Orbit transfer method and system based on deep neural network in the Earth-Moon three-body model

Abstract

A method and system for orbital transfer under the Earth-Moon three-body model based on a deep neural network relates to the technical field of probe transfer design between special Earth-Moon orbits, and is used to solve the technical problem that existing methods cannot solve due to large computational complexity and long time consumption. The technical key points of the present invention include: obtaining a training dataset for transfer between special orbits; constructing a deep neural network and training the deep neural network based on the special transfer training dataset to obtain a trained deep neural network; constructing an optimization model for direct transfer between special orbits of the Earth-Moon system, and iteratively solving the direct transfer optimization model using a particle swarm algorithm and the trained deep neural network until the desired index or the maximum number of iterations is reached, thereby obtaining an iterative index curve and a transfer orbit under the Earth-Moon three-body model. The present invention realizes the calculation and design of optimal transfer pulses between special orbits of the Earth-Moon system.

Description

Technical Field

[0001] The present invention relates to the technical field of design for probe transfer between special Earth-Moon orbits, and in particular to an orbit transfer method and system based on a deep neural network in an Earth-Moon three-body model. Background Art

[0002] As Earth's only natural satellite, the Moon has long been a hot topic in deep space exploration. Demand for missions such as lunar resource exploration, verifying the communication capabilities of deep space probes, and verifying their rendezvous and docking capabilities is increasing rapidly. Designing transfer orbits for probes is fundamental to achieving these goals. Special Earth-Moon system orbits, such as the Halo orbit, NRHO orbit, and DRO, facilitate the implementation of several space missions due to their unique spatial locations and operational characteristics. The rapid and efficient design of transfer orbits between these special orbits has become a research hotspot.

[0003] In the traditional design of deep space exploration orbit transfer schemes, the conic section splicing method is widely used. However, the conic section splicing method is limited by the dynamic model and is only applicable to the two-body problem. It cannot truly describe the gravitational environment and has large errors and uncertainties. Under the three-body dynamic model, when the initial and final states of the transfer orbit are known and the transfer time is determined, it can be described as a three-body Lambert problem. However, due to the strong nonlinearity of the three-body dynamic model, the three-body problem has no analytical solution and the solution process relies on numerical integration. In response to the current situation that the three-body problem is difficult to solve and the amount of calculation is large, the literature [1] proposed a quasi-linearization-local variational iteration method (QL-LVIM). Through the idea of ​​quasi-linearization, the nonlinear two-point boundary value problem is transformed into a series of initial value problems with a certain iterative format and appearing in pairs, and then solved by the local variational iteration method. However, this method requires multiple rounds of iterations, the amount of calculation is still relatively large, and the computational efficiency depends on the initial estimated solution, requiring designers to have certain experience. Reference [2] proposed a local point-matching feedback iteration algorithm to address the shortcomings of traditional numerical integration, which is that the accuracy is heavily dependent on small integral steps and cannot meet the requirements of fast calculations on-orbit for spacecraft. This algorithm can achieve large-step high-speed calculations, which is more than 1.5 times faster than the quasi-linearization-local variation iteration method. However, the solution accuracy still depends on the number of iterations. If a solution that meets the accuracy requirements is to be obtained, multiple rounds of iterations are required. At the same time, this method still does not solve the problem of selecting the initial value of the iteration. If the initial calculation parameters are not set rationally enough, the algorithm's large-step high-speed calculation characteristics will be limited. With the development of intelligent algorithms, neural networks have a unique advantage in solving strong nonlinear problems. Reference [3] completed the orbit recursion of Mars entry, descent and landing based on a deep neural network model, and achieved real-time and fast orbit calculation. Reference [4] used deep learning technology to obtain a real-time optimal control method for the solar sail spacecraft orbit transfer mission with the shortest time, and conducted on-board orbit optimization research under the premise of ensuring convergence and real-time performance. However, the above-mentioned cases using deep neural networks are limited to a single scenario and are not universal. When faced with the problem of transferring between different tracks, traditional methods cannot accurately solve it. Summary of the Invention

[0004] In view of this, the present invention proposes an orbit transfer method and system under the Earth-Moon three-body model based on deep neural network to solve the technical problems that existing methods cannot solve, such as large amount of calculation and long time consumption.

