A method for multi-spacecraft cooperative covert flight trajectory planning

Abstract

The present invention discloses a method for planning the collaborative covert flight trajectories of multiple spacecraft. The method first establishes a dynamic constraint model for the collaborative covert flight of multiple spacecraft, and designs safety and boundary constraints. Based on the dynamic constraint model, safety and boundary constraints, a collaborative covert flight trajectory planning model for the multiple spacecraft is constructed. The collaborative covert flight trajectory planning model is linearized and discretized using a pseudospectral method. Based on convex optimization theory, the linearized and discretized collaborative covert flight trajectory planning model is converted into a convex optimization problem. A collaborative optimization solution strategy is designed, and the collaborative covert flight trajectories of the multiple spacecraft are obtained through a cyclic iterative solution. This method can effectively describe the collaborative covert flight missions of multiple spacecraft and simultaneously achieve collaborative covert approach and collaborative covert departure. It effectively reduces the complexity and computational complexity of the planning problem, improves computational speed, and ensures the optimality and accuracy of the solution.

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 covert flight trajectories of multiple spacecraft. Background Art

[0002] Currently, the widely studied pursuit-and-escape game of spacecraft in orbit is a direct and highly confrontational means of space attack and defense. In this game scenario, both spacecraft possess the ability to make autonomous decisions and maneuver, with one actively seeking to approach while the other strives to evade and escape. This game explores pursuit-and-escape strategies in various scenarios, including one-on-many, many-on-one, and many-on-many. Nash equilibrium solutions are constructed based on differential game theory, using methods such as the HJI equation, the extreme value principle, the Riccati equation, and the calculus of variations.

[0003] 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, which is difficult to solve and difficult to achieve the goal, and the task is difficult. Summary of the Invention

[0004] In response to the above-mentioned limitations of the on-orbit pursuit-and-escape game of spacecraft in the existing technology, the present invention proposes a multi-spacecraft collaborative 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.

[0005] In one aspect, the present invention provides a method for planning multi-spacecraft cooperative covert flight trajectories, comprising the following steps:

[0006] S1. Set a multi-spacecraft coordinated covert flight scenario, where 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;

[0007] S2. Set concealment constraint models for the shielding spacecraft and the hidden spacecraft, set relative motion dynamics models for the hidden spacecraft and the shielding spacecraft according to the TH equation for relative spacecraft dynamics, and establish a dynamic constraint model for the coordinated covert flight based on the concealment constraint model and the relative motion dynamics model;

[0008] 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 based on the safety buffer distance and collision avoidance distance;

[0009] S4. Construct a collaborative covert flight trajectory planning model for multiple spacecraft based on the dynamic constraint model, safety constraints, and boundary constraints of the collaborative covert flight;

[0010] S5. Optimize and solve the collaborative covert flight trajectory planning model to obtain the collaborative covert flight trajectories of multiple spacecraft.

[0011] Preferably, the concealment constraint model for shielding spacecraft and hiding spacecraft is set in S2, specifically including the following:

[0012] S21. Acquire the position of the target spacecraft, and determine the position of the hidden spacecraft based on the position of the target spacecraft;

[0013] S22. Determine the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft based on the position of the target spacecraft and the position of the hidden spacecraft;

[0014] 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.

[0015] Preferably, in S23, a concealment constraint model for shielding the spacecraft and hiding the spacecraft is set. The concealment constraint model can be specifically expressed by the formula:

[0016] r s =νr h

[0017]

[0018] Where 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.

[0019] Preferably, in S2, a dynamic constraint model for cooperative covert flight is established based on the concealment constraint model and the relative motion dynamics model. The dynamic constraint model for cooperative covert flight can be specifically expressed by the formula:

[0020]

[0021] Where r hrepresents the location 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, u h is the control vector of the hidden spacecraft, u s is the control vector for the shielding 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] Where, d bf represents the safety 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 starting time of the coordinated covert flight of multiple spacecraft, t f represents the end time of the coordinated covert flight of multiple spacecraft, r h (t0) represents the hidden spacecraft r h At the initial time t0, For r h The first derivative of (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 r 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.

[0025] Preferably, the cooperative covert flight trajectory planning model in S4 can be specifically expressed as:

[0026]

[0027] ||u h || ∞ ≤u h,max ,||u s || ∞ ≤u s,max

[0028] Where J represents the coordinated energy consumption of multiple spacecraft's 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.

