Multi-spacecraft cooperative hidden flight path planning method

Abstract

The invention discloses a multi-spacecraft collaborative hidden flight path planning method, which comprises the following steps of: firstly, establishing a dynamic constraint model of collaborative hidden flight of a plurality of spacecrafts, and designing a safety constraint and a boundary constraint; constructing a plurality of collaborative hidden flight path planning models of the spacecraft according to the dynamic constraint model, the security constraint and the boundary constraint, and linearizing and discretizing the collaborative hidden flight path planning models by using a pseudo-spectral method, and converting the linearized and discretized collaborative hidden flight path planning model into a convex optimization problem based on a convex optimization theory, designing a collaborative optimization solution strategy, and performing loop iteration solution to obtain a collaborative hidden flight path of a plurality of spacecrafts. According to the method, the cooperative hidden flight tasks of the multiple spacecrafts can be effectively expressed, cooperative hidden approaching and cooperative hidden leaving can be achieved at the same time, the complexity and the calculation amount of a planning problem are effectively reduced, the calculation speed is increased, and meanwhile the optimality and the precision of a solution are guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of spacecraft flight trajectory planning, and in particular to a method for planning the collaborative and concealed flight trajectories of multiple spacecraft. Background Art

[0002] With the continuous development of space on-orbit service technology, my country's space security situation will face increasingly severe tests. Europe, the United States and other countries have widely carried out space missions such as space debris removal and on-orbit life extension. For example, Debris Removal uses "harpoons" and "fishing nets" to capture space debris, and MEV (Mission Extension Vehicle) performs multiple on-orbit life extension missions through long-distance rendezvous, close approach, and on-orbit capture operations to take over the attitude and orbit control mechanism of the service target. While improving space on-orbit service technology, such space missions also have obvious military application prospects. When the mission target is changed to a hostile spacecraft, the so-called debris removal and on-orbit life extension become a means of attack, which puts higher requirements on the development of my country's space attack and defense means for spacecraft.

[0003] At present, the widely studied spacecraft in-orbit pursuit and escape game is a direct and highly confrontational means of space attack and defense. In the pursuit and escape game scenario, both spacecraft have the ability to make autonomous decisions and autonomous maneuvers. One party actively seeks to approach, while the other party strives to avoid and escape. The pursuit and escape game studies the pursuit and escape game means including one-to-many, many-to-one, and many-to-many. The Nash equilibrium solution is constructed based on differential game theory. Its methods include HJI equation solution method, extreme value principle, Riccati equation method, variational method, etc.

[0004] The pursuit and escape game of spacecraft in orbit has three limitations: (1) It is too direct and confrontational, which is not conducive to the peaceful and stable development of space; (2) The pursuit and escape game places higher demands on the maneuverability and fuel reserves of the spacecraft involved; (3) The pursuit and escape game is a multilateral confrontation problem that is difficult to solve and it is difficult to truly achieve the goal, making the task difficult. Summary of the invention

[0005] In view of the above-mentioned limitations of the on-orbit pursuit and escape game of spacecraft in the prior art, the present invention proposes a multi-spacecraft coordinated covert flight strategy, that is, with the cooperation of one or more spacecraft of the own side, other spacecraft of the own side can fly close to or away from (the target) without the target's perception, which can effectively avoid the above-mentioned limitations of the pursuit and escape game.

[0006] The present invention provides a method for planning multi-spacecraft cooperative covert flight trajectories, comprising the following steps:

[0007] S1. Setting a scenario of coordinated covert flight of multiple spacecraft, wherein the multiple spacecraft include a target spacecraft, a shielding spacecraft and a hidden spacecraft, and the shielding spacecraft is located on the line connecting the hidden spacecraft and the target spacecraft;

[0008] S2. Set the concealment constraint model of the shielded spacecraft and the hidden spacecraft, set the relative motion dynamics model corresponding to the hidden spacecraft and the shielded spacecraft according to the spacecraft relative dynamics TH equation, and establish the dynamics constraint model of the coordinated concealed flight according to the concealment constraint model and the relative motion dynamics model;

[0009] S3, preset a safety buffer distance between the shielding spacecraft and the target spacecraft, and a collision avoidance distance between the shielding spacecraft and the hidden spacecraft, and design safety constraints and boundary constraints corresponding to multiple spacecraft according to the safety buffer distance and the collision avoidance distance;

[0010] S4. Construct a collaborative covert flight trajectory planning model for multiple spacecraft based on the dynamic constraint model, safety constraints and boundary constraints of collaborative covert flight;

[0011] S5. Optimize and solve the collaborative covert flight trajectory planning model to obtain the collaborative covert flight trajectories of multiple spacecraft.

[0012] Preferably, a concealment constraint model for shielding spacecraft and hiding spacecraft is set in S2, which specifically includes the following:

[0013] S21, obtaining the position of the target spacecraft, and determining the position of the hidden spacecraft according to the position of the target spacecraft;

[0014] S22, determining the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft according to the position of the target spacecraft and the position of the hidden spacecraft;

[0015] S23. Setting a concealment constraint model of the concealing spacecraft and the hidden spacecraft according to the position of the hidden spacecraft and the position of the concealing spacecraft on the line connecting the hidden spacecraft and the target spacecraft.

[0016] Preferably, in S23, a concealment constraint model for shielding the spacecraft and hiding the spacecraft is set, and the concealment constraint model can be specifically expressed by the formula:

[0017]

[0018] In the formula, r h indicates the location of the hidden spacecraft, and r h The first and second derivatives of r s represents the position of the obscuring spacecraft, and rs The first and second derivatives of , ν represents the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft, and are the first and second derivatives of ν, respectively.

[0019] Preferably, in S2, a dynamic constraint model of the coordinated covert flight is established according to the concealment constraint model and the relative motion dynamics model. The dynamic constraint model of the coordinated covert flight can be specifically expressed by the formula:

[0020]

[0021] In the formula, r h represents the position of the hidden spacecraft, r s represents the position of the shielding spacecraft, ν represents the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft, A is the coefficient matrix of the TH equation of the relative motion of the spacecraft, and u h is the control vector of the hidden spacecraft, u s is the control vector for the obscured spacecraft.

