A multi-spacecraft cooperative escort method based on reachable domain coverage
By employing a multi-spacecraft collaborative defense method based on reachability domain coverage, and utilizing covariance analysis and convex optimization algorithms to design defense strategies, the safety problem of high-orbit spacecraft was solved, achieving efficient collaborative defense among multiple spacecraft and improving the defense success rate and fuel utilization efficiency.
Patent Information
- Application Number
- CN202310829573.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-07-06
- Publication Date
- 2026-08-25
- Estimated Expiration
- 2043-07-06
AI Technical Summary
In existing technologies, the safe operation of high-orbit spacecraft is threatened by the increase in space debris and the uncertainty of the status of ground observation equipment. Furthermore, there is a lack of research on multi-spacecraft collaborative protection strategies, especially for large communication and navigation satellites, where effective protection measures are insufficient.
A multi-spacecraft collaborative protection method based on reachability domain coverage is adopted. By obtaining the relative state of the threat source, the covariance analysis method is used to approximate the terminal reachability domain of the threat source as a spatial ellipsoid. Combining dynamic equations and convex optimization algorithms, the protection plane and protection point are designed, and a multi-spacecraft collaborative trajectory planning model is constructed to minimize fuel consumption and avoid collisions, thereby achieving multi-spacecraft collaborative protection.
It effectively prevents threat sources from approaching high-orbit targets, improves the safety and escort success rate of spacecraft, reduces spacecraft fuel consumption, and enhances defense capabilities in multiple scenarios.
Smart Images
Figure CN116859994B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of spacecraft technology, and in particular to a multi-spacecraft collaborative protection method based on reachability domain coverage. Background Technology
[0002] High-orbit spacecraft play an irreplaceable role in many fields, including satellite communication, early warning and surveillance, space environment monitoring, and exploration of unknown celestial bodies. However, due to the increasing amount of space debris and the uncertainty in ground-based observation equipment's estimation of the state of high-orbit targets, the safe operation of high-orbit spacecraft faces potential threats.
[0003] Due to limitations in maneuverability and mission requirements, high-value targets such as large communication and navigation satellites in high orbits are not suitable for large-scale orbital maneuvers. Therefore, using multiple escort spacecraft to provide coordinated protection for these targets is an effective measure to address threats. Existing literature on spacecraft orbital pursuit and escape problems is mostly based on the assumption of continuous thrust, and there is relatively little research on multi-spacecraft coordinated protection strategies. Summary of the Invention
[0004] Therefore, it is necessary to provide a multi-spacecraft collaborative protection method based on reachability domain coverage to address the above-mentioned technical problems.
[0005] A multi-spacecraft cooperative escort method based on reachability domain coverage, the method comprising:
[0006] Obtain the relative state of the threat source; based on the covariance analysis method and the relative state of the threat source, approximate the terminal reachable domain of the threat source as a spatial ellipsoid, and obtain the projection length of the terminal position of the threat source in three coordinate directions;
[0007] The constraints of the threat source terminal reachability domain solution model are set using dynamic equations, initial boundary conditions and control saturation constraints. The objective function of the threat source terminal reachability domain solution model is set to maximize the projection length. The threat source terminal reachability domain solution model is constructed based on the objective function and constraints.
[0008] The reachability domain of the threat source endpoint is obtained by solving the model using a convex optimization algorithm.
[0009] When the target spacecraft is located within the reachable domain of the threat source, multiple escort spacecraft are used for coordinated protection. The plane perpendicular to the line connecting the target spacecraft to the threat source and passing through the midpoint of the reachable domain is defined as the escort plane. The escort point is calculated based on the maximum radius of the cross section of the ellipsoid of the escort plane and the reachable domain and the radius of the projection of the defense distance of the escort spacecraft onto the escort plane.
[0010] Based on the terminal state constraints of the escort spacecraft set at the escort point, and combined with dynamic constraints, initial state constraints, control saturation constraints and inter-satellite collision avoidance constraints, the constraints of the multi-spacecraft cooperative trajectory planning model are set, and the objective function of the multi-spacecraft cooperative trajectory planning model is set to minimize the fuel consumption of multiple escort spacecraft.