[0029] Preferably, S5 is specifically:

[0030] S51. Rewrite the relative motion dynamics model of the hidden spacecraft and the dynamic constraint model of the cooperative covert flight to obtain the state equation;

[0031] S52. Using the multi-segment Radau pseudospectral method and combining it with the state equation, the cooperative covert flight trajectory planning model is transformed into a linearized and discretized cooperative covert flight trajectory planning model;

[0032] S53. Based on convex optimization theory, the linearized and discretized cooperative covert flight trajectory planning model is transformed into a standard convex optimization model;

[0033] S54. Split the standard convex optimization model into two sub-problems, solve the two sub-problems through cyclic iteration, and obtain a collaborative optimal solution. The collaborative optimal solution is the collaborative covert flight trajectory of multiple spacecraft.

[0034] Preferably, the state equation in S51 is specifically:

[0035]

[0036] in,

[0037]

[0038]

[0039] 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.

[0040] Preferably, the two sub-questions in S54 are specifically:

[0041] First sub-question:

[0042]

[0043] Among them, J1 represents the first collaborative energy consumption of multiple spacecraft coordinated covert flight, and They represent the start and end time of the k-th time domain multi-spacecraft coordinated covert flight, 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 hidden spacecraft’s initial and final states 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 K-th time domain, is the coefficient matrix of the state of the hidden spacecraft at the initial moment of the k+1 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) .

[0044] Second sub-question:

[0045]

[0046] Among them, J2 represents the second collaborative energy consumption of multiple spacecraft coordinated covert flight, is the coefficient matrix of the j-th collocation control quantity of the shielding spacecraft in the k-th time domain, V (k) and are all decision variables for shielding the spacecraft in the kth time domain, and are the coefficient matrices of the affine equation 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 j-th distribution point in the k-th time domain, and are the coefficient matrices of the shielding spacecraft’s initial and final states in 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 shielding spacecraft at the initial moment of the k+1 time domain, V (k+1) is the decision variable for shielding the spacecraft in the k+1th time domain.

[0047] Preferably, in S54, the two sub-problems are solved through loop iteration to obtain a collaborative optimal solution, which specifically includes the following:

[0048] S541. Preset initial parameters and initialize the reference trajectory of the hidden spacecraft and the shielded spacecraft in each time domain and

[0049] S542, based on 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 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 sequences

[0050] S543, based on the preset initial parameters, the updated reference trajectory of the hidden spacecraft in each time domain and reference control sequences 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 difference between them is taken, and 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 sequences

[0051] 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 obscured spacecraft with the second allowable error ξ2. If ΔX < ξ1 and ΔV < ξ2, execute step S545; otherwise, execute step S542 and perform the next round of iterative solution.

[0052] 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.

[0053] The above-mentioned method for collaborative covert flight trajectory planning for multiple spacecraft first establishes a dynamic constraint model for the collaborative covert flight of multiple spacecraft and designs safety and boundary constraints. Based on the dynamic constraint model, safety and boundary constraints, a collaborative covert flight trajectory planning model for multiple spacecraft is constructed. The model is linearized and discretized using a pseudospectral method. Based on convex optimization theory, the linearized and discretized model is transformed into a convex optimization problem. A collaborative optimization solution strategy is designed, and the collaborative covert flight trajectories of the multiple spacecraft are obtained through iterative solution. This method can effectively represent the collaborative covert flight mission of multiple spacecraft and simultaneously achieve collaborative covert approach and retreat. By processing the collaborative covert flight trajectory planning model using a pseudospectral method combined with convex optimization theory, an equivalent model with high discretization accuracy, good convergence, and good optimality is obtained. The proposed collaborative planning solution strategy effectively reduces computational complexity, improves the performance of the planning problem, and increases computational speed while ensuring the optimality and accuracy of the solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] 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;

[0055] Figure 2 This is a schematic diagram of a multi-spacecraft coordinated covert flight mission scenario in one embodiment of the present invention;

[0056] Figure 3 This is a flowchart of a loop iterative solution in one embodiment of the present invention;

[0057] Figure 4 This is a schematic diagram of a multi-spacecraft cooperative covert approach trajectory in one embodiment of the present invention;

[0058] Figure 5 This is a schematic diagram of a multi-spacecraft cooperative concealed escape trajectory according to an embodiment of the present invention;

[0059] Figure 6 This is a schematic diagram of multiple spacecraft cooperating to conceal their trajectories in another embodiment of the present invention. DETAILED DESCRIPTION

[0060] 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 with reference to the accompanying drawings.

