A method and apparatus for density control of a spacecraft swarm

Abstract

The application provides a spacecraft cluster density control method and device, and belongs to the technical field of spacecraft cluster control. The method comprises the following steps: determining the current phase space density of the spacecraft cluster according to a configuration invariant; determining the density migration velocity field of the spacecraft cluster according to the current phase space density and a target phase space density; and determining the control acceleration for controlling the spacecraft cluster to reach the target phase space density in a target region based on the reduced dynamics equation of the spacecraft cluster and the density migration velocity field. The method can flexibly control the spacecraft cluster in the phase space, reduces the calculation complexity, and can improve the control efficiency of the spacecraft cluster.

Description

Technical Field

[0001] This invention relates to the field of spacecraft cluster control technology, and specifically to a density control method and apparatus for spacecraft clusters. Background Technology

[0002] A spacecraft swarm is a group of multiple spacecraft that work together in space to achieve specific mission objectives. In large-scale spacecraft swarms, configuration control presents even more complex challenges.

[0003] Currently, relative motion dynamics methods are used to control the overall configuration of spacecraft swarms, such as controlling the overall configuration based on swarm characteristics like density and energy, to achieve overall swarm migration and designated distribution. However, this method relies on coordination control rules between local individuals within the swarm, resulting in high computational complexity and thus low control efficiency for spacecraft swarms. Summary of the Invention

[0004] This invention proposes a density control method and apparatus for spacecraft clusters, which enables flexible control of spacecraft clusters in phase space, reduces computational complexity, and thus improves the control efficiency of spacecraft clusters.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] In a first aspect, the present invention provides a density control method for a spacecraft swarm, comprising: determining the current phase space density of the spacecraft swarm in phase space based on the configuration invariants of each spacecraft in the swarm; the coordinates of a point in phase space corresponding to the configuration invariants of each spacecraft in the swarm; determining the density migration velocity field of the spacecraft swarm based on the current phase space density and the target phase space density; the target phase space density being the desired phase space density when the spacecraft swarm reaches the target region; determining the control acceleration of the spacecraft swarm based on the reduced dynamic equations of the spacecraft swarm and the density migration velocity field of the spacecraft swarm; the control acceleration being used to control the spacecraft swarm to reach the desired phase space density in the target region.

[0007] The density control method for spacecraft clusters provided by this invention is a method for configuration control of spacecraft clusters in phase space. Compared with the configuration control method using relative motion dynamics, this method does not rely on the coordination control rules between local individuals in the cluster, can flexibly control the density of the spacecraft cluster, and can reduce computational complexity and improve the control efficiency of the spacecraft cluster.

[0008] In one implementation of the first aspect, the current phase space density of the spacecraft cluster is determined in phase space based on the configuration invariants of each spacecraft in the spacecraft cluster, including: processing the configuration invariants of each spacecraft in the spacecraft cluster using a local density estimation algorithm to obtain the current phase space density of the spacecraft cluster.

[0009] In one implementation of the first aspect, the smoothing kernel function in the local density estimation algorithm is a combined Gaussian kernel function, and the current phase space density of the spacecraft cluster satisfies:

[0010]

[0011] Where t represents the current time, z0 represents the coordinates of a point in phase space, ρ(z0,t) represents the phase space density of the spacecraft cluster at coordinate z0 in phase space at time t, N represents the number of spacecraft in the spacecraft cluster, and K G (*,h1) represents the first Gaussian kernel function. Let h1 represent the configuration invariant of the i-th spacecraft in the spacecraft cluster at time t, w represent the weight of the first Gaussian kernel function, and K represent the configuration invariant of the i-th spacecraft in the cluster. G (*,h2) represents the second Gaussian kernel function, h2 represents the bandwidth of the second Gaussian kernel function, and h1>h2, 1-w represents the weight of the second Gaussian kernel function.

[0012] In one implementation of the first aspect, the target phase space density satisfies:

[0013]

[0014] Where, ρ * (z0) represents the phase space density of the spacecraft cluster in the target region at coordinate z0 in phase space, D represents phase space, T represents the target region, DT represents the region outside the target region in phase space, and h out The bandwidth of the Gaussian kernel function used to calculate the target phase space density in the region outside the target region in phase space is denoted by z0, where z0 represents the coordinates of a point in phase space. N represents the minimum distance vector from coordinate z0 to the boundary of the target region. * This indicates the number of markers within the target area. K represents the configuration invariant of the i-th marker point within the target region. G (*, h1) represents the first Gaussian kernel function, h1 represents the bandwidth of the first Gaussian kernel function, w represents the weight of the first Gaussian kernel function, and K G (*,h2) represents the second Gaussian kernel function, h2 represents the bandwidth of the second Gaussian kernel function, and h1>h2, 1-w represents the weight of the second Gaussian kernel function.

[0015] In one implementation of the first aspect, determining the density migration velocity field of the spacecraft cluster based on the current phase space density and the target phase space density includes: determining the velocity field corresponding to the diffusion term based on the current phase space density of the spacecraft cluster; determining the velocity field corresponding to the convection term based on the current phase space density and the target phase space density of the spacecraft cluster; and the sum of the velocity fields corresponding to the diffusion term and the velocity fields corresponding to the convection term is the density migration velocity field.

[0016] In one implementation of the first aspect, the velocity field corresponding to the diffusion term satisfies:

[0017]

[0018] Where t represents the current time, z0 represents the coordinates of a point in the phase space, υ(z0,t) represents the velocity field corresponding to the diffusion term at coordinate z0 in the phase space at time t, and D(z0,t) represents the phase space density diffusion coefficient at coordinate z0 in the phase space at time t. Let ρ(z0,t) represent the gradient, and let ρ(z0,t) represent the phase space density of the spacecraft cluster at coordinate z0 in the phase space at time t.

