Data-driven spacecraft formation configuration reconstruction method and device

Abstract

The invention provides a data-driven spacecraft formation configuration reconstruction method and device, and belongs to the technical field of spaceflight. According to the method, the current relative motion state of each slave spacecraft in a plurality of slave spacecrafts in the spacecraft formation, the target relative motion state after configuration reconstruction and the state auto-encoder are combined to construct the control law of each slave spacecraft for realizing spacecraft formation configuration reconstruction, and the process improves the calculation efficiency of solving the control law and improves the calculation efficiency of the spacecraft formation configuration reconstruction. The method is low in computing power requirement, is easy to achieve on-satellite deployment, achieves autonomous planning, can improve the reconstruction efficiency of the spacecraft formation configuration, and facilitates the spacecraft formation to complete tasks.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aerospace technology, and particularly relates to a data-driven spacecraft formation reconfiguration method and device. BACKGROUND

[0002] Spacecraft formation flight has become a key research topic in space missions, and the goal is to form a coordinated configuration by combining multiple spacecraft (such as satellites, space shuttles, etc.) to work together to achieve specific observation, communication, etc. During the spacecraft formation flight, when the task of the spacecraft formation changes or the configuration of the spacecraft formation changes, the spacecraft formation needs to be reconfigured.

[0003] However, the existing spacecraft formation reconfiguration method has the defects of high computational complexity and time and energy consumption, which makes the efficiency of spacecraft formation reconfiguration low, thereby being not conducive to the spacecraft formation to complete the task. SUMMARY

[0004] The present application provides a data-driven spacecraft formation reconfiguration method and device, which combines the current relative motion state of each slave spacecraft in the spacecraft formation, the target relative motion state after reconfiguration, and the state autoencoder to construct the control law of each slave spacecraft to achieve spacecraft formation reconfiguration. The computational complexity of the above process is low, the consumption of time and energy is low, and the efficiency of spacecraft formation reconfiguration can be improved, thereby being conducive to the spacecraft formation to complete the task.

[0005] In order to achieve the above purpose, the present application adopts the following technical solutions: In a first aspect, the present application provides a data-driven spacecraft formation reconfiguration method, which includes a master spacecraft and multiple slave spacecraft. The master spacecraft and the multiple slave spacecraft maintain the formation of the spacecraft formation to cooperate to complete the task. The method includes: in the case of needing to reconfigure the spacecraft formation, for each slave spacecraft in the multiple slave spacecraft, determining the control law of the slave spacecraft based on the current relative motion state of the slave spacecraft, the target relative motion state of the slave spacecraft after reconfiguration, and the state autoencoder. The relative motion state refers to the motion state of the slave spacecraft relative to the master spacecraft. The state autoencoder is an autoencoder based on Lyapunov-Floquet transformation theorem. The state autoencoder is obtained by training multiple relative motion states of multiple spacecraft. The control law of the slave spacecraft is used to determine the thrust of the slave spacecraft to achieve the target relative motion state, so as to realize the reconfiguration of the spacecraft formation.

[0006] In one implementation of the first aspect, the state autoencoder includes an encoder and a decoder. The encoder is used to encode the relative motion state into a reduced dynamic state, and the decoder is used to decode the reduced dynamic state into a relative motion state. The reduced dynamic state indicates the state that satisfies the time-invariant evolution law from the relative motion state of the spacecraft. The encoder satisfies the following formula; in, z Represents the reduced dynamic state. x Indicates a state of relative motion. t Indicates time, ( x , t ) represents the encoder's output. This represents the boundary value matrix of the encoder. Represents the periodic boundary function of the encoder. This represents the sparse coefficient matrix of the encoder. This represents element-wise multiplication of matrices. Indicates t The first fully connected neural network takes a matrix as input and outputs a matrix. Represents the parameters of the first fully connected neural network; the periodic boundary function of the encoder. The following formula must be satisfied; in, Indicates the first shape parameter. Indicates the second shape parameter. T c Indicates the orbital period of the spacecraft; The decoder satisfies the following formula; in, -1 ( z , t ) represents the output of the decoder. This represents the boundary value matrix of the decoder. Represents the periodic boundary function of the decoder. This represents the sparse coefficient matrix of the decoder. Indicates t The second fully connected neural network takes a matrix as input and outputs a matrix. Represents the parameters of the second fully connected neural network; the periodic boundary function of the decoder. The following formula must be satisfied; in, Indicates the third shape parameter. This represents the fourth shape parameter.