[0022] Preferably, in S3, safety constraints and boundary constraints corresponding to multiple spacecraft are designed according to the safety buffer distance and the collision avoidance distance. The safety constraints and boundary constraints can be specifically expressed by the formula:

[0023]

[0024]

[0025]

[0026]

[0027] Where, d bf represents the safe buffer distance between the shielding spacecraft and the target spacecraft, d cf represents the collision avoidance distance between the shielding spacecraft and the hidden spacecraft, t0 represents the start time of the coordinated hidden flight of multiple spacecraft, and t f represents the end time of the coordinated covert flight of multiple spacecraft, rh(t0) represents the hidden spacecraft r h At the initial time t0, is the first-order derivative of rh(t0), r h (t f ) indicates hidden spacecraft r h At the end time t f location, For r h (t f), ν(t0) represents the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft at the initial time t0, is the first-order derivative of ν(t0), r h,0 represents the initial position of the hidden spacecraft, For r h,0 The first derivative of h,f Indicates the terminal position of the hidden spacecraft, For r h,f The first-order derivative of , ν represents the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft, ν0 represents the initial position of the shielding spacecraft, is the first-order derivative of ν0, and ||.||2 represents the 2-norm of the vector.

[0028] Preferably, the collaborative covert flight trajectory planning model in S4 can be specifically expressed by the formula:

[0029]

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] ||u h || ∞ ≤u h,max ,||u s || ∞ ≤u s,max

[0037] Where J represents the coordinated energy consumption of multiple spacecraft coordinated covert flight, u h,max represents the maximum thrust of the shielding spacecraft, u s,max represents the maximum thrust of the hidden spacecraft, B is the coefficient matrix of the TH equation of relative motion of the spacecraft, ||.|| ∞ Represents the infinity norm of a vector.

[0038] Preferably, S5 is specifically:

[0039] S51. Rewrite the relative motion dynamics model of the hidden spacecraft and the dynamics constraint model of the coordinated hidden flight to obtain the state equation;

[0040] S52, using the multi-segment Radau pseudo-spectral method and combining the state equation to transform the cooperative covert flight trajectory planning model into a linearized and discretized cooperative covert flight trajectory planning model;

[0041] S53. Based on convex optimization theory, the linearized and discretized cooperative covert flight trajectory planning model is transformed into a standard convex optimization model;

[0042] S54. Split the standard convex optimization model into two sub-problems, solve the two sub-problems through cyclic iteration, and obtain the collaborative optimal solution. The collaborative optimal solution is the collaborative covert flight trajectory of multiple spacecraft.

[0043] Preferably, the state equation in S51 is specifically:

[0044]

[0045]

[0046] in,

[0047]

[0048]

[0049] Where x represents the state vector of the hidden spacecraft, is the first-order derivative of x, ν represents the state vector of the shielding spacecraft, and are coefficient matrices of the hidden spacecraft state equation, Q and R are coefficient matrices of the shielded spacecraft state equation, I3 is the 3D identity matrix, 03 is the 3D zero matrix, 0 1×3 is a 1×3 dimensional matrix of zeros.

[0050] Preferably, the two sub-questions in S54 are specifically:

[0051] First sub-question:

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] Among them, J1 represents the first coordinated energy consumption of multiple spacecraft coordinated covert flight, and They represent the start and end time of the coordinated covert flight of multiple spacecraft in the kth time domain, is the Gaussian integral weight coefficient of the jth collocation point in the kth time domain, is the coefficient matrix of the jth collocation point of the hidden spacecraft in the kth time domain, X (k) and are all decision variables of the hidden spacecraft in the kth time domain, and are the coefficient matrices of the affine equations of the j-th collocation point of the hidden spacecraft in the k-th time domain, and are the coefficient matrices of the initial and final states of the hidden spacecraft in the kth time domain, is the state at the initial moment of the kth time domain, is the coefficient matrix of the state at the end of the Kth time domain, is the coefficient matrix of the state of the hidden spacecraft at the initial moment of the k+1th time domain, X (k+1) To hide the decision variables of the spacecraft in the k+1th time domain, is the state at the end of the Kth time domain, K is the total number of time domain segments, k = 1, 2, ..., K, N (k) Indicates the number of points in the k-th time domain, j=1,2,...,N (k) .

[0058] Second sub-question:

[0059]

[0060]

[0061]

[0062]

[0063]

[0064] Among them, J2 represents the second collaborative energy consumption of multiple spacecraft coordinated covert flight, is the coefficient matrix of the jth collocation control quantity of the shielding spacecraft in the kth time domain, V (k) and are the decision variables of the shielding spacecraft in the kth time domain, and are the coefficient matrices of the affine equations of the j-th collocation point of the shielding spacecraft in the k-th time domain, is the position vector coefficient matrix of the hidden spacecraft at the jth distribution point in the kth time domain, is the position vector coefficient matrix of the shielding spacecraft at the jth distribution point in the kth time domain, and are the coefficient matrices of the shielding spacecraft at the initial and final states of the kth time domain, is the state quantity of the shielding spacecraft at the initial moment of the kth time domain, is the coefficient matrix of the state of the shielding spacecraft at the initial moment of the k+1th time domain, V (k+1) is the decision variable for shielding the spacecraft in the k+1th time domain.

[0065] Preferably, in S54, the two sub-problems are solved through loop iteration to obtain a collaborative optimal solution, which specifically includes the following:

[0066] S541, preset initial parameters, initialize the reference trajectory of the hidden spacecraft and the shielded spacecraft in each time domain and

[0067] S542, according to the preset initial parameters and the reference trajectory of the hidden spacecraft in each time domain Solve the first sub-problem and obtain the decision variable X of the hidden spacecraft in each time domain (k) and Calculate the decision variable X of the hidden spacecraft in each time domain (k) and reference trajectory The difference between them is taken, and the largest difference is taken as the iterative error ΔX of the hidden spacecraft. According to the decision variable X of the hidden spacecraft in each time domain, (k) and Update the reference trajectory of the hidden spacecraft in each time domain and reference control sequence

[0068] S543, based on the preset initial parameters, the updated reference trajectory of the hidden spacecraft in each time domain and reference control sequence and the reference trajectory of the obscured spacecraft in each time domain Solve the second sub-problem and obtain the decision variable V of the shielding spacecraft in each time domain (k) and Calculate the decision variable V of the shielding spacecraft in each time domain (k) and reference trajectory The maximum of the differences is taken as the iterative error ΔV of the shielding spacecraft. According to the decision variable V of the shielding spacecraft in each time domain, (k) and Update the reference trajectory of the obscured spacecraft in each time domain and reference control sequence

[0069] S544, preset a first allowable error ξ1 and a second allowable error ξ2, compare the iterative error ΔX of the hidden spacecraft with the first allowable error ξ1, and compare the iterative error ΔV of the shielded spacecraft with the second allowable error ξ2, if ΔX<ξ1 and ΔV<ξ2, execute step S545, otherwise, execute step S542 to perform the next round of iterative solution;

[0070] S545. Output the reference trajectory and reference control sequence corresponding to the hidden spacecraft and the shielded spacecraft after this round of iteration. The reference trajectory and reference control sequence are the collaborative optimal solution.