[0019] The velocity field corresponding to the convection term satisfies:

[0020]

[0021] Where v(z0,t) represents the velocity field corresponding to the convection term at coordinate z0 in the phase space at time t, α(z0,t) represents the velocity influence coefficient of the convection term at coordinate z0 in the phase space at time t, and ρ * (z0) represents the phase space density of the spacecraft cluster in the target region at coordinate z0 in phase space, D represents phase space, T represents the target region, and DT represents the region outside the target region in phase space.

[0022] In one implementation of the first aspect, the reduced kinetic equations include: Where t represents the current time, and z(t) represents the linear transformation of the spacecraft's motion state at time t. Let z(t) denote the derivative of z(t) as a function of t, J denote the Jordan standard matrix of the system matrix, B denote the control acceleration transformation matrix, u(t) denote the control acceleration of the spacecraft cluster at time t, and z0(t) denote the configuration invariant of the spacecraft cluster at time t.

[0023] Based on the above implementation method, the control acceleration of the spacecraft cluster, determined according to the reduced dynamic equations and the density migration velocity field of the spacecraft cluster, satisfies:

[0024]

[0025] Among them, u (i) (t) represents the control acceleration of the i-th spacecraft in the space cluster at time t. Let represent the density migration velocity field of the i-th spacecraft in the space cluster at time t.

[0026] Secondly, the present invention provides a density control device for a spacecraft swarm, comprising a density determination module, a velocity field determination module, and an acceleration determination module. The density determination module is used to determine the current phase space density of the spacecraft swarm in phase space based on the configuration invariants of each spacecraft in the swarm; the configuration invariants of each spacecraft in the swarm correspond to the coordinates of a point in phase space. The velocity field determination module is used to determine the density migration velocity field of the spacecraft swarm based on the current phase space density and the target phase space density; the target phase space density is the desired phase space density when the spacecraft swarm reaches the target region. The acceleration determination module is used to determine the control acceleration of the spacecraft swarm based on the reduced dynamic equations of the spacecraft swarm and the density migration velocity field of the spacecraft swarm; the control acceleration is used to control the spacecraft swarm to reach the desired phase space density in the target region.

[0027] In one implementation of the second aspect, the density determination module is specifically used to: process the configuration invariants of each spacecraft in the spacecraft cluster using a local density estimation algorithm to obtain the current phase space density of the spacecraft cluster.

[0028] In one implementation of the second aspect, the velocity field determination module is specifically used to: determine the velocity field corresponding to the diffusion term based on the current phase space density of the spacecraft cluster; determine the velocity field corresponding to the convection term based on the current phase space density and the target phase space density of the spacecraft cluster; and the sum of the velocity fields corresponding to the diffusion term and the velocity fields corresponding to the convection term is the density migration velocity field.

[0029] Thirdly, the present invention provides an electronic device including a processor and a memory coupled to the processor; the memory is used to store computer instructions, and when the electronic device is running, the processor executes the computer instructions stored in the memory to cause the electronic device to perform the method described in the first aspect above or any implementation thereof.

[0030] Fourthly, the present invention provides a computer-readable storage medium including computer program instructions that, when executed by a computer, cause the computer to perform the method described in the first aspect above or any implementation thereof.

[0031] Fifthly, the present invention provides a computer program product, including computer program instructions, which, when executed on a computer, cause the computer to perform the method described in the first aspect above or any implementation thereof.

[0032] The technical effects corresponding to the second to fifth aspects and their possible implementations can be referred to the above description of the technical effects of the first aspect and its possible implementations, and will not be repeated here. Attached Figure Description

[0033] Figure 1 This is one of the schematic diagrams of the spacecraft cluster density control method provided in the embodiments of this application;

[0034] Figure 2 This is the second schematic diagram of the spacecraft cluster density control method provided in the embodiments of this application;

[0035] Figure 3 This is the third schematic diagram of the spacecraft cluster density control method provided in the embodiments of this application;

[0036] Figure 4 This is a schematic diagram of the density control device for a spacecraft cluster provided in the embodiments of this application. Detailed Implementation

[0037] In the specification and claims of this invention, the terms "first" and "second," etc., are used to distinguish different objects, rather than to describe a specific order of objects.

[0038] In the embodiments of this application, "and / or" indicates a relationship between objects. For example, A and / or B can represent the following three situations: A exists alone, B exists alone, and A and B exist simultaneously.

[0039] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0040] In the description of this invention, unless otherwise stated, "a plurality of" means two or more. For example, a plurality of spacecraft refers to two or more spacecraft in a spacecraft cluster.

[0041] Configuration control of a spacecraft swarm refers to the use of a series of control strategies and technologies to ensure that the individual spacecraft in the swarm can work together effectively according to predetermined trajectories and attitudes. This control technology is of great significance for improving the efficiency of spacecraft swarm mission execution, reducing the burden on individual spacecraft, and enhancing the reliability of spacecraft swarm control.

[0042] The method and apparatus provided in this application relate to spacecraft cluster density control, and can be used to control the density of spacecraft clusters. Specifically, the overall configuration control of the spacecraft cluster is performed based on the density to achieve overall cluster migration and specified distribution.

[0043] Understandably, a spacecraft swarm is a group of multiple spacecraft. These spacecraft can include satellites, drones, and other aircraft. Compared to traditional constellations and formations, spacecraft swarms are much larger in scale. Furthermore, the spacecraft within a swarm exhibit high homogeneity and relative motion characteristics, which makes configuration control of the swarm challenging. Homogeneity refers to the similarity of certain key performance indicators among the spacecraft comprising the swarm, such as size, weight, power consumption, communication capabilities, and payload capacity.

