Multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous

Abstract

The invention relates to a multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous. The multi-spacecraft orbit cooperative control strategy comprises the following steps: step 1, establishing a relative motion equation to describe motion of spacecrafts and non-cooperative targets; 2, establishing a spacecraft orbit control model; 3, solving a spacecraft orbit control strategy; step 4, calculating a state weight matrix of two pursuing parties; and step 5, designing a task allocation scheme of pursuit and escape parties. According to the multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous, the state quantities of pursuing and escaping parties are converted into a weight matrix based on an analytic hierarchy process, the matching problem between trackers and escapers is solved by adopting a KM algorithm, and task redistribution is performed on the remaining trackers on the basis to make up for the deficiency of primary distribution.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and in particular to a multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous. Background Art

[0002] In recent years, the aerospace technology of countries around the world has developed rapidly, the frequency of space launches has continued to increase, and the number of spacecraft in orbit has continued to increase. With the rise of microsatellites and the continuous emergence of large constellation plans, satellites often operate in orbit in the form of multi-satellite networking, which means that it is more common for multiple spacecraft to perform space missions together. In addition, with the development of space rendezvous technology, satellites have the ability to conduct close reconnaissance of non-cooperative targets. With the support of these technologies, a group of satellites in orbit can provide important intelligence through ground observation, and can also approach and interfere with non-cooperative target satellites, thereby affecting their normal functions. Considering the clustering characteristics of current spacecraft in orbit, it is necessary to study the rendezvous problem between multiple spacecraft and non-cooperative targets.

[0003] The rendezvous problem between a spacecraft and a non-cooperative target is essentially an orbital pursuit problem. At present, the spacecraft pursuit problem is mostly limited to the scope of the dual-spacecraft pursuit game, and rarely involves the study of the multi-spacecraft pursuit game. In the multi-spacecraft pursuit game, at least one party has multiple spacecraft, and these spacecraft work together to complete a game target task. Compared with the dual-spacecraft pursuit game, the multi-spacecraft game has more strategies and more complex models, which leads to the optimal game strategy not only determined by control ability and dynamics. Summary of the invention

[0004] The present invention aims to solve the technical problems existing in the orbital rendezvous of non-cooperative targets in the prior art and provide a multi-spacecraft orbital cooperative control strategy for the rendezvous of non-cooperative targets.

[0005] In order to solve the above technical problems, the technical solutions of the present invention are as follows:

[0006] A multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous includes the following steps:

[0007] Step 1, establish the relative motion equation to describe the motion of the spacecraft and the non-cooperative target;

[0008] Step 2: Establishment of spacecraft orbit control model;

[0009] Step 3, solving the spacecraft orbit control strategy;

[0010] Step 4: Calculate the state weight matrix of the two parties in pursuit and escape;

[0011] Step 5: Design a task allocation plan for the pursuit and fugitive parties.

[0012] In the above technical solution, step 1 is specifically as follows:

[0013] Define OXYZ to represent the inertial coordinate system, the OX axis is located in the equatorial plane and points to the vernal equinox; the OZ axis points to the agreed pole along the earth's rotation axis, and the OY axis conforms to the right-handed Cartesian coordinate system; in the process of spacecraft pursuit and escape game, a point close to the pursuit and escape spacecraft is selected as the reference spacecraft, and the reference spacecraft orbits the earth along the Kepler orbit. On this basis, Sxyz is defined as the reference coordinate system; in the reference coordinate system Sxyz, the origin of the coordinate is a point moving on the reference orbit, the Sx axis points from the center of the earth to the reference spacecraft, the Sy axis is along the direction of motion of the reference point, perpendicular to the Sx axis, and the Sz axis is perpendicular to the Sx axis and the Sy axis respectively, satisfying the right-hand rule; the relative motion equation of the spacecraft and the non-cooperative target relative to the reference point is expressed as:

[0014]

[0015] Where: x, y, z are the projection sizes of the relative position vector along the three axes respectively; They are the first-order derivatives of the three-axis relative position vectors, i.e., the relative velocity of the spacecraft; are the second-order derivatives of the three-axis relative position vectors, i.e., the relative acceleration of the spacecraft; u x ,u y ,u z are the three-axis components of the spacecraft acceleration; ω represents the orbital angular velocity of the reference point.

