A three-dimensional cooperative guidance method for multiple missiles based on joint constraints of attack time and angle

Abstract

The present invention discloses a multi-missile three-dimensional cooperative guidance method based on joint constraints of attack time and angle, including: establishing a relative motion model and a relative motion equation group between missiles and targets; introducing a missile remaining flight time variable to construct a three-dimensional cooperative guidance model; obtaining the acceleration of each missile in the missile-target line of sight direction; constructing a fixed-time interference observer of the target acceleration in the pitch direction and the yaw direction and estimating the target acceleration term in the line of sight coordinate system; obtaining the acceleration of the missile in the normal direction of the missile-target line of sight according to the three-dimensional cooperative guidance model and the estimated target acceleration term; obtaining three acceleration components of the missile in the ballistic coordinate system; and continuously updating the speed and position of each missile during flight using the three acceleration components, thereby realizing that multiple missiles arrive at the target at the same time. The present invention can control the line of sight angle of each missile to converge to a set value within a fixed time, and can realize spatial coordination.

Description

Technical Field

[0001] The invention belongs to the technical field of missile guidance and control, and in particular relates to a three-dimensional collaborative guidance method for multiple missiles based on joint constraints of attack time and angle. Background Art

[0002] With the rapid development of aerospace technology and scientific and technological forces, the defense capability and maneuverability of important targets are increasing day by day, and the reaction time to missiles is also shortening. The traditional "one-to-one" strike method is difficult to complete the task of high-precision strike targets. In order to adapt to the complex and changing space environment, a strategy of using multiple missiles to coordinately attack targets is proposed. By adding communication equipment to a single missile body, the information obtained by each missile is collected and fully processed using the communication network to control the guided flight of the missile group, which has given rise to the embryo of a coordinated strike system of multiple missile systems. Coordinated guidance of multiple missiles can not only improve the comprehensive strike capability and the probability of hitting, but also complete tasks that traditional single missiles cannot complete. Therefore, in the execution of modern aerospace missions, the study of the coordinated guidance law of multiple missiles has very important engineering significance and has received widespread attention.

[0003] In the early research of cooperative guidance, the main focus was on attacking stationary or slow-moving targets, and the attack time was preset. In 2006, Jeon et al. first introduced the impact-time control guidance (ITCG) and applied it to salvo missions. Later, Jeon et al. expanded ITCG to simultaneously control the attack time and attack angle. However, since there was no information exchange between the missiles, it was not really cooperative in essence. In order to achieve truly cooperative guidance, multi-agent consistency theory was used to design cooperative guidance laws. At present, most of the relevant consistency cooperative guidance laws are based on finite time control theory. Many literatures design second-order sliding mode guidance laws in the line of sight direction to ensure that multiple missiles reach the target at the same time. In the line of sight normal direction, adaptive laws and terminal sliding modes are used to establish finite time guidance laws, forcing missiles to attack targets at the desired line of sight angles. Although there are many references that have made improvements in the terminal sliding surface, approaching law, and state error, they all combine finite time control theory with terminal sliding mode theory.

[0004] First, the current design of the cooperative guidance law basically adopts the finite time convergence theory. The finite time convergence boundary is related to the initial state of the multi-missile system. In actual guidance, the specific initial motion state of the missile and target cannot be predicted in advance, and the convergence time obtained by different initial conditions is also different. It may be due to the relationship between the initial state of the system that the system cannot converge. Secondly, the current research is basically carried out in two-dimensional space, but the actual guidance occurs in three-dimensional space. Therefore, it is necessary to deeply study the cooperative guidance motion model in three-dimensional space to meet the actual air combat needs. In addition, for large maneuvering targets, the target acceleration is a very important unknown factor for the design of the guidance law, which cannot be directly obtained through the measurement device. The current research on cooperative guidance assumes that the missile can directly obtain the target acceleration, while the actual target maneuver is unknown to the missile. At the same time, the current research has relatively low cooperative interception accuracy in the target large maneuvering scenario. Summary of the invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a three-dimensional collaborative guidance method for multiple missiles based on joint constraints of attack time and angle. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] The present invention provides a three-dimensional collaborative guidance method for multiple missiles based on joint constraints of attack time and angle, comprising:

[0007] Using the relative motion information between the missile and the target, a relative motion model and a relative motion equation group between the missile and the target are established;

[0008] The missile's remaining flight time variable is introduced into the relative motion equations between the missile and the target to construct a three-dimensional cooperative guidance model.

[0009] According to the three-dimensional collaborative guidance model, the acceleration of each missile in the missile-target line of sight direction is obtained so that multiple missiles can reach the target at the same time;

[0010] Construct a fixed-time disturbance observer of the target acceleration in the pitch and yaw directions and estimate the target acceleration term in the line-of-sight coordinate system;

[0011] According to the three-dimensional collaborative guidance model and the estimated target acceleration term, the acceleration of the missile in the normal direction of the missile-target line of sight is obtained so that multiple missiles can reach the target at the same time;

[0012] Using the missile's acceleration in the missile-target line of sight direction and the line of sight normal direction, the three acceleration components of the missile in the ballistic coordinate system are obtained;

[0013] The three acceleration components are used to continuously update the speed and position of each missile during flight, thereby achieving that multiple missiles arrive at the target at the same time.

