Multi-missile dynamic encirclement cooperative guidance method based on dubins escape region

Abstract

The application discloses a kind of multi-missile dynamic encirclement cooperative guidance methods based on Dubins escape domain, comprising: obtaining the relative motion model between missile and target from the relative motion information between missile and target obtained from reconnaissance system, and defining state variable according to the relative motion model to obtain two-dimensional cooperative guidance model;Calculate target Dubins escape domain;Calculate the position of multiple virtual target points;According to the different guidance stages, the constantly changing positions of each virtual target point in the process of approaching the real target are calculated to generate dynamic cooperative hunting strategy;Based on the relative motion model, two-dimensional cooperative guidance model and predetermined time consistency, cooperative guidance law is designed;According to cooperative guidance law, the operational task of multi-missile cooperative hunting maneuvering target or defense intercepting maneuvering target is completed.The application constructs dynamic hunting strategy, does not need to set terminal line-of-sight angle in advance to carry out angle cooperation, can completely cover target escape area, and can quantize control remaining flight time and line-of-sight angle.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of missile guidance and control, and particularly relates to a multi-missile dynamic encirclement cooperative guidance method based on a Dubins escape region. BACKGROUND

[0002] With the rapid development of space technology and scientific and technological strength, the defense capability and maneuverability of important targets are increasingly improved, and the reaction time of missiles is also shortened. The traditional "one-to-one" attack mode is difficult to complete the task of high-precision attack targets. In order to adapt to the complex space environment, a strategy of cooperative attack on targets by multiple missiles is proposed. Through adding communication equipment on a single missile body, the information obtained by each missile is collected and fully processed through a communication network, and then used to control the guidance flight of the missile group. This strategy has given birth to the germination of the multi-missile system cooperative attack system. Multi-missile cooperative guidance not only can improve the comprehensive attack capability and hit probability, but also can complete the task that cannot be completed by traditional single missile. Therefore, in the execution of modern space tasks, the research on multi-missile dynamic encirclement cooperative guidance method has very important engineering significance, and has been widely concerned at present.

[0003] In the early cooperative guidance research, the attack on static or low-speed moving targets was mainly carried out, and the attack time was preset. In 2006, Jeon et al. first introduced the impact-time control guidance (ITCG) and applied it to the salvo task. After that, Jeon et al. also extended the ITCG to control the attack time and attack angle at the same time. However, because there is no information exchange between each missile, it is not a true sense of cooperation. In order to realize the true sense of cooperative guidance, the multi-agent consensus theory is used to design the cooperative guidance law. At present, the consensus cooperative guidance law is mostly based on finite time and fixed time control theory. At the same time, in the realization of angle cooperation, the actual line-of-sight angle is set in advance according to the attack effect, which is called static encirclement. The dynamic encirclement strategy is less studied at present, mainly focusing on the use of intercept missile group reachable region to cover the target maneuvering range, cooperative encirclement guidance method based on wolf pack encirclement mechanism and the like.

[0004] Looking at the prior art, the following shortcomings mainly exist:

[0005] 1) At present, the design of cooperative guidance law basically adopts finite time or fixed time convergence theory, and the boundary of convergence time cannot be directly obtained, lacking specific quantification.

[0006] 2) At present, the cooperative encirclement mainly focuses on the static encirclement direction, and the terminal line-of-sight angle needs to be set in advance. If it is aimed at a large maneuvering target, the line-of-sight angle set in advance may not be the best encirclement situation.

[0007] 3) The target escape path of the existing dynamic encirclement guidance method is relatively fixed, only the classic tail or lateral escape mode is used, and the target escape region cannot be completely covered.

[0008] Therefore, how to propose a new multi-missile dynamic encirclement cooperative guidance method to overcome the above defects is an urgent technical problem in the art. SUMMARY

[0009] In order to solve the above problems existing in the prior art, the present application provides a multi-missile dynamic encirclement cooperative guidance method based on Dubins escape domain. The technical problem to be solved by the present application is solved by the following technical scheme:

[0010] Obtain the relative motion information between the missile and the target from the reconnaissance system, obtain the relative motion model between the missile and the target, and define the state variable according to the relative motion model to obtain a two-dimensional cooperative guidance model;

[0011] Calculate the target Dubins escape domain;

[0012] Calculate the positions of a plurality of virtual target points; wherein, in the scene of n missiles cooperatively attacking the target, the boundary of the target Dubins escape domain is divided into n equal parts to construct a sub-escape domain, and the intersection point of the bisector of the corresponding sub-escape domain and the boundary of the target Dubins escape domain is a virtual target point;

[0013] According to different guidance stages, the changing positions of each virtual target point in the process of approaching the real target are calculated to generate a dynamic cooperative encirclement strategy;

[0014] Design a cooperative guidance law based on the relative motion model, the two-dimensional cooperative guidance model and predetermined time consistency;

[0015] Complete the combat task of multi-missile cooperative encirclement of a maneuvering target or defense interception of a maneuvering target according to the cooperative guidance law.

[0016] In an embodiment of the present application, the relative motion information between the missile and the target is obtained from the reconnaissance system, and the relative motion model between the missile and the target is obtained, which includes:

[0017] Obtain the relative motion information between the missile and the target from the reconnaissance system, and obtain the relative motion equation set:

[0018]

[0019] Differentiate the first two equations of the relative motion equation set with respect to time t to obtain the differential result:

[0020]

[0021]

[0022] Introducing the remaining flight time variable The differential result is differentiated to obtain:

[0023]

[0024] Wherein, M i , T and T vi respectively represent the i-th missile, target and i-th virtual target point; v mi and v t are the speed of the i-th missile and the speed of the target, r i is the distance between the i-th missile and the target; q i is the line-of-sight angle between the i-th missile and the target; θ mi and θ t are the heading angles of the i-th missile and the target; a t is the target normal acceleration; a mf and a mt are the normal and tangential accelerations of the missile; ω r =a t sin(q i -θ t ); ω q =a t cos(q i -θ t ); u ri , u qi are the line-of-sight and line-of-sight normal components of the target and i-th missile acceleration.