[0071] The above-mentioned method for planning the trajectory of cooperative covert flight of multiple spacecrafts first establishes a dynamic constraint model of cooperative covert flight of multiple spacecrafts, and designs safety constraints and boundary constraints. According to the dynamic constraint model of cooperative covert flight, safety constraints and boundary constraints, the trajectory planning model of cooperative covert flight of multiple spacecrafts is constructed. The pseudo-spectral method is used to linearize and discretize the trajectory planning model of cooperative covert flight. Based on the convex optimization theory, the linearized and discretized trajectory planning model of cooperative covert flight is transformed into a convex optimization problem. A collaborative optimization solution strategy is designed. Through cyclic iterative solution, the trajectory of cooperative covert flight of multiple spacecrafts is obtained. The method can effectively describe the cooperative covert flight mission of multiple spacecrafts, and can simultaneously realize cooperative covert approach and cooperative covert departure. By processing the trajectory planning model of cooperative covert flight by pseudo-spectral method and combining with convex optimization theory, an equivalent model with high discrete accuracy, good convergence and good optimality can be obtained. The proposed collaborative planning solution strategy will effectively reduce the computational complexity, improve the performance of solving the planning problem, and improve the calculation speed, while ensuring the optimality and accuracy of the solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 is a flow chart of a method for planning multi-spacecraft cooperative covert flight trajectories in one embodiment of the present invention;

[0073] Figure 2 This is a schematic diagram of a multi-spacecraft cooperative covert flight mission scenario in one embodiment of the present invention;

[0074] Figure 3 is a flow chart of a loop iterative solution in one embodiment of the present invention;

[0075] Figure 4 is a schematic diagram of a multi-spacecraft cooperative covert approach trajectory in one embodiment of the present invention;

[0076] Figure 5 It is a schematic diagram of a multi-spacecraft cooperative concealment away trajectory in one embodiment of the present invention;

[0077] Figure 6It is a schematic diagram of multiple spacecrafts cooperating to conceal their trajectories in another embodiment of the present invention. DETAILED DESCRIPTION

[0078] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings.

[0079] In one embodiment, see Figure 1 and Figure 2 , Figure 1 This is a flow chart of a method for planning multi-spacecraft cooperative covert flight trajectories in one embodiment of the present invention. Figure 2 The present invention is a schematic diagram of a multi-spacecraft cooperative covert flight mission scenario in an embodiment of the present invention. A multi-spacecraft cooperative covert flight trajectory planning method includes the following steps:

[0080] S1. Setting a multiple spacecraft cooperative covert flight scenario, wherein the multiple spacecraft cooperative covert flight scenario includes a target spacecraft, at least one shielding spacecraft and at least one hidden spacecraft. Figure 1 The figure specifically shows a coordinated covert flight scenario when there is one target spacecraft, one shielding spacecraft and one hidden spacecraft. When one shielding spacecraft and one hidden spacecraft perform a task of cooperatively and covertly approaching or moving away from the target spacecraft, the shielding spacecraft always remains on the line connecting the hidden spacecraft and the target spacecraft to block the line of sight of the target spacecraft, so that the hidden spacecraft can achieve visual stealth.

[0081] S2. Obtain the position of the target spacecraft, and based on this, set the concealment constraint model of the shielding spacecraft and the hidden spacecraft, respectively set the relative motion dynamics model of the hidden spacecraft and the relative motion dynamics model of the shielding spacecraft according to the spacecraft relative dynamics TH equation, and establish the dynamics constraint model of the coordinated concealed flight according to the concealment constraint model and the above two relative motion dynamics models;

[0082] S3, preset a safety buffer distance between the shielding spacecraft and the target spacecraft, and a collision avoidance distance between the shielding spacecraft and the hidden spacecraft, and design safety constraints and boundary constraints corresponding to multiple spacecraft according to the safety buffer distance and the collision avoidance distance;

[0083] S4. Construct a collaborative covert flight trajectory planning model for multiple spacecraft based on the dynamic constraint model, safety constraints and boundary constraints of collaborative covert flight;

[0084] S5. Optimize and solve the collaborative covert flight trajectory planning model to obtain the collaborative covert flight trajectories of multiple spacecraft.

[0085] In one embodiment, the concealment constraint model of the shielded spacecraft and the hidden spacecraft is set in S2, which specifically includes the following:

[0086] S21, obtaining the position of the target spacecraft, and determining the position of the hidden spacecraft according to the position of the target spacecraft;

[0087] S22, determining the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft according to the position of the target spacecraft and the position of the hidden spacecraft;

[0088] S23. Setting a concealment constraint model of the concealing spacecraft and the hidden spacecraft according to the position of the hidden spacecraft and the position of the concealing spacecraft on the line connecting the hidden spacecraft and the target spacecraft.

[0089] In one embodiment, a concealment constraint model of the shielded spacecraft and the hidden spacecraft is set in S23. The concealment constraint model can be specifically expressed by the formula:

[0090] r s =vr h

[0091]

[0092]

[0093] In the formula, r h indicates the location of the hidden spacecraft, and r h The first and second derivatives of r s represents the position of the obscuring spacecraft, and r s The first and second derivatives of , ν represents the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft, and are the first and second derivatives of ν, respectively.