[0007] In one implementation of the first aspect, the control law of the spacecraft satisfies the following formula; in, ) indicates thrust; Represents the weight matrix. It is a positive definite matrix. -1 for The inverse matrix; Indicates intermediate variables. T Let represent the transpose matrix of the intermediate variables, and ; Represents a constant matrix; Represents the transformation matrix. for The inverse matrix, , This represents the boundary value matrix of the encoder. Represents the periodic boundary function of the encoder. This represents the sparse coefficient matrix of the encoder. This represents element-wise multiplication of matrices. Indicates t The first fully connected neural network takes a matrix as input and outputs a matrix. Indicates the parameters of the first fully connected neural network; Represents the control input matrix; Describes the initial costate. The initial costate is obtained by solving the two-point boundary value problem of the current relative motion state and the target relative motion state using differential algebraic methods. satisfy: , The reference value representing the initial costate. , For polynomial mapping, It is a polynomial inverse mapping. The deviation value from the configuration invariants of the spacecraft when the relative motion state of the target is achieved.

[0008] In one implementation of the first aspect, the loss function of the state autoencoder during training satisfies the following formula; in, L Represents the loss function. L linear Represents the linear prediction term. Represents the weight parameters. Lreconstruction Represents the reconstruction loss term; Linear predictor L linear The following formula must be satisfied; in, N This indicates the number of multiple relative motion states of multiple spacecraft. k This represents the k-th index in the relative motion state. This represents the k-th relative motion state. This represents the time point of the k-th relative motion state. This represents the (k+1)th relative motion state. This represents the time point of the (k+1)th relative motion state; express and The output of the encoder is the input. Represents a constant matrix; This represents the time interval between the k-th relative motion state and the (k+1)-th relative motion state. ; express and The output of the encoder is the input. Reconstructing the loss term L reconstruction The following formula must be satisfied; in, -1 ( , ) indicates with and The output of the decoder is the input. The second norm of a vector.

[0009] Secondly, this invention provides a data-driven spacecraft formation configuration reconfiguration device. The spacecraft formation includes a master spacecraft and multiple slave spacecraft, which maintain the formation configuration to collaboratively complete tasks. The device includes a control law construction module and a configuration reconfiguration module. The control law construction module, when configuration reconfiguration of the spacecraft formation is required, determines the control law for each of the multiple slave spacecraft based on its current relative motion state, the target relative motion state of the slave spacecraft after configuration reconfiguration, and a state autoencoder. The relative motion state refers to the motion state of the slave spacecraft relative to the master spacecraft. The state autoencoder is an autoencoder based on the Lyapunov-Floquet transform theorem, trained using multiple relative motion states of the multiple spacecraft. The configuration reconfiguration module, using the control law of the slave spacecraft, determines the thrust required for the slave spacecraft to reach the target relative motion state, thereby achieving spacecraft formation configuration reconfiguration.

[0010] 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.

[0011] 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.

[0012] 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.

[0013] 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.

[0014] Compared with the prior art, the present invention has the following beneficial effects.

[0015] In the data-driven spacecraft formation configuration reconfiguration method provided by this invention, when the spacecraft formation needs to be reconfigured, for each of the multiple slave spacecraft included in the spacecraft formation, a control law for the slave spacecraft is constructed based on the current relative motion state of the slave spacecraft, the target relative motion state, and the state autoencoder. Then, the slave spacecraft is made to move from the current relative motion state to the target relative motion state through the control law of the slave spacecraft, thereby realizing the spacecraft formation configuration reconfiguration. Since the state autoencoder used in the above process is an autoencoder based on the Lyapunov-Floquet transform theorem, and this state autoencoder is trained from multiple relative motion states of multiple spacecraft, it can more realistically reflect the dynamic characteristics of the spacecraft. In the process of spacecraft formation configuration reconstruction, only the autoencoder needs to be trained once, and the trained state autoencoder can be reused multiple times to construct the control law required for formation configuration reconstruction. The above process improves the computational efficiency of solving the control law, has low computing power requirements, and is easy to deploy on satellite to achieve autonomous planning, thereby improving the efficiency of spacecraft formation configuration reconstruction and facilitating the spacecraft formation to complete its mission. Attached Figure Description

[0016] Figure 1 This is one of the schematic diagrams of a data-driven spacecraft formation configuration reconfiguration method provided in the embodiments of this application; Figure 2 This is a second schematic diagram of a data-driven spacecraft formation configuration reconfiguration method provided in the embodiments of this application; Figure 3 This is a graph showing the change in training loss of the state autoencoder provided in an embodiment of this application; Figure 4 This is a graph showing the changes in the components of each column of the transformation matrix provided in the embodiments of this application; Figure 5 This is a diagram showing the results of predicting and reconstructing relative motion trajectories using a reduced dynamics model, as provided in an embodiment of this application. Figure 6 This is a control law thrust variation curve provided in the embodiments of this application; Figure 7 This is a schematic diagram of the spacecraft formation reconstructed trajectory provided in the embodiments of this application; Figure 8 This is one of the structural schematic diagrams of a data-driven spacecraft formation configuration reconfiguration device provided in the embodiments of this application; Figure 9 This is the second schematic diagram of a data-driven spacecraft formation configuration reconfiguration device provided in the embodiments of this application. Detailed Implementation

[0017] 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.