[0025] In an embodiment of the present application, the state variable is defined according to the relative motion model to obtain a two-dimensional cooperative guidance model, comprising:

[0026] According to the relative motion model, the state variables x 1i and x 2i are defined:

[0027]

[0028] A two-dimensional cooperative guidance model is obtained:

[0029]

[0030] Wherein, is regarded as the disturbance caused by target maneuver.

[0031] In an embodiment of the present application, the target Dubins escape domain is assumed that the target escape time is Tvmax , the area composed of the boundary points reached by the target flying leftward and rightward; wherein, α v , the radian value corresponding to the flight time of the target flying only with the minimum turning radius, used for measuring the size of the target Dubins escape domain; a tmax , the maximum value of the normal acceleration of the target;

[0032] The calculation of the target Dubins escape domain comprises:

[0033] Under the premise of assuming that the maximum maneuvering angle of the target at a certain time is π, the coordinates of the left and right side circle center points, the coordinates of the points on the left and right side circular arcs, the length of the straight line segment and the coordinates of the target Dubins escape domain boundary points are sequentially calculated, so as to complete the calculation of the target Dubins escape domain.

[0034] In an embodiment of the present application,

[0035] The calculation formula of the coordinates of the left and right side circle center points comprises:

[0036]

[0037] Wherein, (x t ,y t ) is the coordinate of the actual target point; (x tlo ,y tlo ), (x tro ,y tro ) are respectively the coordinates of the left and right side circle center points; R v represents the minimum turning radius of the target;

[0038] The calculation formula of the coordinates of the points on the left and right side circular arcs comprises:

[0039]

[0040] Wherein, (x tlc ,y tlc ), (x trc ,y trc ) are respectively the coordinates of the points on the left and right side circular arcs; The surrounding segment satisfies

[0041] The calculation formula of the length of the straight line segment comprises:

[0042]

[0043] Wherein, L v is the length of the straight line segment; when not entering the converging segment, α v = π;

[0044] The formula for calculating the coordinates of the boundary point of the target Dubins escape domain includes:

[0045]

[0046] Among them, (x tld ,y tld ), (x trd ,y trd The coordinates of the Dubins escape domain boundary points on the left and right sides are respectively.

[0047] In one embodiment of the present invention, when n is 3, the multiple virtual target points are arranged from left to right as T. v1 T v2 T v3 ;

[0048] The calculation of the positions of multiple virtual target points includes:

[0049] By constructing a virtual target triangle, and based on the cosine theorem, the calculation formula for the coordinates of the boundary points of the Dubins escape domain of the target, and the virtual target calculation auxiliary angle ω, the calculation method is applied. v Calculate the virtual target point T v1 Location;

[0050] Using the calculated virtual target point T v1 Location, the virtual target point T v1 and the virtual target point T v3 The symmetry of the virtual target point T is used to calculate the virtual target point T. v3 Location;

[0051] Based on the formula used in the calculation of the target Dubins escape domain, substitute into Calculate the virtual target point T v2 The location.

[0052] In one embodiment of the present invention, the step of calculating the constantly changing positions of each virtual target point as it approaches the real target according to different guidance stages, in order to generate a dynamic cooperative encirclement strategy, includes:

[0053] For each virtual target point, based on the three guidance stages defined in the guidance process, the virtual target escape time T corresponding to that virtual target point is calculated using a preset time-varying virtual target convergence function. v The three guidance phases include an encirclement phase, a convergence phase, and an overlap phase.

[0054] Using the calculated virtual target escape time T v Calculate the corresponding α v ;

[0055] Based on the calculated αv and virtual target calculation auxiliary angle ω v The calculation formula of the virtual target point is calculated in the process of approaching the real target.

[0056] In an embodiment of the present application, the virtual target escape time T v The calculation formula includes:

[0057]

[0058] Wherein, T sta =T go (0) max -T vmax -δ vt is defined as the end time of the trapping segment; T tran =T go (0) max -δ vt is defined as the end time of the convergence segment; T f is the end time of the real guidance; T go (0) max is the maximum value of the initial estimated remaining flight time of each missile; δ vt is the coincidence segment, 0<δ vt ≤T go (0) max .

[0059] In an embodiment of the present application, the cooperative guidance law is designed based on the relative motion model, the two-dimensional cooperative guidance model and the predetermined time consistency, which includes:

[0060] Based on the relative motion model and the two-dimensional cooperative guidance model, a guidance model for cooperative attack of virtual targets by multiple missiles is constructed:

[0061]

[0062] Wherein, r iv and are the distance and distance change between the corresponding missile and the virtual target point, respectively; q iv and are the line of sight angle and the line of sight angle change rate of the corresponding missile and the virtual target point, respectively; (x mi ,y mi ), (x iv ,y iv ) are the coordinates of the i-th missile and the corresponding i-th virtual target, respectively; x 1iv and x 2ivTwo state variables corresponding to the virtual target respectively;

[0063] The method of dynamic inverse is used to decouple the design of guidance law to the line of sight and the normal of line of sight, and the multi-agent pre-determined time consistency theory is introduced to design the guidance law, and the guidance model of the multi-missile cooperative attack of the virtual target is rewritten into the form of continuous nonlinear system:

[0064]

[0065] Wherein, X=[x 1iv x 2iv ] T , U(t)=[u ri u qi ] T ,

[0066] According to the dynamic inverse theory, the calculation method of the control vector is obtained:

[0067] U(t)=G[X(t)] -1 {V(t)-F[X(t)]}

[0068] The control vector obtained is substituted into the continuous nonlinear system form of the guidance model rewritten, and the following is obtained:

[0069]

[0070] According to the multi-agent pre-determined time consistency theory, the change of the state vector is designed:

[0071] V(t)=-K(t)X(t)

[0072] Wherein,

[0073]

[0074] k 1rv >0, η 1v >0, k 2rv >0, η 2v >0, k 1qv >0, k 2qv >0, are all guidance parameters;

[0075] h>2, t0≥0, T * >0 are all positive parameters; is the first order differential of μ(t) with respect to time,

[0076] The control law of the line of sight and the normal of line of sight is obtained:

[0077]

[0078] The line-of-sight and the line-of-sight normal control law is designed as a cooperative guidance law.