[0094] Specifically, firstly, the absolute position of the target spacecraft is obtained, and then the position of the hidden spacecraft is determined according to the position of the target spacecraft, that is, the absolute position of the target spacecraft is used as the coordinate origin O and a new coordinate system is established to determine the position of the hidden spacecraft in the new coordinate system, that is, the position of the hidden spacecraft relative to the target spacecraft; then, the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft is determined according to the position of the target spacecraft and the position of the hidden spacecraft; then, the concealment constraint model of the shielding spacecraft and the hidden spacecraft is set according to the position of the hidden spacecraft and the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft, specifically:

[0095] r s =vr h (1)

[0096] Among them, r s =[x s ,y s ,z s ] T

[0097] r h =[x h ,y h ,z h ] T

[0098] In the formula, r s represents the position of the obstructing spacecraft, that is, the position of the obstructing spacecraft relative to the target spacecraft, x s ,y s ,z s are the position coordinates of the shielding spacecraft on the x, y, and z axes, respectively; ν represents the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft; r h represents the position of the hidden spacecraft, that is, the position of the hidden spacecraft relative to the target spacecraft, x h ,y h ,z h are the position coordinates of the hidden spacecraft on the x, y, and z axes respectively, and T represents transposition.

[0099] Calculate the first-order derivative and the second-order derivative of the above hidden constraint model respectively:

[0100]

[0101]

[0102] In the formula, and r h The first and second derivatives of and r s The first and second derivatives of and are the first and second derivatives of ν, respectively.

[0103] In one embodiment, in S2, a dynamic constraint model of cooperative covert flight is established according to the concealment constraint model and the relative motion dynamics model. The dynamic constraint model of cooperative covert flight can be specifically expressed by the formula:

[0104]

[0105] In the formula, r h represents the position of the hidden spacecraft, r srepresents the position of the shielding spacecraft, ν represents the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft, A is the coefficient matrix of the TH equation of the relative motion of the spacecraft, and u h is the control vector of the hidden spacecraft, u s is the control vector for the obscured spacecraft.

[0106] Specifically, the setting process of the dynamic constraint model of cooperative stealth flight is as follows:

[0107] 1) Set up the relative motion dynamics model according to the TH equation of spacecraft relative motion

[0108] According to the TH equation of relative motion of spacecraft, the relative motion dynamics model of hidden spacecraft is set as follows:

[0109]

[0110] Where A and B are the coefficient matrices of the TH equation for relative motion of the spacecraft, u h is the control vector for the hidden spacecraft.

[0111] According to the TH equation of relative motion of spacecraft, the relative motion dynamics model of shielding spacecraft is set as follows:

[0112]

[0113] In the formula, u s is the control vector for the obscured spacecraft.

[0114] 2) Establish a dynamic constraint model for cooperative concealed flight based on the concealment constraint models of multiple spacecraft, the relative motion dynamics model of hidden spacecraft, and the relative motion dynamics model of shielded spacecraft.

[0115] Specifically, the dynamic constraint model of cooperative stealth flight is derived according to formulas (1), (1)-1, (1)-2, (2)-1 and (2)-2, as follows:

[0116]

[0117] In the formula, r h represents the position coordinates of the hidden spacecraft, r s represents the position coordinates of the shielding spacecraft, ν represents the position coordinates of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft, A is the coefficient matrix of the TH equation of relative motion of the spacecraft, u h is the control vector of the hidden spacecraft, u s is the control vector for the obscured spacecraft.

[0118] In one embodiment, in S3, safety constraints and boundary constraints corresponding to multiple spacecraft are designed according to the safety buffer distance and the collision avoidance distance. The safety constraints and boundary constraints can be specifically expressed by the formula:

[0119]

[0120] Where, d bf represents the safe buffer distance between the shielding spacecraft and the target spacecraft, d cf represents the collision avoidance distance between the shielding spacecraft and the hidden spacecraft, t0 represents the start time of the coordinated hidden flight of multiple spacecraft, and t f represents the end time of the coordinated covert flight of multiple spacecraft, rh(t0) represents the hidden spacecraft r h At the initial time t0, is the first-order derivative of rh(t0), r h (t f ) indicates hidden spacecraft r h At the end time t f location, For r h (t f ), ν(t0) represents the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft at the initial time t0, is the first-order derivative of ν(t0), r h,0 represents the initial position of the hidden spacecraft, For r h,0 The first derivative of h,f Indicates the terminal position of the hidden spacecraft, For r h,f The first-order derivative of , ν represents the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft, ν0 represents the initial position of the shielding spacecraft, is the first-order derivative of ν0, and ||.||2 represents the 2-norm of the vector.

[0121] Specifically, when multiple spacecraft are performing coordinated covert flight, in order to ensure the safety of multiple spacecraft during the coordinated covert flight, the shielding spacecraft and the hidden spacecraft need to maintain a certain distance to prevent collision, and the shielding spacecraft also needs to maintain a certain safety buffer distance with the target spacecraft. First, set the safety buffer distance d between the shielding spacecraft and the target spacecraft. bf , the collision avoidance distance d between the shielding spacecraft and the hidden spacecraft cf Then, we determine the initial and end times of the coordinated covert flight of multiple spacecraft, the initial and terminal positions of the hidden spacecraft, the initial position of the shielded spacecraft, and other parameters, and then according to the safety buffer distance d bf , collision avoidance distance d cf, hidden spacecraft || r h ||2. Set safety constraints and boundary constraints for parameters such as the initial position and terminal position of related spacecraft.

[0122] In one embodiment, the collaborative covert flight trajectory planning model in S4 can be specifically expressed by the formula:

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130] ||u h || ∞ ≤u h,max ,||u s || ∞ ≤u s,max

[0131] Where J represents the coordinated energy consumption of multiple spacecraft coordinated covert flight, u h,max represents the maximum thrust of the shielding spacecraft, u s,max represents the maximum thrust of the hidden spacecraft, B is the coefficient matrix of the TH equation of relative motion of the spacecraft, ||.|| ∞ Represents the infinite norm of a vector, minimize represents minimization, and subject to represents constraints.

[0132] Specifically, multiple spacecraft are in a preset time period [t0,t f ] The goal is to minimize the energy consumption required for coordinated stealth flight, that is:

[0133]

[0134] At the same time, the maximum thrust of the spacecraft is limited: ||u h || ∞ ≤u h,max ,||u s || ∞ ≤u s,max (5)-1

[0135] Combined with the previous constraints (specifically including the relative motion dynamics model of hidden spacecraft (Formula (2)-1), the collaborative covert flight dynamics constraint model of shielded spacecraft (Formula (3)), and safety constraints and boundary constraints (Formula (4)), a collaborative covert flight trajectory planning model for multiple spacecraft is obtained.