[0061] 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 following is a schematic diagram of a multi-spacecraft coordinated covert flight mission scenario in one embodiment of the present invention. A multi-spacecraft coordinated covert flight trajectory planning method includes the following steps:

[0062] S1. Set a multi-spacecraft coordinated covert flight scenario, where the multi-spacecraft coordinated covert flight scenario includes a target spacecraft, at least one shielding spacecraft, and at least one hidden spacecraft. Figure 1 The figure specifically illustrates a coordinated covert flight scenario with one target spacecraft, one shielding spacecraft, and one hidden spacecraft. During a coordinated covert flight mission involving a shielding spacecraft and a hidden spacecraft, the shielding spacecraft always remains on the line connecting the hidden and target spacecraft, obstructing the target spacecraft's line of sight and rendering the hidden spacecraft visually invisible.

[0063] S2. Obtain the position of the target spacecraft and, based on this, set concealment constraint models for the shielding spacecraft and the hidden spacecraft. Set the relative motion dynamics model of the hidden spacecraft and the relative motion dynamics model of the shielding spacecraft according to the TH equation for relative spacecraft dynamics. Establish a dynamic constraint model for coordinated covert flight based on the concealment constraint model and the two relative motion dynamics models.

[0064] 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 based on the safety buffer distance and collision avoidance distance;

[0065] S4. Construct a collaborative covert flight trajectory planning model for multiple spacecraft based on the dynamic constraint model, safety constraints, and boundary constraints of the collaborative covert flight;

[0066] S5. Optimize and solve the collaborative covert flight trajectory planning model to obtain the collaborative covert flight trajectories of multiple spacecraft.

[0067] In one embodiment, the concealment constraint model for shielding spacecraft and hiding spacecraft is set in S2, specifically including the following:

[0068] S21. Acquire the position of the target spacecraft, and determine the position of the hidden spacecraft based on the position of the target spacecraft;

[0069] S22. Determine the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft based on the position of the target spacecraft and the position of the hidden spacecraft;

[0070] 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.

[0071] In one embodiment, a concealment constraint model for shielding spacecraft and hiding spacecraft is set in S23. The concealment constraint model can be specifically expressed as:

[0072] r s =νr h

[0073]

[0074] Where 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.

[0075] Specifically, first, the absolute position of the target spacecraft is obtained, and then the position of the hidden spacecraft is determined based on 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, based on the position of the target spacecraft and the position of the hidden spacecraft, the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft is determined; then, based on the position of the hidden spacecraft and the position of the shielding spacecraft on the line connecting the hidden spacecraft and the target spacecraft, a concealment constraint model of the shielding spacecraft and the hidden spacecraft is set, specifically as follows:

[0076] r s =νr h (1)

[0077] Among them, r s =[x s ,y s ,z s ] T

[0078] r h =[x h ,y h ,z h ] T

[0079] Where r s represents the position of the shielding spacecraft, that is, the position of the shielding 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, and 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.

[0080] Calculate the first-order derivative and the second-order derivative of the above hidden constraint model respectively:

[0081]

[0082]

[0083] Where, 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.

[0084] In one embodiment, in S2, a dynamic constraint model for cooperative stealth flight is established based on the stealth constraint model and the relative motion dynamics model. The dynamic constraint model for cooperative stealth flight can be specifically expressed as follows:

[0085]

[0086] Where r h represents the location 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, u h is the control vector of the hidden spacecraft, u s is the control vector for shielding the spacecraft.

[0087] Specifically, the setting process of the dynamic constraint model of cooperative stealth flight is as follows:

[0088] 1) Set up the relative motion dynamics model according to the TH equation of spacecraft relative motion

[0089] According to the TH equation of relative motion of spacecraft, the relative motion dynamics model of hidden spacecraft is set as follows:

[0090]

[0091] Where A and B are the coefficient matrices of the TH equation of relative motion of spacecraft, u h is the control vector of the hidden spacecraft.

[0092] The relative motion dynamics model of the shielding spacecraft is set according to the TH equation of the relative motion of the spacecraft as follows:

[0093]

[0094] Where u s is the control vector for shielding the spacecraft.

[0095] 2) Establish a dynamic constraint model for cooperative covert flight based on the concealment constraint models of multiple spacecraft, the relative motion dynamics model of the hidden spacecraft, and the relative motion dynamics model of the shielded spacecraft.