[0011] A multi-spacecraft cooperative trajectory planning model is constructed using constraints and objective functions; the optimal control sequence for the multi-spacecraft cooperative trajectory planning model is obtained by solving the model.
[0012] In one embodiment, under the rolling time-domain optimization framework, the first step of the generated optimal control sequence is used as the actual control input to act on the dynamic system, update the relative state of the threat source and the escort spacecraft, and determine whether the threat source is within the interception range of the escort spacecraft. If so, the interception is successful; otherwise, the relative state of the threat source is reacquired to calculate the optimal control sequence for multiple spacecraft until the remaining interception time is zero.
[0013] In one embodiment, the reachability domain of the threat source is approximated as a spatial ellipsoid using covariance analysis to obtain the projected lengths of the threat source's terminal location in three coordinate directions, including:
[0014] Using covariance analysis, the reachable domain of the threat source is approximated as a spatial ellipsoid, yielding the projected lengths of the threat source's terminal location in three coordinate directions.
[0015] J i =n i ·(r f -r e )2
[0016] Where i∈{x,y,z}, n i r represents the unit normal vector in the directions of the three coordinate axes. f =CX w (t f ) represents the location of the threat source endpoint, r e Indicates the relative position of the terminal when the threat source is uncontrolled, C = [I 3×3 0 3×3 ].
[0017] In one embodiment, a solution model for the reachability domain of the threat source endpoint is constructed based on the objective function and constraints, including:
[0018] Based on the objective function and constraints, a solution model for the reachability domain of the threat source terminal is constructed to maximize J. i =||n i ·(r f (N)-r e )||2
[0019] Satisfy X w (k+1)=Φ(T imp )X w (k)+Φ v (T imp )Δv(k)
[0020] X w (0) = X w0
[0021] ||Δv(k)||2≤Δv max
[0022] Where k = 0, 1, ..., N-1 represents the discrete step number, X w (k) represents the relative state of the threat source at step k, T imp X represents the pulse interval time. w0 Let Δv(k) represent the initial relative state of the threat source, Φ and Φ' represent the pulse velocity magnitude, and Φ' ... v This is the transition matrix for relative state and relative velocity.
[0023] In one embodiment, the guard point is calculated based on the maximum radius of the cross section of the ellipsoid of the guard plane and the terminal reachable domain, and the radius of the projection of the defense distance of the guard spacecraft onto the guard plane, including:
[0024] The maximum radius of the cross section of the ellipsoid of the guard plane and the terminal reachable domain is R. p The radius of the projection of the defense distance of the escorting spacecraft onto the escort plane is R. d ,when At that time, the guard points are distributed in a phase-equidistant manner within a radius of R. d On the circumference, when When, the guard point is at a radius of The circumference is arranged in equal phases.
[0025] In one embodiment, inter-satellite collision avoidance constraints include collision avoidance constraints between escort spacecraft and collision avoidance constraints between escort spacecraft and the target; the collision avoidance constraint between escort spacecraft is ||C(X)||. gi (k)-X gj (k))||2>R col Where Rcol is the minimum permissible distance between the two spacecraft, and X gi (k) and X gj (k) represent the relative states of the i-th and j-th escort spacecraft at step k; the collision avoidance constraint between the escort spacecraft and the target is ||C·(X)||. gi (k)-X t (k))||2>R col , where X t(k) represents the relative state of the target spacecraft at step k.
[0026] In one embodiment, a multi-spacecraft cooperative trajectory planning model is constructed using constraints and an objective function, including:
[0027] A multi-spacecraft cooperative trajectory planning model is constructed using constraints and objective functions.
[0028] minimize
[0029] Satisfy X gi (k+1)=A d X gi (k)+B d u i (k)
[0030] X gi (0) = X gi0 r gi (N)=P gi
[0031] ||u i (k)||2≤U max
[0032] ||C(X gi (k)-X gj (k))||2>R col
[0033] ||C·(X gi (k)-X t (k))||2>R col
[0034] Among them, X gi (k) and u i (k) represent the relative state and control quantity of the i-th escort spacecraft at step k, respectively, k = 0, K, N-1, N s And N represents the number of escort spacecraft and the number of distances, A d B represents the discrete state transition matrix. d X represents the discrete control transfer matrix. gi0 Let r represent the initial relative state of the i-th escort spacecraft. gi (N) represents the relative position of the i-th escort spacecraft at step N, P gi U represents the relative position of the i-th guard point. max This indicates the maximum thrust used to protect the spacecraft.
