CN115033024A - Multi-missile three-dimensional cooperative guidance method based on attack time and angle common constraints - Google Patents
Multi-missile three-dimensional cooperative guidance method based on attack time and angle common constraints Download PDFInfo
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Abstract
The invention discloses a multi-missile three-dimensional cooperative guidance method based on attack time and angle joint constraint, which comprises the following steps: establishing a relative motion model and a relative motion equation set of the missile and the target; introducing residual flight time variables of the missile, and constructing a three-dimensional cooperative guidance model; acquiring the acceleration of each missile in the visual line direction of the missile target; constructing a fixed time disturbance observer of the target acceleration in the pitching direction and the yawing direction and estimating a target acceleration item under a sight line coordinate system; acquiring the acceleration of the missile in the normal direction of the missile sight line according to the three-dimensional cooperative guidance model and the estimated target acceleration item; obtaining three acceleration components of the missile in a trajectory coordinate system; and continuously updating the speed and the position of each missile in the flight process by utilizing the three acceleration components, thereby realizing that a plurality of missiles reach the target at the same time. The invention can control the sight angle of each missile to converge to a set value within a fixed time, and can realize the spatial cooperation.
Description
Technical Field
The invention belongs to the technical field of missile guidance and control, and particularly relates to a multi-missile three-dimensional cooperative guidance method based on attack time and angle joint constraint.
Background
With the rapid development of both aerospace technology and technological strength, the defense capability and maneuvering performance of important targets are increasingly improved, and the reaction time for missiles is shortened. The traditional one-to-one hitting mode is difficult to complete the task of hitting a target with high precision, in order to adapt to a complex and changeable space environment, a strategy of cooperatively attacking the target by using a plurality of missiles is provided, communication equipment is added on a single missile body, information obtained by each missile is collected and sufficiently processed by using a communication network, the information is used for controlling guided flight of a missile group, and the sprouting of a cooperative hitting system of a multi-missile system is promoted. The multi-missile cooperative guidance can not only improve the comprehensive hitting capacity and the hit probability, but also can complete the tasks which cannot be completed by the traditional single missile. Therefore, in the process of executing modern aerospace missions, the research on the multi-missile cooperative guidance law has very important engineering significance and receives wide attention.
In the early cooperative Guidance research, static or low-speed moving targets are mainly hit, attack Time is preset, in 2006, Jeon et al introduces an attack-Time Control law (ITCG) for the first Time and applies the ITCG to a flush mission, and then Jeon et al controls the attack Time and the attack angle at the same Time by expanding the ITCG, but because information exchange is not carried out among all missiles, the cooperation is not really true in nature. To achieve true cooperative guidance, a multi-agent consistency theory is used to design a cooperative guidance law. At present, a related consistency cooperative guidance law is mostly based on a finite time control theory, a second-order sliding mode guidance law is designed in a plurality of documents in a sight line direction, a plurality of missiles are guaranteed to arrive at a target at the same time, and the finite time guidance law is established in the sight line direction by utilizing a self-adaptive law and a terminal sliding mode, so that the missiles are forced to attack the target by a desired sight line angle. Although many references improve on the terminal sliding mode surface, the approach law, the state error and the like, the finite time control theory and the terminal sliding mode theory are combined.
Firstly, the current design related to the cooperative guidance law basically adopts a finite time convergence theory, a finite time convergence boundary is related to the initial state of a multi-missile system, in actual guidance, the specific initial motion state of a missile cannot be predicted in advance, the convergence time obtained under different initial conditions is different, and the convergence cannot be caused by the relationship of the initial state of the system. Secondly, the current research is basically carried out in a two-dimensional space, but the actual guidance is carried out in a three-dimensional space, so that the cooperative guidance motion model in the three-dimensional space needs to be deeply researched to adapt to the actual air combat requirement. In addition, for a large maneuvering target, the target acceleration is an important unknown factor for the design of a guidance law and cannot be directly obtained through a measuring device, and at present, the cooperative guidance research assumes that a missile can directly obtain the target acceleration, while the actual maneuvering target is unknown for the missile. Meanwhile, the cooperative interception precision of the current research under the target large maneuvering scene is relatively low.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a multi-missile three-dimensional cooperative guidance method based on attack time and angle joint constraint. The technical problem to be solved by the invention is realized by the following technical scheme:
the invention provides a multi-missile three-dimensional cooperative guidance method based on attack time and angle joint constraint, which comprises the following steps:
establishing a relative motion model and a relative motion equation set of the missile and the target by utilizing the relative motion information of the missile and the target;
introducing a residual flight time variable of the missile into a relative motion equation set of the missile and the target, and constructing a three-dimensional cooperative guidance model;
acquiring the acceleration of each missile in the visual line direction of the missile target according to the three-dimensional cooperative guidance model so that a plurality of missiles can reach the target at the same time;
constructing a fixed time disturbance observer of the target acceleration in the pitching direction and the yawing direction and estimating a target acceleration item under a sight line coordinate system;
acquiring the acceleration of the missile in the normal direction of the target sight line of the missile according to the three-dimensional cooperative guidance model and the estimated target acceleration item so that a plurality of missiles can reach the target at the same time;
acquiring three acceleration components of the missile in a trajectory coordinate system by utilizing the acceleration of the missile in the direction of the visual line of the missile target and the normal direction of the visual line;
and continuously updating the speed and the position of each missile in the flight process by utilizing the three acceleration components, thereby realizing that a plurality of missiles reach the target at the same time.