[0079] In an embodiment of the present application, the combat task of multiple missiles cooperatively surrounding and capturing a maneuvering target or intercepting a maneuvering target is completed according to the cooperative guidance law, and the combat task includes:

[0080] According to the cooperative guidance law, the tangent and normal acceleration components of the missile are obtained through coordinate system conversion to a trajectory system;

[0081] The tangent and normal acceleration components of the missile are used to iteratively update the speed and position of the missile in the cooperative attack task, and the combat task of multiple missiles cooperatively surrounding and capturing a maneuvering target or intercepting a maneuvering target is completed.

[0082] The multi-missile dynamic surrounding and capturing cooperative guidance method based on the Dubins escape domain provided in the embodiments of the present application is different from static surrounding and capturing, and the embodiments of the present application construct a dynamic surrounding and capturing strategy based on a target Dubins escape domain, can realize angle cooperation without pre-setting a terminal line-of-sight angle, form a surrounding and capturing attack posture with a certain spatial dispersion in the escape direction of the maneuvering target, and can be applied to combat tasks of surrounding and capturing or intercepting a large maneuvering target. For the target escape path of the current dynamic surrounding and capturing guidance method being relatively fixed, the embodiments of the present application construct a target Dubins escape domain by introducing a Dubins shortest path; and by equally dividing the target Dubins escape region, introduce a virtual target point concept, design a time-varying virtual target convergence function that varies with real guidance time to make the virtual target point gradually coincide with the real target point, form a dynamic surrounding and capturing guidance strategy, and the target Dubins escape domain constructed in the embodiments of the present application can completely cover all the shortest escape paths of the target, and realize surrounding and capturing of the target. For the problem that the boundary of the convergence time cannot be directly obtained, the embodiments of the present application construct a cooperative guidance model of multiple missiles and multiple virtual targets, design a line-of-sight and line-of-sight normal cooperative guidance law of multiple missiles based on predetermined time stability theory, control the remaining flight time and the line-of-sight angle, and can quantitatively realize cooperative attack on the target. BRIEF DESCRIPTION OF DRAWINGS

[0083] Figure 1 A flowchart of a multi-missile dynamic surrounding and capturing cooperative guidance method based on a Dubins escape domain provided in the embodiments of the present application is shown in the figure;

[0084] Figure 2 A relative motion model diagram of a two-dimensional space multi-missile and a single target / virtual target in the embodiments of the present application is shown in the figure;

[0085] Figure 3A target Dubins escape domain boundary point calculation graph in the embodiment of the present application;

[0086] Figure 4 A virtual target point calculation graph in the embodiment of the present application;

[0087] Figure 5 A convergence segment escape domain change graph in the embodiment of the present application;

[0088] Figure 6 An inter-missile topology structure graph in the embodiment of the present application;

[0089] Figure 7 A missile and target motion trajectory graph in the embodiment of the present application;

[0090] Figure 8 A real and virtual target motion trajectory graph in the embodiment of the present application;

[0091] Figure 9 A missile remaining flight time change curve graph in the embodiment of the present application;

[0092] Figure 10 A missile-target line-of-sight angle change curve graph in the embodiment of the present application;

[0093] Figure 11 A missile line-of-sight direction acceleration command change curve graph in the embodiment of the present application;

[0094] Figure 12 A missile line-of-sight normal acceleration command change curve graph in the embodiment of the present application. DETAILED DESCRIPTION

[0095] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0096] In order to overcome the deficiencies of the prior art, the embodiment of the present application provides a multi-missile dynamic encirclement cooperative guidance method based on Dubins escape domain, which provides a reasonable and feasible solution for encircling a maneuvering target.

[0097] As shown in Figure 1 The multi-missile dynamic encirclement cooperative guidance method based on Dubins escape domain provided by the embodiment of the present application can include the following steps:

[0098] S1, obtaining the relative motion information between the missile and the target from the reconnaissance system, obtaining the relative motion model between the missile and the target, and defining the state variable according to the relative motion model to obtain a two-dimensional cooperative guidance model;

[0099] wherein, the reference Figure 2 two-dimensional space multi-missile and single target / virtual target relative motion model diagram, obtaining the relative motion information between the missile and the target from the reconnaissance system, obtaining the relative motion model between the missile and the target, comprising:

[0100] A1, obtaining the relative motion information between the missile and the target from the reconnaissance system, obtaining the relative motion equation group:

[0101]

[0102] A2, differentiating the first two equations of the relative motion equation group with respect to time t to obtain the differential result:

[0103]

[0104]

[0105] A3, introducing the remaining flight time variable differentiating the differential result to obtain:

[0106]

[0107] wherein, M i , T and T vi represent the i-th missile, target and i-th virtual target point respectively; v mi and v t are the speed of the i-th missile and the speed of the target respectively, r i is the distance between the i-th missile and the target; q i is the line-of-sight angle between the i-th missile and the target; θ mi and θ t are the heading angles of the i-th missile and the target respectively; a t is the target normal acceleration; a mf and a mt are the normal and tangential accelerations of the missile respectively; ω r =a t sin(q i -θ t ); ω q =a t cos(q i -θ t ); u ri , u qiare the components of the target and the i-th missile acceleration along the line-of-sight and the normal direction of the line-of-sight respectively; the dot above the parameter represents derivation.