[0014] In one embodiment of the present invention, the relative motion equations between the missile and the target are:

[0015]

[0016] Among them, r i is the distance between the projectile and the target, is the first-order derivative of the missile-target distance with respect to time, is the second-order derivative of the missile-target distance with respect to time, q εi is the line of sight inclination of the i-th missile, q βi is the line of sight deflection angle of the i-th missile, is the first-order derivative of the line of sight angle of the ith missile with respect to time, is the first-order derivative of the line of sight angle of the ith missile with respect to time, is the second-order derivative of the line of sight inclination of the ith missile with respect to time, is the first-order derivative of the line of sight angle of the ith missile with respect to time, θ mi ,ψ mi are the ballistic inclination and deflection angle of the i-th missile, θ t ,ψ t are the velocity inclination and deflection angle of the target, respectively, Mir ,a Miε ,a Miβ is the acceleration component of the i-th missile on the three axes in the line of sight coordinate system; a Tr ,a Tε ,a Tβ are the components of target acceleration on the three axes in the line of sight coordinate system.

[0017] In one embodiment of the present invention, a missile remaining flight time variable is introduced into the relative motion equations between the missile and the target to construct a three-dimensional collaborative guidance model, including:

[0018] Defining state variables according to a set of relative motion equations between the missile and the target and constructing state equations according to the state variables;

[0019] A missile remaining flight time variable is introduced into the state equation and the state equation is updated to obtain a three-dimensional collaborative guidance model.

[0020] In one embodiment of the present invention, the three-dimensional collaborative guidance model is:

[0021]

[0022] Among them, x 1i =r i , x 3i =q εi -qεid , x 5i =q βi -q βid ,

[0023] represents the missile's remaining flight time variable, represents the first-order derivative of the missile's remaining flight time variable with respect to time, represents the target acceleration term estimated using the i-th missile.

[0024] In one embodiment of the present invention, according to the three-dimensional collaborative guidance model, obtaining the acceleration of each missile in the missile-target line of sight direction so that multiple missiles can reach the target at the same time includes:

[0025] Set the total flight time of the missile t fi =t+t goi , where t goi represents the remaining flight time of the ith missile, and t represents the flight time of the missile;

[0026] Differentiating the total flight time of the missile yields:

[0027]

[0028] in, represents the virtual control quantity;

[0029] According to the fixed time consistency theory, the acceleration in the line of sight direction that can make the total flight time of all missiles converge within a fixed time and make the remaining flight time of all missiles converge to a consistent value within a fixed time is obtained:

[0030]

[0031] in, h0,h1,h2>0,α<β,αγ<1,βγ>1, all are constant coefficients.

[0032] In one embodiment of the present invention, the fixed time convergence interference observer is:

[0033]

[0034] Among them, z 1i , z 2i x 4i , d qεi The estimated value of θ1≥0, η1,η2>0 and z 3i , z 4i x6i , d qβi The estimated value of θ1,θ2≥0,η1,η2,η3,η4>0 and ε1, ε3∈(0.5,1), ε2, ε4∈(1,1.5), t(·) is the nonlinear correction term.

[0035] In one embodiment of the present invention, according to the three-dimensional collaborative guidance model and the estimated target acceleration term, obtaining the acceleration of the missile in the normal direction of the missile-target line of sight so that multiple missiles can reach the target at the same time includes:

[0036] According to the guidance model perpendicular to the line of sight in the pitch plane, the piecewise continuous fixed-time non-singular terminal sliding mode surface and fixed-time convergence approach law in the lateral plane are constructed, and the acceleration control law of the missile in the normal pitch plane of the missile-target line of sight is obtained.

[0037] According to the guidance model in the lateral plane perpendicular to the line of sight, the piecewise continuous fixed-time non-singular terminal sliding mode surface and fixed-time convergence law in the lateral plane are constructed, and the acceleration control law of the missile in the lateral plane normal to the missile-target line of sight is obtained.

[0038] In one embodiment of the present invention, according to the guidance model perpendicular to the line of sight in the pitch plane, a piecewise continuous fixed-time non-singular terminal sliding mode surface and a fixed-time convergence approach law in the lateral plane are constructed, and the acceleration control law of the missile in the normal pitch plane of the missile-target line of sight is obtained, including:

[0039] According to the guidance model perpendicular to the line of sight in the pitch plane, a piecewise continuous fixed-time non-singular terminal sliding surface is constructed:

[0040]

[0041] Among them, δ1, δ2>0, λ1>λ2, 1<λ2<2, are all constant coefficients. ε is a positive number;

[0042] Construct a fixed-time convergence law based on gain parameter adaptation:

[0043]

[0044] Among them, p1,q1>1,k1,k2>0, is the adaptive gain value;

[0045] According to the fixed time convergence approach law, the acceleration control law of the missile in the normal pitch plane of the missile-target line of sight is obtained as follows:

[0046]

[0047] Another aspect of the present invention provides a storage medium storing a computer program for executing the steps of the multi-missile three-dimensional collaborative guidance method based on the joint constraints of attack time and angle as described in any one of the above embodiments.

