A spacecraft cooperative closed-loop interception method based on reachable domain analysis

Abstract

The present invention discloses a method for collaborative closed-loop interception of spacecraft based on reachable domain analysis, which belongs to the field of aerospace technology. The implementation method of the present invention is as follows: using reachable domain theory to analyze the maneuverability boundary of the interceptor and the target, and constructing collaborative interception constraints in the form of a set, reconstructing the collaborative interception constraints using the terminal position error sphere, establishing a collaborative interception problem and completing the solution based on the sequential convex programming framework, forming a closed-loop interception strategy, and realizing the collaborative interception of a weak maneuverability interceptor against a strong maneuverability target through the closed-loop interception strategy. It has the following advantages: (1) It can be applied to the interception of a weak maneuverability interceptor against a strong maneuverability target, using the weak to defeat the strong to reduce the interception miss rate; (2) Based on the reachable domain theory, the collaborative interception constraints are constructed, and the interception accuracy is high; (3) There are no strict restrictions and constraints on the orbital height of the interceptor; (4) The collaborative interception problem is solved by sequential convex programming, and the efficiency of solving the collaborative interception problem is high.

Description

Technical Field

[0001] The present invention relates to a spacecraft collaborative closed-loop interception method based on reachable domain analysis, and in particular to a collaborative closed-loop interception method applicable to multiple weakly maneuverable aircraft against a single strong maneuverable aircraft, belonging to the field of aerospace technology. Background Art

[0002] In recent years, with the advancement of space technology and the improvement of comprehensive national strength, the development and utilization of space resources has become increasingly frequent, and space security issues are becoming increasingly prominent. Space attack and defense are gradually becoming a hot research topic for major space powers around the world. As a key component of space attack and defense, the strategic significance of space interception technology in offensive and defensive confrontations is self-evident. The space interception problem involves achieving space interception by applying appropriate maneuvers outside the Earth's atmosphere, moving an interceptor from its initial position to its target position over a period of time. The space interception problem is essentially a space maneuvering problem. Based on the strength of the target's maneuverability, it can be divided into two categories: those with a target's maneuverability weaker than that of the interceptor, and those with a target's maneuverability stronger than that of the interceptor. For the former, a single aircraft is typically used to intercept a single target, treating the target as non-maneuverable. The target is intercepted by predicting the theoretical intercept point. If the target maneuvers mid-flight, the interceptor re-predicts the intercept point and applies maneuvers to achieve interception of the maneuvering target. For the latter, using the same interception method as above can result in significant misses. This is because the target has strong maneuverability, and if it applies large maneuvers during flight, the interceptor will not be able to intercept it, causing the interception process to fail. Therefore, it is necessary to consider using multiple interceptors to collaboratively intercept the target to ensure a successful interception. However, due to the weak maneuverability of the interceptor, the accuracy of the final collaborative interception of the target is difficult to guarantee. In addition, since the collaborative interception problem involves the dynamics of multiple aircraft, its computational efficiency is low and difficult to apply in real time. Therefore, this patent proposes a spacecraft collaborative closed-loop interception method based on reachable domain analysis. This method can not only use the reachable domain analysis method to ensure the accuracy of intercepting a strong maneuverability target with a weak maneuverability interceptor, but also improve the computational efficiency based on the sequential convex optimization framework, so that the proposed method can meet the real-time performance of the closed-loop solution framework.

[0003] In the prior art of spacecraft interception methods [1] (see: Meng Shaofei, Liu Xinxue, Fu Dan, et al. Iterative algorithm for single-pulse interception trajectory with the lowest energy consumption [J]. Systems Engineering and Electronics, 2016, 38(12): 2821-2826.), the problem of single-pulse single-loop interception with the lowest energy consumption under the condition that the interception starting point is fixed but the interception end point is not fixed in the on-orbit interception is considered. From the perspective of the change law of the transfer velocity increment, a numerical iterative algorithm for the interception trajectory with the lowest energy consumption is designed. This algorithm improves the speed and reliability and avoids the problem of falling into the local optimum. However, multi-layer iteration will increase the computational complexity and solution time, and this method cannot be applied to intercepting targets with strong maneuverability. Summary of the Invention