[0136] In one embodiment, S5 is specifically:

[0137] S51. The relative motion dynamics model of the hidden spacecraft and the dynamic constraint model of the coordinated hidden flight are rewritten to obtain the state equation.

[0138] Furthermore, the state equation in S51 is specifically:

[0139]

[0140] in,

[0141]

[0142]

[0143] Where x represents the state vector of the hidden spacecraft, is the first-order derivative of x, ν represents the state vector of the shielding spacecraft, and Both represent the coefficient matrices of the hidden spacecraft state equation, Q and R both represent the coefficient matrices of the shielded spacecraft state equation, I3 is the 3D identity matrix, 03 is the 3D zero matrix, 0 1×3 is a 1×3 dimensional matrix of zeros.

[0144] S52. Use the multi-segment Radau pseudo-spectral method and combine it with the state equation to transform the cooperative covert flight trajectory planning model into a linearized and discretized cooperative covert flight trajectory planning model.

[0145] Furthermore, in order to make the solution more easily convergent and improve the approximate accuracy, after obtaining the collaborative covert flight trajectory planning model, the multi-segment Radau pseudo-spectral method is used to linearize and discretize the model to obtain the linearized and discretized collaborative covert flight trajectory planning model, as follows:

[0146]

[0147] Where J represents the coordinated energy consumption of multiple spacecraft coordinated covert flight, and They represent the start and end time of the coordinated covert flight of multiple spacecraft in the kth time domain, is the Gaussian integral weight coefficient of the jth collocation point in the kth time domain, N(k) Indicates the number of points in the k-th time domain, j=1,2,...,N (k) , is the control vector of the jth collocation point of the hidden spacecraft in the kth time domain, is the control vector of the jth collocation point of the shielding spacecraft in the kth time domain, represents the pseudo-spectral differential matrix of the approximate variable at the i-th collocation point in the k-th time domain at the j-th collocation point, represents the state vector of the hidden spacecraft at the jth collocation point in the kth time domain, represents the state vector of the shielding spacecraft at the jth collocation point in the kth time domain, and are the state quantities of the hidden spacecraft at the initial and end times of the kth time domain, is the approximate state vector of the hidden spacecraft at the i-th collocation point in the k-th time domain, is the approximate state vector of the shielding spacecraft at the i-th collocation point in the k-th time domain, i=1,2,...,N (k) +1, C h represents the hidden spacecraft state coefficient matrix, C h = [I303], I3 is the 3D identity matrix, 03 is the 3D zero matrix, C s is the shielding spacecraft state coefficient matrix, C s =

[10] , and Indicates that the state variables at the beginning and end of each segmented time domain are equal, ||.||2 indicates the 2-norm of the vector, ||.|| ∞ Represents the infinity norm of a vector.

[0148] S53. Based on convex optimization theory, the linearized and discretized collaborative covert flight trajectory planning model is transformed into a standard convex optimization model.

[0149] Furthermore, based on the convex optimization theory, the linearized and discretized cooperative covert flight trajectory planning model is transformed into a standard convex optimization problem with a theoretical global optimal solution and better optimal convergence. The corresponding standard convex optimization model is as follows:

[0150]

[0151] in, and are the coefficient matrices of the j-th collocation control quantity of the hidden spacecraft and the shielded spacecraft in the k-th time domain, respectively, X (k) and are the decision variables of the hidden spacecraft in the kth time domain, V (k) and are the decision variables of the shielding spacecraft in the kth time domain, and are the coefficient matrices of the affine equations of the hidden spacecraft at the jth collocation point in the kth time domain, and are the coefficient matrices of the affine equations of the shielding spacecraft at the jth collocation point in the kth time domain, is the position vector coefficient matrix of the hidden spacecraft at the jth distribution point in the kth time domain, is the position vector coefficient matrix of the shielding spacecraft at the jth distribution point in the kth time domain, and are the coefficient matrices of the hidden spacecraft at the initial and end times of the kth time domain, and are the coefficient matrices of the shielding spacecraft at the initial and end times of the kth time domain, respectively. The coefficient matrices are used to extract the parameters of each decision variable at the corresponding time.

[0152] Among the above parameters, the decision variable X (k) 、V (k) , and Defined as:

[0153]

[0154] In the formula, represents the position vector of the hidden spacecraft at the first distribution point in the kth time domain, represents the position of the shielding spacecraft at the first distribution point in the kth time domain, represents the control vector of the hidden spacecraft at the first distribution point in the kth time domain, represents the control vector of the shielding spacecraft at the first distribution point in the kth time domain.

[0155] The dynamic constraints of the hidden spacecraft and the dynamic constraints of the cooperative hidden flight can be obtained by processing the state equations obtained in S51 using the pseudo-spectral method, as follows:

[0156] The dynamic constraints of the hidden spacecraft are:

[0157]

[0158] The dynamic constraints of cooperative stealth flight are:

[0159]

[0160] Affine equation coefficient matrix and The above two dynamic constraints can be summarized as follows:

[0161]

[0162] The standard convex optimization model is a pseudo-spectral convex form of the dynamic constraint model of cooperative covert flight. The trajectory planning model of cooperative covert flight is transformed into a standard convex optimization model, which has the characteristics of high discrete accuracy, good convergence and good optimality.

[0163] S54. Split the standard convex optimization model into two sub-problems, solve the two sub-problems through cyclic iteration, and obtain the collaborative optimal solution. The collaborative optimal solution is the collaborative covert flight trajectory of multiple spacecraft.

[0164] Furthermore, the first of the two sub-problems in S54 is expressed as follows:

[0165]

[0166] Among them, J1 represents the first coordinated energy consumption of multiple spacecraft coordinated covert flight, and They represent the start and end time of the coordinated covert flight of multiple spacecraft in the kth time domain, is the Gaussian integral weight coefficient of the jth collocation point in the kth time domain, is the coefficient matrix of the jth collocation point of the hidden spacecraft in the kth time domain, X (k) and are all decision variables of the hidden spacecraft in the kth time domain, and are the coefficient matrices of the affine equations of the j-th collocation point of the hidden spacecraft in the k-th time domain, and are the coefficient matrices of the initial and final states of the hidden spacecraft in the kth time domain, is the coefficient matrix of the state of the hidden spacecraft at the initial moment of the k+1th time domain, X (k+1) To hide the decision variables of the spacecraft in the k+1th time domain, is the state at the initial moment of the kth time domain, is the coefficient matrix of the state at the end of the Kth time domain, is the state at the end of the Kth time domain, K is the total number of time domain segments, k = 1, 2, ..., K, N (k) Indicates the number of points in the k-th time domain, j=1,2,...,N (k) .