[0048] Another aspect of the present invention provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and when the processor calls the computer program in the memory, it implements the steps of the three-dimensional collaborative guidance method for multiple missiles based on the common constraints of attack time and angle as described in any of the above embodiments.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] 1. The present invention extends the commonly used two-dimensional guidance model to three-dimensional space, constructs a three-dimensional space missile-target relative motion model, and decouples the missile guidance model into the line of sight and the line of sight normal direction. In the line of sight direction, a collaborative guidance law is designed based on the fixed time consistency theory, which can realize that each missile attacks the target at the same time; in the line of sight normal direction, an adaptive convergence law is designed, and based on the designed fixed time fast non-singular terminal sliding mode surface, the line of sight angle of each missile can be controlled to converge to a set value within a fixed time, which can realize spatial coordination. The convergence time boundary of the guidance law designed by the present invention is independent of the initial conditions of the system, and is only related to the control parameters, topological structure and the total number of multi-agents. The proposed fixed time interference observer can estimate the target maneuvering acceleration, eliminate the influence of the target maneuvering on the multi-missile system, and does not require assumptions for the guidance system, which is more practical.

[0051] 2. In order to reflect the artificial encirclement and capture strategy, the present invention proposes to set the line of sight inclination angle and line of sight deflection angle of the expected collision to be "symmetrical" in pairs in advance, which can realize the encirclement and capture situation of multi-bullet trajectory space symmetry and better meet the needs of saturation attack.

[0052] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is a flow chart of a method for three-dimensional collaborative guidance of multiple missiles based on joint constraints of attack time and angle provided by an embodiment of the present invention;

[0054] Figure 2 It is a schematic diagram of a three-dimensional collaborative guidance process of multiple missiles based on joint constraints of attack time and angle provided by an embodiment of the present invention;

[0055] Figure 3 A three-dimensional geometric model of relative motion between a missile and a target provided by an embodiment of the present invention;

[0056] Figure 4 It is a communication topology diagram between multiple missiles provided by an embodiment of the present invention;

[0057] Figure 5 A three-dimensional motion trajectory diagram of a missile and a target obtained by using the method of an embodiment of the present invention;

[0058] Figure 6 is a motion trajectory diagram of a missile and a target in a pitch plane obtained by using the method of an embodiment of the present invention;

[0059] Figure 7 is a motion trajectory diagram of a missile and a target horizontal plane obtained by using the method of an embodiment of the present invention;

[0060] Figure 8 is a curve diagram of the change in relative distance between the missile and the target obtained by using the method of the embodiment of the present invention;

[0061] Fig. 9 is a missile remaining flight time variation curve diagram obtained by using the method of an embodiment of the present invention;

[0062] Fig.10 is a curve diagram of the change of the missile sight line inclination angle obtained by using the method of the embodiment of the present invention;

[0063] Fig.11 is a curve diagram of the change of the missile-to-eye sight line deflection angle obtained by using the method of an embodiment of the present invention;

[0064] Fig.12 is a sliding surface variation curve diagram of four missiles in pitch direction obtained by using the method of the embodiment of the present invention;

[0065] Fig.13 is a sliding surface variation curve diagram of four missiles in the lateral deflection direction obtained by using the method of the embodiment of the present invention;

[0066] Fig.14 is the acceleration a in the normal direction of the line of sight of the four missiles obtained by the method of the embodiment of the present invention Mε The change curve diagram of

[0067] Fig.15 is the acceleration a in the normal direction of the line of sight of the four missiles obtained by the method of the embodiment of the present invention Mβ The change curve diagram of

[0068] Fig.16 is the line-of-sight acceleration a of the four missiles obtained by the method of the embodiment of the present invention Mr 's change curve graph. DETAILED DESCRIPTION

[0069] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, the following is a detailed description of a three-dimensional collaborative guidance method for multiple missiles based on the joint constraints of attack time and angle proposed by the present invention, in combination with the accompanying drawings and specific implementation methods.

[0070] The above and other technical contents, features and effects of the present invention are clearly presented in the following detailed description of the specific implementation modes in conjunction with the accompanying drawings. Through the description of the specific implementation modes, the technical means and effects adopted by the present invention to achieve the predetermined purpose can be more deeply and specifically understood. However, the attached drawings are only for reference and explanation purposes and are not used to limit the technical solutions of the present invention.

[0071] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants are intended to cover non-exclusive inclusion, so that an article or device including a series of elements includes not only those elements, but also other elements that are not explicitly listed. In the absence of more restrictions, the elements defined by the statement "including one..." do not exclude the existence of other identical elements in the article or device including the elements.

[0072] See also Figure 1 , Figure 1 1 is a flowchart of a method for three-dimensional coordinated guidance of multiple missiles based on joint constraints of attack time and angle provided by an embodiment of the present invention. The method for three-dimensional coordinated guidance of multiple missiles includes:

[0073] S1: Use the relative motion information between the missile and the target to establish the relative motion model and relative motion equations between the missile and the target.