[0044] To address the problem of high computational complexity and low control efficiency in spacecraft cluster control using relative motion dynamics methods in the prior art, this application provides a density control method and apparatus for spacecraft clusters. In phase space, based on the density of the spacecraft cluster and the desired density when the cluster completes its overall migration, a density migration velocity field is determined. Then, based on this velocity field, the control acceleration of the spacecraft cluster during the overall migration process is further determined, thereby controlling the acceleration to ensure that the cluster density reaches the desired density when it reaches the target region. The technical solution provided in this application enables flexible control of spacecraft clusters in phase space, reduces computational complexity, and improves control efficiency.

[0045] For example, the spacecraft cluster density control method provided in this application embodiment can be executed by an electronic device with processing capabilities, such as a computer or server. Taking a computer as an example, the hardware of the computer may include a processor, memory, network interface, user interface, and communication bus, etc.

[0046] The processor controls the electronic equipment to perform related processing and computational tasks, such as determining the current phase space density, density migration velocity field, and control acceleration of the spacecraft cluster in phase space. The processor may include a central processing unit (CPU) or other processors, and can be single-core or multi-core; for example, a processor may include multiple CPUs.

[0047] Memory is used to store computer instructions and related data, such as configuration invariants of each spacecraft in a spacecraft swarm, the current and target phase space densities of the swarm, and the control accelerations of the swarm. Memory can be random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), flash memory, optical storage, disk storage media, or other magnetic storage devices, or any other medium capable of storing program code or data accessible by a computer. Optionally, memory can be integrated within the processor, or it can be independent of the processor.

[0048] A network interface is used for communication between a computer and other devices or communication networks. A network interface can be a transceiver with transmit and receive capabilities. Optionally, a network interface may include standard wired interfaces or wireless interfaces (such as Wi-Fi interfaces, Bluetooth interfaces, and 5G interfaces).

[0049] The communication bus is used to enable communication between different components. For example, the processor, memory, network interface and user interface mentioned above can be interconnected through the communication bus.

[0050] The user interface may include a display screen and input units (such as a keyboard and mouse). Optionally, the user interface may also include standard wired interfaces and wireless interfaces.

[0051] Those skilled in the art will understand that the computer described above may include more or fewer components, or combine certain components, or have different component arrangements; the embodiments of this application do not limit this.

[0052] The density control method and apparatus for a spacecraft cluster provided in the embodiments of this application will be described in detail below.

[0053] like Figure 1 As shown, the density control method for spacecraft clusters provided in this application includes S101-S103.

[0054] S101. Determine the current phase space density of the spacecraft cluster in phase space based on the configuration invariants of each spacecraft in the spacecraft cluster.

[0055] In this embodiment, the configuration invariant of each spacecraft in the spacecraft cluster corresponds to the coordinates of a point in phase space.

[0056] It should be understood that spacecraft configuration invariants are used to indicate the constant state of motion that a spacecraft maintains during the overall migration of a spacecraft swarm without the application of acceleration. Specifically, spacecraft configuration invariants are quantities that are transformed from the constant state of motion of a spacecraft, which refers to the state of motion in which the spacecraft continuously moves on a predetermined orbit.

[0057] In this embodiment, the spacecraft's motion state includes its position and velocity in a locally vertical and locally horizontal three-dimensional coordinate system. The three axes of the three-dimensional coordinate system are the x-axis, y-axis, and z-axis. Therefore, the spacecraft's motion state specifically includes the spacecraft's position coordinates on the x-axis, y-axis, and z-axis, as well as the velocity of each spacecraft on the x-axis, y-axis, and z-axis. In other words, the spacecraft's motion state is a six-dimensional feature vector.

[0058] Optionally, the center point of the spacecraft cluster is taken as the origin of the aforementioned three-dimensional coordinate system. The direction from the origin to the center of the central celestial body (e.g., Earth) is the positive x-axis. The positive z-axis is aligned with the direction of the instantaneous angular momentum of the reference orbit. The y-axis is perpendicular to the xz plane (the plane containing the x and z axes), and the positive directions of the x, y, and z axes form a right-handed coordinate system. Here, the reference orbit refers to the orbit in which the position of the center point of the spacecraft cluster changes during its motion.

[0059] As described above, a linear transformation of the motion state of each spacecraft in a spacecraft cluster can yield the configuration invariants of each spacecraft, and then a phase space can be constructed based on these configuration invariants. The following describes the linear transformation process of the spacecraft's motion state.

[0060] First, we construct the individual dynamic equations for each spacecraft.

[0061] When using the aforementioned locally vertical and locally horizontal three-dimensional coordinate system to describe the motion state of each spacecraft, for each spacecraft in the spacecraft cluster, the relative motion equation is used to describe the motion state of each spacecraft, and the individual dynamic equation of each spacecraft satisfies:

[0062]

[0063] Where x(t) represents the motion state (six-dimensional vector) of each spacecraft in the spacecraft cluster at time t; This represents the derivative of x(t) with respect to time t. It is also a six-dimensional vector. This includes the velocities and accelerations of each spacecraft along the x, y, and z axes, respectively. The velocities along the x, y, and z axes are obtained by differentiating the position coordinates along the x, y, and z axes in x(t), and the accelerations along the x, y, and z axes are obtained by differentiating the velocities along the x, y, and z axes in x(t); A represents the system matrix; 0 3×1 Let represent a 3×1 zero matrix; u(t) represents the control acceleration of the spacecraft cluster.

[0064] Secondly, when the above system matrix A satisfies the Jordan decomposition condition, Jordan decomposition is performed on system matrix A, decomposing system matrix A into:

[0065] A = QJQ -1 ,

[0066] Where J represents the Jordan standard matrix of the system matrix A, and Q represents the generalized eigenvector.

[0067] Next, the generalized eigenvector Q obtained from the Jordan decomposition of the system matrix A is linearly transformed onto x(t).

[0068] The transformation relationship for the linear transformation of x(t) is: x(t) = Qz(t), where z(t) is the quantity representing the motion state of the spacecraft at time t after the linear transformation, i.e., the six-dimensional vector after the linear transformation of x(t), z(t) = Q -1 x(t).