[0016] In the above technical solution, step 2 is specifically as follows:

[0017] Assume that the state of the spacecraft is The control input is Based on the optimal control theory, the state equation of the spacecraft is as follows:

[0018]

[0019] use and X E Respectively represent the state of the i-th spacecraft and the non-cooperative target, and use and u E denote the control input of the i-th spacecraft and the non-cooperative target, respectively, X i represents the relative state variables of the i-th spacecraft and the non-cooperative target, and the state equations of both parties are written as follows:

[0020]

[0021] Payoff functions for spacecraft and non-cooperative targets and J E Each is:

[0022]

[0023] Where: T f is the terminal moment; S is a semi-positive symmetric matrix, representing the terminal distance weight; and R E They are all positive definite symmetric matrices representing energy weights, and j is the number of the spacecraft closest to the non-cooperative target.

[0024] In the above technical solution, step 3 is specifically as follows:

[0025] After introducing the covariate variable λ(t), the Hamiltonian function is written as:

[0026]

[0027] The cooperative state equation and state equation of the spacecraft and non-cooperative target system are written as:

[0028]

[0029] The optimal control condition Substituting into the above formula, we can get the control strategies of the pursuer and escaper respectively:

[0030]

[0031] Where: u kmax is the acceleration amplitude of each party in pursuit and escape, is the optimal control strategy for both pursuit and escape spacecraft, R k is the corresponding energy weight matrix;

[0032] According to the Pontryagin minimum principle, the optimal control strategy of the closed-loop form of the pursuit system is obtained:

[0033]

[0034] Where: The matrix function P(t) satisfies the Ricatti equation:

[0035]

[0036] in, Q e =B(R E ) -1 B T , is the first-order derivative of the matrix function, P(T f ) is the matrix function value at the terminal moment, S f is a constant matrix.

[0037] In the above technical solution, step 4 is specifically as follows:

[0038] First, construct a judgment matrix. The maneuverability, position and speed of the escaper are the main factors that the tracker needs to consider when selecting the escaper. Compare these three factors in pairs and construct a judgment matrix C=(c ij ) 3×3 , where if the judgment of factor i relative to factor j is c ij , then the judgment of factor j relative to i is c ji =1 / c ij ;

[0039] Then, perform hierarchical single sorting and calculate the maximum characteristic root λ of the judgment matrix max The corresponding eigenvector is normalized to obtain w, where the elements in w represent the importance weight of each factor relative to other factors;

[0040] Next, the consistency test is performed: the consistency ratio CR = CI / RI and the consistency index CI = (λ-n) / (n-1) are defined; the RI value is related to the number of factors n. When CR is less than 0.1, the consistency test is passed, otherwise the judgment matrix needs to be reconstructed;

[0041] After that, calculate the weight of each factor: convert the maneuverability, distance and speed of the pursuit and escape combination into the factor weight according to the following function:

[0042]

[0043] Where: subscripts i and j represent the tracker and escaper numbers; μ a ,μ d ,μ v They represent the weight values ​​of the maneuverability, distance and speed of the pursuit-escape combination respectively; v is the speed; a is the acceleration amplitude; r represents the distance between the current pursuit-escape combination tracker and escaper; D1 and D2 are the closest distance and the farthest distance between the two parties respectively; k d k is the distance calculation coefficient; v is the velocity direction coefficient;

[0044] Finally, calculate the weight matrix: write the factor weight values ​​obtained in the previous step into the weight matrix T according to the following function, T ij Represents the elements in the weight matrix:

[0045]

[0046] In the above technical solution, step 5 is specifically as follows:

[0047] Assume that the number of trackers is M, the number of escapers is N, M>N, and the orbital rendezvous problem of multiple spacecraft and non-cooperative targets is represented by a weighted bipartite graph Graph={P,E,L,S}; where the vertex set P={P1,P2,…,P M} represents the tracker, and the vertex set E = {E1, E2, …, E N} represents the escaper, and the edge set L = {l ij |i=1,2,…,M,j=1,2,…,N} represents the pairing situation. If tracker i selects escaper j, then edge l ij exists, and its weight is given by the hierarchical analysis method in step 4, using s ij express.

[0048] In the above technical solution, in step 5, the specific method of using the KM algorithm to solve the matching solution is as follows:

[0049] The first step is to initialize the top label value; select the side with fewer vertices as the starting set and the other side as the to-be-matched set, and set the top label value for each vertex; at the beginning of matching, set the top label value of all vertices in the starting set to the maximum weight of the edge it can connect to, and set all top label values ​​of the to-be-matched set to 0; during the algorithm, for any edge in the graph, it is necessary to ensure that the sum of the top labels of the left and right vertices connected to the edge is always not less than the weight value of the edge, that is:

[0050] p i +e j ≥s ij

[0051] Among them, p i represents the top label value corresponding to the i-th tracker, e j Indicates the top mark value corresponding to the jth escaper;

[0052] The second step is to find a complete match of the bipartite graph. In a bipartite graph, a path formed by starting from an unmatched point and passing through an unmatched edge, a matched edge, an unmatched edge, and so on in an alternating order is called an alternating path. If an alternating path eventually reaches another unmatched point, then the path is an augmenting path. For each vertex in the starting set, find an augmenting path in the equal subgraph. If an augmenting path is found, go to step 4, otherwise go to step 3.