[0074] The relative motion information between the missile and the target is obtained from the reconnaissance system, such as the missile-target distance (the distance between the missile and the target), the missile's line of sight inclination and deflection, the target speed, the target's speed inclination and deflection, and the relative motion model between the missile and the target is obtained, such as Figure 3 As shown, where M i represents the i-th missile, T represents the target, V mi represents the speed of the ith missile, V t Indicates the target speed.

[0075] According to the relative motion model of the missile and the target, the relative motion equations of the missile and the target are obtained as follows:

[0076]

[0077] Among them, r i is the distance between the projectile and the target, is the first-order derivative of the missile-target distance with respect to time, is the second-order derivative of the missile-target distance with respect to time, q εi is the line of sight inclination of the i-th missile, q βi is the line of sight deflection angle of the i-th missile, is the first-order derivative of the line of sight angle of the ith missile with respect to time, that is, the rate of change of the line of sight angle, is the first-order derivative of the sight angle of the ith missile with respect to time, that is, the rate of change of the sight angle, is the second-order derivative of the line of sight inclination of the ith missile with respect to time, is the first-order derivative of the line of sight angle of the ith missile with respect to time, θ mi ,ψ mi are the ballistic inclination and deflection angle of the i-th missile, θ t ,ψ t are the velocity inclination and deflection angle of the target, respectively, Mir ,a Miε ,a Miβ is the acceleration component of the i-th missile on the three axes in the line of sight coordinate system; a Tr ,a Tε ,a Tβ are the components of target acceleration on the three axes in the line of sight coordinate system.

[0078] It should be noted that the line of sight coordinate system OX L Y L Z L Defined as: the origin of the coordinates is at the instantaneous center of mass of the missile, OX L The positive direction of the axis is the line of sight of the target, OY L The axis is located in the plumb plane and is parallel to OX L Vertical, pointing upward is positive, OZ L Axis and OX L Y L Z L The planes are perpendicular and form a right-handed coordinate system with the other two axes.

[0079] Furthermore, in order to facilitate the calculation of various guidance variables in the relative motion model between the missile and the target, this embodiment provides a calculation method for various state quantities of the missile and the target, and a calculation formula for the missile-target distance and its derivative:

[0080]

[0081] Among them, x r =x t -x m ,y r =yt -y m , z r =z t -z m , x t ,y t and z t are the components of the target position vector on the three axes in the reference inertial coordinate system, x m ,y m and z m They are the components of the missile position vector on the three axes in the reference inertial coordinate system.

[0082] It should be noted that the reference inertial coordinate system (ground coordinate system) OXYZ is defined as: its coordinate origin is at the missile launch point (strictly speaking, it should be taken at the center of mass of the missile at the moment of launch), OX is the intersection of the ballistic plane and the horizontal plane, pointing to the target is positive, OY is located in the plumb plane, perpendicular to OX, OZ is perpendicular to the OXY plane, and forms a right-handed coordinate system with the other two axes.

[0083] Furthermore, the missile's sight inclination angle, sight deflection angle and their corresponding first-order derivative calculation formulas are:

[0084]

[0085] S2: Introduce the missile's remaining flight time variable into the relative motion equations between the missile and the target to construct a three-dimensional collaborative guidance model.

[0086] In this embodiment, step S2 includes:

[0087] S2.1: Define state variables based on the relative motion equations between the missile and the target and construct the state equations of the multi-missile system based on the state variables.

[0088] Specifically, the state variables are defined as follows:

[0089] x 1i =r i , x 3i =q εi -q εid , x 5i =q βi -q βid ,

[0090] Among them, q εid is the expected line of sight inclination angle of the i-th missile, q βid is the expected line of sight deflection angle of the i-th missile.

[0091] Then, the state equation of the multi-missile system is constructed according to the state variables:

[0092]

[0093] S2.2: Introduce the missile remaining flight time variable into the state equation and update the state equation to obtain a three-dimensional collaborative guidance model.

[0094] Specifically, in order to achieve the goal of all missiles attacking the target at the same time, the missile remaining flight time variable is introduced Differentiating it gives:

[0095]

[0096] By taking the remaining flight time as the new state variable of the three-dimensional cooperative guidance model to be constructed, a new set of relative motion equations between the missile and the target can be obtained, namely the three-dimensional cooperative guidance model:

[0097]

[0098] in, For target motion, its acceleration is bounded, so the following assumptions are made: |d ri |<ω r ,|d qεi |<ω qε ,|d qβi |<ω qβ , where ω r ,ω qε ,ω qβ is a positive constant value.

[0099] S3: According to the three-dimensional collaborative guidance model, the acceleration of each missile in the missile-target line of sight direction is obtained, so that multiple missiles can collaboratively attack the target or defend against the target at the same time.

[0100] Specifically, step S3 of this embodiment includes:

[0101] S3.1: Set the total flight time t of the missile fi =t+t goi , where t goi represents the remaining flight time of the ith missile, and t represents the flight time of the missile.

[0102] S3.2: Differentiate the total flight time of the missile and divide t goi Bring in to get:

[0103]

[0104] in, Defined as a virtual control quantity.