[0004] Aiming at the interception problem where the maneuverability of the interceptor is weaker than that of the target, the main purpose of the present invention is to provide a spacecraft cooperative closed-loop interception method based on reachable domain analysis. The reachable domain theory is used to analyze the maneuverability boundary of the interceptor and the target, and the cooperative interception constraint is constructed in the form of a set. The cooperative interception constraint is reconstructed using the terminal position error sphere. The cooperative interception problem is established and solved based on the sequential convex programming framework to form a closed-loop interception strategy. The closed-loop interception strategy is used to achieve the cooperative interception of the weak maneuverability interceptor against the strong maneuverability target. It has the following advantages: (1) It can be applied to the interception of the weak maneuverability interceptor against the strong maneuverability target, and the weak can defeat the strong to reduce the interception miss rate; (2) The cooperative interception constraint is constructed based on the reachable domain theory, and its interception accuracy is high; (3) There is no strict limit and constraint on the orbital height of the interceptor; (4) The cooperative interception problem is solved by sequential convex programming, and the efficiency of solving the cooperative interception problem is high.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] The present invention discloses a method for collaborative closed-loop interception of spacecraft based on reachable domain analysis. The method establishes local vertical and horizontal coordinate systems with the initial position of any interceptor as the origin; establishes dynamic equations of the interceptor and the target in the local vertical and horizontal coordinate systems, uses the reachable domain to analyze the maneuverability boundary of the interceptor and the target, and constructs collaborative interception constraints in a set form; constructs terminal position error spheres of the interceptor and the target, represents the terminal position error sphere of the target with terminal discrete points, and reconstructs the collaborative interception constraints by covering the terminal discrete points of the target with the terminal position error sphere of the interceptor; gives the acceleration range of the interceptor, and combines the dynamic equations of the interceptor and the target and the collaborative interception constraints, establishes a collaborative interception problem with minimizing the maneuver size of the interceptor as a performance indicator; solves the collaborative interception problem based on a sequential convex programming method to obtain control quantities of all interceptors; in each guidance cycle, the interceptor executes the obtained control quantities to form a closed-loop interception strategy, and realizes collaborative interception of a weak-maneuverability interceptor against a strong-maneuverability target through the closed-loop interception strategy.

[0007] The present invention discloses a spacecraft collaborative closed-loop interception method based on reachable domain analysis, comprising the following steps:

[0008] Step 1: Take the initial position of any interceptor as the origin and establish a local vertical and horizontal coordinate system. The construction of the local vertical and horizontal coordinate system facilitates the construction of the cooperative interception constraint in step 2.

[0009] Select the initial position of any interceptor as the coordinate origin, select the direction from the center of the earth to the interceptor position as the x-axis, the z-axis as the cross product direction of the x-axis vector and the interceptor velocity vector, and the y-axis, z-axis and x-axis satisfy the right-hand rule, thus completing the construction of the local vertical and horizontal coordinate systems.

[0010] Step 2: Establish the dynamic equations of the interceptor and the target in the local vertical and horizontal coordinate systems, use the reachable domain to analyze the maneuverability boundaries of the interceptor and the target, and construct the cooperative interception constraints in a set form.

[0011] Step 2.1: Establish the dynamic equations of the interceptor and target in the local vertical and horizontal coordinate systems;

[0012] Considering the total number of interceptors is N, the dynamic equation describing the interceptor and the target is established in the local vertical and local horizontal coordinate system as follows:

[0013]

[0014]

[0015] Among them, r n =[x n ,y n ,z n ] T represents the position vector of the nth spacecraft, v n =[v n,x ,v n,y ,v n,z ] T represents the velocity vector of the nth spacecraft, u n represents the acceleration vector of the nth spacecraft, t0 is the initial time, r n,0 and v n,0 are the initial position vector and velocity vector of the nth spacecraft respectively. T =[x T ,y T ,z T ] T Represents the target position vector, v T =[v T,x ,v T,y ,vT,z ] T represents the target's velocity vector, u T represents the acceleration vector of the target, r T,0 and v T,0 are the initial position vector and velocity vector of the target respectively. The matrices A1 and A2 are expressed as follows:

[0016]

[0017] where ω is the mean orbital angular velocity of the reference interceptor.

[0018] Step 2.2: Use the reachable domain to analyze the maneuverability boundaries of the interceptor and the target, and construct cooperative interception constraints in a set form.

[0019] Interceptor n at interception time t f The terminal position at the reachable domain K n as follows:

[0020]

[0021] in is the reachable domain mapping function, Indicates the initial state of interceptor n, u n,max is the upper limit of the acceleration of interceptor n. Similarly, the target is intercepted at time t f The terminal position at the reachable domain K T as follows:

[0022]

[0023] in represents the initial state of the target, u T,max is the upper limit of the target's acceleration. Using equations (4) and (5), the collaborative interception constraint is constructed in a set form as follows:

[0024]

[0025] in

[0026]

[0027] K1, K2, K N They are interceptor 1, interceptor 2, and interceptor N terminal location reachable domains, is the union of all interceptor terminal position reachable domains. Formula (6) indicates that this union contains the target terminal position reachable domain, that is, the interceptor's maneuvering range can cover the target's maneuvering range. When the interception time t f approaches 0, and Equation (6) always holds true, which means that the interceptor group can collaboratively intercept the target.

[0028] Step 3: Construct the terminal position error sphere of the interceptor and the target, and represent the terminal position error sphere of the target with the terminal discrete points to facilitate convexification in step 4. Use the interceptor's terminal position error sphere to cover the terminal discrete points of the target to reconstruct the cooperative interception constraint, which is convenient for solving the sequential convex programming method in step 4.