[0005] According to one aspect of the present invention, a method for orbit transfer based on a deep neural network in an Earth-Moon three-body model is proposed, comprising the following steps:

[0006] Step 1: Obtain a special inter-track transfer training dataset;

[0007] Step 2: construct a deep neural network and train the deep neural network based on the special inter-track transfer training data set to obtain a trained deep neural network;

[0008] Step 3: Construct an optimization model for direct transfer between special orbits of the Earth-Moon system, and use the particle swarm algorithm and a trained deep neural network to iteratively solve the direct transfer optimization model until the desired index or the maximum number of iterations is reached, and obtain the iterative index curve and the transfer orbit under the Earth-Moon three-body model.

[0009] Furthermore, the specific steps of step one include:

[0010] Step 11: Calculate and obtain discrete data of a special orbit of the Earth-Moon system using a circularly restricted three-body dynamics model; the discrete data of the special orbit of the Earth-Moon system is transfer orbit data of different time lengths from any point in the starting orbit to any point in the target orbit, including position data and velocity data;

[0011] Step 1 and 2: Discretize the expected transfer time range to obtain discrete transfer time;

[0012] Step 13: Calculate the discrete data of the special orbits of the Earth-Moon system using a traversal calculation method to establish a special orbit transfer training set; the special orbit transfer training set includes a starting orbit data set and a target orbit data set.

[0013] Furthermore, the direct transfer optimization model between special orbits of the Earth-Moon system described in step 3 includes an upper optimization model and a lower optimization model; wherein,

[0014] The upper optimization model is:

[0015] The objective function is to minimize the pulse J1: Energy J2 is minimized:

[0016] Where, ||Δv i ||2 represents the amplitude of the i-th pulse; n is the number of pulses;

[0017] The lower layer optimization model is:

[0018]

[0019] Constraints:

[0020] Where, They represent the off-orbit pulses that leave the starting orbit; They represent the pulses entering the target orbit; x c,i ,y c,i ,z c,iRespectively represent the three-axis coordinates of the i-th data point of the starting track, They represent the three-axis velocities of the i-th data point on the starting track; x t,j ,y t,j ,z t,j Represent the three-axis coordinates of the j-th data point of the target track, They represent the three-axis velocities of the jth data point on the target track, t k represents the kth data point of the transfer time; i represents the position of the transfer starting point in the starting trajectory data, j represents the position of the transfer target point in the target trajectory, k represents the position of the transfer time in the transfer time series, p represents the total number of starting trajectory data points, q represents the total number of target trajectory data points, and m represents the total number of transfer time data points; DNN represents the trained deep neural network.

[0021] Furthermore, the iterative solution of the direct transfer optimization model based on the particle swarm algorithm and the trained deep neural network includes: taking the special inter-orbit transfer training set and the discrete transfer time as search conditions, optimizing and solving the upper-level optimization model using the particle swarm algorithm, and calculating the optimal transfer scheme as the output, wherein the optimal transfer scheme includes a combination of the transfer starting point position and speed, the transfer target point position and speed, and the transfer time; for the lower-level optimization model, inputting the optimal transfer scheme output by the upper-level optimization model into the trained deep neural network to obtain the corresponding pulse sequence, and calculating the corresponding index; wherein the corresponding index is the transfer orbit data, the size of the transfer pulse or the amount of energy consumed; feeding the corresponding index back to the upper-level optimization model, reselecting the point using the particle swarm algorithm, and repeating the above steps until the expected index or the maximum number of iterations is reached, thereby obtaining the iterative index curve and the transfer orbit under the Earth-Moon three-body model.