[0053] Step 3: Modify the top mark value. At this time, the matching of the bipartite graph is not a complete match, and the equal subgraph needs to be expanded. The top mark modification rule is: subtract d from the top mark values ​​of the points that are to be matched in the starting set and the points that have been matched, and increase d from the top mark values ​​of the points to be matched in the set to be matched. The variable d = min{p i +e j -s ij};

[0054] The fourth step is to continue to repeat steps 2 and 3 until an augmenting path is found for each vertex in the starting set.

[0055] In the above technical solution, in step 5, the main steps of redistributing tasks to the remaining trackers are as follows:

[0056] First, recalculate the weight matrix; after the initial allocation, count the tracker numbers that have not yet determined the tracking target, and calculate the weight matrix of the remaining trackers and escapers;

[0057] Then, the KM algorithm is used to assign escapers to the current remaining trackers based on the new weight matrix;

[0058] After this allocation, if all trackers have been assigned to escapers, the redistribution ends, otherwise the weight matrices of the remaining spacecraft continue to be calculated and allocated until all trackers have escapers to track.

[0059] In the above technical solution, in step 5, when recalculating the weight matrix, the weight matrix of the remaining trackers and escapers satisfies:

[0060]

[0061] Where: subscripts i and j represent the tracker and escaper numbers; μ a ,μ d ,μ v They represent the weight values ​​of the maneuverability, distance and speed of the pursuit-escape combination respectively; v is the speed; a is the acceleration amplitude; r represents the distance between the current pursuit-escape combination tracker and escaper; D1 and D2 are the closest distance and the farthest distance between the two parties respectively; k d k is the distance calculation coefficient; v is the velocity direction coefficient.

[0062] The present invention has the following beneficial effects:

[0063] The multi-spacecraft orbit collaborative control strategy for non-cooperative target rendezvous of the present invention converts the state quantities of the pursuer and escaper into a weight matrix based on the hierarchical analysis method, adopts the KM algorithm to solve the matching problem between the pursuer and the escaper, and on this basis, redistributes tasks to the remaining pursuers to make up for the shortcomings of the initial allocation.

[0064] Compared with the dual-spacecraft pursuit and escape control strategy, the multi-spacecraft orbit collaborative control strategy for non-cooperative target rendezvous of the present invention proves that the effect of joint pursuit is better than single pursuit. Increasing the number of trackers can improve the success rate of interception missions. At the same time, the pursuit and escape task redistribution based on the KM algorithm can complement the initial allocation, and the pursuer can dispatch additional trackers to track and intercept escapees that are more difficult to intercept. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0066] Figure 1 Schematic diagram of pursuit trajectories corresponding to different pursuit methods.

[0067] Figure 2 Schematic diagram of distance and time for different pursuit methods.

[0068] Figure 3 Schematic diagram of the change in the x-position component of the pursuing and escaping parties.

[0069] Figure 4 Schematic diagram of the change in the y position component of the pursuing and fleeing parties.

[0070] Figure 5 Schematic diagram of the change in the z position component of the pursuing and fleeing parties.

[0071] Figure 6 This is a schematic diagram of the change in relative distance between the two parties in static matching.

[0072] Figure 7 This is a schematic diagram of the trajectory changes of the two parties in static matching.

[0073] Figure 8 This is a schematic diagram of the dynamic matching of the change in relative distance between the two parties in pursuit.

[0074] Fig. 9 A schematic diagram of the dynamic matching of the trajectory changes of the pursuing and fugitive parties.

[0075] Fig.10 Schematic diagram of the change in the x-axis position components of the pursuing and fleeing parties under dynamic matching.

[0076] Fig.11 Schematic diagram of the change in the x-axis position components of the chasing and fleeing parties under static matching.

[0077] Fig.12 Schematic diagram of the change in the y-axis position components of the pursuing and fleeing parties under dynamic matching.

[0078] Fig.13 Schematic diagram of the change in the y-axis position components of the chasing and fleeing parties under static matching.

[0079] Fig.14 Schematic diagram of the change of z-axis position components of the pursuing and fleeing parties under dynamic matching.