In one embodiment of the invention, the system of relative motion equations of the missile and the target is:
wherein r is i The distance between the two eyes is the distance of the bullet,
the first derivative of the shot distance with respect to time,
second derivative of the distance to the bullet eye with respect to time, q εi Is the line of sight inclination of the ith missile, q βi Is the view declination of the ith missile,
the first derivative of line-of-sight inclination with respect to time for the ith missile,
is a first derivative of the line-of-sight declination of the ith missile with respect to timeThe number of the first and second groups is,
the second derivative of the line-of-sight inclination of the ith missile with respect to time,
is the first derivative of the line-of-sight declination of the ith missile with respect to time, theta mi ,ψ mi The trajectory inclination angle and deflection angle theta of the ith missile t ,ψ t Respectively the target speed dip and slip angle, a Mir ,a Miε ,a Miβ The components of the acceleration of the ith missile on three axes under the sight line coordinate system; a is Tr ,a Tε ,a Tβ Are the components of the target acceleration in three axes under the line-of-sight coordinate system.
In one embodiment of the invention, the missile residual flight time variable is introduced into a relative motion equation system of a missile and a target, and a three-dimensional cooperative guidance model is constructed, wherein the three-dimensional cooperative guidance model comprises the following steps:
defining a state variable according to a relative motion equation set of the missile and the target and constructing a state equation according to the state variable;
and introducing a missile residual flight time variable into the state equation and updating the state equation to obtain a three-dimensional cooperative guidance model.
In an embodiment of the present invention, the three-dimensional cooperative guidance model is:
wherein x is 1i ＝r i ，
x 3i ＝q εi -q εid ，
x 5i ＝q βi -q βid ，
A variable representing the time of flight remaining for the missile,
representing the first derivative of the missile time-of-flight residual variable with respect to time,
representing the target acceleration term estimated with the ith missile.
In an embodiment of the present invention, acquiring the acceleration of each missile in the direction of the visual line of the missile target according to the three-dimensional cooperative guidance model so that multiple missiles can reach the target at the same time includes:
setting the Total time of flight t of the missile fi ＝t+t goi Wherein, t goi Representing the residual flight time of the ith missile, and t representing the flying time of the missile;
differentiating the total flight time of the missile to obtain:
wherein the content of the first and second substances,
representing a virtual control quantity;
according to the fixed time consistency theory, obtaining the acceleration which can make the total flight time of all missiles converge in the fixed time and make the residual flight time of all missiles converge to the consistent sight line direction in the fixed time:
wherein the content of the first and second substances,
h 0 ,h 1 ,h 2 the coefficients are constant values when alpha is more than 0, alpha is more than beta, alpha gamma is more than 1, and beta gamma is more than 1.
In one embodiment of the invention, the fixed-time convergent disturbance observer is:
wherein, z 1i ，z 2i Are respectively x 4i ，d qεi Estimated value of theta 1 ≥0，η 1 ,η 2 Is greater than 0 and
z 3i ，z 4i are respectively x 6i ，d qβi Estimated value of theta 1 ,θ 2 ≥0，η 1 ,η 2 ,η 3 ,η 4 Is greater than 0 and
ε 1 ，ε 3 ∈(0.5,1)，ε 2 ，ε 4 e (1,1.5), and t (·) is a nonlinear correction term.
In an embodiment of the present invention, obtaining the acceleration of the missile in the normal direction of the missile sight line according to the three-dimensional cooperative guidance model and the estimated target acceleration term so that multiple missiles can reach the target at the same time includes:
according to a guidance model which is vertical to the sight direction in the pitching plane, constructing a segmented continuous fixed time nonsingular terminal sliding mode surface and a fixed time convergence approximation law in the lateral plane, and obtaining an acceleration control law of the missile in the missile target sight normal direction to the pitching plane;
and according to a guidance model which is perpendicular to the sight direction in the lateral plane, constructing a segmented continuous fixed-time nonsingular terminal sliding mode surface and a fixed-time convergence approximation law in the lateral plane, and obtaining an acceleration control law of the missile in the missile eye sight direction to the lateral plane.
In an embodiment of the invention, according to a guidance model in a pitching plane perpendicular to a sight line direction, a segmented continuous fixed time nonsingular terminal sliding mode surface and a fixed time convergence approach law in a lateral plane are constructed, and an acceleration control law of a missile in a missile target sight line normal direction pitching plane is obtained, and the method comprises the following steps:
constructing a segmented continuous fixed-time nonsingular terminal sliding mode surface according to a guidance model perpendicular to the sight direction in the pitching plane:
wherein, delta 1 ，δ 2 ＞0，λ 1 ＞λ 2 ，1＜λ 2 Less than 2, are all constant value coefficients,
ε is a positive number;
constructing a fixed time convergence approximation law based on gain parameter self-adaptation:
wherein p is 1 ,q 1 ＞1,k 1 ,k 2 ＞0，
Is an adaptive gain value;
and obtaining an acceleration control law of the missile in the normal pitching plane of the missile eye sight according to the fixed time convergence approach law, wherein the acceleration control law comprises the following steps:
another aspect of the present invention provides a storage medium, in which a computer program is stored, the computer program being configured to execute the steps of the multi-missile three-dimensional collaborative guidance method based on the attack time and angle joint constraint in any one of the above embodiments.