[0029] Step 3.1: Construct the terminal error sphere between the interceptor and the target;

[0030] For the linear dynamic system shown in equations (1) and (2), it is discretized into the following discrete linear dynamic system:

[0031] s[k+1]=A s [k]s[k]+B s [k]u[k] (8)

[0032] Where k is the kth discrete time node, matrix A s [k], B s [k] is the system matrix, s[k] and u[k] are the nominal state and control variables of the system at the kth discrete time node. Definition is the disturbed state of the kth discrete time node, and the dynamic equation of the disturbed state is as follows:

[0033]

[0034] Where Δu[k] is the control deviation. Subtract equation (9) from equation (8) and let The following expression is obtained:

[0035] Δs[k+1]=A s [k]Δs[k]+B s [k]Δu[k] (10)

[0036] The state deviation Δs[k] at step k is obtained by recursion from formula (10) as follows:

[0037]

[0038] because as well as definition:

[0039]

[0040]

[0041] Under definitions (12) and (13), equation (11) becomes:

[0042]

[0043] in, is the position deviation of the kth step, is the speed deviation of the kth step, as well as The matrices The weight, and and

[0044] The matrices The weight, and The initial state deviations are The following boundary relationship is determined according to formula (14):

[0045]

[0046] Among them, ||Δs1[1]|| and ||Δs2[1]|| represent the initial position deviation and initial velocity deviation of the system, and their values ​​are zero; considering that the nominal control quantity Δu[j] is 0, the upper limit value of ||Δu[j]|| is u max ,u max is the maximum acceleration allowed by the system, so Equation (15) can be further rewritten as:

[0047]

[0048] in is the interfered position, s1[k] represents the nominal position. Equation (16) shows that the scatter of the interceptor and target positions at the terminal moment is described by a sphere.

[0049] Step 3.2: Use terminal discrete points to represent the terminal error sphere of the target, which facilitates convexification in step 4.

[0050] From formula (16), we know that the terminal position of the target is scattered in a sphere centered on the nominal position, and N random points are drawn from the sphere according to uniform distribution. c The discrete points are as follows:

[0051]

[0052] Among them, r ob,j represents the jth discrete point of the target, The target is recursively extended to the terminal time t without control f The nominal position of . Equation (17) expresses the terminal error sphere of the target with terminal discrete points, which is convenient for convexification in step 4.

[0053] Step 3.3: Reconstruct the cooperative interception constraints by covering the terminal discrete points of the target with the terminal error sphere of the interceptor.

[0054] The terminal error sphere of interceptor n can cover the target terminal j-th discrete point r ob,j , expressed as the following formula:

[0055]

[0056] in, represents the nominal position of the interceptor n at the terminal moment without control, and R n is the radius of the terminal position error sphere of interceptor n. Using the representation method shown in formula (18), the cooperative interception constraint (6) is reconstructed as:

[0057]

[0058] Equation (19) indicates that the terminal discrete point of the target is covered by at least one terminal error sphere of the interceptor. Although Equation (19) and Equation (6) have the same meaning, Equation (19) facilitates convexification in step 4.

[0059] Step 4: Given the interceptor's acceleration range, combined with the interceptor and target dynamics equations obtained in step 2 and the cooperative interception constraints obtained in step 3, a cooperative interception problem is established with minimizing the interceptor's maneuver size as the performance indicator; the cooperative interception problem is solved using a sequential convex programming method to obtain the control variables of all interceptors. The efficiency of solving the interceptor control variables is improved through the sequential convex programming method.

[0060] Step 4.1: Given the interceptor's acceleration range, and combining the interceptor and target dynamics equations obtained in step 2 and the cooperative interception constraints obtained in step 3, establish a cooperative interception problem with minimizing the interceptor's maneuver size as the performance indicator.

[0061] The current discrete time point is 1, and the state of the interceptor is x n [1], the target state is x T [1], predict the state x of the target at the second discrete time point T [2]As follows:

[0062] x T [2] = A s [1]x T [1] (20)

[0063] Then take the second discrete point as the starting point and the last discrete point k as the end point, and the terminal position discrete point of the target is obtained by formula (17) as r ob,j ,j=1,2,...,N c For interceptor n, the control it exerts at the current discrete time point 1 is u n [1], whose size satisfies:

[0064] ||un [1]||≤u n,max (twenty one)

[0065] Using formula (21), we can get the state x of interceptor n at the second discrete point: n [2] is:

[0066] x n [2] = A s [1]x n [1]+B s [1]u n [1] (22)

[0067] Taking the second discrete point as the starting point and the last discrete point k as the end point, the collaborative interception constraint is constructed through formula (19) as follows:

[0068]

[0069] Taking minimizing the interceptor maneuver size as the performance indicator, the cooperative interception problem P0 is constructed as follows:

[0070] Question P0:

[0071] st equation (20)-(23)(25)

[0072] Step 4.2: Solve the cooperative interception problem based on a sequential convex programming method to obtain the control variables of all interceptors, and improve the efficiency of solving the interceptor control variables through the sequential convex programming method.

[0073] In the collaborative interception problem P0, the performance index shown in formula (24) is convex, and the constraints in formulas (20) to (22) are also convex. Only the constraint in formula (23) is non-convex. Therefore, this constraint is convexified. Given a reference profile, and the corresponding After that, Equation (23) is convexified to become as follows:

[0074]

[0075]

[0076] in Represents the required covering discrete point r ob,j The interceptor is in the best terminal position when Represents The corresponding terminal position error sphere radius, at this time, the convex optimization problem P1 is as follows:

[0077] Question P1:

[0078] st equations (20)-(22), (26) and (27)(29)

[0079] The sequence iteratively solves problem P1 until convergence, and the solution of problem P0 is obtained, that is, the control quantity u of the interceptor is obtained. n [1].