[0080] Fig.15 Schematic diagram of the change of z-axis position components of the chasing and fleeing parties under static matching. DETAILED DESCRIPTION

[0081] The inventive concept of the present invention is:

[0082] The present invention provides a multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous. Aiming at the tracker redundancy problem in the scenario of more chasing and fewer escaping, a many-to-one pursuit and escape control strategy is derived. The coordination of trackers can improve the game results and increase the success rate of interception missions.

[0083] The multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous of the present invention is expanded on the basis of two-person zero-sum differential game theory, and realizes cooperative control of multiple spacecraft performing non-cooperative target rendezvous missions, maximizes the advantages of each spacecraft, and improves the mission success rate.

[0084] The present invention is described in detail below with reference to the accompanying drawings.

[0085] The multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous of the present invention comprises the following steps:

[0086] Step 1, establish the relative motion equation to describe the motion of the spacecraft and the non-cooperative target:

[0087] Define OXYZ to represent an inertial coordinate system, with the OX axis located in the equatorial plane and pointing to the vernal equinox; the OZ axis points to the agreed pole along the earth's rotation axis, and the OY axis conforms to the right-handed Cartesian coordinate system. In the spacecraft pursuit and escape game, a point close to the pursuit and escape spacecraft is selected as the reference spacecraft. The reference spacecraft orbits the earth along the Kepler orbit, and on this basis, Sxyz is defined as the reference coordinate system. In the reference coordinate system Sxyz, the origin of the coordinates is a point moving on the reference orbit, the Sx axis points from the center of the earth to the reference spacecraft, the Sy axis is along the direction of motion of the reference point, perpendicular to the Sx axis, and the Sz axis is perpendicular to the Sx axis and the Sy axis, respectively, satisfying the right-hand rule. In the context of the non-cooperative target rendezvous problem studied in the present invention, the initial distance between the two parties is on the order of ten kilometers, which is much smaller than the reference orbit radius. Then the relative motion equation of the spacecraft and the non-cooperative target relative to the reference point is expressed as:

[0088]

[0089] Where: x, y, z are the projection sizes of the relative position vector along the three axes respectively; They are the first-order derivatives of the three-axis relative position vectors, i.e., the relative velocity of the spacecraft; are the second-order derivatives of the three-axis relative position vectors, i.e., the relative acceleration of the spacecraft; u x ,u y ,u z are the three-axis components of the spacecraft acceleration; ω represents the orbital angular velocity of the reference point.

[0090] Step 2: Establishment of spacecraft orbit control model:

[0091] According to the relative motion equation, the control force acting on the spacecraft controls the motion of the spacecraft by changing the three-axis acceleration of the spacecraft. Considering only the gravitational force between the earth and the spacecraft, the dynamic equation of the spacecraft is linear. Assume that the state quantity of the spacecraft is The control input is The state equation of the spacecraft can be obtained based on the optimal control theory as follows:

[0092]

[0093] Consider the problem of n spacecraft simultaneously performing orbital rendezvous with a non-cooperative target, using and X E Respectively represent the state of the i-th spacecraft and the non-cooperative target, and use and u E denote the control input of the i-th spacecraft and the non-cooperative target, respectively, X i represents the relative state variables of the i-th spacecraft and the non-cooperative target, from which the state equations of both parties can be written:

[0094]

[0095] In the present invention, non-cooperative targets give priority to avoiding the spacecraft closest to them. Then, considering the terminal distance and fuel consumption, the payment function of the spacecraft and the non-cooperative target is and J E Each is:

[0096]

[0097] Where: T f is the terminal moment; S is a semi-positive symmetric matrix, representing the terminal distance weight; and R E They are all positive definite symmetric matrices representing energy weights, and j is the number of the spacecraft closest to the non-cooperative target.

[0098] Step 3, solving the spacecraft orbit control strategy:

[0099] After introducing the co-state variable λ(t), the Hamiltonian function of equation (6) can be written as:

[0100]

[0101] The spacecraft and the non-cooperative target can be regarded as a pursuit-escape system. The spacecraft performing the pursuit mission is regarded as the pursuer, and the non-cooperative target needs to avoid the spacecraft and is regarded as the escaper. The cooperative state equation and state equation of this system can be written as:

[0102]

[0103] The optimal control condition Substituting into equation (8), we can obtain the control strategies of the pursuer and escaper respectively:

[0104]

[0105] Where: u kmax is the acceleration amplitude of each party in pursuit and escape, is the optimal control strategy for both pursuit and escape spacecraft, R k is the corresponding energy weight matrix.