[0105] S3.3: According to the fixed time consistency theory, the acceleration in the line of sight direction that can make the total flight time of all missiles converge within a fixed time and make the remaining flight time of all missiles converge to a consistent value within a fixed time is obtained.

[0106] In order to achieve the convergence of the multi-missile system within a fixed time, according to the fixed time consistency theory, the control protocol is designed as follows:

[0107]

[0108] Among them, h0, h1, h2>0, α<β, αγ<1, βγ>1, the above are all constant coefficients, x i =t fi .

[0109] Based on this, we can get the total flight time t of each missile fi Converges within a fixed time and makes the remaining flight time of all missiles t goi The coordinated acceleration converges to a consistent line of sight in a fixed time:

[0110]

[0111] Among them, a Mri represents the acceleration of the ith missile in the direction of the missile-target line of sight,

[0112]

[0113] S4: Construct a fixed-time disturbance observer of the target acceleration in the pitch and yaw directions and estimate the target acceleration term in the line-of-sight coordinate system.

[0114] The target acceleration term is an unknown factor in the guidance law design in the actual guidance system and cannot be directly measured. Therefore, a fixed-time disturbance observer is proposed to estimate the two components of the target normal acceleration in the line of sight normal direction in the state equation. According to the fixed-time observer theory, the fixed-time convergent disturbance observers in the pitch direction and the yaw direction are designed as follows:

[0115]

[0116] Among them, z 1i , z 2i They are x 4i , d qεi The estimated value of θ1≥0, η1,η2>0 and z 3i , z 4i They are x 6i , d qβiThe estimated value of θ1,θ2≥0,η1,η2,η3,η4>0 and ε1, ε3∈(0.5,1), while ε2, ε4∈(1,1.5), t(·) is a nonlinear correction term, expressed as follows:

[0117]

[0118] Therefore, the target acceleration term d estimated by the i-th missile can be obtained according to the above formula: qεi and d qβi .

[0119] S5: According to the three-dimensional collaborative guidance model and the estimated target acceleration term, the acceleration of the missile in the normal direction of the missile-target line of sight is obtained, so that multiple missiles can collaboratively attack the target or defend against the interception target at the same time.

[0120] In this embodiment, step S5 includes:

[0121] S5.1: Based on the guidance model in the pitch plane perpendicular to the line of sight, a piecewise continuous fixed-time non-singular terminal sliding mode surface and a fixed-time convergence law are constructed, and the acceleration control law of the missile in the pitch plane normal to the missile-target line of sight is obtained.

[0122] From step S2, the guidance model perpendicular to the line of sight in the pitch plane can be obtained as follows:

[0123]

[0124] In order to solve the singularity problem and make all missile sight angles converge to the specified angle within a fixed time, this embodiment uses the above guidance model to construct a piecewise continuous fixed-time non-singular terminal sliding mode surface:

[0125]

[0126]

[0127] Among them, δ1, δ2>0, λ1>λ2, 1<λ2<2, all of which are constant coefficients, and their values ​​are given in the simulation experiment later. ε is a small positive number.

[0128] In order to reduce the chattering of the guidance system and enable the multi-missile system to converge within a fixed time, this embodiment also proposes a fixed-time convergence law based on gain parameter adaptation:

[0129]

[0130] Among them, p1, q1>1, k1, k2>0, and in order to ensure the convergence speed, k1 and k2 are generally taken as larger values. is the adaptive gain value, which is mainly used to adjust the sliding mode switch term The size of , its convergence direction is mainly related to the line of sight angle change rate and the sliding surface, and is a decreasing function. By selecting a larger initial value, the convergence speed is guaranteed. At the same time, it is accompanied by the line of sight angle change rate and the sliding surface. The continuous decrease ensures that no large control amount will be generated in the final convergence stage, so that the system state will not continuously pass through the sliding surface to generate chattering, which can weaken the chattering problem caused by the huge control gain. The adaptive gain is adjusted by the following function:

[0131]

[0132] Among them, κ1 represents the set intermediate parameter.

[0133] Therefore, the acceleration control law of the missile in the normal pitch plane of the missile-target line of sight is:

[0134]

[0135] Among them, the time differential term of the continuous symbol term is:

[0136]

[0137] S5.2: Based on the guidance model in the lateral plane perpendicular to the line of sight, construct the piecewise continuous fixed-time non-singular terminal sliding mode surface and fixed-time convergence law in the lateral plane, and obtain the acceleration control law of the missile in the lateral plane normal to the missile-target line of sight.

[0138] The guidance model in the lateral plane can be obtained from step S2, which has certain similarities with the pitch plane. The design principle of the acceleration command in this direction is the same as that of the pitch plane acceleration command. The guidance model in the lateral plane perpendicular to the line of sight is:

[0139]

[0140] Its piecewise continuous fixed-time non-singular terminal sliding mode surface is:

[0141]

[0142] Among them, δ3, δ4>0, λ3>λ4, 1<λ4<2, ε is a small positive number.

[0143] In order to suppress the chattering of the guidance system and make the system converge within a fixed time, the reaching law of the lateral deviation direction is designed as follows:

[0144]

[0145] Among them, p2, q2>1, k3, k4>0, and in order to ensure the convergence speed, k3 and k4 are generally taken as larger values. is the adaptive gain value, and the adaptive gain is adjusted by the following function:

[0146]

[0147] Among them, κ2 represents the set intermediate parameter.