[0080] Step 5: In each guidance cycle, the interceptor executes the control quantity obtained in step 4 to form a closed-loop interception strategy, through which the weak maneuverability interceptor can achieve coordinated interception of the strong maneuverability target.

[0081] In each guidance cycle, the interceptor solves the cooperative interception problem P0 to obtain the control amount, and all interceptors apply the control amount u n [1] After flying a guidance cycle Δt, a closed-loop interception strategy is formed and the interception time is updated to:

[0082] t f =t f -Δt (30)

[0083] Check that the following stop conditions are met:

[0084] t f ≤δ (31)

[0085] Where δ is the stopping threshold. If Equation (31) is not satisfied, the next guidance cycle is entered; when Equation (31) is satisfied, the closed-loop interception process ends, and the coordinated interception of the strong maneuverability target by the weak maneuverability interceptor is achieved.

[0086] Beneficial effects:

[0087] 1. The present invention discloses a method for collaborative closed-loop interception of spacecraft based on reachable domain analysis. By using the reachable domain to analyze the maneuverability boundary of the interceptor and the target, and constructing collaborative interception constraints in a set form, a problem of collaboratively intercepting a target with strong maneuverability by an interceptor with weak maneuverability is established, thereby achieving an interception effect of the weak defeating the strong, thereby reducing the number of misses in the interception.

[0088] 2. The present invention discloses a method for collaborative closed-loop interception of spacecraft based on reachable domain analysis. Through reachable domain analysis, the terminal position error sphere is used to characterize the maneuverability boundary of the aircraft, effectively improving the construction accuracy of the maneuverability boundary between the interceptor and the target, and thereby establishing collaborative interception constraints, thereby achieving high interception accuracy.

[0089] 3. The present invention discloses a spacecraft collaborative closed-loop interception method based on reachable domain analysis. The closed-loop interception can be completed by establishing a coordinate system with the initial position of any interceptor. Therefore, there are no strict requirements on the orbital heights of the interceptor and the target, which has obvious advantages.

[0090] 4. The present invention discloses a spacecraft collaborative closed-loop interception method based on reachable domain analysis, which solves the collaborative interception problem through a sequential convex programming method, greatly improving the computational efficiency. Therefore, under the condition of limited onboard computing resources, it can effectively improve the real-time performance of the calculation.

[0091] 5. The present invention discloses a spacecraft collaborative closed-loop interception method based on reachable domain analysis. On the basis of beneficial effects 1, 2, 3, and 4, it can realize the collaborative interception of highly maneuverable targets with weakly maneuverable interceptors. Therefore, compared with traditional one-to-one interception, it has higher flexibility, richer application scenarios, and a wider range of applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 This is a flow chart of a spacecraft collaborative closed-loop interception method based on reachable domain analysis of the present invention;

[0093] Figure 2 is a schematic diagram of the local vertical and horizontal coordinate systems in step 1 of the present invention;

[0094] Figure 3 is the coverage of the target terminal error sphere by the interceptor at the initial moment of interception in this embodiment;

[0095] Figure 4 It is the flight trajectory of the interceptor and the target during the closed-loop interception process of this embodiment. DETAILED DESCRIPTION

[0096] In order to better illustrate the purpose and advantages of the present invention, the present invention is explained in detail below by analyzing the implementation of a spacecraft collaborative closed-loop interception method based on reachable domain analysis.

[0097] Example 1:

[0098] like Figure 1 As shown, this embodiment discloses a spacecraft collaborative closed-loop interception method based on reachable domain analysis, and the specific implementation method is as follows:

[0099] Step 1: Take the initial position of any interceptor as the origin and establish a local vertical and horizontal coordinate system. The construction of the local vertical and horizontal coordinate system facilitates the construction of the cooperative interception constraint in step 2.

[0100] The initial position of any interceptor is selected as the coordinate origin, the direction from the center of the earth to the interceptor position is selected as the x-axis, the z-axis is the cross product direction of the x-axis vector and the interceptor velocity vector, and the y-axis, z-axis and x-axis satisfy the right-hand rule, such as Figure 2 As shown, the construction of the local vertical and horizontal coordinate systems is completed.

[0101] Step 2: Establish the dynamic equations of the interceptor and the target in the local vertical and horizontal coordinate systems, use the reachable domain to analyze the maneuverability boundaries of the interceptor and the target, and construct the cooperative interception constraints in a set form.