[0106] According to the Pontryagin minimum principle, the optimal control strategy of the closed-loop form of the pursuit system can be obtained:

[0107]

[0108] Where: The matrix function P(t) satisfies the Ricatti equation:

[0109]

[0110] in, Q e =B(R E ) -1 B T , is the first-order derivative of the matrix function, P(T f ) is the matrix function value at the terminal moment, S f is a constant matrix.

[0111] Step 4: Calculate the state weight matrix of the two parties:

[0112] In the orbital rendezvous problem of multiple spacecraft and non-cooperative targets studied in the present invention, all trackers need to track escapers, that is, all non-cooperative targets need to be mission targets, and there are no redundant trackers and escapers. To deal with this problem, the present invention quantifies the states of spacecraft participating in the game into a weight matrix with the help of hierarchical analysis method, and then uses the Kuhn-Munkres algorithm (KM algorithm) to match the pursuit and escape tasks. Since the KM algorithm can only perform one-to-one matching, and the actual problem of more pursuits and fewer escapes is a combination of the problem of more pursuits and one escape and the problem of one pursuit and one escape, it is necessary to consider using the KM algorithm for redistribution to generate a complete matching solution.

[0113] First, construct a judgment matrix. The maneuverability, position and speed of the escaper are the main factors that the tracker needs to consider when selecting the escaper. Compare these three factors in pairs and construct a judgment matrix C=(c ij ) 3×3, where if the judgment of factor i relative to factor j is c ij , then the judgment of factor j relative to factor i is c ji =1 / c ij .

[0114] Then, perform hierarchical single sorting and calculate the maximum characteristic root λ of the judgment matrix max The corresponding eigenvector is normalized to obtain w, where the elements in w represent the importance weight of each factor relative to other factors.

[0115] Next, the consistency test is performed: the consistency ratio CR = CI / RI and the consistency index CI = (λ-n) / (n-1) are defined. The RI value is related to the number of factors n. When CR is less than 0.1, the consistency test is passed, otherwise the judgment matrix needs to be reconstructed.

[0116] After that, calculate the weight of each factor: convert the maneuverability, distance and speed of the pursuit and escape combination into the factor weight according to the following function:

[0117]

[0118] Where: subscripts i and j represent the tracker and escaper numbers; μ a ,μ d ,μ v They represent the weight values ​​of the maneuverability, distance and speed of the pursuit-escape combination respectively; v is the speed; a is the acceleration amplitude; r represents the distance between the current pursuit-escape combination tracker and escaper; D1 and D2 are the closest distance and the farthest distance between the two parties respectively; k d k is the distance calculation coefficient, which is determined based on experience and is generally 0.01; v is the velocity direction coefficient, which is taken as 0.25.

[0119] Finally, calculate the weight matrix: Write the factor weight values ​​obtained in step 4 into the weight matrix T according to the following function, T ij Represents the elements in the weight matrix:

[0120]

[0121] Step 5: Design of task allocation plan for both parties:

[0122] For the orbital rendezvous problem of multiple spacecraft and non-cooperative targets studied in this invention, let the number of trackers be M and the number of escapers be N (M>N), the problem can be represented by a weighted bipartite graph Graph={P,E,L,S}. M} represents the tracker, and the vertex set E = {E1, E2, …, E N} represents the escaper, and the edge set L = {lij |i=1,2,…,M,j=1,2,…,N} represents the pairing situation. If tracker i selects escaper j, then edge l ij exists, and its weight is given by the hierarchical analysis method in the previous section, using s ij Before the matching starts, all trackers can choose any escaper to track. The specific method of using the KM algorithm to solve the matching solution is as follows:

[0123] The first step is to initialize the top-label value. Select the side with fewer vertices as the starting set and the other side as the to-be-matched set, and set the top-label value for each vertex. At the beginning of the match, set the top-label value of all vertices in the starting set to the maximum weight of the edge it can connect to, and set all top-label values ​​of the to-be-matched set to 0. During the algorithm, for any edge in the graph, it is necessary to ensure that the sum of the top labels of the left and right vertices connected to the edge is always not less than the weight value of the edge, that is:

[0124] p i +e j ≥s ij (16)

[0125] Among them, p i represents the top label value corresponding to the i-th tracker, e j Indicates the top label value corresponding to the j-th escaper.

[0126] The second step is to find a complete match of the bipartite graph. In a bipartite graph, a path formed by starting from an unmatched point and passing through an unmatched edge, a matched edge, an unmatched edge, and so on in an alternating order is called an alternating path. If an alternating path eventually reaches another unmatched point, then the path is an augmenting path. For each vertex in the starting set, find an augmenting path in the equal subgraph. If an augmenting path is found, go to step 4, otherwise go to step 3.