[0167] The second of the two sub-problems is stated as follows:

[0168]

[0169] Among them, J2 represents the second collaborative energy consumption of multiple spacecraft coordinated covert flight, is the coefficient matrix of the jth collocation control quantity of the shielding spacecraft in the kth time domain, V (k) and are the decision variables of the shielding spacecraft in the kth time domain, and are the coefficient matrices of the affine equations of the j-th collocation point of the shielding spacecraft in the k-th time domain, is the position vector coefficient matrix of the hidden spacecraft at the jth distribution point in the kth time domain, is the position vector coefficient matrix of the shielding spacecraft at the jth distribution point in the kth time domain, and are the coefficient matrices of the shielding spacecraft at the initial and final states of the kth time domain, is the state quantity of the shielding spacecraft at the initial moment of the kth time domain, is the coefficient matrix of the state of the shielding spacecraft at the initial moment of the k+1th time domain, V (k+1) is the decision variable for shielding the spacecraft in the k+1th time domain.

[0170] The above two sub-problems are solved through cyclic iteration to obtain the coordinated optimal solution, that is, the coordinated covert flight trajectory of all spacecraft under the condition of the lowest coordinated energy consumption.

[0171] In one embodiment, see Figure 3 , Figure 3 This is a flow chart of iterative solution in an embodiment of the present invention. In S54, two sub-problems are solved iteratively to obtain a collaborative optimal solution, which specifically includes the following:

[0172] S541. Preset initial parameters, including boundary conditions, number of pseudo-spectrum segments, start time and end time, number of points for each segment, safety distance parameters, control capability amplitude and allowable error, and initialize reference trajectories of hidden and shielded spacecraft. and To hide the reference trajectory of the spacecraft in the kth time domain, To mask the reference trajectory of the spacecraft in the kth time domain, K is the total number of time domain segments, that is, the number of pseudo-spectrum segments k = 1, 2, ..., K;

[0173] S542, according to the preset initial parameters and the reference trajectory of the hidden spacecraft in each time domain Solve the first sub-problem and obtain the decision variable X of the hidden spacecraft in each time domain (k) and Calculate the decision variable X of the hidden spacecraft in each time domain (k) and reference trajectory The maximum difference between them is taken as the iterative error ΔX of the hidden spacecraft. According to the decision variables X of the hidden spacecraft in each time domain (k) and Update the reference trajectory of the hidden spacecraft in each time domain and reference control sequence The specific update formula is:

[0174] S543, based on the preset initial parameters, the updated reference trajectory of the hidden spacecraft in each time domain and reference control sequence and the reference trajectory of the obscured spacecraft in each time domain Solve the second sub-problem and obtain the decision variable V of the shielding spacecraft in each time domain (k) and Calculate the decision variable V of the shielding spacecraft in each time domain (k) and reference trajectory The largest of the differences is taken as the iterative error ΔV of the shielding spacecraft. According to the decision variable V of the shielding spacecraft in each time domain (k) and Update the reference trajectory of the obscured spacecraft in each time domain and reference control sequence The specific update formula is:

[0175] S544, preset a first allowable error ξ1 and a second allowable error ξ2, compare the iterative error ΔX of the hidden spacecraft with the first allowable error ξ1, and compare the iterative error ΔV of the shielded spacecraft with the second allowable error ξ2, if ΔX<ξ1 and ΔV<ξ2, execute step S545, otherwise, execute step S542 to perform the next round of iterative solution;

[0176] S545. Output the reference trajectory and reference control sequence of the hidden spacecraft and the shielded spacecraft after this round of iteration. The reference trajectory and reference control sequence are the collaborative optimal solution.

[0177] In one embodiment, a multi-spacecraft cooperative covert flight system includes a target spacecraft, a shielding spacecraft, a hidden spacecraft, and a computer system. The target spacecraft, the shielding spacecraft, and the hidden spacecraft are respectively connected to the computer system for communication. The shielding spacecraft is located on a line connecting the hidden spacecraft and the target spacecraft, wherein:

[0178] The computer system is used to obtain the position information corresponding to the target spacecraft, the shielding spacecraft, and the hidden spacecraft, and execute the above-mentioned multi-spacecraft cooperative covert flight trajectory planning method to plan the flight trajectory of the shielding spacecraft and the hidden spacecraft relative to the target spacecraft;

[0179] The shielding spacecraft and the hidden spacecraft respectively receive their respective flight trajectories relative to the target spacecraft planned by the computer system to achieve coordinated covert flight.

[0180] For the specific limitations of a multi-spacecraft collaborative covert flight system, please refer to the limitations of a multi-spacecraft collaborative covert flight trajectory planning method mentioned above, which will not be repeated here.

[0181] Furthermore, a multi-spacecraft collaborative covert flight trajectory planning method proposed in the present invention was verified through experiments.

[0182] See also Figure 4 , Figure 5 and Figure 6 , Figure 4 This is a schematic diagram of the collaborative covert approach trajectory of multiple spacecraft in one embodiment of the present invention. Figure 5 This is a schematic diagram of multiple spacecraft working together to conceal their trajectory in one embodiment of the present invention.

[0183] Figure 4 Specifically, it shows a schematic diagram of the trajectory of a hidden spacecraft and a shielding spacecraft cooperatively approaching a target spacecraft in a covert manner. Figure 5 The figure specifically shows a schematic diagram of the trajectories of a hidden spacecraft and a shielding spacecraft working together to conceal themselves from a target spacecraft.

[0184] Depend on Figure 4 and Figure 5 It can be seen that during the entire process of the hidden spacecraft approaching or moving away from the target spacecraft, the shielding spacecraft cooperates with it and always remains on the connecting line between the target spacecraft and the hidden spacecraft, making it impossible for the target spacecraft to observe and perceive the existence of the hidden spacecraft, and the hidden spacecraft achieves covert maneuvering flight.