[0108] Specifically, Figure 2 wherein T is the target; a t is the normal acceleration of the target; v t is the velocity of the target; θ t is the heading angle of the target; T v1 , T vi and T vn are the first, i-th and n-th virtual target points respectively; M1, M i , M n are the first, i-th and n-th missiles respectively; a1, a mi , a n are the normal accelerations of the first, i-th and n-th missiles respectively; v1, v mi , v n are the velocities of the first, i-th and n-th missiles respectively; θ1, θ i , θ n are the heading angles of the first, i-th and n-th missiles respectively; r1, r i , r n are the distances between the first, i-th and n-th missiles and the target respectively; r 1v , r iv , r nv are the distances between the first, i-th and n-th missiles and the corresponding virtual targets respectively; q 1v , q iv , q nv are the line-of-sight angles between the first, i-th and n-th missiles and the corresponding virtual targets respectively; in the embodiment of the present application, the subscript mi of the physical quantity represents that it is a physical quantity of a missile, the i alone represents that it is a physical quantity between a missile and a target, and iv represents that it is a physical quantity between a missile and a virtual target.

[0109] wherein the state variable is defined according to the relative motion model to obtain a two-dimensional cooperative guidance model, including:

[0110] B1, the state variables x 1i and x 2i are defined according to the relative motion model:

[0111]

[0112] B2, the two-dimensional cooperative guidance model is obtained:

[0113]

[0114] wherein, considered as the interference brought by the target maneuver.

[0115] S2, calculating the target Dubins escape region;

[0116] The target Dubins escape region is calculated by a plurality of target Dubins escape curves, which are composed of a circular arc with the same radius and a corresponding tangent segment. There are three typical target Dubins escape curves in the target Dubins escape region, i.e., the target continuously turns left or right with constant maximum overload, and the target flies straight. The target Dubins escape region is composed of the farthest boundary points reached by the target flying in the manner of Dubins escape curve within a specific time period, as shown in the middle lattice-shaped shaded part. Figure 3

[0117] The target Dubins escape region is assumed that the target escape time is T vmax , and the region composed of the boundary points reached by the target flying left and right; see Figure 3 for details, where the boundary of the shaded area is assumed that the target escape time is T vmax , and the region composed of the boundary points reached by the target flying left and right. T vmax can be calculated by the following formula:

[0118]

[0119] wherein, α v is the radian value corresponding to the flight time of the target flying only with the minimum turning radius (excluding the straight segment), which can be used to measure the size of the target Dubins escape region; a tmax is the maximum value of the target normal acceleration; it is assumed that the maximum maneuvering angle of the target at a certain moment is set to π, at this time α v = π, and the minimum turning radius of the target

[0120] wherein, the target Dubins escape region is calculated, including:

[0121] Under the premise that the maximum maneuvering angle of the target at a certain moment is π, the coordinates of the left and right center points of the Dubins escape region, the coordinates of the points on the left and right circular arcs, the length of the straight segment, and the coordinates of the boundary points of the target Dubins escape region are calculated in sequence, and the calculation of the target Dubins escape region is completed.

[0122] Specifically, as mentioned above, under the premise that the maximum maneuvering angle of the target at a certain moment is π, at this time α v = π, and the minimum turning radius

[0123] According to​Figure 3 The boundary points on the left and right sides are calculated, including the following steps:

[0124] (1) Calculate the coordinates of the center points of the left and right sides of the Dubins escape domain:

[0125] This step is calculated according to the actual target point and the minimum turning radius of the target.

[0126] The calculation formula of the coordinates of the center points of the left and right sides includes:

[0127]

[0128] Where (x t ,y t ) is the coordinate of the actual target point; (x tlo ,y tlo ), (x tro ,y tro ) are the coordinates of the center points of the left and right sides, respectively; R v represents the minimum turning radius of the target.

[0129] (2) Calculate the coordinates of the points on the left and right side arcs:

[0130] This step is calculated according to the center points of the left and right sides and the radian value corresponding to the target arc segment flight.

[0131] The calculation formula of the coordinates of the points on the left and right side arcs includes:

[0132]

[0133] Where (x tlc ,y tlc ), (x trc ,y trc ) are the coordinates of the points on the left and right side arcs, respectively; is the radian value corresponding to the target arc segment flight, In the pursuit segment, satisfies

[0134] (3) Calculate the length of the straight line segment:

[0135] The target flight time of the entire escape path is T vmax , the arc segment flight time is The target flight time in the straight line segment is On this basis, the calculation formula of the length of the straight line segment can be obtained.

[0136] The calculation formula of the length of the straight line segment includes:

[0137]

[0138] Wherein, L v is a straight line length; when not entering the converging section, alpha v = pi;

[0139] (4) Calculate the target Dubins escape domain boundary point coordinates:

[0140] Wherein, the calculation formula of the target Dubins escape domain boundary point coordinates includes:

[0141]

[0142] Wherein, (x tld ,y tld ), (x trd ,y trd ) are respectively left and right target Dubins escape domain boundary point coordinates.

[0143] Referring to Figure 3 It is understood that the target Dubins escape domain boundary point coordinates (x tld ,y tld ) and (x trd ,y trd ) are connected to form the outermost escape domain boundary.