[0022] According to another aspect of the present invention, an orbit transfer system based on a deep neural network under the Earth-Moon three-body model is proposed, comprising:

[0023] a data acquisition module configured to acquire a special inter-track transfer training dataset;

[0024] A neural network training module is configured to construct a deep neural network and train the deep neural network according to the special inter-track transfer training dataset to obtain a trained deep neural network;

[0025] The model solving module is configured to construct an optimization model for direct transfer between special orbits of the Earth-Moon system, and iteratively solve the direct transfer optimization model using a particle swarm algorithm and a trained deep neural network until the desired index or the maximum number of iterations is reached, thereby obtaining an iterative index curve and a transfer orbit under the Earth-Moon three-body model.

[0026] Furthermore, the data acquisition module acquires a special track transfer training data set including:

[0027] Step 11: Calculate and obtain discrete data of a special orbit of the Earth-Moon system using a circularly restricted three-body dynamics model; the discrete data of the special orbit of the Earth-Moon system is transfer orbit data of different time lengths from any point in the starting orbit to any point in the target orbit, including position data and velocity data;

[0028] Step 1 and 2: Discretize the expected transfer time range to obtain discrete transfer time;

[0029] Step 13: Calculate the discrete data of the special orbits of the Earth-Moon system using a traversal calculation method to establish a special orbit transfer training set; the special orbit transfer training set includes a starting orbit data set and a target orbit data set.

[0030] Furthermore, the direct transfer optimization model between special orbits of the Earth-Moon system in the model solving module includes an upper optimization model and a lower optimization model; wherein,

[0031] The upper optimization model is:

[0032] The objective function is to minimize the pulse J1: Energy J2 is minimized:

[0033] Where, ||Δv i ||2 represents the amplitude of the i-th pulse; n is the number of pulses;

[0034] The lower layer optimization model is:

[0035]

[0036] Constraints:

[0037] Where, They represent the off-orbit pulses that leave the starting orbit; They represent the pulses entering the target orbit; x c,i ,y c,i ,z c,i Respectively represent the three-axis coordinates of the i-th data point of the starting track, They represent the three-axis velocities of the i-th data point on the starting track; x t,j ,y t,j ,z t,j They represent the three-axis coordinates of the j-th data point of the target track, and they represent the three-axis speed of the j-th data point of the target track, t krepresents the kth data point of the transfer time; i represents the position of the transfer starting point in the starting trajectory data, j represents the position of the transfer target point in the target trajectory, k represents the position of the transfer time in the transfer time series, p represents the total number of starting trajectory data points, q represents the total number of target trajectory data points, and m represents the total number of transfer time data points; DNN represents the trained deep neural network.

[0038] Furthermore, the iterative solution of the direct transfer optimization model based on the particle swarm algorithm and the trained deep neural network includes: taking the special inter-orbit transfer training set and the discrete transfer time as search conditions, optimizing and solving the upper-level optimization model using the particle swarm algorithm, and calculating the optimal transfer scheme as the output, wherein the optimal transfer scheme includes a combination of the transfer starting point position and speed, the transfer target point position and speed, and the transfer time; for the lower-level optimization model, inputting the optimal transfer scheme output by the upper-level optimization model into the trained deep neural network to obtain the corresponding pulse sequence, and calculating the corresponding index; wherein the corresponding index is the transfer orbit data, the size of the transfer pulse or the amount of energy consumed; feeding the corresponding index back to the upper-level optimization model, reselecting the point using the particle swarm algorithm, and repeating the above steps until the expected index or the maximum number of iterations is reached, thereby obtaining the iterative index curve and the transfer orbit under the Earth-Moon three-body model.

[0039] The beneficial technical effects of the present invention are:

[0040] The present invention proposes an orbit transfer method and system under the Earth-Moon three-body model based on a deep neural network. First, a special inter-orbit transfer training data set is obtained; then, a deep neural network is constructed and the deep neural network is trained according to the special inter-orbit transfer training data set to obtain a trained deep neural network; then, an optimization model for direct transfer between special orbits of the Earth-Moon system is constructed, and the direct transfer optimization model is iteratively solved based on a particle swarm algorithm and the trained deep neural network until the expected index or the maximum number of iterations is reached, thereby obtaining an iterative index curve and a transfer orbit under the Earth-Moon three-body model.