[0096] Specifically, the dynamic constraint model of cooperative stealth flight is derived based on formulas (1), (1)-1, (1)-2, (2)-1, and (2)-2, as follows:

[0097]

[0098] Where 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 the relative motion of the spacecraft, u h is the control vector of the hidden spacecraft, u s is the control vector for shielding the spacecraft.

[0099] In one embodiment, in S3, safety constraints and boundary constraints corresponding to multiple spacecraft are designed based on the safety buffer distance and the collision avoidance distance. The safety constraints and boundary constraints can be specifically expressed by the formula:

[0100]

[0101] Where, d bf represents the safety 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 starting time of the coordinated covert flight of multiple spacecraft, t f represents the end time of the coordinated covert flight of multiple spacecraft, r h (t0) represents the hidden spacecraft r h At the initial time t0, For r h The first derivative of (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 r 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.

[0102] 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 , collision avoidance distance d between shielding spacecraft and hidden spacecraft cf Then, 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 are determined, and then the safety buffer distance d is used to calculate the initial and end times of the coordinated covert flight of multiple spacecraft. 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.

[0103] In one embodiment, the cooperative covert flight trajectory planning model in S4 can be specifically expressed as follows:

[0104]

[0105] ||u h || ∞ ≤u h,max ,||u s || ∞ ≤u s,max

[0106] Where J represents the coordinated energy consumption of multiple spacecraft's 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 the constraints.

[0107] Specifically, multiple spacecraft are set to travel in a preset time period [t0,t f ] The goal is to minimize the energy consumption required for coordinated covert flight, namely:

[0108]

[0109] At the same time, the maximum thrust of the spacecraft is limited: ||u h || ∞ ≤u h,max ,||u s || ∞ ≤u s,max (5)-1

[0110] Combined with the previous constraints (specifically including the relative motion dynamics model of the hidden spacecraft (Formula (2)-1), the cooperative covert flight dynamics constraint model of the shielding spacecraft (Formula (3)), and the safety constraints and boundary constraints (Formula (4)), a cooperative covert flight trajectory planning model for multiple spacecraft is obtained.

[0111] In one embodiment, S5 is specifically:

[0112] S51. Rewrite the relative motion dynamics model of the hidden spacecraft and the dynamic constraint model of the cooperative covert flight to obtain the state equation.

[0113] Furthermore, the state equation in S51 is specifically:

[0114]

[0115] in,

[0116]

[0117]

[0118] 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.

[0119] 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.

[0120] Furthermore, in order to make the solution more convergent and improve the approximation accuracy, after obtaining the cooperative 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 cooperative covert flight trajectory planning model, as follows:

[0121]

[0122] Where J represents the coordinated energy consumption of multiple spacecraft's coordinated covert flight. and They represent the start and end time of the k-th time domain multi-spacecraft coordinated covert flight, 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 shielded 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.

[0123] S53. Based on convex optimization theory, the linearized and discretized cooperative covert flight trajectory planning model is transformed into a standard convex optimization model.

[0124] Furthermore, based on convex optimization theory, the linearized and discretized cooperative covert flight trajectory planning model is transformed into a standard convex optimization problem with a theoretically global optimal solution and better optimal convergence. The corresponding standard convex optimization model is as follows:

[0125]

[0126] 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 all decision variables of the hidden spacecraft in the kth time domain, V (k) and are all decision variables for shielding the 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 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 j-th distribution point in the k-th time domain, and are the coefficient matrices of the hidden spacecraft at the initial and end moments of the kth time domain, and are the coefficient matrices of the shielding spacecraft at the initial and end moments of the kth time domain, respectively. The coefficient matrices are used to extract the parameters of each decision variable at the corresponding moment.

[0127] Among the above parameters, the decision variable X (k) 、V (k) 、 and Defined as:

[0128]

[0129] Where, 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.

[0130] 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:

[0131] The dynamic constraints of the hidden spacecraft are:

[0132]

[0133] The dynamic constraints of cooperative stealth flight are:

[0134]

[0135] Affine equation coefficient matrix and and The above two dynamic constraints can be summarized as follows:

[0136]

[0137] The standard convex optimization model is a pseudo-spectral convex form of the dynamic constraint model of cooperative covert flight. It transforms the cooperative covert flight trajectory planning model into a standard convex optimization model, which has the characteristics of high discrete accuracy, good convergence and good optimality.

[0138] S54. Split the standard convex optimization model into two sub-problems, solve the two sub-problems through cyclic iteration, and obtain a collaborative optimal solution. The collaborative optimal solution is the collaborative covert flight trajectory of multiple spacecraft.