[0069] Finally, configuration invariants for each spacecraft are determined based on the results of the linear transformation.

[0070] Based on the above transformation relationship, the individual dynamic equations of a spacecraft can be transformed into reduced dynamic equations, which satisfy the following:

[0071]

[0072] in, Let z(t) denote the derivative of z(t) as a function of t, J denote the Jordan standard matrix of system matrix A, B denote the control acceleration transformation matrix, and u(t) denote the control acceleration of the spacecraft cluster in phase space.

[0073] The above control acceleration transformation matrix B satisfies:

[0074] B = Q -1 ·[0 3×3I 3×3 ] T ,

[0075] Among them, I 3×3 This represents a 3×3 identity matrix.

[0076] It should be understood that the general solution form of the relative motion described by the individual dynamic equations is:

[0077] x(t)=e Jt x(t0)

[0078] Where x(t) represents the motion state of each spacecraft in the spacecraft cluster at time t, x(t0) represents the motion state of the spacecraft at the initial time (time t0), and e Jt This represents an exponential function with Jt as the exponent.

[0079] Based on the above, the general solution form of the relative motion described by the reduced dynamic equations is as follows:

[0080] z(t) = e Jt z0(t),

[0081] Where z0(t) represents the configuration invariant of each spacecraft in the spacecraft cluster at time t.

[0082] Optionally, the above e Jt satisfy:

[0083]

[0084] Where q1 represents the instantaneous center of relative motion, q2 indicates the spacecraft's drift motion along the orbital direction, q3 indicates the spacecraft's first periodic motion along the orbital plane, q4 indicates the spacecraft's second periodic motion along the orbital plane, q5 indicates the spacecraft's first periodic motion perpendicular to the orbital plane, and q6 indicates the spacecraft's second periodic motion perpendicular to the orbital plane. In this case, z0(t) represents the scaling factor of the six fundamental modes of relative motion indicated by q1, q2, ..., q6.

[0085] Let z0 represent the configuration invariant of the i-th spacecraft in the spacecraft cluster. (i) (t), then according to the above formula z(t)=Q -1 Given x(t), we can see that the motion state of the i-th spacecraft is represented as:

[0086] z (i) (t)=Q -1 x(t) Formula (1)

[0087] According to the above formula z(t=e JtGiven z0(t), we can see that the linear transformation of the motion state of the i-th spacecraft is represented as follows:

[0088]

[0089] According to the above formula x(t)=e Jt From x(t0), we can see that the motion state of the i-th spacecraft is represented as:

[0090] x (i) (t)=e Jt x i (t0) Formula (3)

[0091] Substituting formula (1) into formula (2), we get:

[0092]

[0093] Substituting formula (3) into formula (4), we obtain the configuration invariant z0 of the i-th spacecraft in the spacecraft cluster. (i) (t):

[0094] z0 (i) (t)=e -Jt Q -1 e Jt x (i) (t0) Formula (5)

[0095] Among them, e -Jt Let x represent an exponential function with respect to -Jt, where x is the exponent. (i) (t0) represents the motion state of the i-th spacecraft in the spacecraft cluster at time t0.

[0096] After deriving the spacecraft's configuration invariants as described above, a phase space is constructed based on these invariants. Specifically, the spacecraft's configuration invariants (i.e., the six-dimensional vector z0) are... (i) If (t) is taken as the coordinates of a point in phase space, then the dimension of phase space is the same as the dimension of configuration invariants. The boundary of phase space is related to the range of motion of spacecraft in the spacecraft swarm, which is determined by the overall migration mission performed by the spacecraft swarm. The coordinates of a point on the boundary of phase space are configuration invariants of spacecraft in the spacecraft swarm at the boundary of their range of motion.

[0097] Furthermore, the current phase space density of the spacecraft swarm is determined within phase space. Understandably, the phase space density of a spacecraft swarm refers to the number of spacecraft per unit volume cell in phase space.

[0098] The integral of the phase space density of a spacecraft cluster with respect to the entire phase space satisfies:

[0099] ∫D ρ(z0,t)dz0=1 Formula (6)

[0100] Where z0 represents the coordinates of a point in phase space (which can be any point in phase space), ρ(z0,t) represents the phase space density of the spacecraft cluster at time t, which is the number of spacecraft per unit volume at the point corresponding to z0 (i.e., the number of spacecraft per unit volume centered at the point corresponding to z0), and D represents phase space, and This indicates that phase space is a six-dimensional space. It represents the set of real numbers.

[0101] Optionally, combined Figure 1 ,like Figure 2 As shown, the above-mentioned S101 (i.e., determining the current phase space density of the spacecraft cluster) can be achieved through S1011.

[0102] S1011. The configuration invariants of each spacecraft in the spacecraft cluster are processed using a local density estimation algorithm to obtain the current phase space density of the spacecraft cluster.

[0103] In this embodiment, the local density estimation algorithm uses a smoothing kernel function to estimate the phase space density, and the phase space density ρ(z0,t) satisfies:

[0104]

[0105] Where N represents the number of spacecraft in the spacecraft cluster, and K(·) represents the smoothing kernel function. Let zi represent the configuration invariant of the i-th spacecraft in the spacecraft cluster at time t (i.e., the point in phase space corresponding to the configuration invariant), and z0 represent the coordinates of a point in phase space. Indicates the point corresponding to z0 and The distance between corresponding points (the point corresponding to z0 relative to...) The offset of the corresponding point.

[0106] It should be noted that the phase space density ρ(z0,t) calculated by formula (7) satisfies formula (6) above.

[0107] In the prior art, the phase space density is determined by calculating the number of spacecraft in each volume unit after phase space discretization. However, the phase space density calculated by this method has the defect of discontinuity. Compared with the prior art, the embodiments of this application use a local density estimation algorithm to calculate the phase space density of the spacecraft cluster, which can avoid the problem of discontinuity in phase space density.