[0018] 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.

[0019] In the description of this invention, unless otherwise stated, "a plurality of" means two or more. For example, a plurality of slave spacecraft means two or more slave spacecraft.

[0020] The method and apparatus provided in this application relate to spacecraft formation configuration reconfiguration. They can be used to determine the control law by the current relative motion state of each slave spacecraft in the spacecraft formation and the target relative motion state of the slave spacecraft after configuration reconfiguration, and then realize the spacecraft formation configuration reconfiguration through the control law.

[0021] Understandably, during the spacecraft formation configuration reconfiguration process, the relative motion relationships between multiple slave spacecraft and the master spacecraft within the formation are divided into multiple one-to-one relative motion relationships. Each of these one-to-one relative motion relationships refers to the relative motion relationship between a slave spacecraft and the master spacecraft. Then, for each one-to-one relative motion relationship, a control law is designed for the slave spacecraft, and the motion state of the slave spacecraft is adjusted to achieve the spacecraft formation configuration reconfiguration.

[0022] To address the shortcomings of existing spacecraft formation configuration reconfiguration methods in the background art, which suffer from high computational complexity and high time and computing power consumption, resulting in low efficiency and hindering spacecraft formations from completing their missions, this application provides a data-driven spacecraft formation configuration reconfiguration method and apparatus. This method combines the current relative motion state of each slave spacecraft in a spacecraft formation, the target's relative motion state after configuration reconfiguration, and a state autoencoder to construct a control law for each slave spacecraft to achieve spacecraft formation configuration reconfiguration. This process has low computational complexity and low time and computing power consumption, thereby improving the efficiency of spacecraft formation configuration reconfiguration and facilitating spacecraft formation mission completion.

[0023] For example, the data-driven spacecraft formation configuration reconfiguration method provided in this embodiment of the invention can be executed by an electronic device with processing capabilities, such as a computer or server. Taking a computer as an example, the hardware components of the computer may include: a processor, memory, a network interface, a user interface, a communication bus, etc.

[0024] The processor is used to control electronic devices to perform related processing and calculation tasks, such as determining the control law of the spacecraft and determining the thrust required for the spacecraft to reach a target relative motion state. The processor may include a central processing unit (CPU) or other processors, and may be single-core or multi-core; for example, the processor may include multiple CPUs.

[0025] Memory is used to store computer instructions and related data, such as storing the relative motion states, reduced dynamic states, and control laws of multiple spacecraft. Memory can be random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), flash memory, optical storage, magnetic 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 into the processor, or it can be independent of the processor.

[0026] 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).

[0027] 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.

[0028] The user interface may include a display screen and an input unit (such as a keyboard). Optionally, the user interface may also include a standard wired interface or a wireless interface.

[0029] 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.

[0030] In this embodiment, the spacecraft formation includes a master spacecraft and multiple slave spacecraft. The master spacecraft and the multiple slave spacecraft maintain a spacecraft formation configuration to collaboratively complete the mission. For example, as shown... Figure 1 As shown in the figure, an embodiment of this application provides a data-driven spacecraft formation configuration reconfiguration method, including S101-S102.

[0031] In one implementation, combined with Figure 1 ,like Figure 2 As shown, before S101, the above method also includes S103.

[0032] S103. Construct a dynamic model of the relative motion of spacecraft in a spacecraft formation.

[0033] It is understood that the master spacecraft and slave spacecraft in the above-mentioned spacecraft formation can refer to satellites, spacecraft, space shuttles, etc., or other types of spacecraft. This application embodiment does not limit them here.

[0034] The construction process of the above relative motion dynamics model is given below.

[0035] Step 1: Construct the relative motion relationship between the spacecraft and the host spacecraft in the spacecraft formation.

[0036] In the relative motion of a spacecraft formation, typically one or more slave spacecraft fly relative to a master spacecraft. A Local Vertical-Local Horizontal (LVLH) coordinate system is defined to describe the relative motion of the spacecraft formation. The origin of this coordinate system is located at the center of mass of the master spacecraft, and the coordinate system's... x The axis points radially towards the orbital radial direction of the main spacecraft (i.e., from the Earth's center of mass towards the orbital position of the main spacecraft). This coordinate system... z The axis points to the normal to the orbital plane of the main spacecraft; this coordinate system... y The axial directions satisfy the right-hand rule of the coordinate system.

[0037] Based on the known dynamics of relative motion, if the relative motion is a linear time-varying periodic system, then the dynamics model of relative motion can be described by the following ordinary differential equations.

[0038] in, Relative motion state The vectors are six-dimensional, representing the spacecraft's position in the local vertical and horizontal coordinate systems. x axis, y shaft and z The position components of the axis, the spacecraft in the local vertical and horizontal coordinate system. x axis, y shaft and z The velocity component of the shaft;t Indicates time, For the system matrix, To control the input matrix, The control force applied externally. The system matrix is ​​a periodic matrix function with a period of... In the spacecraft formation control scenario addressed in the embodiments of this application, For orbital period.