[0144] S3, calculate the positions of a plurality of virtual target points;

[0145] The difference between the dynamic encirclement cooperative guidance and the static encirclement cooperative guidance according to the embodiment of the application lies in whether the terminal line-of-sight angle constraint needs to be preset in advance. In the static encirclement cooperative guidance strategy, the preset line-of-sight angle of each missile needs to be determined by estimating the collision point in advance, and once determined, it will not change with the target maneuvering. If the target maneuvering changes greatly during the guidance process, the set line-of-sight angle constraint may not be the best cooperative encirclement guidance strategy. According to the embodiment of the application, a plurality of virtual target points are calculated according to the motion of the real target, and the plurality of virtual target points gradually approach the real target from different directions, so that the dynamic cooperative encirclement strategy without presetting the line-of-sight angle constraint can be realized.

[0146] According to the embodiment of the application, the virtual target point is defined as the intersection point of the bisector of the corresponding sub-escape domain and the boundary of the target Dubins escape domain in the scene of n-missile cooperative attack target.

[0147] Specifically, in a coordinated attack scenario, assuming n missiles are coordinating an attack on a target, the target's Dubins escape boundary is divided into n equal parts according to the number of missiles and their angles, constructing n sub-escape domains. The bisecting line of the angle of each sub-escape domain intersects the escape boundary at a point; this intersection is defined as a virtual target point. For ease of understanding, the following embodiments of this invention will use n=3 as an example. Please refer to [link to previous documentation]. Figure 4 The two dashed lines represent the trisections of the entire escape domain, dividing the target's Dubins escape boundary into three sub-escape domains. For each sub-escape domain, the angle is bisected using the corresponding bisection line. The three intersections of these bisection lines with the outermost boundary of the target's Dubins escape domain are the virtual target points. Figure 4 In the diagram, the three virtual target points are T from left to right. v1 T v2 and T v3 .

[0148] Based on this, the positions of multiple virtual target points are calculated, including:

[0149] S31, by constructing a virtual target triangle, and based on the cosine theorem, the calculation formula for the coordinates of the boundary points of the target's Dubins escape domain, and the virtual target's auxiliary angle ω, the calculation method is applied. v Calculate the virtual target point T v1 Location;

[0150] See Figure 4 Define the angle ω between the bisecting line and the lines containing the centers of the left and right circles as the auxiliary angle for virtual target calculation. v The calculation formula is as follows:

[0151]

[0152] Given a fixed maximum turning overload and speed, the target's Dubins escape boundary point is determined solely by α. v and It depends on whether the virtual target point can be calculated. Then its location can be calculated, and the problem is transformed into how to calculate its location given ω. v Solve under the following circumstances

[0153] For the virtual target point T on the left v1 ,according to Figure 4 A virtual target triangle can be constructed, given by T(x) t ,y t ), T lo (x tlo ,y tlo ), Tv1 (x tld ,y tld Composed of three points, apply the Law of Cosines within the virtual target triangle:

[0154]

[0155] Among them T, T lo T v1 The coordinates of all three points can be calculated using the formula for calculating the coordinates of the boundary points of the target Dubins escape domain in S2. As the variable to be solved, it is unknown, while ω v It is known. The above equations constitute a univariate trigonometric function equation, which can be solved using the vpasolve function in MATLAB to find the virtual target point T. v1 Corresponding Then the virtual target point T can be determined. v1 The location.

[0156] S32, using the calculated virtual target point T v1 Location, virtual target point T v1 and virtual target point T v3 The symmetry of the virtual target point T is used to calculate the virtual target point T. v3 Location;

[0157] Due to the virtual target point T v1 and virtual target point T v3 It is symmetrical, therefore, according to the virtual target point T v1 Calculated T can be obtained v3 of Thus, the virtual target point T is determined. v3 The location coordinates.

[0158] S33, based on the formula used in the calculation of the target Dubins escape domain, substitute into Calculate the virtual target point T v2 The location.

[0159] For the virtual target point T in the middle v2 can Substituting the formula used in S2 and performing another calculation, its position can be calculated.

[0160] It is understandable that the position of the virtual target point calculated in S3 is equivalent to its initial position in the process of gradually approaching the real target, and the position of the virtual target point is constantly changing in the process of approaching the real target.

[0161] It should be noted that for the remaining values of n, the corresponding ω v can be calculated according to the calculation formula of the virtual target v , so as to calculate the position of the virtual target point, which is not described one by one here.

[0162] S4, according to different guidance stages, the changing position of each virtual target point in the process of approaching the real target is calculated to generate a dynamic cooperative hunting strategy;

[0163] As described above, S2-S3 gives the calculation method of the target Dubins escape domain and the corresponding virtual target point, wherein the escape time of the target is: T v = T vmax .

[0164] In S4, the guidance process is divided into three stages, including the hunting segment, the convergence segment and the coincidence segment. The division of guidance stages is mainly based on the real guidance time. By designing a time-varying virtual target convergence function that changes with the real guidance time, the virtual target point is constantly close to the real target point and finally coincides. This time-varying virtual target convergence function is mainly used to calculate the escape time T v of the virtual target point; then, according to the escape time T v of the virtual target point, the size of the target escape domain α v = πT v / T vmax .

[0165] In an optional implementation, S4 can include:

[0166] S41, for each virtual target point, according to the three guidance stages divided by the guidance process, the preset time-varying virtual target convergence function is used to calculate the virtual target escape time T v corresponding to the virtual target point;

[0167] The calculation formula of the virtual target escape time T v includes:

[0168]

[0169] The calculation formula of the virtual target escape time T v above is the preset time-varying virtual target convergence function; T sta = T go (0) max -T vmax -δ vt is defined as the end time of the hunting segment; T tran = T go (0) max -δvt T is defined as the time when the convergence segment ends; T f T is defined as the time when the real target is hit; T go (0) max T is defined as the maximum value of the remaining flight time of each missile; δ vt T is defined as the time when the convergence segment ends; T vt T is defined as the time when the convergence segment ends; T go (0) max To ensure the success rate of guidance, δ vt needs to be selected according to T go (0) max appropriately.