[0108] In one implementation, the smoothing kernel function in the local density estimation algorithm is a combined Gaussian kernel function, which is a weighted combination of at least two Gaussian kernel functions.

[0109] Specifically, the Gaussian kernel function K G The specific form of (·) satisfies:

[0110]

[0111] In this context, the variable y in the Gaussian kernel function represents the offset of one point from another point (zero), h represents the bandwidth of the Gaussian kernel function, and d represents the dimension of the variable, i.e., the dimension of variable y. In the Gaussian kernel function, the bandwidth h determines the trade-off between bias and variance during density estimation.

[0112] Based on the description of the Gaussian kernel function, in this embodiment, two Gaussian kernel functions with different bandwidths are combined to estimate the current phase space density of the spacecraft cluster. The current phase space density of the spacecraft cluster then satisfies:

[0113]

[0114] In the above formula, t represents the current time, N represents the number of spacecraft in the spacecraft cluster, and K... G (*, h1) represents the first Gaussian kernel function, h1 represents the bandwidth of the first Gaussian kernel function, and K G (*, h2) denotes the second Gaussian kernel function, h2 represents the bandwidth of the second Gaussian kernel function, w represents the weight of the first Gaussian kernel function, 1-w represents the weight of the second Gaussian kernel function, and h1 > h2; z0 represents the coordinates of a point in the phase space. This represents the configuration invariant of the i-th spacecraft in the spacecraft cluster at time t. Indicates the point corresponding to z0 and The distance between corresponding points (i.e., the distance between the points corresponding to z0 and z0 relative to z0) (Offset of the point corresponding to the zero point). Indicates the variable is The first Gaussian kernel function with bandwidth h1; Indicates the variable is The second Gaussian kernel function with bandwidth h2.

[0115] Furthermore, by substituting formula (8) into formula (9), the phase space density of the spacecraft cluster can be obtained:

[0116]

[0117] It should be noted that the phase space density ρ(z0,t) obtained by formula (10) satisfies the above formula (6).

[0118] In summary, this embodiment selects a combined Gaussian kernel function to calculate the phase space density of a spacecraft swarm. This preserves the non-zero values ​​of Gaussian kernel functions with different bandwidths, combining the characteristics of these functions to create a combined Gaussian kernel function with a steep peak value and a wider range of influence. In particular, when multiple spacecraft in a swarm approach each other during migration, a smaller bandwidth can, to some extent, prevent collisions. Based on this, this embodiment uses a combined Gaussian kernel function to calculate the phase space density of the spacecraft swarm, ensuring that the integral value of the phase space density with respect to the entire phase space is always 1.

[0119] S102. Based on the current phase space density and the target phase space density of the spacecraft cluster, determine the density migration velocity field of the spacecraft cluster. The target phase space density is the expected phase space density when the spacecraft cluster reaches the target region.

[0120] In this embodiment, the phase space density is related to the density migration velocity field of the spacecraft cluster, and the relationship between the phase space density and the density migration velocity field of the spacecraft cluster is described by the density migration equation of the spacecraft cluster.

[0121] Optionally, the density migration equation for a spacecraft swarm satisfies:

[0122]

[0123] in, This represents the partial derivative of the phase space density ρ(z0,t) with time t. Represents the gradient. Indicates to For finding the gradient, Let z0 represent the configuration invariant of the i-th spacecraft. (i) The derivative of (t) with respect to t, this derivative That is, the density migration velocity field of the i-th spacecraft in the space cluster at time t.

[0124] In the density migration equation of the aforementioned spacecraft cluster, This reflects the change in phase space density caused by the velocity field in phase space. When the i-th spacecraft is uncontrolled or perturbed, z0 (i) If (t) is a constant value, then According to the density migration equation of the spacecraft swarm described above, the phase space density of the spacecraft swarm remains unchanged, indicating that the spacecraft maintain a fixed density distribution in phase space. Therefore, it can be concluded that during the migration of the spacecraft swarm, the change in phase space density is caused by the density migration velocity field. Directly induced, thus, by controlling the density migration velocity field This allows spacecraft clusters to be distributed on demand to achieve a set density, thereby enabling the deployment, maintenance, and reconfiguration of spacecraft clusters.

[0125] In this embodiment of the application, given the desired density of the spacecraft cluster, the target density migration velocity field when the density of the spacecraft cluster is the desired density can be calculated using the density migration equation described above. Therefore, the density of the spacecraft cluster can be changed by altering the density migration velocity field of the spacecraft cluster, thereby achieving density control of the spacecraft cluster.

[0126] Optionally, in this embodiment of the application, the density migration velocity field of the spacecraft cluster may include the velocity field corresponding to the diffusion term and the velocity field corresponding to the convection term. The density migration velocity field of the spacecraft cluster is the sum of the velocity field corresponding to the diffusion term and the velocity field corresponding to the convection term. The above determination of the density migration velocity field of the spacecraft cluster includes determining the velocity field corresponding to the diffusion term and the velocity field corresponding to the convection term.

[0127] Understandably, the velocity field corresponding to the diffusion term is used to describe the dispersion effect of a spacecraft cluster in space. The dispersion effect refers to a diffusion phenomenon of a spacecraft cluster caused by changes in density gradient. The velocity field corresponding to the diffusion term can cause the spacecraft cluster to diffuse. The velocity field corresponding to the convection term is used to describe the transmission effect generated by the motion of the spacecraft cluster in space. The convection process represented by the velocity field corresponding to the convection term describes the attraction of different coordinate points within the target area to the spacecraft in the cluster. The velocity field corresponding to the convection term can guide the spacecraft cluster to migrate towards the target area and distribute evenly within the target area.

[0128] Based on the above descriptions of the velocity fields corresponding to the diffusion term and the convection term, optionally, combined with... Figure 2 ,like Figure 3 As shown, the above S102 can be implemented by S1021-S1022.