[0139] Furthermore, the first of the two subproblems in S54 is formulated as follows:

[0140]

[0141] Among them, J1 represents the first collaborative energy consumption of multiple spacecraft coordinated covert flight, and They represent the start and end time of the k-th time domain multi-spacecraft coordinated covert flight, 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 hidden spacecraft’s initial and final states in the kth time domain, is the coefficient matrix of the hidden spacecraft state at the initial moment of the k+1 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 K-th 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) .

[0142] The second of the two subproblems is stated as follows:

[0143]

[0144] Among them, J2 represents the second collaborative energy consumption of multiple spacecraft coordinated covert flight, is the coefficient matrix of the j-th collocation control quantity of the shielding spacecraft in the k-th time domain, V (k) and are all decision variables for shielding the spacecraft in the kth time domain, and are the coefficient matrices of the affine equation 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 j-th distribution point in the k-th time domain, and are the coefficient matrices of the shielding spacecraft’s initial and final states in 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 shielding spacecraft at the initial moment of the k+1 time domain, V (k+1) is the decision variable for shielding the spacecraft in the k+1th time domain.

[0145] The above two sub-problems are solved through cyclic iteration to obtain the collaborative optimal solution, that is, the collaborative covert flight trajectory of all spacecraft under the condition of lowest collaborative energy consumption.

[0146] In one embodiment, see Figure 3 , Figure 3 This is a flowchart of a loop iterative solution in one embodiment of the present invention. In S54, two sub-problems are solved through loop iterative solution to obtain a collaborative optimal solution, which specifically includes the following:

[0147] S541. Preset initial parameters, including boundary conditions, number of pseudo-spectrum segments, start and end times, number of points assigned to 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;

[0148] S542, based on 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 sequences The specific update formula is:

[0149] S543, based on the preset initial parameters, the updated reference trajectory of the hidden spacecraft in each time domain and reference control sequences 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 sequences The specific update formula is:

[0150] 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 obscured 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.

[0151] 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.

[0152] In one embodiment, a multi-spacecraft coordinated covert flight system includes a target spacecraft, a shielding spacecraft, a concealed spacecraft, and a computer system. The target spacecraft, the shielding spacecraft, and the concealed spacecraft are each communicatively connected to the computer system. The shielding spacecraft is located on a line connecting the concealed spacecraft and the target spacecraft, wherein:

[0153] The computer system is used to obtain the corresponding position information of the target spacecraft, the shielding spacecraft, and the hidden spacecraft, and execute the above-mentioned multi-spacecraft coordinated covert flight trajectory planning method to plan the flight trajectory of the shielding spacecraft and the hidden spacecraft relative to the target spacecraft;

[0154] 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.

[0155] For the specific limitations of a multi-spacecraft cooperative covert flight system, please refer to the limitations of a multi-spacecraft cooperative covert flight trajectory planning method mentioned above, which will not be repeated here.

[0156] Furthermore, the multi-spacecraft collaborative covert flight trajectory planning method proposed in the present invention was verified through experiments.

[0157] 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 Schematic diagram of multiple spacecraft cooperatively concealing their trajectories in one embodiment of the present invention.

[0158] Figure 4 Specifically, it shows a trajectory diagram of a hidden spacecraft and a shielding spacecraft cooperatively approaching a target spacecraft. Figure 5 The figure specifically shows a schematic diagram of the trajectory of a hidden spacecraft and a shielding spacecraft working together to hide away from a target spacecraft.

[0159] 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.

[0160] 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.

[0161] Figure 6 Specifically shown are the flight trajectories of two hidden spacecraft and one shielding spacecraft relative to the target spacecraft, wherein the shielding spacecraft is always located on the line connecting the two hidden spacecraft and the target spacecraft.

[0162] Depend on Figure 6 It 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 unable 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.

[0163] The above-mentioned method for collaborative covert flight trajectory planning for multiple spacecraft first establishes a dynamic constraint model for the collaborative covert flight of multiple spacecraft and designs safety and boundary constraints. Based on the dynamic constraint model, safety and boundary constraints, a collaborative covert flight trajectory planning model for multiple spacecraft is constructed. The model is linearized and discretized using a pseudospectral method. Based on convex optimization theory, the linearized and discretized model is transformed into a convex optimization problem. A collaborative optimization solution strategy is designed, and the collaborative covert flight trajectories of the multiple spacecraft are obtained through iterative solution. This method can effectively represent the collaborative covert flight mission of multiple spacecraft and simultaneously achieve collaborative covert approach and retreat. By processing the collaborative covert flight trajectory planning model using a pseudospectral method combined with convex optimization theory, an equivalent model with high discretization accuracy, good convergence, and good optimality is obtained. The proposed collaborative planning solution strategy effectively reduces computational complexity, improves the performance of the planning problem, and increases computational speed while ensuring the optimality and accuracy of the solution.