Yet another aspect of the present invention provides an electronic device, which includes a memory and a processor, where the memory stores a computer program, and the processor, when calling the computer program in the memory, implements the steps of the multi-missile three-dimensional collaborative guidance method based on attack time and angle joint constraints as described in any one of the above embodiments.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the invention, a common two-dimensional guidance model is expanded to a three-dimensional space, a three-dimensional space missile-target relative motion model is constructed, a missile guidance model is decoupled to the direction of a sight line and a sight line, a cooperative guidance law is designed on the basis of a fixed time consistency theory in the sight line direction, and each missile can simultaneously attack a target; a self-adaptive approach law is designed in the direction of a line-of-sight method, based on a designed fixed-time fast nonsingular terminal sliding mode surface, the line-of-sight angle of each missile can be controlled to be converged to a set value in fixed time, and spatial cooperation can be realized. The fixed time interference observer can estimate the maneuvering acceleration of the target, can eliminate the influence of the maneuvering of the target on a multi-missile system, does not need to assume for a guidance system, and is more practical.
2. In order to embody the manual trapping strategy, the invention proposes that the sight inclination angle and the sight declination angle expected to collide are set to be in a pairwise 'symmetrical' mode in advance, so that the spatially symmetrical trapping situation of the multi-missile trajectory can be realized, and the requirement of saturation attack can be met better.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
FIG. 1 is a flow chart of a multi-missile three-dimensional cooperative guidance method based on attack time and angle joint constraints provided by an embodiment of the invention;
FIG. 2 is a schematic diagram of a multi-missile three-dimensional cooperative guidance process based on joint constraints of attack time and angle, provided by the embodiment of the invention;
FIG. 3 is a three-dimensional geometric model of the relative motion of a missile and a target provided by an embodiment of the invention;
FIG. 4 is a diagram of a topology of communications among multiple missiles in accordance with an embodiment of the present invention;
FIG. 5 is a three-dimensional trajectory of the missile and target obtained using the method of an embodiment of the invention;
FIG. 6 is a diagram of the trajectory of the missile and target pitch planes obtained using the method of an embodiment of the invention;
FIG. 7 is a graph of the trajectory of the missile and target level obtained using the method of an embodiment of the invention;
FIG. 8 is a graph of the relative distance change between the missile and target obtained using the method of an embodiment of the invention;
FIG. 9 is a graph of the change in the residual flight time of a missile using the method of an embodiment of the invention;
FIG. 10 is a graph of the variation of the inclination of the line of sight of a bullet eye obtained by the method of an embodiment of the present invention;
FIG. 11 is a graph of the variation of the declination of a bullet eye using a method according to an embodiment of the present invention;
FIG. 12 is a graph of the variation of the sliding mode surfaces in the pitching direction of four missiles obtained by the method of the embodiment of the invention;
FIG. 13 is a graph of the variation of the slip form surfaces in the lateral deviation direction of four missiles obtained by the method of the embodiment of the invention;
FIG. 14 shows the normal directional accelerations a of four missile sight lines obtained by the method of the embodiment of the invention Mε A graph of variation of (d);
FIG. 15 shows the normal directional accelerations a of four missile sight lines obtained by the method of the embodiment of the invention Mβ A graph of variation of (d);
FIG. 16 shows the acceleration a of the four missile in the direction of the line of sight obtained by the method of the embodiment of the invention Mr Graph of the variation of (c).
Detailed Description
In order to further explain the technical means and effects of the present invention adopted to achieve the predetermined invention purpose, the following detailed description is made with reference to the accompanying drawings and the specific embodiments for a multi-missile three-dimensional cooperative guidance method based on attack time and angle common constraints according to the present invention.
The foregoing and other technical matters, features and effects of the present invention will be apparent from the following detailed description of the embodiments, which is to be read in connection with the accompanying drawings. The technical means and effects of the present invention adopted to achieve the predetermined purpose can be more deeply and specifically understood through the description of the specific embodiments, however, the attached drawings are provided for reference and description only and are not used for limiting the technical scheme of the present invention.
It should be noted that, in this document, relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that an article or device that comprises a list of elements does not include only those elements but may include other elements not expressly listed. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of additional like elements in the article or device comprising the element.
Referring to fig. 1, fig. 1 is a flowchart of a multi-missile three-dimensional cooperative guidance method based on joint constraints of attack time and angle according to an embodiment of the present invention. The multi-missile three-dimensional cooperative guidance method comprises the following steps:
s1: and establishing a relative motion model and a relative motion equation set of the missile and the target by utilizing the relative motion information of the missile and the target.
Obtaining the relative motion information between the missile and the target from the reconnaissance system, for example, the missile-eye distance (distance between the missile and the target), the line-of-sight inclination angle and the deflection angle of the missile, the target speed, and the speed inclination angle and the deflection angle of the target, to obtain a relative motion model between the missile and the target, as shown in fig. 3, wherein M is i Denotes the ith missile, T denotes the target, V mi Indicates the velocity, V, of the ith missile t Representing the target speed.