[0102] Step 2.1: Establish the dynamic equations of the interceptor and target in the local vertical and horizontal coordinate systems;

[0103] Considering the total number of interceptors is N = 6, the dynamic equation describing the interceptor and the target is established in the local vertical and local horizontal coordinate system as follows:

[0104]

[0105]

[0106] Among them, r n =[x n ,y n ,z n ] T represents the position vector of the nth spacecraft, v n =[v n,x ,v n,y ,v n,z ] T represents the velocity vector of the nth spacecraft, u n represents the acceleration vector of the nth spacecraft, t0 is the initial time, r n,0 and v n,0 are the initial position vector and velocity vector of the nth spacecraft, respectively, as shown in Table 1. T =[x T ,y T ,z T ] T Represents the target position vector, v T =[v T,x ,v T,y ,v T,z ] T represents the target's velocity vector, u T represents the acceleration vector of the target, r T,0 and v T,0 are the initial position vector and velocity vector of the target, respectively, as shown in Table 1.

[0107] Table 1 Initial states of interceptors and targets

[0108] Initial position vector (m) Initial velocity vector (m / s) Interceptor 1 <![CDATA[[0,0,0] T ]]> <![CDATA[[0.99,0.88,0] T ]]> Interceptor 2 <![CDATA[[200,400,0] T ]]> <![CDATA[[-0.04,-0.99,0] T ]]> Interceptor 3 <![CDATA[[400,0,0] T ]]> <![CDATA[[-0.84,0.98,0] T ]]> Interceptor 4 <![CDATA[[0,0,0] T ]]> <![CDATA[[0.69,1,14,0] T ]]> Interceptor 5 <![CDATA[[200,400,0] T ]]> <![CDATA[[0.03,1.14,0] T ]]> Interceptor 6 <![CDATA[[400,0,0] T ]]> <![CDATA[[-1.13,0.99,0] T ]]> Target <![CDATA[[500,500,0] T ]]> <![CDATA[[-1.7,-1.7,0] T ]]>

[0109] The matrices A1 and A2 are expressed as follows:

[0110]

[0111] where ω is the mean orbital angular velocity of the reference interceptor.

[0112] Step 2.2: Use the reachable domain to analyze the maneuverability boundaries of the interceptor and the target, and construct cooperative interception constraints in a set form.

[0113] Interceptor n at interception time t f The terminal position at the reachable domain K n as follows:

[0114]

[0115] in is the reachable domain mapping function, Indicates the initial state of interceptor n, u n,max is the upper limit of the acceleration of interceptor n, which is 5N. Similarly, the target is intercepted at time t f = The terminal position at 180s can reach the domain K T as follows:

[0116]

[0117] in represents the initial state of the target, u T,max is the upper limit of the target acceleration, which is 7 N. Using equations (35) and (36), the collaborative interception constraint is constructed in a set form as follows:

[0118]

[0119] in

[0120]

[0121] K1, K2, K N They are interceptor 1, interceptor 2, and interceptor N terminal location reachable domains, is the union of all interceptor terminal position reachable domains, and Equation (37) indicates that this union includes the target terminal position reachable domain, that is, the interceptor's maneuvering range can cover the target's maneuvering range. When the interception time t f approaches 0, and Equation (37) always holds true, which means that the interceptor group can collaboratively intercept the target.

[0122] Step 3: Construct the terminal position error sphere of the interceptor and the target, and represent the terminal position error sphere of the target with the terminal discrete points to facilitate convexification in step 4. Use the interceptor's terminal position error sphere to cover the terminal discrete points of the target to reconstruct the cooperative interception constraint, which is convenient for solving the sequential convex programming method in step 4.

[0123] Step 3.1: Construct the terminal error sphere between the interceptor and the target;

[0124] For the linear dynamic system shown in Equations (32) and (33), it is discretized into the following discrete linear dynamic system:

[0125] s[k+1]=A s [k]s[k]+B s [k]u[k] (39)

[0126] Where k is the kth discrete time node, matrix A s [k], B s [k] is the system matrix, s[k] and u[k] are the nominal state and control variables of the system at the kth discrete time node. Definition is the disturbed state of the kth discrete time node, and the dynamic equation of the disturbed state is as follows:

[0127]

[0128] Where Δu[k] is the control deviation. Subtract equation (9) from equation (8) and let The following expression is obtained:

[0129] Δs[k+1]=A s [k]Δs[k]+B s [k]Δu[k] (41)

[0130] The state deviation Δs[k] at step k is obtained by recursion from formula (41) as follows:

[0131]

[0132] because as well as definition:

[0133]

[0134]

[0135] Under definitions (43) and (44), equation (42) becomes:

[0136]

[0137] in, is the position deviation of the kth step, is the speed deviation of the kth step, as well as The matrices The weight, and and The matrices The weight, and The initial state deviations are The following boundary relationship is determined according to formula (45):

[0138]

[0139] Among them, ||Δs1[1]|| and ||Δs2[1]|| represent the initial position deviation and initial velocity deviation of the system, and their values ​​are zero; considering that the nominal control quantity Δu[j] is 0, the upper limit value of ||Δu[j]|| is u max ,u max is the maximum acceleration allowed by the system, so Equation (46) can be further rewritten as:

[0140]

[0141] in is the interfered position, s1[k] represents the nominal position. Equation (47) shows that the scatter of the interceptor and target positions at the terminal moment is described by a sphere.