[0164] The above describes in detail the method for planning the multi-spacecraft coordinated covert flight trajectories 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 intended to help understand the core concept of the present invention. It should be noted that those skilled in the art can make various improvements and modifications to the present invention without departing from the principles of the present invention, and such 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 concealment constraint models for the shielding spacecraft and the hidden spacecraft, setting relative motion dynamics models corresponding to the hidden spacecraft and the shielding spacecraft according to the spacecraft relative dynamics TH equation, and establishing a dynamic constraint model for coordinated covert flight based on the concealment constraint model and the relative motion dynamics model; 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 a plurality of safety constraints and boundary constraints corresponding to the spacecraft based on 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 dynamic constraint model of the collaborative covert flight 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 multi-spacecraft cooperative covert flight trajectory planning method according to 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, obtaining 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 based on the position of the target spacecraft and the position of the hidden spacecraft; S23. Set 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 multi-spacecraft cooperative covert flight trajectory planning method according to 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 Where 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 multi-spacecraft cooperative covert flight trajectory planning method according to claim 3, characterized in that: In S2, a dynamic constraint model of cooperative covert flight is established based on the concealment constraint model and the relative motion dynamic model. The dynamic constraint model of cooperative covert flight can be specifically expressed by the formula: Where r h represents the location 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, u h is the control vector of the hidden spacecraft, u s is the control vector for the shielding spacecraft.

5. The multi-spacecraft cooperative covert flight trajectory planning method according to 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 safety 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 starting time of the coordinated covert flight of multiple spacecraft, t f represents the end time of the coordinated covert flight of multiple spacecraft, r h (t0) represents the hidden spacecraft r h At the initial time t0, For r h The first derivative of (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 r 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 according to claim 5, wherein: The cooperative covert flight trajectory planning model described in S4 can be specifically expressed as follows: ||in h || ∞ in h,max ,||in s || ∞ in s,max Where J represents the coordinated energy consumption of multiple spacecraft's 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 multi-spacecraft cooperative covert flight trajectory planning method according to claim 6, characterized in that: The S5 is specifically: S51, rewriting the relative motion dynamics model of the hidden spacecraft and the dynamic constraint model of the coordinated covert flight to obtain a state equation; S52, using a multi-segment Radau pseudospectral method in combination with 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. Split the standard convex optimization model into two sub-problems, and solve the two sub-problems through cyclic iteration to obtain a collaborative optimal solution, where the collaborative optimal solution is the collaborative covert flight trajectory of the multiple spacecraft.

8. The multi-spacecraft cooperative covert flight trajectory planning method according to 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 according to claim 8, wherein: The two sub-problems in S54 are specifically: First sub-question: Among them, J1 represents the first collaborative energy consumption of multiple spacecraft coordinated covert flight, and They represent the start and end time of the k-th time domain multi-spacecraft coordinated covert flight, 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 hidden spacecraft’s initial and final states in the kth time domain, is the coefficient matrix of the hidden spacecraft state at the initial moment of the k+1 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 K-th 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 j-th collocation control quantity of the shielding spacecraft in the k-th time domain, V (k) and are all decision variables for shielding the spacecraft in the kth time domain, and are the coefficient matrices of the affine equation 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 j-th distribution point in the k-th time domain, and are the coefficient matrices of the shielding spacecraft’s initial and final states in 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 shielding spacecraft at the initial moment of the k+1 time domain, V (k+1) is the decision variable for shielding the spacecraft in the k+1th time domain.

10. The multi-spacecraft cooperative covert flight trajectory planning method according to 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 and 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 difference between them is taken, and 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 sequences S543, based on the preset initial parameters, the updated reference trajectory of the hidden spacecraft in each time domain and reference control sequences 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, and the decision variable V of the shielding spacecraft in each time domain is calculated. (k) and Update the reference trajectory of the obscured spacecraft in each time domain and reference control sequences 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 obscured spacecraft with the second allowable error ξ2. If ΔX < ξ1 and ΔV < ξ2, execute step S545; otherwise, execute step S542 and 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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