[0041] In response to the demand for rapid design of transfer orbits between special orbits in Earth-Moon space, the present invention proposes a universal method capable of rapid real-time calculation. By combining intelligent algorithms with deep learning, the algorithm's solution efficiency is guaranteed, the simplicity of the algorithm structure is improved, and the solution process no longer relies on complex dynamic models and boundary condition constraints. This provides strong technical support for the rapid design of orbits for future lunar exploration missions, improves the feasibility of on-orbit real-time orbit optimization design, and realizes the rapid calculation and design of minimum pulse transfer orbits between various types of special orbits under the three-body dynamics model in the Earth-Moon system.

[0042] The present invention directly generates an algorithm for the transfer pulse scheme based on the state quantities of the transfer starting point, the transfer target point, and the transfer time, solving the problem of using a large amount of computing resources when solving the three-body Lambert problem using traditional methods. Taking into account the strict requirements for solution efficiency of rapid design tasks and the computing power constraints of onboard computers, the present invention, based on the requirements of rapid transfer orbit design tasks in lunar exploration missions and a certain degree of on-orbit real-time optimization, uses a computational method with fast solution speed, small computational load, and sufficiently high solution accuracy - a deep neural network (DNN) built based on deep learning. Only a sufficient training set is needed to train the deep neural network to achieve rapid calculation of the transfer orbit. The deep neural network calculation method for transfer orbit design used in the present invention optimizes the input and output quantities separately. The input quantity is searched using intelligent algorithms such as particle swarm optimization and genetic algorithm; the output quantity optimization uses the deep neural network to solve the Lambert problem. This achieves the goal of using fewer computing resources and obtains the transfer orbit between special Earth-Moon orbits while consuming as little fuel as possible. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The present invention can be better understood by referring to the description given below in conjunction with the accompanying drawings, which together with the following detailed description are included in this specification and form a part of this specification, and are used to further illustrate the preferred embodiments of the present invention and explain the principles and advantages of the present invention.

[0044] Figure 1 This is a flow chart of an orbit transfer method based on a deep neural network in an Earth-Moon three-body model according to an embodiment of the present invention;

[0045] Figure 2 Schematic diagram of the rotating coordinate system of the center of mass of the Earth-Moon system in an embodiment of the present invention;

[0046] Figure 3 Schematic diagram of the relationship between various coordinate systems in an embodiment of the present invention;

[0047] Figure 4 Schematic diagram of the libration point and nearby special orbits in the Earth-Moon three-body system of the present invention;

[0048] Figure 5 This is a graph showing the mean square error change during the deep neural network training process according to an embodiment of the present invention;

[0049] Figure 6 This is an evolution curve diagram of iteration indicators in an embodiment of the present invention;

[0050] Figure 7 This is an example diagram of the transfer orbit in the mass-rotating coordinate system of the Earth-Moon system according to an embodiment of the present invention;

[0051] Figure 8 A comparison chart of the iterative index evolution curves obtained by the embodiment of the present invention, the traditional sequential quadratic programming method, and the multi-point shooting method;

[0052] Figure 9 This figure is a comparison example of the transfer orbits in the Earth-Moon system's center-of-mass rotating coordinate system obtained by the embodiment of the present invention and the traditional sequential quadratic programming method and multi-point shooting method. DETAILED DESCRIPTION

[0053] In order to enable those skilled in the art to better understand the present invention, exemplary embodiments or examples of the present invention will be described below with reference to the accompanying drawings. Obviously, the described embodiments or examples are only some of the embodiments or examples of the present invention, and not all of them. Based on the embodiments or examples of the present invention, all other embodiments or examples obtained by those skilled in the art without creative work should fall within the scope of protection of the present invention.

[0054] The embodiment of the present invention proposes an orbit transfer method based on a deep neural network under the Earth-Moon three-body model. Figure 1 As shown, the method includes the following steps:

[0055] Step 1: Obtain a special inter-track transfer training dataset;

[0056] Step 2: construct a deep neural network and train the deep neural network based on the special inter-track transfer training data set to obtain a trained deep neural network;

[0057] Step 3: Construct an optimization model for direct transfer between special orbits of the Earth-Moon system, and use the particle swarm algorithm and a trained deep neural network to iteratively solve the direct transfer optimization model until the desired index or the maximum number of iterations is reached, and obtain the iterative index curve and the transfer orbit under the Earth-Moon three-body model.