[0129] S1021. Determine the velocity field corresponding to the diffusion term based on the current phase space density of the spacecraft cluster.

[0130] In this embodiment of the application, the velocity field corresponding to the diffusion term can be calculated based on the current phase space density of the spacecraft cluster.

[0131] Optionally, the velocity field corresponding to the diffusion term satisfies:

[0132]

[0133] Where t represents the current time, z0 represents the coordinates of a point in the phase space, υ(z0,t) represents the velocity field corresponding to the diffusion term at coordinate z0 in the phase space at time t, and D(z0,t) represents the phase space density diffusion coefficient at coordinate z0 in the phase space at time t (a known quantity). This indicates the gradient of the phase space density ρ(z0,t).

[0134] Substituting the current phase space density of the spacecraft cluster into the above formula, the velocity field corresponding to the diffusion term can be calculated.

[0135] S1022. Determine the velocity field corresponding to the convection term based on the current phase space density and the target phase space density of the spacecraft cluster.

[0136] In this embodiment, during the overall migration mission of the spacecraft cluster, to ensure that each spacecraft in the cluster can effectively coordinate according to a predetermined trajectory and attitude, it is desirable that the multiple spacecraft in the cluster be evenly distributed within the target region, and that every spacecraft outside the target region converges to the target region. Based on this, the target phase space density of the spacecraft cluster should satisfy:

[0137]

[0138] Where, ρ * (z0) represents the target phase space density of the spacecraft cluster in the target region at coordinate z0 in phase space, where D represents phase space, T represents the target region, and DT represents the region outside the target region in phase space. When coordinate z0 is outside the target region, the target phase space density is estimated using a Gaussian kernel function with a bandwidth of h. out The variables of the Gaussian kernel function are This represents the minimum distance from coordinate z0 to the boundary of the target region. When coordinate z0 is located within the target region, the target phase space density is estimated using a combined Gaussian kernel function, where N... * This represents the number of markers (N) within the target area. * (where h is an integer greater than or equal to 1), the bandwidth of the first Gaussian kernel function is h1, and the variable is... The weight of the first Gaussian kernel function is w; the bandwidth of the second Gaussian kernel function is h2, and the variable is... This represents the coordinates of the i-th marker point within the target area. Indicates the point corresponding to z0 and The distance between the corresponding points is h1 > h2, and the weight of the second Gaussian kernel function is 1 - w. The formula for the Gaussian kernel function can be found in formula (8) above.

[0139] Combining the above formula (13), when the spacecraft is outside the target area, the target phase space density is controlled by a Gaussian kernel function based on the minimum distance, which can effectively guide the spacecraft to move towards the target area and limit the spacecraft's activity to prevent it from escaping. When the spacecraft is within the target area, the target phase space density is controlled by a combined Gaussian kernel function, which helps the spacecraft cluster achieve a uniform distribution within the target area.

[0140] Optionally, the velocity field corresponding to the convection term is related to the target phase space density and the current phase space density of the spacecraft cluster, and the velocity field corresponding to the convection term satisfies:

[0141]

[0142] Where v(z0,t) represents the velocity field corresponding to the convection term at coordinate z0 in the phase space at time t, α(z0,t) represents the velocity influence coefficient of the convection term at coordinate z0 in the phase space at time t, D(z0,t) is the density diffusion coefficient of the phase space at coordinate z0 in the phase space at time t, D represents the phase space, T represents the target region, and DT represents the region outside the target region in the phase space.

[0143] According to the above formula, when coordinate z0 is outside the target area, based on the target phase space density ρ of the spacecraft cluster... * (z0) determines the velocity field v(z0,t) corresponding to the convection term. This velocity field can guide spacecraft in the spacecraft cluster to the target region, reducing the probability of isolated events (i.e., spacecraft leaving the cluster). When coordinate z0 is within the target region, based on the target phase space density ρ... * The velocity field v(z0,t) corresponding to the convection term is determined by (z0) and the current phase space density ρ(z0,t) of the spacecraft cluster, and the velocity field corresponding to the convection term is in the opposite direction to the velocity field corresponding to the diffusion term.

[0144] In this embodiment of the application, the velocity fields corresponding to the determined diffusion term and the velocity fields corresponding to the convection term are summed to obtain the density migration velocity field of the spacecraft cluster, i.e.

[0145] S103. Based on the reduced dynamic equations of the spacecraft cluster and the density migration velocity field of the spacecraft cluster, determine the control acceleration of the spacecraft cluster. The control acceleration is used to control the spacecraft cluster to reach the desired phase space density in the target region.

[0146] In this embodiment of the application, the control acceleration includes the control acceleration acting on each spacecraft in the spacecraft cluster. After being subjected to the control acceleration, the motion state of each spacecraft in the spacecraft cluster will change, and thus the spacecraft will begin to migrate, that is, the spacecraft's orbit will change.

[0147] Based on the above embodiments, the reduced kinetic equations are: The general solution for the relative motion described by the reduced dynamic equation is z(t) = e Jt z0(t).

[0148] Where z(t) represents the linear transformation of the spacecraft's motion state at time t. Let z(t) denote the derivative of z(t) as a function of t, J denote the Jordan standard matrix of the system matrix, B denote the control acceleration transformation matrix, u(t) denote the control acceleration of the spacecraft cluster at time t, and z0(t) denote the configuration invariant of the spacecraft cluster at time t.