[0148] Therefore, the acceleration control law of the missile on the normal lateral deflection plane of the missile-target line of sight is obtained as:

[0149]

[0150] Among them, the time differential term of the continuous symbol term is:

[0151]

[0152] It should be noted that the sliding mode approach law and acceleration command form of the lateral plane are basically similar to those of the pitch plane. However, since the lateral plane acceleration command is coupled with the pitch plane, and the coupling term and the target motion acceleration estimation term are negative, the parameter selection is slightly different. Replace the switching function to reduce the generation of chattering.

[0153] S6: Using the missile's acceleration in the missile-target line of sight direction and the line of sight normal direction, obtain the three acceleration components of the missile in the ballistic coordinate system.

[0154] According to steps S3, S4 and S5, three acceleration instructions of the missile in the line of sight coordinate system can be obtained. The conversion matrix between the reference inertial coordinate system and the ballistic coordinate system is:

[0155]

[0156] The transformation matrix between the reference inertial coordinate system and the line of sight coordinate system:

[0157]

[0158] Among them, θ k ,ψ k (k = mi, t) is the missile's ballistic inclination and deflection angle and the target's velocity inclination and deflection angle. Specifically, θ mi and ψ mi is the ballistic inclination and ballistic deviation of the ith missile, θ t and ψ t Respectively represent the target's track inclination and deflection. ε and qβ They respectively represent the missile's line of sight inclination angle and line of sight deflection angle.

[0159] It should be noted that the ballistic coordinate system OX v Y v Z v Defined as: Its coordinate origin is at the instantaneous center of mass of the missile, OX v The axis coincides with the missile velocity vector, OY v The axis lies in the plumb plane containing the velocity vector and is perpendicular to OX v Axis, pointing upward is positive, OZ v Axis and OX v Y v The planes are perpendicular and form a right-handed coordinate system with the other two axes.

[0160] Furthermore, the two components of the tangential acceleration and the normal acceleration in the direction of movement of the missile can be obtained from the acceleration components in the line of sight coordinate system obtained in steps S3, S4 and S5 through the above two conversion matrices:

[0161]

[0162] Among them, a mix ,a miy ,a miz are the acceleration components of the ith missile along the three coordinate axes in the ballistic coordinate system.

[0163] S7: According to the three acceleration components in the ballistic coordinate system obtained in step S6, the missile speed and position in the coordinated attack mission are iteratively updated, so that multiple missiles can arrive at the target at the same time, so as to complete the combat mission of multi-missile distributed coordinated attack on large mobile targets or defense and interception of mobile targets.

[0164] The following is a further description of the multi-missile three-dimensional collaborative guidance method according to an embodiment of the present invention in conjunction with the accompanying drawings and embodiments.

[0165] (1) Suppose a multi-missile distributed system consisting of four missiles cooperates to intercept a high-speed and highly maneuverable target. The topology of the communication network between the missiles is as follows: Figure 4 As shown in Table 1, the communication network is undirected and connected. The initial motion state parameters of the missile and the target are shown in Table 1:

[0166] Table 1 Initial motion state parameters of missile and target

[0167]

[0168] (2) Other parameter settings.

[0169] In order to meet the guidance requirements, it is necessary to set the parameters in the guidance law. The final sight direction parameters are set to: h0 = 7, h1 = h2 = 1.5, α = 0.4, β = 1.6, γ = 0.9; the guidance parameters in the sight normal pitch direction are set to: δ1 = 5, δ2 = 8, λ1 = 3, λ2 = 1.1, k1 = 2500, k2 = 2500, p1 = 1.4, q1 = 0.89, κ1=10.9,ν1=50,ν2=50,ν3=50,ε=0.001; the guidance parameters in the normal lateral direction of the line of sight are set as follows:δ3=9,δ4=8,λ3=2,λ4=1.7,k3=250,k4=250,p2=1.5,q2=0.9, κ2=5,ν4=50,ν5=50,ν6=50. The upper limit of missile acceleration is set to 35g, g=9.8m / s 2 . Target maneuver parameter design:

[0170] Table 2 Simulation results of miss distance, guidance time and angle error

[0171]