[0142] Step 3.2: Use terminal discrete points to represent the terminal error sphere of the target, which facilitates convexification in step 4.

[0143] From formula (47), we can see that the terminal position of the target is scattered in a sphere centered on the nominal position, and N random points are drawn from the sphere according to uniform distribution. c =763 discrete points as follows:

[0144]

[0145] Among them, r ob,j represents the jth discrete point of the target, The target is recursively extended to the terminal time t without control f Nominal position, u T,max is the upper limit of the acceleration allowed by the target. Equation (48) expresses the terminal error sphere of the target with terminal discrete points, which facilitates the convexification in step 4.

[0146] Step 3.3: Reconstruct the cooperative interception constraints by covering the terminal discrete points of the target with the terminal error sphere of the interceptor.

[0147] The terminal error sphere of interceptor n can cover the target terminal j-th discrete point r ob,j , expressed as the following formula:

[0148]

[0149] in, represents the nominal position of the interceptor n at the terminal moment without control, and Rn is the radius of the terminal position error sphere of interceptor n. Using the representation method shown in formula (49), the cooperative interception constraint (37) is reconstructed as:

[0150]

[0151] Equation (50) indicates that the terminal discrete point of the target is covered by at least one terminal error sphere of the interceptor. Although Equation (50) and Equation (37) have the same meaning, Equation (50) facilitates convexification in step 4.

[0152] Step 4: Given the interceptor's acceleration range, combined with the interceptor and target dynamics equations obtained in step 2 and the cooperative interception constraints obtained in step 3, a cooperative interception problem is established with minimizing the interceptor's maneuver size as the performance indicator; the cooperative interception problem is solved using a sequential convex programming method to obtain the control variables of all interceptors. The efficiency of solving the interceptor control variables is improved through the sequential convex programming method.

[0153] Step 4.1: Given the interceptor's acceleration range, and combining the interceptor and target dynamics equations obtained in step 2 and the cooperative interception constraints obtained in step 3, establish a cooperative interception problem with minimizing the interceptor's maneuver size as the performance indicator.

[0154] The current discrete time point is 1, and the state of the interceptor is x n [1], the target state is x T [1], predict the state x of the target at the second discrete time point T [2]As follows:

[0155] x T [2] = A s [1]x T [1] (51)

[0156] Then, taking the second discrete point as the starting point and the last discrete point k=150 as the end point, the terminal position discrete point of the target is obtained by formula (48) as r ob,j ,j=1,2,...,N c For interceptor n, the control it exerts at the current discrete time point 1 is u n [1], whose size satisfies:

[0157] ||u n [1]||≤u n,max (52)

[0158] Using formula (39), we can get the state x of interceptor n at the second discrete point: n [2] is:

[0159] x n[2] = A s [1]x n [1]+B s [1]u n [1] (53)

[0160] Then, taking the second discrete point as the starting point and the last discrete point k as the end point, the collaborative interception constraint is constructed through formula (50) as follows:

[0161]

[0162] Taking minimizing the interceptor maneuver size as the performance indicator, the cooperative interception problem P0 is constructed as follows:

[0163] Question P0:

[0164] st equation (51)-(54)(56)

[0165] Step 4.2: Solve the cooperative interception problem based on a sequential convex programming method to obtain the control variables of all interceptors, and improve the efficiency of solving the interceptor control variables through the sequential convex programming method.

[0166] In the collaborative interception problem P0, the performance index shown in equation (55) is convex, and the constraints in equations (51) to (53) are also convex. Only the constraint in equation (54) is non-convex. Therefore, this constraint is convexified. Given a reference profile, and the corresponding After that, Equation (54) is convexified to become as follows:

[0167]

[0168]

[0169] in Represents the required covering discrete point r ob,j The interceptor is in the best terminal position when Represents The corresponding terminal position error sphere radius. At this point, the convex optimization problem P1 is as follows:

[0170] Question P1:

[0171] st equations (51)-(53), (57) and (58) (60) The sequence iteratively solves problem P1 until convergence, and the solution of problem P0 is obtained, that is, the control quantity u of the interceptor is obtained. n [1].

[0172] Step 5: In each guidance cycle, the interceptor executes the control quantity obtained in step 4 to form a closed-loop interception strategy, through which the weak maneuverability interceptor can achieve coordinated interception of the strong maneuverability target.

[0173] In each guidance cycle, the interceptor solves the cooperative interception problem P0 to obtain the control amount, and all interceptors apply the control amount u n [1] After a guidance cycle Δt = 1.2s, a closed-loop interception strategy is formed and the interception time is updated to:

[0174] t f =t f -Δt (61)

[0175] Repeat the above process again until the following stop conditions are met:

[0176] t f ≤δ (62)

[0177] Where δ is the stopping threshold, which is 0.1s. If Equation (62) is not satisfied, the next guidance cycle is entered; when Equation (62) is satisfied, the closed-loop interception process ends, and the coordinated interception of the strong maneuverability target by the weak maneuverability interceptor is achieved.