[0170] Among them, the three guidance segments are as follows:

[0171] 1) The flight time of the virtual target in the encirclement segment is T v =T vmax , and the size of the target Dubins escape domain is α v =π, at this time, the target escape domain range is maximum, and n missiles respectively fly towards n virtual target points to form the encirclement trend.

[0172] 2) In the convergence segment, the escape time T v <T vmax , therefore the corresponding target escape domain will also be reduced accordingly, as shown in Figure 5 The area surrounded by the outer long dashed line is the escape domain of the encirclement segment, and the area surrounded by the inner short dashed line and the solid curve is the escape domain of the convergence segment. The corresponding virtual target points T' v1 , T' v2 , T' v3 are also marked in the figure. In this process, the virtual target points gradually converge to the real target point until they coincide with the real target point, and enter the coincidence segment.

[0173] 3) In the coincidence segment, the virtual target point coincides with the real target point, and the missile attacks the real target, completing the encirclement guidance containing time constraint and angle constraint.

[0174] S42, the calculated virtual target escape time T v is used to calculate the corresponding α v ;

[0175] As can be understood from the above, the virtual target escape time T v of a virtual target point is variable, and each T v calculated can be substituted into the calculation formula of α v α v =πT v / T vmax to calculate the corresponding α v.

[0176] S43, based on the calculated alpha v and the virtual target calculation auxiliary angle ω v The calculation formula is used to calculate the changing position of the virtual target point in the process of approaching the real target.

[0177] In this step, the calculated alpha v is substituted into the calculation formula of the virtual target calculation auxiliary angle ω v The calculation formula of ω v is as follows: Then the ω v of each position of the virtual target point can be calculated.

[0178] S5, based on the relative motion model, the two-dimensional cooperative guidance model and the predetermined time consistency design cooperative guidance law;

[0179] Wherein, S5 can include:

[0180] S51, based on the relative motion model, the two-dimensional cooperative guidance model, the guidance model for multiple missile cooperative attack virtual target is constructed:

[0181]

[0182] Wherein, r iv and are the distance between the corresponding missile and the virtual target point and the distance change; q iv and are the line of sight angle and the line of sight angle change rate of the corresponding missile and the virtual target point; (x mi ,y mi ), (x iv ,y iv ) are the coordinates of the i-th missile and the corresponding i-th virtual target; x 1iv and x 2iv are two state variables corresponding to the virtual target; The subscript v is added to the above formula parameters in the embodiment of the application to indicate that it is for the virtual target, so as to be distinguished.

[0183] S52, the method of dynamic inverse is used to decouple the design of the guidance law to the line of sight and the line of sight normal, and the multi-agent predetermined time consistency theory is introduced to design the guidance law, and the guidance model for multiple missile cooperative attack virtual target is rewritten into the form of continuous nonlinear system:

[0184]

[0185] Wherein, X=[x1iv x 2iv ] T , U(t) = [u ri u qi ] T ,

[0186] S53, according to the dynamic inverse theory, the calculation method of the control vector is obtained:

[0187] U(t) = G[X(t)] -1 {V(t)-F[X(t)]}

[0188] Wherein, the calculation method of V(t) is described in detail hereinafter.

[0189] S54, the obtained control vector is substituted into the continuous nonlinear system form rewritten from the guidance model, and the following is obtained:

[0190]

[0191] S55, according to the multi-agent predetermined time consensus theory, the change of the state vector is designed:

[0192] V(t) = -K(t)X(t)

[0193] Wherein,

[0194] k 1rv >0, η 1v >0, k 2rv >0, η 2v >0, k 1qv >0, k 2qv >0, are all guidance parameters, which are determined through simulation experiment; h>2, t0≥0, T * >0 are all positive parameters; is the first order differential of μ(t) with respect to time,

[0195] S56, the control law of line of sight and line of sight normal is obtained:

[0196]

[0197] Wherein, the above-mentioned control law of line of sight and line of sight normal can be obtained by comprehensively considering the foregoing steps; the control law of line of sight and line of sight normal is designed as the cooperative guidance law, which is referred to as PsTCG.

[0198] It should be noted that, based on the above cooperative guidance law, all state variables will tend to be consistent, x 1iv→ 0 means that the flight time of all missiles will tend to the same value, achieving the purpose of attacking the target at the same time; x 2iv → 0 can guarantee that all missiles hit the target. Due to the adoption of the consistency theory of predetermined time, the convergence speed of the state variable is slow in the initial stage, and when the guidance time t→ T * , the convergence speed gradually increases, which avoids a large amount of control input in the initial stage and is more conducive to engineering implementation.

[0199] S6, completing the combat task of cooperative hunting of a mobile target or defense interception of a mobile target according to the cooperative guidance law.

[0200] S6 can include:

[0201] S61, obtaining tangent and normal acceleration components of the missile through coordinate system conversion to the trajectory system according to the cooperative guidance law;

[0202] S62, iteratively updating the speed and position of the missile in the cooperative attack task by using the tangent and normal acceleration components of the missile, and completing the combat task of cooperative hunting of a mobile target or defense interception of a mobile target.

[0203] The embodiment of the present application can realize the combat task of hunting a large mobile target or defense interception of a large mobile target.