Obtaining a relative motion equation set of the missile and the target according to the relative motion model of the missile and the target as follows:
wherein r is i The distance between the two eyes is the distance of the bullet,
the first derivative of the shot distance with respect to time,
second derivative of the distance to the bullet eye with respect to time, q εi Is the line of sight inclination of the ith missile, q βi Is the line-of-sight declination of the ith missile,
the first derivative of the sight line inclination angle of the ith missile with respect to time, namely the change rate of the sight line inclination angle,
the first derivative of the view angle of the ith missile with respect to time, namely the change rate of the view angle,
the second derivative of the line-of-sight inclination angle of the ith missile with respect to time,
is the first derivative of the line-of-sight declination of the ith missile with respect to time, theta mi ,ψ mi The trajectory inclination angle and deflection angle theta of the ith missile t ,ψ t Respectively the target speed dip and slip angle, a Mir ,a Miε ,a Miβ The components of the acceleration of the ith missile on three axes under the sight line coordinate system; a is a Tr ,a Tε ,a Tβ The components of the target acceleration in three axes under the sight line coordinate system.
Note that the line-of-sight coordinate system OX L Y L Z L Is defined as: origin of coordinates on missile instantaneous centroid, OX L The positive axial direction being the direction of sight of the target, OY L The axis lying in the plane of the plumb and OX L Perpendicular, pointing upwards as positive, OZ L Shaft and OX L Y L Z L The plane is vertical, and a right-hand coordinate system is formed by the other two axes.
Further, in order to conveniently calculate each guidance variable in the relative motion model between the missile and the target, the embodiment provides a calculation mode of each state quantity of the missile and the target, and a calculation formula of the missile-target distance and a derivative thereof:
wherein x is r ＝x t -x m ，y r ＝y t -y m ，z r ＝z t -z m ，x t 、y t And z t The components of the target position vector on three axes in the reference inertial coordinate system, x m 、y m And z m The components of the missile position vector on three axes in the reference inertial coordinate system are respectively.
It should be noted that the reference inertial coordinate system (ground coordinate system) xyz is defined as: the origin of coordinates is on the missile launching point (strictly speaking, the origin of coordinates is on the centroid of the launched instantaneous missile), OX is the intersection line of the missile path surface and the horizontal plane, the pointing target is positive, OY is positioned in the plane of the plumb and is vertical to OX, OZ is vertical to the plane of OXY, and a right-hand coordinate system is formed by OZ and other two axes.
Further, the line of sight inclination angle, the line of sight declination angle and the corresponding first derivative of the line of sight declination angle of the missile are calculated according to the formula:
s2: and introducing the residual flight time variable of the missile in a relative motion equation set of the missile and the target to construct a three-dimensional cooperative guidance model.
In the present embodiment, step S2 includes:
s2.1: and defining state variables according to a relative motion equation set of the missile and the target, and constructing a state equation of the multi-missile system according to the state variables.
Specifically, the state variables are defined as follows:
x 1i ＝r i ，
x 3i ＝q εi -q εid ，
x 5i ＝q βi -q βid ，
wherein q is εid Is the desired line of sight inclination, q, of the ith missile βid The expected line of sight declination of the ith missile.
And then, constructing a state equation of the multi-missile system according to the state variables:
s2.2: and introducing a missile residual flight time variable into the state equation and updating the state equation to obtain a three-dimensional cooperative guidance model.
Specifically, in order to achieve the purpose that all missiles attack the target simultaneously, the residual flight time variable of the missiles is introduced
Differentiating it gives:
and (3) taking the residual flight time as a new state variable of the three-dimensional cooperative guidance model to be constructed, and obtaining a new bullet relative motion equation set, namely the three-dimensional cooperative guidance model:
wherein the content of the first and second substances,
for target motion, the accelerations are bounded, so the following assumptions are made: | d ri |＜ω r ,|d qεi |＜ω qε ,|d qβi |＜ω qβ Wherein, ω is r ,ω qε ,ω qβ Is a positive constant value.
S3: and acquiring the acceleration of each missile in the visual line direction of the missile target according to the three-dimensional cooperative guidance model, so that a plurality of missiles can cooperatively attack the target or defend the interception target at the same time.
Specifically, step S3 of the present embodiment includes:
s3.1: setting the Total time of flight t of the missile fi ＝t+t goi Wherein, t goi The remaining flight time of the ith missile is shown and t is the time of flight of the missile.
S3.2: differentiating the total time of flight of the missile and dividing t goi The carry-in may result in:
wherein the content of the first and second substances,
defined as a virtual control quantity.
S3.3: according to the fixed time consistency theory, the acceleration which can enable the total flight time of all missiles to be converged in the fixed time and enable the residual flight time of all missiles to be converged to the consistent sight line direction in the fixed time is obtained.
In order to realize the convergence of the multi-missile system in fixed time, according to the fixed time consistency theory, a control protocol is designed as follows:
wherein h is 0 ,h 1 ,h 2 More than 0, alpha is less than beta, alpha gamma is less than 1, beta gamma is more than 1, all of which are constant coefficients, x i ＝t fi 。
Based on this, the total time of flight t that enables each missile can be obtained fi Converge in a fixed time and allow the remaining flight times t of all missiles goi Cooperative acceleration converging to a consistent line of sight direction over a fixed time:
wherein, a Mri Represents the acceleration of the ith missile in the direction of the line of sight of the missile,
s4: and constructing a fixed time disturbance observer of the target acceleration in the pitching direction and the yawing direction and estimating a target acceleration term in a sight line coordinate system.