[0039] According to the Lyapunov-Floquet theorem, for the above linear time-varying periodic system, there exists a theorem with respect to... Periodic transformation matrix This allows the transformation of the original relative motion state into a reduced dynamic state. The aforementioned transformation matrix... It satisfies the following formula.

[0040] in, The reduced dynamic state Also a six-dimensional vector, reducing the dynamic state. It refers to the relative motion state By transforming the matrix The reduced dynamical state obtained by transforming to the reduced space. and transformation matrix The unknowns can be obtained through subsequent training with a state autoencoder. The evolution model of the reduced dynamic state satisfies the following ordinary differential equation.

[0041] in, Let be a constant matrix, representing the system matrix under the reduced dynamic state. Therefore, the original relative motion state changes from... The dominant time-varying dynamic state of motion has transformed into a state dominated by... The dominant time-invariant reduced dynamical state. Therefore, when the external input is 0, the solution of the reduced dynamical state is... ,in The initial reduced dynamic state at time 0, It is also known as configuration invariant.

[0042] S101. When it is necessary to reconfigure the spacecraft formation, for each of the multiple slave spacecraft, the control law of the slave spacecraft is determined based on the current relative motion state of the slave spacecraft, the target relative motion state of the slave spacecraft after configuration reconfiguration, and the state autoencoder.

[0043] The aforementioned relative motion state refers to the motion state of the spacecraft relative to the host spacecraft. The state autoencoder is an autoencoder based on the Lyapunov-Floquet transform theorem.

[0044] Specifically, the aforementioned state autoencoder includes an encoder and a decoder. The encoder encodes the relative motion state into a reduced dynamic state, and the decoder decodes the reduced dynamic state back into a relative motion state. The reduced dynamic state indicates a state that satisfies the time-invariant evolution law from the relative motion state of the spacecraft. This reduced dynamic state represents the state of the spacecraft that does not change over time while moving in its orbit. It should be understood that the aforementioned reduced dynamic state, as a state description method equivalent to the original state and satisfying the time-invariant system evolution law, simplifies the description of the system and the prediction of its evolution.

[0045] In this embodiment, the encoder and decoder in the state autoencoder are constructed based on the relative motion dynamics model obtained in S103 above and the evolution model of the reduced dynamic state. The encoder then satisfies the following formula.

[0046] in, z Represents the reduced dynamic state. x Indicates a state of relative motion. t Indicates time, ( x , t ) represents the encoder's output. This represents the boundary value matrix of the encoder. Represents the periodic boundary function of the encoder. This represents the sparse coefficient matrix of the encoder. This represents element-wise multiplication of matrices. Indicates t The first fully connected neural network takes a matrix as input and outputs a matrix. Represents the parameters of the first fully connected neural network; the periodic boundary function of the encoder. It satisfies the following formula.

[0047] in, Indicates the first shape parameter. Indicates the second shape parameter. T c This indicates the orbital period of the spacecraft.

[0048] The decoder described above satisfies the following formula.

[0049] in, -1 ( z , t ) represents the output of the decoder. This represents the boundary value matrix of the decoder. Represents the periodic boundary function of the decoder. This represents the sparse coefficient matrix of the decoder. Indicates t The second fully connected neural network takes a matrix as input and outputs a matrix. Represents the parameters of the second fully connected neural network; the periodic boundary function of the decoder. The following formula must be satisfied; in, Indicates the third shape parameter. This represents the fourth shape parameter.

[0050] It should be noted that both the encoder and decoder described above add a sparse coefficient matrix to the structure of the standard autoencoder. and The purpose of this sparse coefficient matrix is ​​to enable neural networks to... and The output features whose partial output values ​​are close to 0 are fixed at 0 to simulate the coordinate transformation matrix. P The components that may always be 0 in the neural network serve to simplify the training process, avoid overfitting, and improve generalization ability.

[0051] Since the embodiments of this application do not improve the neural network hierarchical structure of the encoder and decoder, and the neural network in the structure of the encoder and the neural network in the structure of the decoder in the autoencoder are existing technologies, the embodiments of this application will not elaborate on the hierarchical structure of the encoder and decoder in the autoencoder.

[0052] Furthermore, the aforementioned state autoencoder is trained using multiple relative motion states of multiple spacecraft. The training process of the aforementioned state autoencoder is described in detail below.

[0053] Step 1: Construct a relative motion trajectory dataset.

[0054] Multiple spacecraft motion trajectories are collected, and multiple relative motion states are obtained from each of these trajectories. A relative motion trajectory dataset is then constructed using these multiple relative motion states. It should be noted that the aforementioned multiple spacecraft motion trajectories may include multiple trajectories from a single spacecraft, or one trajectory from each of multiple spacecraft. This application does not limit the source or acquisition method of the aforementioned multiple spacecraft motion trajectories.