[0204] The multi-missile dynamic hunting cooperative guidance method based on the Dubins escape domain provided by the embodiment of the present application is different from static hunting. The embodiment of the present application constructs a dynamic hunting strategy based on the target Dubins escape domain, can realize angle cooperation without pre-setting the terminal line-of-sight angle, forms a certain spatial dispersion hunting attack posture of the mobile target in the escape direction of the mobile target, and can be applied to the combat task of hunting or intercepting a large mobile target. For the target escape path of the current dynamic hunting guidance method, the embodiment of the present application constructs a target Dubins escape domain by introducing a Dubins shortest path; and by equally dividing the target Dubins escape region, introduces the concept of a virtual target point, designs a time-varying virtual target convergence function that changes with the real guidance time to make the virtual target point gradually coincide with the real target point, forms a dynamic hunting guidance strategy, and the target Dubins escape domain constructed by the embodiment of the present application can completely cover all the shortest escape paths of the target, and realize hunting of the target. For the problem that the boundary of the convergence time cannot be directly obtained, the embodiment of the present application constructs a cooperative guidance model of multiple missiles and multiple virtual targets, designs a line-of-sight and line-of-sight normal cooperative guidance law of multiple missiles based on the predetermined time stability theory, controls the remaining flight time and the line-of-sight angle, and can realize cooperative attack on the target through specific quantization.

[0205] In order to verify the effect of the embodiment of the present application, the following is described by experimental data.

[0206] The combat scene of the embodiment of the application is designed as three missiles cooperatively attacking a high-speed and large-maneuvering target, the communication network topology structure among the missiles is as shown in the figure Figure 6 , the network is undirected and connected. In order to meet the guidance requirement, the related parameters need to be set. The related parameter settings of the final guidance law are: k 1rv =1, η 1v =0.1, k 2rv =1, η 2v =0.05, k 1qv =0.5, k 2qv =1; the related parameter settings of μ(t) are: h=3, t0=3, T * =25; the related parameter settings in the calculation formula of the escape time of the virtual target point are: δ vt =10.

[0207] The target maneuvering is set as:

[0208] The simulation initial parameter settings of the missile and target position, velocity and heading angle are as shown in Table 1:

[0209] Table 1 Guidance initial condition

[0210]

[0211] Table 2 Miss distance and guidance time error under experimental conditions

[0212]

[0213] The simulation results of the multi-missile cooperative dynamic hunting guidance law based on the target escape domain of the embodiment of the application are shown in Table 2, and it can be seen that the control of the cooperative guidance law based on the embodiment of the application has the same guidance time of each missile under different target maneuvering conditions, and the miss distance at the collision time is within a reasonable range, and has high guidance precision.

[0214] Figures 7-12 The simulation diagram of the cooperative dynamic hunting guidance law designed by the embodiment of the application for attacking a large-maneuvering target. Among them, PsTCG-M1, PsTCG-M2, PsTCG-M3, PsTCG-T and PsTCG-Collision Point represent missile 1, missile 2, missile 3, target and collision point respectively. Figure 7 The trajectory diagram of the missile and target can be seen, and it can be seen that the three missiles have completed the task of attacking the target. Figure 8 The trajectory diagram of the real target and the virtual target point is shown in the figure, in which T, T LEFT , T G , T RIGHTThe real target, the virtual target point on the left border, the virtual target point in the middle and the virtual target point on the right border, respectively, can be seen that the virtual target points in different directions are far away from the real target in the encircling segment, and are close to the real target in the converging segment, and finally coincide with the real target, which well guides the three missiles to complete the encircling situation and attack the target from different directions. Figure 9 The figure of the change of the remaining flight time, it can be clearly seen that even if the initial remaining flight time of the three missiles is different, they can converge to zero at the same time under the control of u r It can be seen that the designed cooperative guidance law realizes the time cooperation. Figure 10 The figure of the change of the line-of-sight angle, it can be seen that even if there is no preset expected line-of-sight angle in advance, the missiles will attack the target from different directions to achieve the purpose of saturation attack. Figures 11-12 The figure of the change of the acceleration command of the line-of-sight and the normal line-of-sight, it shows that even under the constraint of available overload, the three missiles can complete the requirements of cooperative guidance, after 10 seconds, there are slight fluctuations in the acceleration curves of the line-of-sight and the normal line-of-sight, which is caused by the maneuver of the virtual target approaching the real target, and after 25 seconds, they are consistent with the target maneuver.

Claims

1. A multi-missile dynamic encirclement cooperative guidance method based on Dubins escape region, characterized in that, The method comprises the following steps: obtaining the relative motion information between the missile and the target from a reconnaissance system, obtaining the relative motion model between the missile and the target, and defining the state variable according to the relative motion model to obtain a two-dimensional cooperative guidance model; calculating the Dubins escape domain of the target; The positions of a plurality of virtual target points are calculated; wherein the virtual target points are In the scene of the coordinated attack of multiple missiles on a target, the boundary of the target Dubins escape domain is determined according to the angle After the bisecting construction of the sub-escape domain, the intersection point of the bisector of the corresponding sub-escape domain and the boundary of the target Dubins escape domain; According to different guidance stages, the positions of each virtual target point in the process of approaching the real target are calculated to generate a dynamic cooperative hunting strategy, including: for each virtual target point, according to three guidance stages divided by the guidance process, a preset time-varying virtual target convergence function is used to calculate the virtual target escape time corresponding to the virtual target point ; wherein the three guidance stages include a hunting segment, a convergence segment and a coincidence segment; the calculated virtual target escape time is used to calculate the corresponding ; based on the calculated and the calculation formula of the auxiliary angle of the virtual target, the position of the virtual target point in the process of approaching the real target is calculated; the calculation formula of the virtual target escape time includes: wherein, is the arc value corresponding to the flight time of the target when it flies with the minimum turning radius only, which is used to measure the size of the Dubins escape region of the target; is defined as the time when the encirclement segment ends; is defined as the time when the convergence segment ends; is the time when the real guidance ends; is the maximum value of the initial estimated remaining flight time of each missile; is the overlapping segment, ; designing the cooperative guidance law based on the relative motion model, the two-dimensional cooperative guidance model and the predetermined time consistency; completing the combat task of cooperative hunting of a mobile target or defensive interception of a mobile target by multiple missiles according to the cooperative guidance law.