[0035] The aforementioned multi-spacecraft collaborative protection method based on reachability domain coverage first approximates the terminal reachability domain of the threat source as a spatial ellipsoid based on covariance analysis and the relative state of the threat source, obtaining the projected lengths of the threat source's terminal position in three coordinate directions. Then, it sets constraints on the threat source terminal reachability domain solution model using dynamic equations, initial boundary conditions, and control saturation constraints. The objective function of the solution model is set to maximize the projected length. Based on the objective function and constraints, the threat source terminal reachability domain solution model is constructed, modeling the threat source reachability domain problem as a convex optimization problem to be solved. Under the dynamic optimization framework, based on the dynamically updated reachable domain of the threat source terminal, a collaborative escort plane and escort points are designed. Based on the escort points, dynamic constraints, initial and terminal state constraints, control saturation constraints, and inter-satellite collision avoidance constraints for multi-spacecraft collaborative escort are set to minimize the control quantities of multiple escort spacecraft and set the objective function of the multi-spacecraft collaborative trajectory planning model. Using the dynamic constraints, initial and terminal state constraints, control saturation constraints, inter-satellite collision avoidance constraints, and objective function, the multi-spacecraft collaborative trajectory planning model is constructed to generate the corresponding escort trajectories. Based on the escort trajectories, multi-spacecraft collaborative escort can be achieved. Attached Figure Description
[0036] Figure 1 This is a flowchart illustrating a multi-spacecraft cooperative protection method based on reachability domain coverage in one embodiment;
[0037] Figure 2 This is a schematic diagram of a multi-spacecraft collaborative escort scenario in one embodiment;
[0038] Figure 3 This is a schematic diagram of the defense distance and collision avoidance distance in one embodiment;
[0039] Figure 4 This is a schematic diagram of the terminal reachable domain in another embodiment;
[0040] Figure 5 This is a schematic diagram of the guard plane in one embodiment;
[0041] Figure 6 This is a map showing the distribution of guard points in one embodiment;
[0042] Figure 7 This is a schematic diagram of a complete multi-spacecraft collaborative escort process in one embodiment. Detailed Implementation
[0043] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.
[0044] In one embodiment, such as Figure 1 As shown, a multi-spacecraft cooperative escort method based on reachability domain coverage is provided, including the following steps:
[0045] Step 102: Obtain the relative state of the threat source; based on the covariance analysis method and the relative state of the threat source, approximate the terminal reachable domain of the threat source as a spatial ellipsoid, and obtain the projection length of the terminal position of the threat source in three coordinate directions.
[0046] like Figure 2 As shown, limited by the maneuverability and perception capabilities of the escort spacecraft, when a threat source approaches within a few kilometers of our high-value high-orbit targets, multiple escort spacecraft will coordinate to protect them and prevent the threat source from maneuvering around or hovering at close range.
[0047] The defense range R of the spacecraft d And collision avoidance distance R col like Figure 3 As shown. If the distance between the threat source and the escort spacecraft is less than or equal to R... d If the threat source is considered to have entered the defense range of the escort spacecraft, and the escort spacecraft successfully intercepts the threat source, then...
[0048]
[0049] In the formula: C = [I 3×3 0 3×3 ], X g and X w These represent the relative states of the spacecraft being protected and the threat source, respectively.
[0050] To avoid collisions between spacecraft, the distance between the escort spacecraft and the target spacecraft, as well as other escort spacecraft, must be greater than the collision avoidance distance R. col .
[0051]
[0052] In the formula: i,j=1,2,…,N s i≠j, X t N represents the relative state of the target spacecraft. s To protect the number of spacecraft.
[0053] Because the state of a threat source is uncertain, the target spacecraft can estimate the relative reachability of the threat source at the terminal moment based on the observed relative state of the threat source, providing a reference for the design of the escort point for the spacecraft. The terminal reachability of the threat source can be approximated as a space ellipsoid based on the covariance analysis method, and is defined by the center r of the ellipsoid. e =[x e ,y e ,z e ] TThe semi-axis lengths a, b, and c are used to characterize this.