[0055] Step 2: Train the state autoencoder using the relative motion trajectory dataset.

[0056] Multiple relative motion states from the aforementioned relative motion trajectory dataset are input into the encoder of the state autoencoder. The encoder outputs the encoded result and inputs it into the decoder. After the decoder outputs the decoded result, the loss function value is calculated using the encoded and decoded results. When the loss function value is greater than the acceptable error threshold, the trainable parameters in the state autoencoder are optimized using the gradient descent method, thereby realizing the training of the state autoencoder.

[0057] For example, the trainable parameters of the above autoencoder can be: .

[0058] The loss function of the above state autoencoder during the training process satisfies the following formula.

[0059] in, L Represents the loss function. L linear Represents a linear forecast term. L linear Used to measure whether the encoding result conforms to the characteristics of a linear time-invariant system. Represents the weight parameters. L reconstruction Represents the reconstruction loss term. L reconstruction It is used to measure the degree of deviation between the decoding result and the input content of the encoder.

[0060] The above linear prediction term L linear It satisfies the following formula.

[0061] in, N This indicates the number of multiple relative motion states of multiple spacecraft. k This represents the k-th index in the relative motion state. This represents the k-th relative motion state. This represents the time point of the k-th relative motion state. This represents the (k+1)th relative motion state. This represents the time point of the (k+1)th relative motion state; express and The output of the encoder is the input. Represents a constant matrix; This represents the time interval between the k-th relative motion state and the (k+1)-th relative motion state. ; express and The output of the encoder is the input.

[0062] It should be understood that the above constant matrix There are multiple possible values ​​for , and in this embodiment of the application, a system matrix is ​​used. If the standard type is taken as The value of . Optional, if Completely unknown, including any similarity matrices, or if the canonical form is unknown, then... Also used as a trainable parameter, that is, let .

[0063] The above reconstruction loss item L reconstruction It satisfies the following formula.

[0064] in, -1 ( , ) indicates with and The output of the decoder is the input. The second norm of a vector.

[0065] The gradient descent method described above satisfies the following formula.

[0066] in, Represents the trainable parameters at the j-th training round. This represents the loss function value calculated under the trainable parameters of the current round. Set the learning rate (e.g., 0.001). Repeat the above process until the loss function value is below the error threshold, then stop training. In practical applications, the error threshold should be set to a specific value based on the accuracy requirements. The value of the learning rate affects the speed and stability of training convergence. The higher the value, the faster the convergence speed, but the greater the possibility of training divergence.

[0067] Understandably, a spacecraft's control law refers to a set of mathematical algorithms or logical rules that calculate the control commands (such as engine thrust) to be applied based on the spacecraft's current state (such as position, velocity, etc.) and desired objectives, so that the spacecraft moves or remains stable in the required manner.

[0068] In this embodiment, the control law of the slave spacecraft can calculate the thrust to be applied based on the current relative motion state of the slave spacecraft and the relative motion state of the target. Optionally, the control law of the slave spacecraft satisfies the following formula.

[0069] Formula (1) in, ) indicates thrust; Represents the weight matrix. It is a positive definite matrix. -1 for The inverse matrix; Indicates intermediate variables. T Let represent the transpose matrix of the intermediate variables, and ; Represents a constant matrix; Represents the transformation matrix. for The inverse matrix, Indicates t The first fully connected neural network takes a matrix as input and outputs a matrix. Indicates the parameters of the first fully connected neural network; Represents the control input matrix; This represents the initial costate.

[0070] The derivation process of the control law of the spacecraft is given below.

[0071] Step 1: Define the optimization objective.

[0072] In the formation reconfiguration maneuver, the initial relative motion state of the stars is defined as follows: The target's relative motion state is The start time of the reconfiguration maneuver is The stopping time of the reconfiguration maneuver is The reconfiguration of satellite formations follows the principle of energy optimization (i.e., minimizing fuel consumption), therefore, an optimization objective is defined. as follows.

[0073] in, Let be the weight matrix, and be a positive definite matrix. In practical applications, the value can be set according to specific needs. In general, under full-drive conditions, it can be taken as the identity matrix.

[0074] Step 2: Using the aforementioned state autoencoder, both the current relative motion state of the spacecraft and the relative motion state of the target are transformed into reduced dynamic states, and the corresponding configuration invariants are calculated.

[0075] The current relative motion state, which is transformed into a reduced dynamic state, is named the initial reduced dynamic state. The relative motion state of the target, which is transformed into a reduced dynamic state, is named the target reduced dynamic state. The initial reduced dynamic state is then... Reduced dynamic state of the target It satisfies the following formula.