[0185] See also Figure 6 , Figure 6 This is a schematic diagram of multiple spacecraft working together to conceal their trajectory in another embodiment of the present invention.

[0186] Figure 6 Specifically, the flight trajectories of two hidden spacecraft and one shielding spacecraft relative to the target spacecraft are shown, wherein the shielding spacecraft is always located on the line connecting the two hidden spacecraft and the target spacecraft.

[0187] Depend on Figure 6It can be seen that in the process of the two hidden spacecraft maneuvering away from the target spacecraft, the shielding spacecraft, the two hidden spacecraft and the target spacecraft are always in a straight line, and the shielding spacecraft always blocks the line of sight of the target spacecraft, making it impossible for it to observe and perceive the existence of the two hidden spacecraft. The two hidden spacecraft and one shielding spacecraft achieved coordinated covert flight away from the target spacecraft.

[0188] The above-mentioned method for planning the trajectory of cooperative covert flight of multiple spacecrafts first establishes a dynamic constraint model of cooperative covert flight of multiple spacecrafts, and designs safety constraints and boundary constraints. According to the dynamic constraint model of cooperative covert flight, safety constraints and boundary constraints, the trajectory planning model of cooperative covert flight of multiple spacecrafts is constructed. The pseudo-spectral method is used to linearize and discretize the trajectory planning model of cooperative covert flight. Based on the convex optimization theory, the linearized and discretized trajectory planning model of cooperative covert flight is transformed into a convex optimization problem. A collaborative optimization solution strategy is designed. Through cyclic iterative solution, the trajectory of cooperative covert flight of multiple spacecrafts is obtained. The method can effectively describe the cooperative covert flight mission of multiple spacecrafts, and can simultaneously realize cooperative covert approach and cooperative covert departure. By processing the trajectory planning model of cooperative covert flight by pseudo-spectral method and combining with convex optimization theory, an equivalent model with high discrete accuracy, good convergence and good optimality can be obtained. The proposed collaborative planning solution strategy will effectively reduce the computational complexity, improve the performance of solving the planning problem, and improve the calculation speed, while ensuring the optimality and accuracy of the solution.

[0189] The above is a detailed introduction to a multi-spacecraft collaborative covert flight trajectory planning method provided by the present invention. This article uses specific examples to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the core idea of ​​the present invention. It should be pointed out that for ordinary technicians in this technical field, without departing from the principles of the present invention, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A method for planning multi-spacecraft cooperative covert flight trajectories, characterized in that: The method comprises the following steps: S1. Setting a scenario of coordinated covert flight of multiple spacecraft, wherein the multiple spacecraft include a target spacecraft, a shielding spacecraft and a hidden spacecraft, and the shielding spacecraft is located on a line connecting the hidden spacecraft and the target spacecraft; S2, setting the concealment constraint models of the shielded spacecraft and the hidden spacecraft, setting the relative motion dynamics models corresponding to the hidden spacecraft and the shielded spacecraft respectively according to the spacecraft relative dynamics TH equation, and establishing the dynamics constraint model of the coordinated concealed flight according to the concealment constraint model and the relative motion dynamics model; S3, presetting a safety buffer distance between the shielding spacecraft and the target spacecraft, and a collision avoidance distance between the shielding spacecraft and the hidden spacecraft, and designing a plurality of safety constraints and boundary constraints corresponding to the spacecraft according to the safety buffer distance and the collision avoidance distance; S4, constructing a collaborative covert flight trajectory planning model for a plurality of the spacecraft according to the collaborative covert flight dynamics constraint model and the safety constraints and boundary constraints; S5. Optimize and solve the collaborative covert flight trajectory planning model to obtain the collaborative covert flight trajectories of multiple spacecraft.

2. The method for planning multi-spacecraft cooperative covert flight trajectories as claimed in claim 1, characterized in that: In S2, the concealment constraint model of the shielding spacecraft and the hidden spacecraft is set, which specifically includes the following: S21, acquiring the position of the target spacecraft, and determining the position of the hidden spacecraft according to the position of the target spacecraft; S22, determining the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft according to the position of the target spacecraft and the position of the hidden spacecraft; S23, setting a concealment constraint model of the shielding spacecraft and the hidden spacecraft according to the position of the hidden spacecraft and the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft.

3. The method for planning multi-spacecraft cooperative covert flight trajectories as claimed in claim 2, characterized in that: In S23, a concealment constraint model of the shielded spacecraft and the hidden spacecraft is set. The concealment constraint model can be specifically expressed by the formula: r s =νr h In the formula, r h indicates the location of the hidden spacecraft, and r h The first and second derivatives of r s represents the position of the obscuring spacecraft, and r s The first and second derivatives of , ν represents the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft, and are the first and second derivatives of ν, respectively.

4. The method for planning multi-spacecraft cooperative covert flight trajectories as claimed in claim 3, characterized in that: In S2, a dynamic constraint model of cooperative concealed flight is established according to the concealed constraint model and the relative motion dynamic model. The dynamic constraint model of cooperative concealed flight can be specifically expressed by the formula: In the formula, r h represents the position of the hidden spacecraft, r s represents the position of the shielding spacecraft, ν represents the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft, A is the coefficient matrix of the TH equation of the relative motion of the spacecraft, and u h is the control vector of the hidden spacecraft, u s is the control vector for the obscured spacecraft.

5. The method for planning multi-spacecraft cooperative covert flight trajectories as claimed in claim 4, characterized in that: In S3, safety constraints and boundary constraints corresponding to multiple spacecraft are designed according to the safety buffer distance and the collision avoidance distance. The safety constraints and boundary constraints can be specifically expressed by the formula: Where, d bf represents the safe buffer distance between the shielding spacecraft and the target spacecraft, d cf represents the collision avoidance distance between the shielding spacecraft and the hidden spacecraft, t0 represents the start time of the coordinated hidden flight of multiple spacecraft, and t f represents the end time of the coordinated covert flight of multiple spacecraft, rh(t0) represents the hidden spacecraft r h At the initial time t0, is the first-order derivative of rh(t0), r h (t f ) indicates hidden spacecraft r h At the end time t f location, For r h (t f ), ν(t0) represents the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft at the initial time t0, is the first-order derivative of ν(t0), r h,0 represents the initial position of the hidden spacecraft, For r h,0 The first derivative of h,f Indicates the terminal position of the hidden spacecraft, For r h,f The first-order derivative of , ν represents the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft, ν0 represents the initial position of the shielding spacecraft, is the first-order derivative of ν0, and ||.||2 represents the 2-norm of the vector.