[0054]
[0055] In the formula: r e =CΦ(t) N ,t0)X t0 This represents the relative position of the endpoint in an uncontrolled state of the threat source. Therefore, solving for the reachable region of the threat source's endpoint is transformed into solving for the lengths of the three semi-axis. The projected length J of the threat source's endpoint position in the three coordinate directions is... i It can be represented as
[0056] J i =||n i ·(r f -r e )||2
[0057] In the formula: i∈{x,y,z}, n i r represents the unit normal vector in the directions of the three coordinate axes. f =CX w (t f () indicates the location of the threat source endpoint. (By...) Figure 4 It can be seen that J x The value corresponding to the maximum value is the semi-axis a of the ellipsoid. Similarly, b = max J y c = max J z .
[0058] Step 104: Set the constraints of the threat source terminal reachability domain solution model using the dynamic equation, initial boundary conditions and control saturation constraints, and set the objective function of the threat source terminal reachability domain solution model to maximize the projection length. Construct the threat source terminal reachability domain solution model based on the objective function and constraints.
[0059] Taking into account the dynamic equations, initial boundary conditions, and control saturation constraints, the solution of the terminal reachability domain of the threat source can be modeled as a discrete trajectory planning problem. The dynamic equations and initial boundary conditions are affine functions, which need to be further transformed into convex optimization problems before they can be solved.
[0060] Step 106: Solve the threat source terminal reachability domain solution model using a convex optimization algorithm to obtain the threat source terminal reachability domain.
[0061] Using convex optimization algorithms to solve the reachability domain model of threat source terminals is an existing technology, so it will not be elaborated on in this application. The local optimal solution of the convex optimization problem is the global optimal solution, and no initial value needs to be provided during the solution. This can avoid the shortcomings of traditional nonlinear optimization algorithms that are prone to getting trapped in local optima and improve the accuracy of the solution.
[0062] Step 108: When the target spacecraft is located within the reachable domain of the threat source terminal, multiple escort spacecraft are used for coordinated protection. The plane perpendicular to the line connecting the target spacecraft to the threat source and passing through the midpoint of the reachable domain terminal is defined as the escort plane. The escort point is calculated based on the maximum radius of the cross section of the ellipsoid of the escort plane and the reachable domain terminal and the radius of the projection of the defense distance of the escort spacecraft onto the escort plane.
[0063] Within a given alert period, if the target spacecraft is within the reachability of the threat source, the escort spacecraft will engage in coordinated protection. Under the same initial conditions and maneuvers, if The source of the threat is The relative position at any given moment is One of the points, namely According to the definition of the reachable domain of the threat source endpoint, D(t) N ,t0) is The set of positions of all state points after N-N1 steps, therefore As time progresses and the remaining steps decrease, the threat source in t N The relative reachability domain gradually decreases over time. If the terminal reachability domain of the threat source is estimated solely based on the initial state, a large number of escort spacecraft would be needed to cover it, resulting in wasted spacecraft fuel and reduced lifespan. In the rolling time-domain optimization framework, the target spacecraft designs escort points for each escort spacecraft at each discrete time step based on updated threat source information. The escort spacecraft solves the open-loop optimal control problem based on the updated terminal boundary conditions and applies the first step of the generated optimal control sequence as the actual control input to the dynamic system. Rolling time-domain optimization iteratively solves the optimal control strategy using updated state information to reduce the impact of environmental uncertainties on the control results, which is the essential difference between it and traditional optimization methods.
[0064] After determining the terminal reachability domain of the threat source, a plane perpendicular to the line connecting the target spacecraft to the threat source and passing through the midpoint of the relative reachability domain is defined as the guard plane, such as... Figure 5 As shown. The maximum radius of the cross section between the guard plane and the terminal reachable ellipsoid is defined as R. p The projection of the defense distance of the escorting spacecraft onto the escort plane has a radius of R. d If the circle is defined, then the multi-star collaborative defense problem can be transformed into a multi-circle coverage problem.
[0065] Taking three scenarios of escorting spacecraft as examples, such as Figure 6 As shown, when If the coordinated defense area of the escort spacecraft cannot completely cover the escort plane, then the escort points are distributed in an equal-phase manner on a radius of R. d The circumference of the circle allows for a larger area of coordinated defense. When When the coordinated defense area of the three escort spacecraft can completely cover the escort plane, then the escort point is at a radius of... The circumference is arranged in equal phases.