[0149] In this embodiment of the application, taking the derivative of z(t) with respect to t in the above general solution form, we obtain... Will and z(t) = e Jt Substituting z0(t) into the approximate dynamic equation, we get:

[0150]

[0151] Further solving yields:

[0152]

[0153] Furthermore, we obtain:

[0154]

[0155] Solving the above equation, the least squares solution for the control acceleration u(t) of the spacecraft cluster is obtained as follows:

[0156]

[0157] In summary, the control acceleration of the i-th spacecraft in the spacecraft cluster is:

[0158] As can be seen from the description of the above embodiments, in the above formula... This formula represents the density migration velocity field of the spacecraft cluster, describing the relationship between the density migration velocity field and the control acceleration of the spacecraft cluster. Furthermore, combining the relationship between the density of the spacecraft cluster and its density migration velocity field described in the above embodiments (referring to the density migration equation of the spacecraft cluster), it can be seen that applying a certain control acceleration to the spacecraft cluster can make its density migration velocity field reach the target density migration velocity field, thereby making the density of the spacecraft cluster reach the desired density, thus achieving density control of the spacecraft cluster.

[0159] In summary, the spacecraft cluster density control method provided in this application, within a phase space constructed based on the configuration invariants of the spacecraft, determines a control acceleration that enables the phase space density of the spacecraft cluster to reach the desired density (i.e., the target phase space density) based on the relationship between the phase space density of the spacecraft cluster, the density migration velocity field of the spacecraft cluster, and the control acceleration of the spacecraft cluster. Applying this control acceleration to the spacecraft cluster achieves density control. This density control method is a method for configuration control of a spacecraft cluster in phase space. Compared with configuration control methods using relative motion dynamics, this method does not rely on coordination control rules between local individuals in the cluster, allows for flexible control of the spacecraft cluster density, reduces computational complexity, and improves the control efficiency of the spacecraft cluster.

[0160] Accordingly, embodiments of this application provide a density control device for a spacecraft cluster, such as... Figure 4 As shown, it includes a density determination module 401, a velocity field determination module 402, and an acceleration determination module 403.

[0161] The density determination module 401 is used to determine the current phase space density of the spacecraft cluster in phase space based on the configuration invariants of each spacecraft in the spacecraft cluster; the configuration invariants of each spacecraft in the spacecraft cluster correspond to the coordinates of a point in phase space. For example, the density determination module 401 is used to implement S101 of the above-mentioned density control method for the spacecraft cluster.

[0162] The velocity field determination module 402 is used to determine the density migration velocity field of the spacecraft cluster based on the current phase space density and the target phase space density; the target phase space density is the desired phase space density when the spacecraft cluster reaches the target region. For example, the velocity field determination module 402 is used to implement S102 of the above-mentioned density control method for spacecraft clusters.

[0163] The acceleration determination module 403 is used to determine the control acceleration of the spacecraft cluster based on the reduced dynamic equations of the spacecraft cluster and the density migration velocity field of the spacecraft cluster; the control acceleration is used to control the spacecraft cluster to achieve the desired phase space density in the target region. For example, the acceleration determination module 403 is used to implement S103 of the above-mentioned density control method for the spacecraft cluster.

[0164] Optionally, the density determination module 401 is specifically used to: process the configuration invariants of each spacecraft in the spacecraft cluster using a local density estimation algorithm to obtain the current phase space density of the spacecraft cluster. For example, the density determination module 401 is specifically used to implement S101 of the density control method for the aforementioned spacecraft cluster.

[0165] Optionally, the velocity field determination module 402 is specifically used to: determine the velocity field corresponding to the diffusion term based on the current phase space density of the spacecraft cluster; determine the velocity field corresponding to the convection term based on the current phase space density and the target phase space density of the spacecraft cluster; the sum of the velocity fields corresponding to the diffusion term and the velocity fields corresponding to the convection term is the density migration velocity field. For example, the velocity field determination module 402 is specifically used to implement S1021-S1022 of the above-mentioned density control method for spacecraft clusters.

[0166] Each module of the density control device of the aforementioned spacecraft cluster can also be used to perform other steps in the above method embodiments. All relevant content involved in the above method embodiments can be referred to in the functional description of the corresponding functional module, and will not be repeated here.

[0167] This application also provides an electronic device, including: a processor and a memory coupled to the processor; the memory is used to store computer instructions, and when the electronic device is running, the processor executes the computer instructions stored in the memory to cause the electronic device to perform the methods in the above embodiments. The processor can implement the density determination module 401, the velocity field determination module 402, and the acceleration determination module 403; the memory can also be used to store configuration invariants and control acceleration for each spacecraft in a spacecraft cluster.

[0168] This application also provides a computer-readable storage medium including a computer program that, when run on a computer, performs the methods described in the above embodiments.

[0169] This application also provides a computer program product, which includes computer program instructions that, when run on a computer, execute the methods described in the above embodiments.

[0170] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0171] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A density control method for a spacecraft cluster, characterized in that, include: Based on the configuration invariants of each spacecraft in the spacecraft cluster, determine the current phase space density of the spacecraft cluster in phase space; The configuration invariant of each spacecraft in the spacecraft cluster corresponds to the coordinates of a point in the phase space; Determining the density migration velocity field of the spacecraft cluster based on its current phase space density and target phase space density includes: determining the velocity field corresponding to the diffusion term based on the current phase space density of the spacecraft cluster; determining the velocity field corresponding to the convection term based on the current phase space density of the spacecraft cluster and the target phase space density; the sum of the velocity fields corresponding to the diffusion term and the velocity fields corresponding to the convection term is the density migration velocity field; the target phase space density is the expected phase space density when the spacecraft cluster reaches the target region. The velocity field corresponding to the diffusion term satisfies: ， in, t Indicates the current moment. z 0 represents the coordinates of a point in the phase space. Indicates in t Coordinates in phase space at time specified z The velocity field corresponding to the diffusion term at 0, express t Coordinates in phase space at time specified z The phase space density diffusion coefficient at 0, Represents the gradient. Indicates in t Coordinates in phase space at time specified z Phase space density of the spacecraft cluster at point 0; The velocity field corresponding to the convection term satisfies: ， in, Indicates in t Coordinates in phase space at time specified z The velocity field corresponding to the convection term at 0, express t Coordinates in phase space at time specified z The velocity influence coefficient of the convection term at point 0. Represents coordinates in phase space z The phase space density of the spacecraft cluster in the target region at location 0. Represents the phase space, This refers to the target area. This refers to the region outside the target region in the phase space; Based on the reduced dynamic equations of the spacecraft cluster and the density migration velocity field of the spacecraft cluster, the control acceleration of the spacecraft cluster is determined; the control acceleration is used to control the spacecraft cluster to reach the desired phase space density in the target region.

