating the steering deflection angle control quantity delta of the missile rolling rudder y Indicating the steering deflection angle control quantity delta of the pitching rudder of the missile z The control amount of the yaw rudder deflection angle of the missile is represented, R represents a Redburg constant, dt represents differentiation of time t, x (t) represents a state vector at time t, u (t) represents a control vector at time t, t represents time t,represents the derivative of x (t) over time, f (·) represents the integrated control model, x 3 Third term of representing state vector, θ d Representing the falling angle constraint value.
7. The terminal guidance phase trajectory planning method based on view angle constraints of claim 5, wherein the guidance engagement model is represented by the following formula:
；
wherein V is m Representing missile velocity, cos representing cosine function, θ v Indicating the velocity dip angle of the missile, theta L Representing the inclination angle of the sight of the missile, V t Representing the speed, sigma, of the hit object t Represents the yaw rake angle of the hit target, sin represents a sine function, r represents the distance between the missile and the hit target,indicating r is derived over time, and is added to>Represents θ L And (5) deriving time.
8. The terminal guidance phase trajectory planning method based on view angle constraints of claim 5, wherein the flight control model is represented by the following formula:
；
wherein m represents missile mass, X represents aerodynamic resistance received during missile flight, g represents gravitational acceleration, sin represents sine function, cos represents cosine function, and theta v Representing the inclination angle of the missile speed, vm representing the missile speed, Y representing the lift force applied during the missile flight, omega z The angular velocity of the missile at the yaw axis is represented, tan represents a tangent function, beta represents the sideslip angle of the missile, omega x The angular velocity of the missile on the rolling shaft is represented, alpha represents the attack angle of the missile, and omega y The angular velocity of the missile at the pitching axis is represented, Z represents the lateral force applied to the missile during the flying process, Q represents the dynamic pressure applied to the missile warhead, S represents the reference area of the missile warhead,representing the average aerodynamic chord length of the missile, C l Representing roll direction aerodynamic moment coefficient function, C m Representing pitch aerodynamic moment coefficient function, C n Representing the aerodynamic moment coefficient function in yaw direction, I xx The moment of inertia representing the rolling direction of the missile, I yy Indicating moment of inertia in pitch direction of missile, I zz Representing moment of inertia, delta, of the yaw direction of the missile x Indicating the steering deflection angle control quantity delta of the missile rolling rudder y Indicating the steering deflection angle control quantity delta of the pitching rudder of the missile z Indicating the steering angle control of the yaw rudder of the missile, < +.>Meaning Vm is derived over time and is added to>Represents θ v Time derivative, add to>Indicating alpha as a derivative of time,>representing beta as a derivative of time, the following is added>Represents ω x The time is derived from the time of day,represents ω y Time derivative, add to>Represents ω z And (5) deriving time.
9. The terminal guidance phase trajectory planning method based on view angle constraints of claim 5, wherein the view angle model is represented by the following formula:
|η|=|α+θ v -θ L |；
wherein eta represents the missile field angle, alpha represents the missile attack angle and theta v Indicating the velocity dip angle of the missile, theta L Representing the inclination angle of the missile sight, and the symbol of absolute value is represented by the I.
10. An end-guidance stage trajectory planning system based on field angle constraints, wherein the end-guidance stage trajectory planning system, when run by a computer, performs an end-guidance stage trajectory planning method based on field angle constraints as claimed in any one of claims 1 to 9.
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