[0066] Step 110: Based on the guard point, set the terminal state constraints of the escort spacecraft, and combine the dynamic constraints, initial state constraints, control saturation constraints and inter-satellite collision avoidance constraints to set the constraints of the multi-spacecraft cooperative trajectory planning model, so as to minimize the fuel consumption of multiple escort spacecraft and set the objective function of the multi-spacecraft cooperative trajectory planning model.
[0067] The dynamic constraints, initial and terminal state constraints, control saturation constraints, and inter-satellite collision avoidance constraints of multi-spacecraft collaborative escort mainly reflect spatial coordination, temporal coordination, and inter-satellite collision avoidance. Spatial coordination is reflected in the selection of escort points, maximizing the collaborative escort area of the escort spacecraft. Temporal coordination is reflected in the simultaneous arrival of multiple escort spacecraft at the preset escort points. Inter-satellite collision avoidance constraints include collision avoidance between escort spacecraft and collision avoidance between escort spacecraft and the target, enabling efficient and safe operation within the maximum collaborative escort area during subsequent multi-spacecraft collaborative escort operations.
[0068] Step 112: Construct a multi-spacecraft cooperative trajectory planning model using constraints and objective function; solve the multi-spacecraft cooperative trajectory planning model to obtain the optimal control sequence for the multi-spacecraft.
[0069] This application primarily utilizes convex optimization methods to solve the multi-spacecraft cooperative trajectory planning model. This process is existing technology and will not be elaborated upon further in this application. The complete multi-spacecraft cooperative escort process is as follows: Figure 7 As shown in the figure and through simulation, this application can quickly calculate the reachable domain of the threat source terminal. The cooperative protection strategy can effectively block the threat source in multiple scenarios, and the protection success rate increases with the increase of the maneuverability of the escort spacecraft.
[0070] In the aforementioned multi-spacecraft collaborative protection method based on reachability domain coverage, the terminal reachability domain of the threat source is first approximated as a spatial ellipsoid based on covariance analysis and the relative state of the threat source, obtaining the projected lengths of the threat source's terminal position in three coordinate directions. Constraints are then set for the threat source terminal reachability domain solution model using dynamic equations, initial boundary conditions, and control saturation constraints. The objective function of the solution model is set to maximize the projected length. Based on the objective function and constraints, the threat source terminal reachability domain solution model is constructed, modeling the threat source reachability domain problem as a convex optimization problem. Under the rolling optimization framework, based on the dynamically updated reachable domain of the threat source terminal, a cooperative escort plane and escort points are designed. Based on the escort points, dynamic constraints, initial and terminal state constraints, control saturation constraints, and inter-satellite collision avoidance constraints for multi-spacecraft cooperative escort are set to minimize the control quantities of multiple escort spacecraft and set the objective function of the multi-spacecraft cooperative trajectory planning model. Using the dynamic constraints, initial and terminal state constraints, control saturation constraints, inter-satellite collision avoidance constraints, and objective function, the multi-spacecraft cooperative trajectory planning model is constructed to generate the corresponding escort trajectories. Based on the escort trajectories, multi-spacecraft cooperative escort can be achieved.
[0071] In one embodiment, under the rolling time-domain optimization framework, the first step of the generated optimal control sequence is used as the actual control input to act on the dynamic system, update the relative state of the threat source and the escort spacecraft, and determine whether the threat source is within the interception range of the escort spacecraft. If so, the interception is successful; otherwise, the relative state of the threat source is reacquired to calculate the optimal control sequence for multiple spacecraft until the remaining interception time is zero.
[0072] In one embodiment, the reachability domain of the threat source is approximated as a spatial ellipsoid using covariance analysis to obtain the projected lengths of the threat source's terminal location in three coordinate directions, including:
[0073] Using covariance analysis, the reachable domain of the threat source is approximated as a spatial ellipsoid, yielding the projected lengths of the threat source's terminal location in three coordinate directions.