2. The method according to claim 1, characterized in that, Determining the current phase space density of the spacecraft cluster in phase space based on the configuration invariants of each spacecraft in the cluster includes: The configuration invariants of each spacecraft in the spacecraft cluster are processed using a local density estimation algorithm to obtain the current phase space density of the spacecraft cluster.

3. The method according to claim 2, characterized in that, The smoothing kernel function in the local density estimation algorithm is a combined Gaussian kernel function, and the current phase space density of the spacecraft cluster satisfies: ， in, t Indicates the current moment. z 0 represents the coordinates of a point in the phase space. Indicates in t Coordinates in phase space at time specified z The phase space density of the spacecraft cluster at point 0, N This indicates the number of spacecraft in the spacecraft cluster. K G ( , h 1) represents the first Gaussian kernel function. Indicates in t The spacecraft cluster at the specified time i The configuration invariants of each spacecraft h 1 represents the bandwidth of the first Gaussian kernel function. w This represents the weight of the first Gaussian kernel function. K G ( , h 2) represents the second Gaussian kernel function. h 2 represents the bandwidth of the second Gaussian kernel function, and ,1- w This represents the weight of the second Gaussian kernel function.

4. The method according to claim 1, characterized in that, The target phase space density satisfies: ， in, Represents coordinates in phase space z The phase space density of the spacecraft cluster in the target region at location 0. Represents the phase space, This refers to the target area. This refers to the region outside the target region in the phase space. h out The bandwidth of the Gaussian kernel function used to calculate the target phase space density of the region outside the target region in the phase space is represented. z 0 represents the coordinates of a point in the phase space. Representing coordinates z The minimum distance vector from point 0 to the boundary of the target region. This indicates the number of markers within the target area. Indicates the first within the target area i Configuration invariants of each marker point K G ( , h 1) represents the first Gaussian kernel function. h 1 represents the bandwidth of the first Gaussian kernel function. w This represents the weight of the first Gaussian kernel function. K G ( , h 2) represents the second Gaussian kernel function. h 2 represents the bandwidth of the second Gaussian kernel function, and ,1- w This represents the weight of the second Gaussian kernel function.

5. The method according to claim 1, characterized in that, The reduced kinetic equations include: , ; in, t Indicates the current moment. z ( t ) indicates in t The quantity representing the linear transformation of the spacecraft's motion state at any given moment. express z ( t ) t The changing derivative, J The Jordan standard matrix representing the system matrix, B This represents the control acceleration transformation matrix. u ( t ) indicates in t The control acceleration of the spacecraft cluster at that moment, Indicates in t The configuration invariants of the spacecraft cluster at any given time; The control acceleration of the spacecraft cluster, determined based on the reduced dynamic equations and the density migration velocity field of the spacecraft cluster, satisfies: ， in, Indicates in t The first in the space cluster mentioned at the time i The control acceleration of a spacecraft Indicates in t The first in the space cluster mentioned at the time i Density migration velocity field of a spacecraft.

6. A density control device for a spacecraft cluster, characterized in that, It includes a density determination module, a velocity field determination module, and an acceleration determination module; The density determination module is used to determine the current phase space density of the spacecraft cluster in phase space based on the configuration invariants of each spacecraft in the spacecraft cluster. The configuration invariant of each spacecraft in the spacecraft cluster corresponds to the coordinates of a point in the phase space; The velocity field determination module is used to determine the density migration velocity field of the spacecraft cluster based on the current phase space density and the target phase space density of the spacecraft cluster; including: determining the velocity field corresponding to the diffusion term based on the current phase space density of the spacecraft cluster; determining the velocity field corresponding to the convection term based on the current phase space density and the target phase space density of the spacecraft cluster; the sum of the velocity field corresponding to the diffusion term and the velocity field corresponding to the convection term is the density migration velocity field; the target phase space density is the expected phase space density when the spacecraft cluster reaches the target region; The velocity field corresponding to the diffusion term satisfies: ， in, t Indicates the current moment. z 0 represents the coordinates of a point in the phase space. Indicates in t Coordinates in phase space at time specified z The velocity field corresponding to the diffusion term at 0, express t Coordinates in phase space at time specified z The phase space density diffusion coefficient at 0, Represents the gradient. Indicates in t Coordinates in phase space at time specified z Phase space density of the spacecraft cluster at point 0; The velocity field corresponding to the convection term satisfies: ， in, Indicates in t Coordinates in phase space at time specified z The velocity field corresponding to the convection term at 0, express t Coordinates in phase space at time specified z The velocity influence coefficient of the convection term at point 0. Represents coordinates in phase space z The phase space density of the spacecraft cluster in the target region at location 0. Represents the phase space, This refers to the target area. This refers to the region outside the target region in the phase space; The acceleration determination module is used to determine the control acceleration of the spacecraft cluster based on the reduced dynamic equations of the spacecraft cluster and the density migration velocity field of the spacecraft cluster; the control acceleration is used to control the spacecraft cluster to reach the desired phase space density in the target region.

7. An electronic device, characterized in that, The device includes a processor and a memory coupled to the processor; the memory is used to store computer instructions, which, when the electronic device is running, are executed by the processor to cause the electronic device to perform the method as described in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that, It includes computer program instructions that, when executed by a computer, cause the computer to perform the method as described in any one of claims 1 to 5.

Images