[0178] also, Figure 3 It shows that at the beginning of the interception, the interceptor terminal position error sphere covers the target terminal discrete points. It can be seen that the union formed by the interceptor terminal position error sphere has covered all the target terminal discrete points, which demonstrates the accuracy of this method for interception. Figure 4 The final intercept trajectory is shown, and it can be seen that interceptor 2 and interceptor 5 finally intercepted the target.

[0179] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention, which is used to explain the present invention and is not used to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A spacecraft collaborative closed-loop interception method based on reachable domain analysis, characterized by: The following steps are included: Step 1: Take the initial position of any interceptor as the origin and establish a local vertical and horizontal coordinate system. The construction of the local vertical and horizontal coordinate system facilitates the construction of the cooperative interception constraint in step 2. Step 2: Establish the dynamic equations of the interceptor and target in the local vertical and horizontal coordinate systems, use the reachable domain to analyze the maneuverability boundaries of the interceptor and target, and construct the cooperative interception constraints in a set form; Step 3: Construct the terminal position error sphere of the interceptor and the target. The terminal discrete points represent the terminal position error sphere of the target, which facilitates convexification in step 4. The terminal discrete points of the target are covered with the terminal position error sphere of the interceptor to reconstruct the cooperative interception constraint, which facilitates the sequential convex programming method in step 4. Step 4: Given the interceptor's acceleration range, the dynamic equations of the interceptor and target obtained in Step 2 and the cooperative interception constraints obtained in Step 3 are combined to establish a cooperative interception problem with minimizing the interceptor's maneuver size as the performance indicator. The cooperative interception problem is solved using a sequential convex programming method to obtain the control variables of all interceptors. The sequential convex programming method is used to improve the efficiency of solving the interceptor control variables. Step 5: In each guidance cycle, the interceptor executes the control quantity obtained in step 4 to form a closed-loop interception strategy, through which the weak maneuverability interceptor can achieve coordinated interception of the strong maneuverability target.

2. The spacecraft cooperative closed-loop interception method based on reachable domain analysis according to claim 1, characterized in that: The implementation method of step one is: Select the initial position of any interceptor as the coordinate origin, select the direction from the center of the earth to the interceptor position as the x-axis, the z-axis as the cross product direction of the x-axis vector and the interceptor velocity vector, and the y-axis, z-axis and x-axis satisfy the right-hand rule, thus completing the construction of the local vertical and horizontal coordinate systems.

3. The spacecraft cooperative closed-loop interception method based on reachable domain analysis according to claim 2, characterized in that: The implementation method of step 2 is: Step 2.1: Establish the dynamic equations of the interceptor and target in the local vertical and horizontal coordinate systems; Considering the total number of interceptors is N, the dynamic equation describing the interceptor and the target is established in the local vertical and local horizontal coordinate system as follows: Among them, r n =[x n ,y n ,z n ] T represents the position vector of the nth spacecraft, v n =[v n,x ,v n,y ,v n,z ] T represents the velocity vector of the nth spacecraft, u n represents the acceleration vector of the nth spacecraft, t0 is the initial time, r n,0 and v n,0 are the initial position vector and velocity vector of the nth spacecraft respectively; r T =[x T ,y T ,z T ] T Represents the target position vector, v T =[v T,x ,v T,y ,v T,z ] T represents the target's velocity vector, u T represents the acceleration vector of the target, r T,0 and v T,0 are the initial position vector and velocity vector of the target respectively; matrices A1 and A2 are expressed as follows: where ω is the mean orbital angular velocity of the reference interceptor; Step 2.2: Use the reachable domain to analyze the maneuverability boundaries of the interceptor and the target, and construct cooperative interception constraints in a set form; Interceptor n at interception time t f The terminal position at the reachable domain K n as follows: in is the reachable domain mapping function, Indicates the initial state of interceptor n, u n,max is the upper limit of the acceleration of the interceptor n; similarly, the target is at the interception time t f The terminal position at the reachable domain K T as follows: in represents the initial state of the target, u T,max is the upper limit of the target acceleration; using equations (4) and (5) and constructing the collaborative interception constraint in a set form as follows: in K1, K2, K N They are the terminal location reachable domains of interceptor 1, interceptor 2, and interceptor N respectively. is the union of all interceptor terminal position reachable domains; Formula (6) indicates that this union contains the target terminal position reachable domain, that is, the interceptor's maneuvering range can cover the target's maneuvering range; when the interception time t f approaches 0, and Equation (6) always holds true, which means that the interceptor group can collaboratively intercept the target.