[0127] Step 3: Modify the top mark value. At this time, the matching of the bipartite graph is not a complete match, and the equal subgraph needs to be expanded. The top mark modification rule is: subtract d from the top mark value of the point that is to be matched in the starting set and the point that has been matched, and increase the top mark value of the point to be matched in the set by d. The variable d = min{p i +e j -s ij}.

[0128] The fourth step is to continue to repeat steps 2 and 3 until an augmenting path is found for each vertex in the starting set.

[0129] Since the number of trackers is greater than that of escapers, one KM allocation can only determine the tracking target for some trackers. To ensure that all trackers have targets to track, tasks need to be redistributed for the remaining trackers. The main steps of redistribution in the present invention are as follows:

[0130] First, recalculate the weight matrix. After the initial allocation, count the numbers of the trackers whose targets have not been determined, and calculate the weight matrix of the remaining trackers and escapers. Since the trackers give priority to escapers with weaker maneuverability, closer distance, and lower speed during the initial allocation, additional trackers should be assigned to track escapers with stronger maneuverability, longer distance, and higher speed during the redistribution. Otherwise, all trackers will be more inclined to track weak escapers, and strong escapers will not receive the attention of the pursuers. Note that during the initial allocation, it is considered that the various factors of the pursuit and escape combination are ranked from weak to strong in order of importance: maneuverability, distance, and speed; during the redistribution, in order to complement the initial allocation plan, the importance of the various factors of the pursuit and escape combination is ranked from weak to strong in order of importance: speed, distance, and maneuverability. In addition, in the redistribution, equations (12) to (14) should be changed to:

[0131]

[0132] Then, the KM algorithm is used to assign escapers to the remaining trackers based on the new weight matrix. After this assignment, if all trackers have been assigned to escapers, the redistribution ends. Otherwise, the weight matrix of the remaining spacecraft is calculated and assigned again until all trackers have escapers to track.

[0133] The multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous of the present invention is further described in detail below with reference to the accompanying drawings.

[0134] The parameter settings of the payment function in the present invention are shown in Table 1, where r p and r e is the control weight parameter, s r and v is the terminal weight parameter, the reference point orbit altitude is 800km, and the simulation step length is 1s.

[0135] Table 1 Parameter value table

[0136]

[0137] 1. Verification of the effectiveness of collaborative control strategy

[0138] In order to verify the effectiveness of the track coordination control strategy proposed in this invention, a two-chasing-one-escaping example is set up to compare the game results corresponding to different pursuit and escape strategies. In this invention, the strategy of multiple trackers intercepting one escaper at the same time is called joint pursuit, and the one-to-one interception is called single pursuit. The initial states of the two parties of pursuit and escape are shown in Table 2. The spatial trajectory changes of P1, P2 and E under different pursuit modes are shown in Table 2. Figure 1 The relative distance curve between the chasing and escaping parties is shown in Figure 2 shown. Figure 3 to Figure 5 The pattern of how the three-axis position components of the pursuing and fleeing parties change with time is demonstrated.

[0139] Table 2 Initial status of the two parties in pursuit

[0140]

[0141] II. Orbital Control of Multiple Spacecraft and Non-cooperative Target Rendezvous

[0142] The orbital cooperative control strategy of the present invention can solve the orbital intersection problem of multiple trackers and multiple escapers. In this example, the number of trackers is 5, the number of escapers is 3, the initial state of the pursuit and escape spacecraft is shown in Table 3, the game time is 1000s, and the time interval of dynamic matching is 125s. If only one allocation is performed at the initial moment, such allocation is called a static matching scheme. If the tracking target is reassigned to the tracker at regular intervals according to the current state of the pursuit and escape parties, the matching scheme generated thereby is called a dynamic matching. Figure 6 to Figure 9 The relative distance changes and spatial trajectories between the pursuing and fugitives under static matching and dynamic matching schemes are shown respectively. Figure 10 to Figure 15 It reflects the changes in the three-axis position of the spacecraft under different matching schemes.

[0143] Table 3 Initial status of the two parties in pursuit

[0144]

[0145] The multi-spacecraft orbit collaborative control strategy for non-cooperative target rendezvous of the present invention converts the state quantities of the pursuer and escaper into a weight matrix based on the hierarchical analysis method, adopts the KM algorithm to solve the matching problem between the pursuer and the escaper, and on this basis, redistributes tasks to the remaining pursuers to make up for the shortcomings of the initial allocation.