6. The method for planning multi-spacecraft cooperative covert flight trajectories as claimed in claim 5, characterized in that: The cooperative covert flight trajectory planning model described in S4 can be specifically expressed by the formula: ||in h || ∞ in h,max ,||in s || ∞ in s,max Where J represents the coordinated energy consumption of multiple spacecraft coordinated covert flight, u h,max represents the maximum thrust of the shielding spacecraft, u s,max represents the maximum thrust of the hidden spacecraft, B is the coefficient matrix of the TH equation of relative motion of the spacecraft, ||.|| ∞ Represents the infinity norm of a vector.

7. The method for planning multi-spacecraft cooperative covert flight trajectories as claimed in claim 6, characterized in that: The S5 is specifically: S51, rewriting the relative motion dynamics model of the hidden spacecraft and the dynamics constraint model of the cooperative concealed flight to obtain a state equation; S52, using a multi-segment Radau pseudo-spectral method and combining the state equation to transform the cooperative covert flight trajectory planning model into a linearized and discretized cooperative covert flight trajectory planning model; S53, based on convex optimization theory, converting the linearized and discretized cooperative covert flight trajectory planning model into a standard convex optimization model; S54, splitting the standard convex optimization model into two sub-problems, solving the two sub-problems through loop iteration to obtain a collaborative optimal solution, where the collaborative optimal solution is the collaborative covert flight trajectory of the multiple spacecraft.

8. The method for planning multi-spacecraft cooperative covert flight trajectories as claimed in claim 7, characterized in that: The state equation described in S51 is specifically: in, Where x represents the state vector of the hidden spacecraft, is the first-order derivative of x, ν represents the state vector of the shielding spacecraft, and are coefficient matrices of the hidden spacecraft state equation, Q and R are coefficient matrices of the shielded spacecraft state equation, I3 is the 3D identity matrix, 03 is the 3D zero matrix, 0 1×3 is a 1×3 dimensional matrix of zeros.

9. The method for planning multi-spacecraft cooperative covert flight trajectories as claimed in claim 8, characterized in that: The two sub-questions in S54 are specifically: First sub-question: Among them, J1 represents the first coordinated energy consumption of multiple spacecraft coordinated covert flight, and They represent the start and end time of the coordinated covert flight of multiple spacecraft in the kth time domain, is the Gaussian integral weight coefficient of the jth collocation point in the kth time domain, is the coefficient matrix of the jth collocation point of the hidden spacecraft in the kth time domain, X (k) and are all decision variables of the hidden spacecraft in the kth time domain, and are the coefficient matrices of the affine equations of the j-th collocation point of the hidden spacecraft in the k-th time domain, and are the coefficient matrices of the initial and final states of the hidden spacecraft in the kth time domain, is the coefficient matrix of the state of the hidden spacecraft at the initial moment of the k+1th time domain, X (k+1) To hide the decision variables of the spacecraft in the k+1th time domain, is the state at the initial moment of the kth time domain, is the coefficient matrix of the state at the end of the Kth time domain, is the state at the end of the Kth time domain, K is the total number of time domain segments, k = 1, 2, ..., K, N (k) Indicates the number of points in the k-th time domain, j=1,2,...,N (k) . Second sub-question: Among them, J2 represents the second collaborative energy consumption of multiple spacecraft coordinated covert flight, is the coefficient matrix of the jth collocation control quantity of the shielding spacecraft in the kth time domain, V (k) and are the decision variables of the shielding spacecraft in the kth time domain, and are the coefficient matrices of the affine equations of the j-th collocation point of the shielding spacecraft in the k-th time domain, is the position vector coefficient matrix of the hidden spacecraft at the jth distribution point in the kth time domain, is the position vector coefficient matrix of the shielding spacecraft at the jth distribution point in the kth time domain, and are the coefficient matrices of the shielding spacecraft at the initial and final states of the kth time domain, is the state quantity of the shielding spacecraft at the initial moment of the kth time domain, is the coefficient matrix of the state of the shielding spacecraft at the initial moment of the k+1th time domain, V (k+1) is the decision variable for shielding the spacecraft in the k+1th time domain.

10. The method for planning multi-spacecraft cooperative covert flight trajectories as claimed in claim 9, characterized in that: In S54, the two sub-problems are solved through loop iteration to obtain a collaborative optimal solution, which specifically includes the following: S541, preset initial parameters, initialize the reference trajectory of the hidden spacecraft and the shielded spacecraft in each time domain and S542: according to the preset initial parameters and the reference trajectory of the hidden spacecraft in each time domain Solve the first sub-problem and obtain the decision variable X of the hidden spacecraft in each time domain (k) and Calculate the decision variable X of the hidden spacecraft in each time domain (k) and reference trajectory The maximum of the differences is taken as the iterative error ΔX of the hidden spacecraft. According to the decision variable X of the hidden spacecraft in each time domain, (k) and Update the reference trajectory of the hidden spacecraft in each time domain and reference control sequence S543, based on the preset initial parameters, the updated reference trajectory of the hidden spacecraft in each time domain and reference control sequence and the reference trajectory of the shielding spacecraft in each time domain Solve the second sub-problem and obtain the decision variable V of the shielding spacecraft in each time domain (k) and Calculate the decision variable V of the shielding spacecraft in each time domain (k) and reference trajectory The maximum of the differences is taken as the iterative error ΔV of the shielding spacecraft. According to the decision variable V of the shielding spacecraft in each time domain, (k) and Update the reference trajectory of the obscured spacecraft in each time domain and reference control sequence S544, preset a first allowable error ξ1 and a second allowable error ξ2, compare the iterative error ΔX of the hidden spacecraft with the first allowable error ξ1, and compare the iterative error ΔV of the shielded spacecraft with the second allowable error ξ2, if ΔX<ξ1 and ΔV<ξ2, execute step S545, otherwise, execute step S542 to perform the next round of iterative solution; S545. Output the reference trajectory and reference control sequence corresponding to the hidden spacecraft and the shielded spacecraft after this round of iteration. The reference trajectory and reference control sequence are the collaborative optimal solution.

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