4. The spacecraft cooperative closed-loop interception method based on reachable domain analysis according to claim 3, characterized in that: The implementation method of step three is: Step 3.1: Construct the terminal error sphere between the interceptor and the target; For the linear dynamic system shown in equations (1) and (2), it is discretized into the following discrete linear dynamic system: s[k+1]=A s [k]s[k]+B s [k]u[k] (8) Where k is the kth discrete time node, matrix A s [k], B s [k] is the system matrix, s[k] and u[k] are the nominal state and control variables of the system at the kth discrete time node respectively; definition is the disturbed state of the kth discrete time node, and the dynamic equation of the disturbed state is as follows: Where Δu[k] is the control deviation; make the difference between equation (9) and equation (8), and let The following expression is obtained: Δs[k+1]=A s [k]Δs[k]+B s [k]Δu[k] (10) The state deviation Δs[k] at step k is obtained by recursion from formula (10) as follows: because as well as definition: Under definitions (12) and (13), equation (11) becomes: in, is the position deviation of the kth step, is the speed deviation of the kth step, as well as The matrices The weight, and and The matrices The weight, and The initial state deviations are Components; According to formula (14), the following boundary relationship is determined: Among them, ||Δs1[1]|| and ||Δs2[1]|| represent the initial position deviation and initial velocity deviation of the system, and their values ​​are zero; considering that the nominal control quantity Δu[j] is 0, the upper limit value of ||Δu[j]|| is u max ,u max is the maximum acceleration allowed by the system, so Equation (15) can be further rewritten as: in is the interfered position, s1[k] represents the nominal position; Equation (16) represents the dispersion of the positions of the interceptor and the target at the terminal moment described by a sphere; Step 3.2: Use terminal discrete points to represent the terminal error sphere of the target, which facilitates convexification in step 4. From formula (16), we know that the terminal position of the target is scattered in a sphere centered on the nominal position, and N random points are drawn from the sphere according to uniform distribution. c The discrete points are as follows: Among them, r ob,j represents the jth discrete point of the target, The target is recursively extended to the terminal time t without control f The nominal position of the target; Equation (17) uses terminal discrete points to represent the terminal error sphere of the target, which is convenient for convexification in step 4; Step 3.3: Reconstruct the cooperative interception constraints by covering the terminal discrete points of the target with the terminal error sphere of the interceptor; The terminal error sphere of interceptor n can cover the target terminal j-th discrete point r ob,j , expressed as the following formula: in, represents the nominal position of the interceptor n at the terminal moment without control, and R n is the radius of the terminal position error sphere of interceptor n; using the representation method shown in formula (18), the cooperative interception constraint (6) is reconstructed as: Formula (19) indicates that the terminal discrete point of the target is covered by at least one terminal error sphere of the interceptor. Although Formula (19) and Formula (6) have the same meaning, Formula (19) is convenient for convexification in step 4.

5. The spacecraft cooperative closed-loop interception method based on reachable domain analysis according to claim 4, characterized in that: The implementation method of step 4 is: Step 4.1: Given the interceptor's acceleration range, and combining the interceptor-target dynamics equations obtained in Step 2 with the cooperative interception constraints obtained in Step 3, establish a cooperative interception problem with minimizing the interceptor's maneuver size as the performance indicator. The current discrete time point is 1, and the state of the interceptor is x n [1], the target state is x T [1], predict the state x of the target at the second discrete time point T [2]As follows: x T [2]=A s [1]x T [1] (20) Then take the second discrete point as the starting point and the last discrete point k as the end point, and the terminal position discrete point of the target is obtained by formula (17) as r ob,j ,j=1,2,...,N c ; For interceptor n, the control it applies at the current discrete time point 1 is u n [1], whose size satisfies: ||in n [1]||≤u n,max (21) Using formula (21), we can get the state x of interceptor n at the second discrete point: n [2] is: x n [2]=A s [1]x n [1]+B s [1]u n [1] (22) Taking the second discrete point as the starting point and the last discrete point k as the end point, the collaborative interception constraint is constructed through formula (19) as follows: Taking minimizing the interceptor maneuver size as the performance indicator, the cooperative interception problem P0 is constructed as follows: Question P0: st equations (20)-(23) (25) Step 4.2: Solve the cooperative interception problem based on a sequential convex programming method to obtain control variables of all interceptors, and improve the efficiency of solving the interceptor control variables by using the sequential convex programming method; In the collaborative interception problem P0, the performance index shown in formula (24) is convex, and the constraints in formulas (20) to (22) are also convex. Only the constraint in formula (23) is non-convex. Therefore, this constraint is convexified. Given a reference profile, and the corresponding After that, Equation (23) is convexified to become as follows: in Represents the required covering discrete point r ob,j The interceptor is in the best terminal position when Represents The corresponding terminal position error sphere radius, at this time, the convex optimization problem P1 is as follows: Question P1: st equations (20)-(22), (26) and (27) (29) The sequence iteratively solves problem P1 until convergence, and the solution of problem P0 is obtained, that is, the control quantity u of the interceptor is obtained. n [1].

6. The spacecraft cooperative closed-loop interception method based on reachable domain analysis according to claim 5, characterized in that: The implementation method of step five is: In each guidance cycle, the interceptor solves the cooperative interception problem P0 to obtain the control amount, and all interceptors apply the control amount u n [1] After flying a guidance cycle Δt, a closed-loop interception strategy is formed and the interception time is updated to: t f =t f -Δt (30) Check that the following stop conditions are met: t f ≤δ (31) Where δ is the stopping threshold; if equation (31) is not satisfied, the next guidance cycle is entered; when equation (31) is satisfied, the closed-loop interception process ends, that is, the coordinated interception of the strong maneuverability target by the weak maneuverability interceptor is realized.

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