The target acceleration item is an unknown factor for the design of a guidance law in an actual guidance system and cannot be directly measured, so that a fixed time interference observer is provided to respectively estimate two components of the target normal acceleration in a state equation in the normal direction of a sight line, and according to the theory of the fixed time observer, the fixed time convergence interference observers in the pitching direction and the yawing direction are respectively designed as follows:
wherein z is 1i ，z 2i Are each x 4i ，d qεi Estimated value of θ 1 ≥0，η 1 ,η 2 Is greater than 0 and
z 3i ，z 4i are each x 6i ，d qβi Estimated value of theta 1 ,θ 2 ≥0，η 1 ,η 2 ,η 3 ,η 4 Is greater than 0 and
ε 1 ，ε 3 e (0.5,1) and e 2 ，ε 4 E (1,1.5), t (·) is a nonlinear correction term expressed as follows:
so that the target acceleration term d estimated by the ith missile can be obtained according to the formula qεi And d qβi 。
S5: and acquiring the acceleration of the missile in the normal direction of the missile sight line according to the three-dimensional cooperative guidance model and the estimated target acceleration item, so that a plurality of missiles can cooperatively attack a target or defend an interception target at the same time.
In the present embodiment, step S5 includes:
s5.1: and according to a guidance model which is perpendicular to the sight direction in the pitching plane, constructing a segmented continuous fixed-time nonsingular terminal sliding mode surface and a fixed-time convergence approximation law, and obtaining an acceleration control law of the missile in the missile target sight normal direction to the pitching plane.
The guidance model perpendicular to the direction of the line of sight in the pitch plane can be obtained from step S2 as follows:
in order to solve the singularity problem and make all missile sight line inclination angles converge to a specified angle within a fixed time, the embodiment constructs a segmented continuous fixed-time nonsingular terminal sliding mode surface by using the guidance model:
wherein delta 1 ，δ 2 ＞0，λ 1 ＞λ 2 ，1＜λ 2 < 2, all the above are constant coefficients, the values of which are given in the later simulation experiments,
epsilon is a small positive number.
In order to reduce the buffeting of the guidance system and enable the multi-missile system to converge in a fixed time, the embodiment further provides a fixed time convergence approximation law based on the gain parameter adaptation:
wherein p is 1 ,q 1 ＞1,k 1 ,k 2 > 0, and to ensure convergence speed, typically k 1 ,k 2 The values of the two signals are all taken to be larger values,
for adaptive gain values, primarily for adjusting sliding-mode switching terms
The convergence direction of the variable-angle sliding mode is mainly related to the change rate of the sight angle and the sliding mode surface, and is a continuously decreasing function, the convergence speed is ensured by selecting a larger initial value, and the change rate of the sight angle and the sliding mode surface are continuously reduced, so that the final convergence later stage can not generate larger control quantity, the system state can not continuously pass through the sliding mode surface to generate buffeting, and the large-control mode can weaken the defect that the buffeting is generated due to huge controlThe adaptive gain is adjusted by the following function:
wherein, κ 1 Indicating the set intermediate parameters.
Therefore, the acceleration control law of the missile in the pitching plane of the missile normal line is as follows:
wherein, the time differential terms related to the continuous symbol terms are:
s5.2: and according to a guidance model which is vertical to the sight direction in the lateral plane, constructing a segmented continuous fixed-time nonsingular terminal sliding mode surface and a fixed-time convergence approach law in the lateral plane, and obtaining an acceleration control law of the missile from a missile sight method to the lateral plane.
From step S2, a guidance model in the lateral plane can be obtained, which has a certain similarity to the pitch plane, the design principle of the directional acceleration command is the same as that of the pitch plane acceleration command, and the guidance model in the lateral plane perpendicular to the direction of the line of sight is:
the non-singular terminal sliding mode surface with the segmented continuous fixed time is as follows:
wherein, delta 3 ,δ 4 ＞0,λ 3 ＞λ 4 ,1＜λ 4 ＜2，
Epsilon is a small positive number.
In order to suppress the chattering of the guidance system and to make the system converge in a fixed time, the approximation law of the yaw direction is designed as follows:
wherein p is 2 ,q 2 ＞1,k 3 ,k 4 > 0, and to guarantee convergence speed, k is normal 3 ,k 4 The values of the two are all taken to be larger,
for the adaptive gain value, the adaptive gain is adjusted by the function:
wherein, κ 2 Indicating the set intermediate parameters.
Therefore, the acceleration control law of the missile on the missile normal lateral deviation plane is obtained as follows:
wherein, the time differential terms related to the successive symbol terms are:
to be explainedThe sliding mode approach law of the lateral plane and the form of the acceleration command are basically similar to those of the pitch plane, but the parameters are slightly different in selection because the lateral plane acceleration command is coupled with the pitch plane and the coupling term and the target motion acceleration estimation term are negative values. Secondly, consider using a Gaussian error function
The generation of chattering is reduced instead of the switching function.
S6: and obtaining three acceleration components of the missile in a trajectory coordinate system by utilizing the acceleration of the missile in the direction of the visual line of the missile and the normal direction of the visual line.