[0076] The initial configuration invariants corresponding to the initial reduced dynamic state The target configuration invariants corresponding to the target reduced dynamic state It satisfies the following formula.

[0077] The differential equations for changes in configuration invariants satisfy the following formula.

[0078] Step 3: Based on the Pontryagin extreme value principle and the differential equation for the change of the above configuration invariants, the optimal control law that satisfies the above optimization objective can be obtained, i.e., the above formula (1). In the above formula (1)... It is obtained from the state autoencoder after training. satisfy: The initial costate in formula (1) It is an unknown quantity.

[0079] Due to the initial costate in the above formula (1) For unknowns, the initial costate described above is given below. The solution process.

[0080] The problem of solving the energy-optimal control law for formation configuration reconfiguration is transformed into solving configuration invariants. The two-point boundary value problem (TPBVP) is the problem of optimizing the objective function. Find a suitable initial costate while minimizing the minimum. , making Under the dynamic evolution law determined by the differential equation of configuration invariant changes, from Evolved into The above process satisfies the following formula (2).

[0081] Formula (2) In this embodiment of the application, the initial costate This solution utilizes the differential algebraic method (hereinafter referred to as the DA method) to solve the two-point boundary value problem of the current relative motion state and the target relative motion state. It should be understood that the DA method can represent arbitrary variables and continuously differentiable functions as Taylor expansion polynomials. Through algebraic operations on the polynomials, the expansion polynomial of the solution to the ordinary differential equation relative to the initial state is calculated. A mature toolkit (DACE) for the DA method is available; its specific principles and detailed operation steps will not be elaborated upon in this scheme.

[0082] First, within the DA computation framework, the initial configuration invariants and initial costate are represented as biased DA variables, namely: in This represents the Taylor expansion polynomial of the variable within the parentheses, i.e., DA variables. and Let represent the reference values ​​of the initial configuration invariants and the initial costate, respectively, i.e., the center of the Taylor expansion. and These represent the initial configuration invariants and the initial costate deviation variables, respectively.

[0083] Then, within the DA computational framework, based on the differential equations of configuration invariant changes, using... As the initial value, and Substitute into the above formula (1). Then, use a numerical integrator (e.g., the fourth-order Runge-Kutta method) to perform the integrator over the time interval. arrive Integrating on the above, we get The terminal configuration invariant at time t is expressed as: in Indicates and Taylor expansion polynomial as independent variable This represents the constant part of the Taylor expansion polynomial corresponding to the terminal configuration invariant. Represents a polynomial mapping that does not contain a constant part.

[0084] Finally, the Taylor expansion polynomial of the terminal configuration invariants obtained by integration is used to solve for the initial costate that satisfies the aforementioned two-point boundary value problem. Setting the initial configuration invariant deviation variable to 0, the above equation can be rewritten as: in, This is a polynomial mapping, specifically a mapping polynomial from the initial costate deviation to the terminal configuration invariant deviation. This is a polynomial inverse mapping. The error in calculating the terminal configuration invariant to the target configuration invariant is shown in the following equation.

[0085] By inverting the above polynomial mapping, we obtain the initial costate that meets the requirements, namely: in, This is a polynomial inverse mapping, which can be calculated using built-in functions in the DACE toolkit. It should be noted that the polynomial inverse mapping in this step... Once the calculations are complete, the method can be reused for different reconstruction targets. It only requires calculating the deviation from the spacecraft's configuration invariants when the target's relative motion state is achieved, based on the new target configuration invariants. You can substitute it into The initial costate that satisfies the reconstruction condition under the corresponding objective is obtained. Then, the initial costate obtained from the solution... Substitute into the above formula (1) to complete the construction of the control law.

[0086] S102. Using the control law of the spacecraft, determine the thrust required for the spacecraft to reach the target relative motion state in order to realize the reconfiguration of the spacecraft formation.

[0087] Specifically, for each of the multiple slave spacecraft, in the process of reconfiguring the spacecraft formation by performing state control on the slave spacecraft, the current moment is substituted into the above formula (1) to obtain the thrust of the slave spacecraft at the current moment until the slave spacecraft reaches the target relative motion state.

[0088] Understandably, in the implementation of the above data-driven spacecraft formation configuration reconfiguration method, if the spacecraft formation is equipped with an onboard computer with sufficient computing power, the calculation processes of S101-S103 can all be implemented by the onboard computer to reduce the time delay caused during transmission. Otherwise, the calculation processes of S103 and S102 can be implemented by ground equipment, and the calculated control law can be transmitted to the onboard computer via ground injection, and then the calculation process of S103 can be implemented by the onboard computer.

[0089] To verify the effectiveness of the data-driven spacecraft formation configuration reconstruction method provided in the embodiments of this application, the following technical verification is performed using the method provided in the embodiments of this application on the reconstruction problem of a binary star formation in an elliptical orbit.