[0074] J i =||n i ·(r f -r e )||2
[0075] Where i∈{x,y,z}, n i r represents the unit normal vector in the directions of the three coordinate axes. f =CX w (t f ) represents the location of the threat source endpoint, r e Indicates the relative position of the terminal when the threat source is uncontrolled, C = [I 3×3 03×3 ].
[0076] In one embodiment, a solution model for the reachability domain of the threat source endpoint is constructed based on the objective function and constraints, including:
[0077] Based on the objective function and constraints, a solution model for the reachability domain of threat sources and endpoints is constructed as follows:
[0078] Maximize J i =||n i ·(r f (N)-r e )||2
[0079] Satisfy X w (k+1)=Φ(T imp )X w (k)+Φ v (T imp )Δv(k)
[0080] X w (0) = X w0
[0081] ||Δv(k)||2≤Δv max
[0082] Where k = 0, 1, ..., N-1 represents the discrete step number, X w (k) represents the relative state of the threat source at step k, T imp X represents the pulse interval time. w0 Let Δv(k) represent the initial relative state of the threat source, Φ and Φ' represent the pulse velocity magnitude, and Φ' ... v This is the transition matrix for relative state and relative velocity.
[0083] In one embodiment, the guard point is calculated based on the maximum radius of the cross section of the ellipsoid of the guard plane and the terminal reachable domain, and the radius of the projection of the defense distance of the guard spacecraft onto the guard plane, including:
[0084] The maximum radius of the cross section of the ellipsoid of the guard plane and the terminal reachable domain is R. p The radius of the projection of the defense distance of the escorting spacecraft onto the escort plane is R. d ,when At that time, the guard points are distributed in a phase-equidistant manner within a radius of R. d On the circumference, when When, the guard point is at a radius of The circumference is arranged in equal phases.
[0085] In one embodiment, inter-satellite collision avoidance constraints include collision avoidance constraints between escort spacecraft and collision avoidance constraints between escort spacecraft and the target; the collision avoidance constraint between escort spacecraft is ||C(X)||.gi (k)-X gj (k))||2>R col , where R col X is the minimum permissible distance between two spacecraft. gi (k) and X gj (k) represent the relative states of the i-th and j-th escort spacecraft at step k; the collision avoidance constraint between the escort spacecraft and the target is ||C·(X)||. gi (k)-X t (k))||2>R col , where X t (k) represents the relative state of the target spacecraft at step k.
[0086] In one embodiment, a multi-spacecraft cooperative trajectory planning model is constructed using constraints and an objective function, including:
[0087] A multi-spacecraft cooperative trajectory planning model is constructed using constraints and objective functions.
[0088] minimize
[0089] Satisfy X gi (k+1)=A d X gi (k)+B d u i (k)
[0090] X gi (0) = X gi0 r gi (N)=P gi
[0091] ||u i (k)||2≤U max
[0092] ||C(X gi (k)-X gj (k))||2>R col
[0093] ||C·(X gi (k)-X t (k))||2>R col
[0094] Among them, X gi (k) and u i (k) represent the relative state and control quantity of the i-th escort spacecraft at step k, respectively, k = 0, K, N-1, N s And N represents the number of escort spacecraft and the number of distances, A dB represents the discrete state transition matrix. d X represents the discrete control transfer matrix. gi0 Let r represent the initial relative state of the i-th escort spacecraft. gi (N) represents the relative position of the i-th escort spacecraft at step N, P gi U represents the relative position of the i-th guard point. max This indicates the maximum thrust used to protect the spacecraft.
[0095] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.
[0096] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0097] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.