[0058] The method begins with step 1, in which a training dataset for transfers between special orbits is obtained. Specifically, the following process is used to obtain the training dataset: first, discrete data of the special orbit is calculated using a circularly constrained three-body dynamics model; the discrete data of the special orbit is the transfer trajectory data of varying lengths of time from any point on the starting orbit to any point on the target orbit, including position data and velocity data; then, the desired transfer time range is discretized to obtain discrete transfer times; finally, the discrete data of the special orbit is calculated using a traversal calculation method to establish a training dataset for transfers between special orbits; the training dataset for transfers between special orbits includes the starting orbit dataset and the target orbit dataset. Specifically, the circular restricted three-body dynamics model (CRTBP model) equation is established in the Earth-Moon barycentric rotating coordinate system, and the discrete data of the starting orbit and the target orbit under the CRTBP model are calculated. The expected transfer time range is discretized, and the transfer orbit data of different time lengths from any point in the starting orbit to any point in the target orbit are traversed and saved to establish a special inter-orbit transfer data set, that is, a transfer training set between each orbit type is established; there are p groups of data for the starting orbit, q groups of data for the target orbit, and m groups of data for the time series, and p×q×m groups of training set data can be established.

[0059] According to an embodiment of the present invention, in order to facilitate the description of transfer orbits between special Earth-Moon orbits, relevant concepts are defined and an Earth-Moon barycenter rotating coordinate system is established as follows:

[0060] Earth-Moon barycenter rotating coordinate system / reunion coordinate system: In the Earth-Moon three-body system, a reunion coordinate system B-xyz can be defined, whose coordinate origin is at the barycenter of the three-body system, that is, the common center B of the Earth and the Moon. The x-axis points from the system barycenter B to the barycenter of the second main celestial body, that is, the moon. The xy coordinate plane is the relative motion plane of the two main celestial bodies. The x-axis, y-axis, and z-axis form a right-handed coordinate system, such as Figure 2 The relationship diagram of each coordinate system is shown as follows. Figure 3 shown.

[0061] In order to conveniently characterize the special orbits in the Earth-Moon system, the circular restricted three-body dynamics equation is established in the Earth-Moon mass center rotating coordinate system as follows:

[0062]

[0063] Where x, y, and z represent the position of the spacecraft in the three-body coordinate system; μ represents the mass ratio of the two main celestial bodies; and r1 and r2 represent the distances from the spacecraft to the two main celestial bodies. The initial and target orbital datasets are as follows:

[0064]

[0065] Where: p and q are the number of discrete points of the starting track and the target track respectively; X ci and X tj They correspond to discrete orbital data respectively.

[0066] At the same time, the transfer time is discretized, and the expected transfer time range [0, T] is discretized into {0, t1, t2, ..., t m}, considering that the transfer time cannot be 0, the 0 value of the above time series is replaced by 0.001, and the time series is obtained

[0067] T={0.001,t1,t2,...,t m}

[0068] Where: m represents the number of discrete points in the transfer time, T k Corresponding to a certain transfer time.

[0069] The circular restricted three-body dynamical model has five libration points, also known as equilibrium points. There are also many special periodic solutions around the libration points and the main celestial body, which constitute the special periodic and quasi-periodic orbits in the three-body model. Figure 4 The main special orbits are drawn in the figure, namely the large-scale retrograde orbit (DRO orbit family) and the periodic orbit family around the libration point (Halo orbit family). Generally, the speed and distance in the coordinate system are normalized. The units of distance in the simulation diagram are all taken as normalized units, i.e. 1L EM =384400km.

[0070] Through the existing special orbit design method, the discrete special orbit data under the three-body dynamics model can be obtained and represented by the following matrix:

[0071]

[0072] The transfer time series is expressed as: [t0 t1 t2...t m ].