[0172] Under the above parameter setting conditions, the collaborative guidance simulation results are shown in Table 2. It can be seen that the collaborative guidance law constructed by the embodiment of the present invention has the same guidance time for each interceptor missile, and the miss distance and line of sight angle error at the interception time are both within a reasonable range, with high guidance accuracy. Figures 5 to 7 shown. Figures 5 to 7 The three-dimensional flight trajectory diagrams of the four missiles attacking the target and the trajectory diagrams decomposed into the horizontal plane and the pitch plane respectively show that the missiles have a large maneuver adjustment in the initial stage, and the trajectory changes in the later stage tend to be gentle. The four missiles also achieve the effect of coordinated interception of the target from both sides of the target. Figure 8 and Fig. 9 It can be clearly seen that the remaining flight time of the four missiles is different at the initial moment. Under the fixed time control protocol, they reach the same value after 0.5s and can finally intercept the maneuvering target at the same time. Fig.10 and Fig.11 It shows that despite the different initial situations and target maneuvers, the line of sight inclination and deflection angles of the four missiles converge to near the expected values ​​within a fixed time. Fig.12 and Fig.13 It is shown that even when encountering a large maneuvering target, the sliding surface of all missiles converges to zero within a fixed time. Fig.16 It shows that the acceleration instructions of the four missiles in the line of sight direction in the three cases are all within a reasonable range, and gradually converge to a curve similar to the acceleration in the line of sight direction of the target as the guidance time increases after a short period of saturation. Fig.15It can be seen that the acceleration instructions of the four missiles in the line of sight normal direction are also within a reasonable range. The larger acceleration in the initial guidance stage can make the line of sight angular velocity converge to zero quickly within a fixed time, and as the line of sight angular velocity approaches zero, the acceleration instruction decreases accordingly.

[0173] The embodiment of the present invention mainly studies the problem of coordinated attack of multiple missiles on maneuvering targets in three-dimensional space, and designs a fixed-time cooperative guidance law with line of sight angle and attack time constraints. First, the missile-target relative motion equation in three-dimensional space is constructed, and a cooperative guidance model considering line of sight angle constraints and attack time constraints is established. Secondly, corresponding cooperative guidance laws are designed for the line of sight direction and the line of sight normal direction, respectively. Among them, a cooperative guidance law is designed in the line of sight direction based on the fixed-time consistency theory of multi-agents to ensure that each missile attacks the target at the same time; a novel fixed-time fast non-singular terminal sliding surface is designed in the line of sight normal direction, which has the characteristics of non-singularity. By designing an adaptive approaching law, it is ensured that the line of sight angle of each missile converges to the set value within a fixed time, and spatial coordination is achieved. At the same time, a fixed-time interference observer is constructed to estimate the target acceleration. Finally, the effectiveness of the guidance law is verified by simulation.

[0174] The embodiment of the present invention designs an adaptive convergence law in the line of sight normal direction, and based on the designed fixed-time fast non-singular terminal sliding surface, the line of sight angle of each missile can be controlled to converge to a set value within a fixed time, and spatial coordination can be achieved. The convergence time boundary of the guidance law designed by the present invention is independent of the initial conditions of the system, and is only related to the control parameters, topological structure and the total number of multi-agents. The proposed fixed-time interference observer can estimate the acceleration of the target maneuvering, and can eliminate the influence of the target maneuvering on the multi-missile system. No assumptions are required for the guidance system, which is more practical.

[0175] Another embodiment of the present invention provides a storage medium, wherein a computer program is stored in the storage medium, and the computer program is used to execute the steps of the three-dimensional collaborative guidance method for multiple missiles based on the joint constraints of attack time and angle described in the above embodiment. Another aspect of the present invention provides an electronic device, including a memory and a processor, wherein a computer program is stored in the memory, and when the processor calls the computer program in the memory, the steps of the three-dimensional collaborative guidance method for multiple missiles based on the joint constraints of attack time and angle as described in the above embodiment are implemented. Specifically, the above-mentioned integrated module implemented in the form of a software function module can be stored in a computer-readable storage medium. The above-mentioned software function module is stored in a storage medium, including several instructions for enabling an electronic device (which can be a personal computer, a server, or a network device, etc.) or a processor (processor) to execute some steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a disk or an optical disk.