2. The Dubins escape region based multi-projectile dynamic pursuit cooperative guidance method according to claim 1, wherein, The method of obtaining the relative motion information between the missile and the target from the reconnaissance system, obtaining the relative motion model between the missile and the target, comprises the following steps: obtaining the relative motion information between the missile and the target from the reconnaissance system to obtain a relative motion equation group: Differentiating the first two equations of the relative motion equations with respect to time t respectively gives the differential results as Introducing a residual flight time variable The differential result is differentiated to give: in, , and Representing the first Missiles, targets and the first One virtual target point; and The first The speed of the missile and the speed of the target, For the first The distance between each missile and the target; For the first The line-of-sight angle between the missile and the target; and The first The heading angles of the missiles and the target; For target normal acceleration; and These are the missile's normal and tangential accelerations, respectively. ; ; , The target and the first The components of a missile's acceleration in the line of sight and the line-of-sight normal.

3. The Dubins-escape-region-based multi-projectile dynamic pursuit cooperative guidance method according to claim 2, wherein The method of defining the state variable according to the relative motion model, obtaining the two-dimensional cooperative guidance model, comprises the following steps: According to the relative motion model, a state variable is defined and : ， obtaining the two-dimensional cooperative guidance model: wherein , considered as interference caused by the target maneuver.

4. The Dubins-escape-region-based multi-projectile dynamic pursuit cooperative guidance method according to claim 3, wherein, The target Dubins escape region is a region composed of boundary points reached by the target flying leftward and rightward with the assumption that the target escape time is ; ; is an arc value corresponding to the flight time of the target flying only with the minimum turning radius, used to measure the size of the target Dubins escape region; is the maximum value of the target normal acceleration; The method of calculating the Dubins escape domain of the target, comprises the following steps: Under the premise that the maximum maneuvering angle of the target at a certain time is On this basis, the coordinates of the center points on the left and right sides of the Dubins escape region, the coordinates of the points on the left and right circular arcs, the length of the straight line segment, and the coordinates of the boundary points of the target Dubins escape region are calculated in sequence to complete the calculation of the target Dubins escape region.

5. The Dubins escape domain-based multi-missile dynamic hunting cooperative guidance method according to claim 4, characterized in that, the calculation formula of the coordinates of the left and right side circle center points comprises: wherein, is the coordinate of the actual target point; , are the coordinates of the left and right circle center points, respectively; denotes the minimum turning radius of the target; the calculation formula of the coordinates of the points on the left and right side circular arcs comprises: wherein, , are the coordinates of the points on the left and right circular arcs, respectively; The trapping section satisfies ; the calculation formula of the length of the straight line segment comprises: wherein is the length of the straight segment; at the entry into the converging segment, ; the calculation formula of the coordinates of the target Dubins escape domain boundary points comprises: wherein, , are the coordinates of the left and right target Dubins escape region boundary points, respectively.

6. The Dubins-escape-region-based multi-projectile dynamic pursuit cooperative guidance method according to claim 5, wherein When the value of i is 3, the multiple virtual target points are sequentially from left to right , , ; the method of calculating the positions of the multiple virtual target points comprises: By constructing a virtual target triangle, and based on the cosine theorem, the calculation formula for the coordinates of the boundary points of the target's Dubins escape domain, and the auxiliary angle calculation for the virtual target, the calculation method is applied. Calculate the virtual target point Location; using the calculated position of the virtual target point , the virtual target point , and the symmetry of the virtual target point , calculate a position of the virtual target point ; Based on the formula used in the target Dubins escape region calculation process, substitute the position of the virtual target point .

7. The Dubins-escape-region-based multi-projectile dynamic pursuit cooperative guidance method according to claim 6, wherein, The method of designing the cooperative guidance law based on the relative motion model, the two-dimensional cooperative guidance model and the predetermined time consistency comprises the following steps: constructing a guidance model of cooperative attack of the virtual target by the multiple missiles based on the relative motion model and the two-dimensional cooperative guidance model: wherein, and are the distance and the distance variation between the corresponding missile and the virtual target point, respectively; ; ; and are the line-of-sight angle and the line-of-sight angle rate of change of the corresponding missile and the virtual target point, respectively; ; ; , are the coordinates of the first missile and the corresponding first virtual target, respectively; and are the two state variables corresponding to the virtual target, respectively; ; ; the guidance law is decoupled into the line-of-sight and the line-of-sight normal by using the dynamic inverse method, and the multi-agent predetermined time consistency theory is introduced to design the guidance law, and the guidance model of the cooperative attack of the virtual target by the multiple missiles is rewritten into the form of a continuous nonlinear system: wherein , , , ; According to the dynamic inverse theory, the calculation method of the control vector is obtained: the control vector obtained is substituted into the continuous nonlinear system rewritten from the guidance model to obtain: According to the multi-agent predetermined time consistency theory, the change of the state vector is designed: wherein ; , , , , , , are guidance parameters; ; , , are positive parameters; is first order differential with respect to time, ; the line-of-sight and line-of-sight normal control law is obtained: The line-of-sight and line-of-sight normal control law is used as the designed cooperative guidance law.

8. The Dubins-escape-region-based multi-projectile dynamic pursuit cooperative guidance method according to claim 7, wherein, The method of completing the combat task of cooperative hunting of a mobile target or defensive interception of a mobile target by multiple missiles according to the cooperative guidance law comprises the following steps: According to the cooperative guidance law, the tangent and normal acceleration components of the missile are obtained through coordinate system conversion to the trajectory system; the missile speed and position in the cooperative attack task are iteratively updated by using the tangent and normal acceleration components of the missile to complete the combat task of cooperative hunting of a mobile target or defensive interception of a mobile target by multiple missiles.

Images