[0073] Considering that there are p discrete points in the transfer starting trajectory, q discrete points in the target trajectory, and m discrete points in the transfer time, a p×q×m set of training data sets can be constructed by traversal.

[0074] The input quantity consisting of the transfer starting point, transfer target point and transfer time is:

[0075]

[0076] Among them, i, j, k are the starting orbit, target orbit and transfer time discrete point sequence numbers respectively, x c,i ,y c,i ,zc,i Respectively represent the three-axis coordinates of the i-th data point of the starting track, They represent the three-axis velocities of the i-th data point on the starting track;

[0077] x t,j ,y t,j ,z t,j Represent the three-axis coordinates of the j-th data point of the target track, They represent the three-axis velocities of the jth data point on the target track, t k Represents the kth discrete point of transfer time.

[0078] By using the existing method for solving the three-body Lambert problem, the transfer pulse corresponding to each set of input quantities is solved as the output quantity, that is:

[0079] OUTPUT l =[Δu c ,Δv c ,Δw c ,Δu t ,Δv t ,Δw t ]

[0080] Where Δu c ,Δv c ,Δw c are the three-axis pulses transferred off-orbit, Δu t ,Δv t ,Δw t They are the three-axis pulses transferred into orbit.

[0081] Then, step 2 is executed. In step 2, a deep neural network is constructed and trained based on the special inter-track transfer training data set to obtain a trained deep neural network.

[0082] According to an embodiment of the present invention, a deep neural network is established and trained using a training set; a total of 13-dimensional data, including a 6-dimensional transfer starting point state quantity, a 6-dimensional transfer target point state quantity, and a 1-dimensional transfer time, is used as input, and a total of 6-dimensional data, including a 3-dimensional transfer off-orbit pulse and a 3-dimensional on-orbit pulse, is used as a training set label; a deep neural network with 13 input nodes, five fully connected hidden layers (each fully connected layer has 1024 nodes and uses a ReLU function as an activation function), and 6 output nodes is established, and training is performed using the constructed training set.

[0083] Furthermore, the deep neural network structure established in step 2 is as follows:

[0084] A deep neural network consists of an input layer, a hidden layer, and an output layer. The structure of each layer is as follows:

[0085] Input layer: The input layer includes 13 nodes and 13-dimensional input variables. The 13 parameters of the 13-dimensional input variables include the 6-dimensional variables of the three-axis position and velocity of the starting point of the starting orbit transfer, the 6-dimensional variables of the three-axis position and velocity of the target point of the target orbit transfer, and the transfer time. They are:

[0086]

[0087] The input data needs to be normalized before input to ensure that all input feature data are at the same scale.

[0088] Hidden layer: The hidden layer contains multiple levels. The number of layers can be increased or decreased appropriately according to the complexity of the problem. Here, five fully connected layers are selected as hidden layers. Each fully connected layer has 1024 nodes and the ReLU function is used as the activation function to introduce nonlinearity.

[0089] Dropout layer: A Dropout layer is added between hidden layers to prevent overfitting, and the dropout rate is set to 0.2.

[0090] Output layer: The output layer includes 6 nodes and 6-dimensional output variables. The 6 parameters of the 6-dimensional output variables include: a 3-dimensional variable for the three-axis de-orbit pulse at the transfer starting point and a 3-dimensional variable for the three-axis on-orbit pulse at the transfer target point. For this type of regression problem, a linear activation function is used.

[0091] Settings for other parameters of deep neural network:

[0092] Loss function and optimizer selection: Considering the accuracy requirements of the transfer trajectory, such as Figure 5 As shown in the figure, the mean square error (MSE) is used as the loss function, which imposes heavier penalties on larger errors to achieve a smaller allowable error and higher output accuracy of the model. The optimizer uses the Adam optimizer that combines the advantages of the adaptive learning rate algorithm to provide good convergence performance.