Claims
1. A multi-spacecraft cooperative escort method based on reachability domain coverage, characterized in that, The method includes: Obtain the relative state of the threat source; based on the covariance analysis method and the relative state of the threat source, approximate the terminal reachable domain of the threat source as a spatial ellipsoid, and obtain the projection length of the terminal position of the threat source in three coordinate directions; The constraints of the threat source terminal reachability domain solution model are set using dynamic equations, initial boundary conditions, and control saturation constraints. The objective function of the threat source terminal reachability domain solution model is set to maximize the projection length. The threat source terminal reachability domain solution model is constructed based on the objective function and constraints. The reachability domain of the threat source terminal is obtained by solving the model using a convex optimization algorithm. When the target spacecraft is located within the reachable domain of the threat source terminal, multiple escort spacecraft are used for coordinated protection. A plane perpendicular to the line connecting the target spacecraft to the threat source and passing through the midpoint of the reachable domain terminal is defined as the protection plane. The protection point is calculated based on the maximum radius of the cross section of the ellipsoid of the protection plane and the reachable domain terminal and the radius of the projection of the defense distance of the escort spacecraft onto the protection plane. Based on the guard points, set the terminal state constraints of the escort spacecraft, and combine dynamic constraints, initial state constraints, control saturation constraints and inter-satellite collision avoidance constraints to set the constraints of the multi-spacecraft cooperative trajectory planning model, so as to minimize the fuel consumption of the multiple escort spacecraft and set the objective function of the multi-spacecraft cooperative trajectory planning model. A multi-spacecraft cooperative trajectory planning model is constructed using the aforementioned constraints and objective function; the optimal control sequence for the multi-spacecraft is obtained by solving the multi-spacecraft cooperative trajectory planning model. The guard point is calculated based on the maximum radius of the cross section of the ellipsoid of the guard plane and the terminal reachable domain, and the radius of the projection of the defense distance of the guard spacecraft onto the guard plane, including: The maximum radius of the cross-section of the ellipsoid of the guard plane and the terminal reachable domain is R p The radius of the projection of the defense distance of the escort spacecraft onto the escort plane is... R d ,when At that time, the guard points are distributed in a phase-equidistant manner within a radius of [missing information]. R d On the circumference, when When, the guard point is at a radius of The circumference is arranged in equal phases.
2. The method according to claim 1, characterized in that, The method further includes: Under the rolling time-domain optimization framework, the first step of the generated optimal control sequence is used as the actual control input to act on the dynamic system, update the relative state of the threat source and the escort spacecraft, and determine whether the threat source is within the interception range of the escort spacecraft. If so, the interception is successful; otherwise, the relative state of the threat source is reacquired to calculate the optimal control sequence for multiple spacecraft until the remaining interception time is zero.
3. The method according to claim 1, characterized in that, Using covariance analysis, the reachable domain of a threat source is approximated as a spatial ellipsoid, yielding the projected lengths of the threat source's terminal location in three coordinate directions, including: Using covariance analysis, the reachable domain of the threat source is approximated as a spatial ellipsoid, yielding the projected lengths of the threat source's terminal location in three coordinate directions. in, , This represents the unit normal vector in the directions of the three coordinate axes. For the location of the threat source terminal, This indicates the relative location of the terminal when the threat source is uncontrolled. .
4. The method according to claim 3, characterized in that, Based on the objective function and constraints, a solution model for the reachability domain of the threat source endpoint is constructed, including: Based on the objective function and constraints, a solution model for the reachability domain of threat source terminals is constructed as follows: maximize satisfy in, Indicates the distance from the walk. Indicates the first k The relative state of the threat sources of the step, Indicates the pulse interval time. The initial relative state of the threat source. Indicates the pulse velocity magnitude. and This is the transition matrix for relative state and relative velocity.
5. The method according to claim 3, characterized in that, The inter-satellite collision avoidance constraints include collision avoidance constraints between escort spacecraft and collision avoidance constraints between escort spacecraft and the target; the collision avoidance constraints between escort spacecraft are... ,in, The minimum permissible distance between two spacecraft and They represent the first i The and the first j The relative states of the escort spacecraft at step k; the collision avoidance constraints between the escort spacecraft and the target are as follows: ,in, Indicates the first The relative state of the target spacecraft.
6. The method according to claim 5, characterized in that, A multi-spacecraft cooperative trajectory planning model is constructed using the aforementioned constraints and objective function, including: A multi-spacecraft cooperative trajectory planning model is constructed using the aforementioned constraints and objective function. Minimize satisfy in, X gi ( k )and They represent the first i The first escort spacecraft k The relative state and control variables of the step. , N s and N To protect the number of spacecraft and the number of departures, Represents the discrete state transition matrix. Represents the discrete control transfer matrix. Indicates the first i Initial relative states of the escort spacecraft Indicates the first i The escort spacecraft in the N The relative position of the steps, Indicates the first i The relative positions of the guard points This indicates the maximum thrust used to protect the spacecraft.