According to the steps S3, S4 and S5, three acceleration commands of the missile in the line-of-sight coordinate system can be obtained, according to the transformation matrix of the reference inertial coordinate system and the ballistic coordinate system:
referring to a transformation matrix between the inertial coordinate system and the line of sight coordinate system:
wherein, theta k ,ψ k (k-mi, t) is the trajectory inclination, deviation angle of the missile and the speed inclination and deviation angle of the target, in particular θ mi And psi mi Is the trajectory inclination and trajectory deviation angle of the ith missile t And psi t Respectively representing the track inclination and the drift angle of the target. q. q.s ε And q is β Respectively representing the sight line inclination angle and the sight line deflection angle of the missile.
Note that the ballistic coordinate system OX v Y v Z v Is defined as: with origin of coordinates at the missile's instantaneous centroid, OX v Axis coincident with missile velocity vector, OY v The axis lying in the plumb plane containing the velocity vector and perpendicular to OX v Axis, pointing upwards positive, OZ v Shaft and OX v Y v The planes are vertical, and a right-hand coordinate system is formed by the other two axes.
Further, two components of the tangential acceleration and the normal acceleration of the missile moving direction can be obtained from the acceleration components in the line-of-sight coordinate system obtained in steps S3, S4, and S5 by the two transformation matrices described above:
wherein, a mix ,a miy ,a miz Acceleration components of the ith missile along three coordinate axes in a ballistic coordinate system are respectively shown.
S7: and according to the three acceleration components under the ballistic coordinate system obtained in the step S6, iteratively updating the speed and the position of the missile in the cooperative attack task, so that a plurality of missiles arrive at the target at the same time, and the multi-missile distributed cooperative attack large maneuvering target or defense interception maneuvering target battle task is completed.
The multi-missile three-dimensional cooperative guidance method of the embodiment of the invention is further explained with reference to the drawings and the embodiment.
(1) A multi-missile distributed system consisting of four missiles is arranged to cooperatively intercept a task of a high-speed large maneuvering target, the topological structure of a communication network among the missiles is shown in figure 4, and the communication network is undirected and communicated. The initial motion state parameters of the missile and the target are shown in table 1:
TABLE 1 initial State of motion parameters for missile and target
(2) And setting other parameters.
In order to meet the guidance requirement, parameters in the guidance law need to be set, and finally, the sight line direction parameters are set as follows: h is 0 ＝7,h 1 ＝h 2 1.5, α ═ 0.4, β ═ 1.6, γ ═ 0.9; normal pitch system of line of sightThe parameters are set as: delta 1 ＝5,δ 2 ＝8，λ 1 ＝3,λ 2 ＝1.1，k 1 ＝2500,k 2 ＝2500，p 1 ＝1.4，q 1 ＝0.89，
κ 1 ＝10.9,ν 1 ＝50,ν 2 ＝50,ν 3 50, 0.001; the guidance parameters in the normal-to-lateral-deviation direction of the sight line are set as follows: delta 3 ＝9，δ 4 ＝8，λ 3 ＝2，λ 4 ＝1.7，k 3 ＝250,k 4 ＝250，p 2 ＝1.5,q 2 ＝0.9，
κ 2 ＝5,ν 4 ＝50,ν 5 ＝50,ν 6 50. The upper bound of the acceleration of the missile is set to 35g, and g is 9.8m/s 2 . Designing target maneuvering parameters:
TABLE 2 simulation results of miss distance, guidance time and angle error
Under the condition of the parameter setting, the cooperative guidance simulation result is shown in the table 2, and it can be seen that the guidance time of each intercepting missile is the same, the miss distance and the line-of-sight angle error at the intercepting moment are in a reasonable range, and the cooperative guidance law constructed by the embodiment of the invention has higher guidance precision. The simulation results are shown in fig. 5 to 7. Fig. 5 to 7 are a three-dimensional flight trajectory diagram of four missiles attacking a target and a trajectory diagram decomposed into a horizontal plane and a pitching plane, respectively, and it can be seen that the missiles have large maneuvering adjustment in the initial stage, the change of the rear section trajectory tends to be smooth, and the four missiles also achieve the effect of cooperatively intercepting the target from both sides of the target. As is clear from fig. 8 and 9, the remaining flight times of the four missiles at the initial time are all different, and the four missiles can simultaneously intercept the maneuvering target after reaching the same value after 0.5s under the action of the fixed time control protocol. Fig. 10 and 11 show that, despite the different initial situations and different target maneuvers, the line-of-sight inclination and declination of the four missiles converge to the vicinity of the expected values in a fixed time. Fig. 12 and 13 show that the slip-form surfaces of all missiles converge to zero within a fixed time even when large maneuvering targets are encountered. FIG. 16 shows that the acceleration commands of four missiles in the sight-line direction are all in a reasonable range under three conditions, and the four missiles gradually converge to a curve similar to the acceleration of the target sight-line direction along with the guidance time after the four missiles are briefly saturated. It can be seen from the graph and fig. 15 that the acceleration commands of the four missiles in the normal direction of the line of sight are also in a reasonable range, the acceleration of the initial guidance segment is large, so that the angular velocity of the line of sight can be rapidly converged to zero in a fixed time, and the acceleration command is correspondingly reduced as the angular velocity of the line of sight approaches zero.