[0090] The validation results of the training effect of the state autoencoder are as follows: Figures 3 to 5 As shown, Figure 3 The study demonstrates that the loss function, reconstruction loss term, and linear prediction loss term of the state autoencoder gradually decrease with the increase of training rounds, verifying the successful convergence of the training results. Figure 4 The training results of the state autoencoder are shown, and the change trajectories of each column component in the transformation matrix are displayed. Figure 5 This paper demonstrates how a reduced dynamic model can be used to predict and reconstruct random relative motion trajectories. The results show that the predicted trajectory accurately approximates the actual trajectory, proving the effectiveness of the data-driven reduced dynamic model. These results demonstrate the effectiveness of the state autoencoder in the method provided in the embodiments of this application.

[0091] The results of solving the control law and verifying its control effect are as follows: Figure 6 and Figure 7 As shown, Figure 6 The thrust curve obtained from the solved control law is shown. Figure 7 The trajectory of formation reconstruction under the action of the obtained optimal control law is shown. The results show that the formation successfully transitioned from the initial configuration to the target configuration, verifying the effectiveness of the solved control law and its control effect.

[0092] In summary, the data-driven spacecraft formation configuration reconfiguration method provided in this application embodiment, when it is necessary to reconfigure the spacecraft formation, for each of the multiple slave spacecraft included in the spacecraft formation, a control law for the slave spacecraft is constructed based on the current relative motion state of the slave spacecraft, the target relative motion state, and the state autoencoder. Then, the control law of the slave spacecraft is used to make the slave spacecraft reach the target relative motion state from the current relative motion state, thereby realizing the spacecraft formation configuration reconfiguration. Since the state autoencoder used in the above process is an autoencoder based on the Lyapunov-Floquet transform theorem, and this state autoencoder is trained from multiple relative motion states of multiple spacecraft, it can more realistically reflect the dynamic characteristics of the spacecraft. In the process of spacecraft formation configuration reconstruction, only the autoencoder needs to be trained once, and the trained state autoencoder can be reused multiple times to construct the control law required for formation configuration reconstruction. The above process improves the computational efficiency of solving the control law, has low computing power requirements, and is easy to deploy on satellite to achieve autonomous planning, thereby improving the efficiency of spacecraft formation configuration reconstruction and facilitating the spacecraft formation to complete its mission.

[0093] Accordingly, embodiments of this application provide a data-driven spacecraft formation configuration reconfiguration device, such as... Figure 7As shown, the device includes a control law construction module 501 and a configuration reconstruction module 502.

[0094] The control law construction module 501 is used to determine the control law for each of the multiple slave spacecraft when configuration reconfiguration of the spacecraft formation is required. This is based on the current relative motion state of the slave spacecraft, the target relative motion state of the slave spacecraft after configuration reconfiguration, and the state autoencoder. The relative motion state refers to the motion state of the slave spacecraft relative to the master spacecraft. The state autoencoder is an autoencoder based on the Lyapunov-Floquet transform theorem and is trained using multiple relative motion states of the multiple spacecraft. For example, the control law construction module 501 is used to implement S101 of the above method.

[0095] The configuration reconfiguration module 502 is used to determine the thrust required for the spacecraft to reach the target relative motion state by employing the control law of the spacecraft, thereby achieving spacecraft formation configuration reconfiguration. For example, the configuration reconfiguration module 502 is used to implement S102 of the above method.

[0096] Optionally, combined Figure 8 ,like Figure 9 As shown, the above-mentioned device also includes a dynamic model construction model 503.

[0097] The dynamic model construction model 503 is used to construct a dynamic model of the relative motion of spacecraft in a spacecraft formation. For example, the dynamic model construction model 503 is used to implement S103 of the above method.

[0098] The modules of the aforementioned data-driven spacecraft formation configuration reconfiguration device 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.

[0099] 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 described in the above embodiments. The processor can implement the control law construction module 501 and the configuration reconstruction module 502; the memory can also be used to store multiple relative motion states, reduced dynamic states, and control laws of a spacecraft.

[0100] 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.

[0101] 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.

[0102] 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.

[0103] 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 data-driven spacecraft formation configuration reconfiguration method, wherein the spacecraft formation includes a master spacecraft and multiple slave spacecraft, the master spacecraft and the multiple slave spacecraft maintaining the configuration of the spacecraft formation to collaboratively complete a mission; characterized in that, The method includes: In cases where configuration reconfiguration of the spacecraft formation is required, for each of the plurality of slave spacecraft, a control law for the slave spacecraft is determined based on its current relative motion state, the target relative motion state of the slave spacecraft after configuration reconfiguration, and a state autoencoder; wherein, the relative motion state refers to the motion state of the slave spacecraft relative to the master spacecraft; the state autoencoder is an autoencoder based on the Lyapunov-Floquet transform theorem; the state autoencoder is trained through multiple relative motion states of the multiple spacecraft; Using the control law of the slave spacecraft, the thrust required for the slave spacecraft to reach the relative motion state of the target is determined, so as to realize the reconfiguration of the spacecraft formation.