[0176] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A three-dimensional collaborative guidance method for multiple missiles based on joint constraints of attack time and angle, characterized in that: include: Using the relative motion information between the missile and the target, a relative motion model and a relative motion equation group between the missile and the target are established; The missile's remaining flight time variable is introduced into the relative motion equations between the missile and the target, and a three-dimensional cooperative guidance model is constructed. According to the three-dimensional collaborative guidance model, the acceleration of each missile in the missile-target line of sight direction is obtained so that multiple missiles can reach the target at the same time; Construct a fixed-time disturbance observer of the target acceleration in the pitch and yaw directions and estimate the target acceleration term in the line-of-sight coordinate system; According to the three-dimensional collaborative guidance model and the estimated target acceleration term, the acceleration of the missile in the normal direction of the missile-target line of sight is obtained so that multiple missiles can reach the target at the same time; Using the missile's acceleration in the missile-target line of sight direction and the line of sight normal direction, the three acceleration components of the missile in the ballistic coordinate system are obtained; The three acceleration components are used to continuously update the speed and position of each missile during flight, so that multiple missiles can arrive at the target at the same time; According to the three-dimensional collaborative guidance model, the acceleration of each missile in the missile-target line of sight direction is obtained so that multiple missiles can reach the target at the same time, including: Set the total flight time of the missile t fi =t+t goi , where t goi represents the remaining flight time of the ith missile, and t represents the flight time of the missile; Differentiating the total flight time of the missile yields: in, represents the virtual control quantity, x 1i =r i , r i is the distance between the projectile and the target, is the first-order derivative of the missile-target distance with respect to time, q εi is the line of sight inclination angle of the i-th missile, is the first-order derivative of the line of sight angle of the ith missile with respect to time, q βi is the line of sight deflection angle of the i-th missile, is the first-order derivative of the line of sight angle of the ith missile with respect to time, a Mir ,a Miε ,a Miβ are the components of the acceleration of the i-th missile on the three axes in the line-of-sight coordinate system; According to the fixed time consistency theory, the acceleration in the line of sight direction that can make the total flight time of all missiles converge within a fixed time and make the remaining flight time of all missiles converge to a consistent value within a fixed time is obtained: in, h0,h1,h2>0,α<β,αγ<1,βγ>1, all are constant coefficients, t fi represents the total flight time of the ith missile, t fj represents the total flight time of the jth missile, The fixed-time convergent disturbance observer is: Among them, z 1i , z 2i x 4i , d qεi The estimated value of θ1≥0, η1,η2>0 and z 3i , z 4i x 6i , d qβi The estimated value of θ1,θ2≥0,η1,η2,η3,η4>0 and ε1, ε3∈(0.5,1), ε2, ε4∈(1,1.5), t(·) is a nonlinear correction term, According to the three-dimensional collaborative guidance model and the estimated target acceleration term, the acceleration of the missile in the normal direction of the missile-target line of sight is obtained so that multiple missiles can reach the target at the same time, including: According to the guidance model perpendicular to the line of sight in the pitch plane, the piecewise continuous fixed-time non-singular terminal sliding mode surface and fixed-time convergence approach law in the lateral plane are constructed, and the acceleration control law of the missile in the normal pitch plane of the missile-target line of sight is obtained. According to the guidance model in the lateral plane perpendicular to the line of sight, the piecewise continuous fixed-time non-singular terminal sliding mode surface and the fixed-time convergence approach law in the lateral plane are constructed, and the acceleration control law of the missile in the lateral plane normal to the missile-target line of sight is obtained. According to the guidance model perpendicular to the line of sight in the pitch plane, the piecewise continuous fixed-time non-singular terminal sliding mode surface and the fixed-time convergence approach law in the lateral plane are constructed, and the acceleration control law of the missile in the normal pitch plane of the missile-target line of sight is obtained, including: According to the guidance model perpendicular to the line of sight in the pitch plane, a piecewise continuous fixed-time non-singular terminal sliding surface is constructed: Among them, δ1,δ2>0,λ1>λ2,1<λ2<2 are all constant coefficients. ε is a positive number; Construct a fixed-time convergence law based on gain parameter adaptation: Among them, p1,q1>1,k1,k2>0, is the adaptive gain value; According to the fixed time convergence approach law, the acceleration control law of the missile in the normal pitch plane of the missile-target line of sight is obtained as follows:

2. The method for three-dimensional coordinated guidance of multiple missiles based on joint constraints of attack time and angle according to claim 1 is characterized in that: The relative motion equations between the missile and the target are: Among them, r i is the distance between the projectile and the target, is the first-order derivative of the missile-target distance with respect to time, is the second-order derivative of the missile-target distance with respect to time, q εi is the line of sight inclination of the i-th missile, q βi is the line of sight deflection angle of the i-th missile, is the first-order derivative of the line of sight angle of the ith missile with respect to time, is the first-order derivative of the line of sight angle of the ith missile with respect to time, is the second-order derivative of the line of sight inclination of the ith missile with respect to time, is the first-order derivative of the line of sight angle of the ith missile with respect to time, θ mi ,ψ mi are the ballistic inclination and deflection angle of the i-th missile, θ t ,ψ t are the velocity inclination and deflection angle of the target, respectively, Mir ,a Miε ,a Miβ is the acceleration component of the i-th missile on the three axes in the line of sight coordinate system; a Tr ,a Tε ,a Tβ are the components of target acceleration on the three axes in the line of sight coordinate system.

3. The multi-missile three-dimensional collaborative guidance method based on joint constraints of attack time and angle according to claim 2 is characterized in that: The missile's remaining flight time variable is introduced into the relative motion equations between the missile and the target, and a three-dimensional collaborative guidance model is constructed, including: Defining state variables according to a set of relative motion equations between the missile and the target and constructing state equations according to the state variables; A missile remaining flight time variable is introduced into the state equation and the state equation is updated to obtain a three-dimensional collaborative guidance model.

4. The multi-missile three-dimensional collaborative guidance method based on joint constraints of attack time and angle according to claim 3 is characterized in that: The three-dimensional collaborative guidance model is: Among them, x 1i =r i , x 3i =q εi -q εid , x 5i =q βi -q βid , represents the missile's remaining flight time variable, represents the first-order derivative of the missile's remaining flight time variable with respect to time, represents the target acceleration term estimated using the i-th missile.

5. A storage medium, characterized in that: The storage medium stores a computer program for executing the steps of the multi-missile three-dimensional collaborative guidance method based on joint constraints of attack time and angle as described in any one of claims 1 to 4.

6. An electronic device, characterized in that: It comprises a memory and a processor, wherein the memory stores a computer program, and when the processor calls the computer program in the memory, it implements the steps of the multi-missile three-dimensional collaborative guidance method based on the joint constraints of attack time and angle as claimed in any one of claims 1 to 4.

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