The embodiment of the invention mainly researches the problem of cooperative attack of a plurality of missiles on a maneuvering target in a three-dimensional space, and designs a fixed time cooperative guidance law with a sight angle and attack time constraint. Firstly, a three-dimensional space missile-target relative motion equation is constructed, and a cooperative guidance model considering the line-of-sight angle constraint and the attack time constraint is established. Secondly, corresponding cooperative guidance laws are respectively designed in the sight line direction and the sight line normal direction, wherein the cooperative guidance laws are designed in the sight line direction based on the multi-agent fixed time consistency theory, and the condition that each missile attacks a target at the same time is guaranteed; a novel fixed-time rapid nonsingular terminal sliding mode surface is designed in the direction of a line-of-sight method, has the nonsingular characteristic, and ensures that the line-of-sight angle of each missile is converged to a set value in fixed time through designing a self-adaptive approach law, so that spatial cooperation is realized. Meanwhile, a fixed-time disturbance observer is constructed to estimate the target acceleration. Finally, the effectiveness of the guidance law is verified through simulation.
The embodiment of the invention designs a self-adaptive approach law in the direction of a line of sight method, and based on a designed fixed-time fast nonsingular terminal sliding mode surface, the line of sight angle of each missile can be controlled to be converged to a set value in fixed time, and spatial cooperation can be realized. The fixed time interference observer can estimate the maneuvering acceleration of the target, can eliminate the influence of the maneuvering of the target on a multi-missile system, does not need to assume for a guidance system, and is more practical.
Still another embodiment of the present invention provides a storage medium, wherein the storage medium stores a computer program for executing the steps of the multi-missile three-dimensional collaborative guidance method based on the attack time and angle joint constraints in the above embodiments. Still another aspect of the present invention provides an electronic device, which includes a memory and a processor, where the memory stores a computer program, and the processor implements the steps of the multi-missile three-dimensional cooperative guidance method based on attack time and angle joint constraints, as described in the above embodiment, when calling the computer program in the memory. Specifically, the integrated module implemented in the form of a software functional module may be stored in a computer readable storage medium. The software functional module is stored in a storage medium and includes several instructions to enable an electronic device (which may be a personal computer, a server, or a network device) or a processor (processor) to execute some steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.
Claims (10)
1. A multi-missile three-dimensional cooperative guidance method based on attack time and angle joint constraint is characterized by comprising the following steps:
establishing a relative motion model and a relative motion equation set of the missile and the target by utilizing the relative motion information of the missile and the target;
introducing a residual flight time variable of the missile into a relative motion equation set of the missile and the target, and constructing a three-dimensional cooperative guidance model;
acquiring the acceleration of each missile in the visual line direction of the missile target according to the three-dimensional cooperative guidance model so that a plurality of missiles can reach the target at the same time;
constructing a fixed time disturbance observer of the target acceleration in the pitching direction and the yawing direction and estimating a target acceleration item under a sight line coordinate system;
acquiring the acceleration of the missile in the normal direction of the target sight line of the missile according to the three-dimensional cooperative guidance model and the estimated target acceleration item so that a plurality of missiles can reach the target at the same time;
acquiring three acceleration components of the missile in a trajectory coordinate system by using the acceleration of the missile in the direction of the sight line of the missile and the normal direction of the sight line;
and continuously updating the speed and the position of each missile in the flight process by utilizing the three acceleration components, thereby realizing that a plurality of missiles reach the target at the same time.
2. The multi-missile three-dimensional cooperative guidance method based on attack time and angle joint constraints is characterized in that the relative motion equation system of the missile and the target is as follows:
wherein r is i The distance between the two eyes is the distance of the bullet,
the first derivative of the shot distance with respect to time,
as the second derivative of the distance of the bullet eyes with respect to time, q εi Is the line of sight inclination of the ith missile, q βi Is the view declination of the ith missile,
the first derivative of the line of sight inclination of the ith missile with respect to time,
the first derivative of the line-of-sight declination of the ith missile with respect to time,
the second derivative of the line-of-sight inclination angle of the ith missile with respect to time,
is the first derivative of the line of sight declination of the ith missile with respect to time, theta mi ,ψ mi The trajectory inclination angle and deflection angle theta of the ith missile t ,ψ t Respectively the target speed dip and slip angle, a Mir ,a Miε ,a Miβ The components of the acceleration of the ith missile on three axes under the sight line coordinate system; a is Tr ,a Tε ,a Tβ Are the components of the target acceleration in three axes under the line-of-sight coordinate system.
3. The multi-missile three-dimensional cooperative guidance method based on attack time and angle common constraints as claimed in claim 2 is characterized in that a missile residual flight time variable is introduced into a relative motion equation set of a missile and a target to construct a three-dimensional cooperative guidance model, and the method comprises the following steps:
defining a state variable according to a relative motion equation set of the missile and the target and constructing a state equation according to the state variable;
and introducing a missile residual flight time variable into the state equation and updating the state equation to obtain a three-dimensional cooperative guidance model.
4. The multi-missile three-dimensional cooperative guidance method based on attack time and angle joint constraints as claimed in claim 3, wherein the three-dimensional cooperative guidance model is as follows:
wherein x is 1i ＝r i ，
x 3i ＝q εi -q εid ，
x 5i ＝q βi -q βid ，
A variable representing the time of flight remaining for the missile,
representing the first derivative of the missile time-of-flight residual variable with respect to time,
representing the target acceleration term estimated with the ith missile.