[0146] Compared with the dual-spacecraft pursuit and escape control strategy, the multi-spacecraft orbit collaborative control strategy for non-cooperative target rendezvous of the present invention proves that the effect of joint pursuit is better than single pursuit. Increasing the number of trackers can improve the success rate of interception missions. At the same time, the pursuit and escape task redistribution based on the KM algorithm can complement the initial allocation, and the pursuer can dispatch additional trackers to track and intercept escapees that are more difficult to intercept.

[0147] Obviously, the above embodiments are merely examples for the purpose of clear explanation, and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived therefrom are still within the scope of protection of the invention.

Claims

1. A multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous, characterized in that: The following steps are involved: Step 1, establish the relative motion equation to describe the motion of the spacecraft and the non-cooperative target; Step 2: Establishment of spacecraft orbit control model; Step 3, solving the spacecraft orbit control strategy; Step 4: Calculate the state weight matrix of the two parties in pursuit and escape; Step 5: Design a task allocation plan for the pursuit and fugitive parties.

2. The multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous according to claim 1 is characterized in that: Step 1 is as follows: Define OXYZ to represent the inertial coordinate system, the OX axis is located in the equatorial plane and points to the vernal equinox; the OZ axis points to the agreed pole along the earth's rotation axis, and the OY axis conforms to the right-handed Cartesian coordinate system; in the process of spacecraft pursuit and escape game, a point close to the pursuit and escape spacecraft is selected as the reference spacecraft, and the reference spacecraft orbits the earth along the Kepler orbit. On this basis, Sxyz is defined as the reference coordinate system; in the reference coordinate system Sxyz, the origin of the coordinate is a point moving on the reference orbit, the Sx axis points from the center of the earth to the reference spacecraft, the Sy axis is along the direction of motion of the reference point, perpendicular to the Sx axis, and the Sz axis is perpendicular to the Sx axis and the Sy axis respectively, satisfying the right-hand rule; the relative motion equation of the spacecraft and the non-cooperative target relative to the reference point is expressed as: Where: x, y, z are the projection sizes of the relative position vector along the three axes respectively; They are the first-order derivatives of the three-axis relative position vectors, i.e., the relative velocity of the spacecraft; are the second-order derivatives of the three-axis relative position vectors, i.e., the relative acceleration of the spacecraft; u x ,u y ,u z are the three-axis components of the spacecraft acceleration; ω represents the orbital angular velocity of the reference point.

3. The multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous according to claim 1 is characterized in that: Step 2 is as follows: Assume that the state of the spacecraft is The control input is Based on the optimal control theory, the state equation of the spacecraft is as follows: use and X E Respectively represent the state of the i-th spacecraft and the non-cooperative target, and use and u E denote the control input of the i-th spacecraft and the non-cooperative target, respectively, X i represents the relative state variables of the i-th spacecraft and the non-cooperative target, and the state equations of both parties are written as follows: Payoff functions for spacecraft and non-cooperative targets and J E Each is: Where: T f is the terminal moment; S is a semi-positive symmetric matrix, representing the terminal distance weight; and R E They are all positive definite symmetric matrices representing energy weights, and j is the number of the spacecraft closest to the non-cooperative target.

4. The multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous according to claim 3 is characterized in that: Step 3 is as follows: After introducing the covariate variable λ(t), the Hamiltonian function is written as: The cooperative state equation and state equation of the spacecraft and non-cooperative target system are written as: The optimal control condition Substituting into the above formula, we can get the control strategies of the pursuer and escaper respectively: ||in k ||≤u kmax Where: u kmax is the acceleration amplitude of each party in pursuit and escape, is the optimal control strategy for both pursuit and escape spacecraft, R k is the corresponding energy weight matrix; According to the Pontryagin minimum principle, the optimal control strategy of the closed-loop form of the pursuit system is obtained: Where: The matrix function P(t) satisfies the Ricatti equation: in, Q e =B(R E ) -1 B T , The first derivative of the matrix function, P(T f ) is the matrix function value at the terminal moment, S f is a constant matrix.