2. The method as described in claim 1, characterized in that, The state autoencoder includes an encoder and a decoder. The encoder is used to encode the relative motion state into a reduced dynamic state, and the decoder is used to decode the reduced dynamic state into a relative motion state. The reduced dynamic state indicates the state that satisfies the time-invariant evolution law from the relative motion state of the spacecraft. The encoder satisfies the following formula; in, z Represents the reduced dynamic state. x Indicates a state of relative motion. t Indicates time, ( x , t ) represents the output result of the encoder. This represents the boundary value matrix of the encoder. This represents the periodic boundary function of the encoder. This represents the sparse coefficient matrix of the encoder. This represents element-wise multiplication of matrices. Indicates t The first fully connected neural network takes a matrix as input and outputs a matrix. The parameters of the first fully connected neural network are represented; the periodic boundary function of the encoder is also represented. The following formula must be satisfied; in, Indicates the first shape parameter. Indicates the second shape parameter. T c Indicates the orbital period of the spacecraft; The decoder satisfies the following formula; in, -1 ( z , t ) represents the output of the decoder. This represents the boundary value matrix of the decoder. This represents the periodic boundary function of the decoder. This represents the sparse coefficient matrix of the decoder. Indicates t The second fully connected neural network takes a matrix as input and outputs a matrix. The parameters of the second fully connected neural network are represented; the periodic boundary function of the decoder is also represented. The following formula must be satisfied; in, Indicates the third shape parameter. This represents the fourth shape parameter.

3. The method as described in claim 1 or 2, characterized in that, The control law of the spacecraft satisfies the following formula; in, ) indicates thrust; Represents the weight matrix. It is a positive definite matrix. -1 for The inverse matrix; Indicates intermediate variables. T Let represent the transpose matrix of the intermediate variables, and ; Represents a constant matrix; Represents the transformation matrix. for The inverse matrix, , This represents the boundary value matrix of the encoder. This represents the periodic boundary function of the encoder. This represents the sparse coefficient matrix of the encoder. This represents element-wise multiplication of matrices. Indicates t The first fully connected neural network takes a matrix as input and outputs a matrix. Indicates the parameters of the first fully connected neural network; Represents the control input matrix; Denotes the initial costate, the initial costate The initial costate is obtained by solving the two-point boundary value problem of the current relative motion state and the target relative motion state using differential algebraic methods. satisfy: , The reference value representing the initial costate. , For polynomial mapping, It is a polynomial inverse mapping. The deviation value from the configuration invariants of the spacecraft when the relative motion state of the target is achieved.

4. The method as described in claim 1, characterized in that, The loss function of the state autoencoder during training satisfies the following formula; in, L Represents the loss function. L linear Represents the linear prediction term. Represents the weight parameters. L reconstruction Represents the reconstruction loss term; The linear prediction term L linear The following formula must be satisfied; in, N This indicates the number of multiple relative motion states of multiple spacecraft. k This represents the k-th index in the relative motion state. This represents the k-th relative motion state. This represents the time point of the k-th relative motion state. This represents the (k+1)th relative motion state. This represents the time point of the (k+1)th relative motion state; express and The output of the encoder is the input. Represents a constant matrix; This represents the time interval between the k-th relative motion state and the (k+1)-th relative motion state. ; express and The output of the encoder is the input. The reconstruction loss term L reconstruction The following formula must be satisfied; in, -1 ( , ) indicates with and The output of the decoder is the input. The second norm of a vector.

5. A data-driven spacecraft formation configuration reconfiguration device, wherein the spacecraft formation includes a master spacecraft and multiple slave spacecraft, the master spacecraft and the multiple slave spacecraft maintaining the configuration of the spacecraft formation to collaboratively complete a mission; characterized in that, The device includes a control law construction module and a configuration reconstruction module; The control law construction module is used to determine the control law for each of the multiple slave spacecraft when the configuration reconfiguration of the spacecraft formation is required. This determination is based on the current relative motion state of the slave spacecraft, the target relative motion state of the slave spacecraft after configuration reconfiguration, and a state autoencoder. The relative motion state refers to the motion state of the slave spacecraft relative to the master spacecraft. The state autoencoder is an autoencoder based on the Lyapunov-Floquet transform theorem and is trained using multiple relative motion states of the multiple spacecraft. The configuration reconfiguration module is used to determine the thrust required for the slave spacecraft to reach the target relative motion state by adopting the control law of the slave spacecraft, so as to realize the configuration reconfiguration of the spacecraft formation.

6. 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 4.

7. 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 4.

8. A computer program product, characterized in that, It includes computer program instructions that, when executed on a computer, cause the computer to perform the method as described in any one of claims 1 to 4.

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