5. The multi-missile three-dimensional cooperative guidance method based on attack time and angle joint constraint according to claim 4, wherein the step of obtaining the acceleration of each missile in the direction of the visual line of the missile target according to the three-dimensional cooperative guidance model so that the multiple missiles can reach the target at the same time comprises the following steps:
setting the Total time of flight t of the missile fi ＝t+t goi Wherein, t goi Representing the residual flight time of the ith missile, and t representing the flying time of the missile;
differentiating the total flight time of the missile to obtain:
wherein, the first and the second end of the pipe are connected with each other,
representing a virtual control quantity;
according to the fixed time consistency theory, obtaining the acceleration which can make the total flight time of all missiles converge in the fixed time and make the residual flight time of all missiles converge to the consistent sight line direction in the fixed time:
wherein, the first and the second end of the pipe are connected with each other,
h 0 ,h 1 ,h 2 the coefficients are constant values when alpha is more than 0, alpha is more than beta, alpha gamma is more than 1, and beta gamma is more than 1.
6. The multi-missile three-dimensional cooperative guidance method based on attack time and angle joint constraints according to claim 5, wherein the fixed time convergence disturbance observer is:
wherein, z 1i ，z 2i Are respectively x 4i ，d qεi Estimated value of θ 1 ≥0，η 1 ,η 2 Is greater than 0 and
z 3i ，z 4i are respectively x 6i ，d qβi Estimated value of theta 1 ,θ 2 ≥0，η 1 ,η 2 ,η 3 ,η 4 Is greater than 0 and
ε 1 ，ε 3 ∈(0.5,1)，ε 2 ，ε 4 e (1,1.5), and t (·) is a nonlinear correction term.
7. The multi-missile three-dimensional cooperative guidance method based on attack time and angle joint constraints as recited in claim 4, wherein the step of obtaining the acceleration of the missile in the normal direction of the missile target sight line according to the three-dimensional cooperative guidance model and the estimated target acceleration term so that a plurality of missiles can reach the target at the same time comprises the following steps:
according to a guidance model which is vertical to the sight direction in the pitching plane, constructing a segmented continuous fixed time nonsingular terminal sliding mode surface and a fixed time convergence approximation law in the lateral plane, and obtaining an acceleration control law of the missile in the missile target sight normal direction to the pitching plane;
and according to a guidance model which is perpendicular to the sight direction in the lateral plane, constructing a segmented continuous fixed-time nonsingular terminal sliding mode surface and a fixed-time convergence approximation law in the lateral plane, and obtaining an acceleration control law of the missile in the missile eye sight direction to the lateral plane.
8. The multi-missile three-dimensional cooperative guidance method based on attack time and angle joint constraints as claimed in claim 7 is characterized in that according to a guidance model perpendicular to a sight line direction in a pitching plane, a segmented continuous fixed-time nonsingular terminal sliding mode surface and a fixed-time convergence approximation law in a lateral plane are constructed, and an acceleration control law of a missile in a missile target sight line direction to the pitching plane is obtained, and the method comprises the following steps:
constructing a segmented continuous fixed-time nonsingular terminal sliding mode surface according to a guidance model perpendicular to the sight direction in the pitching plane:
wherein, delta 1 ，δ 2 ＞，λ 1 ＞λ 2 ，1＜λ 2 Less than 2, are all constant value coefficients,
ε is a positive number;
constructing a fixed time convergence approximation law based on gain parameter self-adaptation:
wherein p is 1 ,q 1 ＞1,k 1 ,k 2 ＞0，
Is an adaptive gain value;
and obtaining an acceleration control law of the missile in the pitching plane by the missile sight line method according to the fixed time convergence approach law, wherein the acceleration control law comprises the following steps:
9. a storage medium, characterized in that the storage medium stores a computer program for executing the steps of the multi-missile three-dimensional cooperative guidance method based on the attack time and angle joint constraint according to any one of claims 1 to 8.
10. An electronic device, characterized by comprising a memory and a processor, wherein the memory stores a computer program, and the processor, when calling the computer program in the memory, implements the steps of the multi-missile three-dimensional cooperative guidance method based on the attack time and angle joint constraint according to any one of claims 1 to 8.
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| CN115268503A (en) * | 2022-09-28 | 2022-11-01 | 中国人民解放军国防科技大学 | Multi-aircraft three-dimensional cooperative guidance method for removing singularity |
| CN117193336A (en) * | 2023-09-12 | 2023-12-08 | 中国船舶集团有限公司第七一九研究所 | Underwater vehicle cooperative guidance method based on time and angle constraint |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115268503A (en) * | 2022-09-28 | 2022-11-01 | 中国人民解放军国防科技大学 | Multi-aircraft three-dimensional cooperative guidance method for removing singularity |
| CN115268503B (en) * | 2022-09-28 | 2023-01-10 | 中国人民解放军国防科技大学 | Multi-aircraft three-dimensional cooperative guidance method for removing singularity |
| CN117193336A (en) * | 2023-09-12 | 2023-12-08 | 中国船舶集团有限公司第七一九研究所 | Underwater vehicle cooperative guidance method based on time and angle constraint |
| CN117193336B (en) * | 2023-09-12 | 2024-03-22 | 中国船舶集团有限公司第七一九研究所 | Underwater vehicle cooperative guidance method based on time and angle constraint |
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