5. The multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous according to claim 1, characterized in that: Step 4 is as follows: First, construct a judgment matrix. The maneuverability, position and speed of the escaper are the main factors that the tracker needs to consider when selecting the escaper. Compare these three factors in pairs and construct a judgment matrix C=(c ij ) 3×3 , where if the judgment of factor i relative to factor j is c ij , then the judgment of factor j relative to i is c ji =1 / c ij ; Then, perform hierarchical single sorting and calculate the maximum characteristic root λ of the judgment matrix max The corresponding eigenvector is normalized to obtain w, where the elements in w represent the importance weight of each factor relative to other factors; Next, the consistency test is performed: the consistency ratio CR = CI / RI and the consistency index CI = (λ-n) / (n-1) are defined; the RI value is related to the number of factors n. When CR is less than 0.1, the consistency test is passed, otherwise the judgment matrix needs to be reconstructed; After that, calculate the weight of each factor: convert the maneuverability, distance and speed of the pursuit and escape combination into the factor weight according to the following function: Where: subscripts i and j represent the tracker and escaper numbers; μ a ,μ d ,μ v They represent the weight values ​​of the maneuverability, distance and speed of the pursuit-escape combination respectively; v is the speed; a is the acceleration amplitude; r represents the distance between the current pursuit-escape combination tracker and escaper; D1 and D2 are the closest distance and the farthest distance between the two parties respectively; k d k is the distance calculation coefficient; v is the velocity direction coefficient; Finally, calculate the weight matrix: write the factor weight values ​​obtained in the previous step into the weight matrix T according to the following function, T ij Represents the elements in the weight matrix:

6. The multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous according to claim 5 is characterized in that: Step 5 is as follows: Assume that the number of trackers is M, the number of escapers is N, M>N, and the orbital rendezvous problem of multiple spacecraft and non-cooperative targets is represented by a weighted bipartite graph Graph={P,E,L,S}; where the vertex set P={P1,P2,…,P M } represents the tracker, and the vertex set E = {E1, E2, …, E N } represents the escaper, and the edge set L = {l ij |i=1,2,…,M,j=1,2,…,N} represents the pairing situation. If tracker i selects escaper j, then edge l ij exists, and its weight is given by the hierarchical analysis method in step 4, using s ij express.

7. The multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous according to claim 6, characterized in that: In step 5, the specific method of using the KM algorithm to solve the matching solution is as follows: The first step is to initialize the top label value; select the side with fewer vertices as the starting set and the other side as the to-be-matched set, and set the top label value for each vertex; at the beginning of matching, set the top label value of all vertices in the starting set to the maximum weight of the edge it can connect to, and set all top label values ​​of the to-be-matched set to 0; during the algorithm, for any edge in the graph, it is necessary to ensure that the sum of the top labels of the left and right vertices connected to the edge is always not less than the weight value of the edge, that is: p i +e j ≥s ij Among them, p i represents the top label value corresponding to the i-th tracker, e j Indicates the top mark value corresponding to the jth escaper; The second step is to find a complete match of the bipartite graph. In a bipartite graph, a path formed by starting from an unmatched point and passing through an unmatched edge, a matched edge, an unmatched edge, and so on in an alternating order is called an alternating path. If an alternating path eventually reaches another unmatched point, then the path is an augmenting path. For each vertex in the starting set, find an augmenting path in the equal subgraph. If an augmenting path is found, go to step 4, otherwise go to step 3. Step 3: Modify the top mark value. At this time, the matching of the bipartite graph is not a complete match, and the equal subgraph needs to be expanded. The top mark modification rule is: subtract d from the top mark values ​​of the points that are to be matched in the starting set and the points that have been matched, and increase d from the top mark values ​​of the points to be matched in the set to be matched. The variable d = min{p i +e j -s ij }; The fourth step is to continue to repeat steps 2 and 3 until an augmenting path is found for each vertex in the starting set.

8. The multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous according to claim 6, characterized in that: In step 5, the main steps of task redistribution for the remaining trackers are as follows: First, recalculate the weight matrix; after the initial allocation, count the tracker numbers that have not yet determined the tracking target, and calculate the weight matrix of the remaining trackers and escapers; Then, the KM algorithm is used to assign escapers to the current remaining trackers based on the new weight matrix; After this allocation, if all trackers have been assigned to escapers, the redistribution ends, otherwise the weight matrices of the remaining spacecraft continue to be calculated and allocated until all trackers have escapers to track.

9. The multi-spacecraft orbit cooperative control strategy for non-cooperative target rendezvous according to claim 8, characterized in that: In step 5, when recalculating the weight matrix, the weight matrix of the remaining trackers and escapers satisfies: Where: subscripts i and j represent the tracker and escaper numbers; μ a ,μ d ,μ v They represent the weight values ​​of the maneuverability, distance and speed of the pursuit-escape combination respectively; v is the speed; a is the acceleration amplitude; r represents the distance between the current pursuit-escape combination tracker and escaper; D1 and D2 are the closest distance and the farthest distance between the two parties respectively; k d k is the distance calculation coefficient; v is the velocity direction coefficient.

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