[0093] As an example, when using MATLAB for deep learning training, the training options are set as follows:

[0094] Gradient clipping threshold GradientThreshold: The maximum number of iterations of model training MaxEpochs is set to 30, that is, the model uses the training set for 30 complete learning; the initial value of the learning rate InitialLearnRate is set to 0.001. This parameter determines the step size of the model parameter update. If it is too large, the model will not be able to find the optimal solution. If it is too small, the model will converge too slowly; the mini-batch data size MiniBatchSize is set to 16. Using mini-batches can increase the randomness of the training process, improve the generalization ability of the model, and help prevent the model from overfitting; the learning rate adjustment strategy LearnRateSchedule uses the piecewise constant strategy 'piecewis e', that is, at a specific number of iterations, the learning rate will be multiplied by a factor; the learning rate adjustment factor LearnRateDropFactor is set to 0.9, which is the factor by which the learning rate is multiplied at the specific number of iterations mentioned above; the learning rate adjustment period LearnRateDropPeriod is set to 10, which means that after each iteration, the learning rate is adjusted according to the adjustment factor; the sequence processing method SequenceLength is set to 'Longest', that is, the longest sequence length is used; the training data shuffling strategy Shuffle is set to 'every-epoch' for each generation, and the training data is reshuffled at the beginning of each iteration to increase the randomness of the training, which helps to improve the generalization ability of the model.

[0095] Finally, execute step three. In step three, construct an optimization model for direct transfer between special orbits of the Earth-Moon system: iteratively solve the direct transfer optimization model based on the upper-layer particle swarm algorithm and the lower-layer trained deep neural network until the expected index or the maximum number of iterations is reached, and obtain the iterative index curve and the transfer orbit under the Earth-Moon three-body model.

[0096] According to an embodiment of the present invention, a direct transfer optimization model combining a particle swarm algorithm and a deep neural network is used to perform an iterative solution until the desired index or the maximum number of iterations is reached, and an iterative index curve and a transfer trajectory under the three-body model are obtained; specifically, the method includes: using the particle swarm algorithm to search for input conditions, obtaining a selected transfer starting point, a transfer target point, and a transfer time, and constructing a three-body Lambert problem; solving the three-body Lambert problem based on a deep neural network, obtaining a corresponding pulse sequence, and calculating the corresponding index; feeding the index back to the upper-level problem, reselecting points using the particle swarm algorithm optimization mechanism, and repeating the iteration until the desired index or the maximum number of iterations is reached, and outputting an index iterative evolution curve and a transfer trajectory, such as Figure 6 、 Figure 7 shown.

[0097] Then, a particle swarm optimization method is selected, and the transfer starting point, transfer target point, and transfer time are used as search variables. The corresponding three-body Lambert problem is established, and a deep neural network is used to solve the three-body Lambert problem. The transfer pulse and transfer trajectory data are output, and the transfer pulse is used to construct the optimization index of the particle swarm optimization. Specifically, the following are included:

[0098] The transfer starting point, transfer target point and transfer time are used as the variables to be optimized to construct a transfer optimization problem;

[0099] Use the trained deep neural network to solve the output pulse problem, take the input as a known quantity, solve the corresponding pulse sequence, and use the pulse size or energy consumption (expressed as the sum of squared pulses) as the optimization indicator;

[0100] The indicators are fed back to the particle swarm optimization input optimization problem, and the search for the transfer starting point, transfer target point and transfer time is re-performed. A deep neural network is used to solve the pulse problem. The above steps are repeated repeatedly, and the indicators obtained in each round are compared to obtain the optimal transfer pulse and transfer trajectory data.

[0101] According to the above method of this embodiment, the optimization problem is solved iteratively based on the particle swarm algorithm and the deep neural network algorithm until the desired index or the maximum number of iterations is reached. The input optimization problem can be reconstructed as follows:

[0102] minimize or

[0103] Constraints

[0104] Where i represents the position of the transfer starting point in the starting orbit data, j represents the position of the transfer target point in the target orbit, k represents the position of the transfer time in the transfer time series, p represents the total number of starting orbit data points, q represents the total number of target orbit data points, and m represents the total number of transfer time data points.

[0105] For each combination of transfer starting point, transfer target point and transfer time searched by the particle swarm optimization algorithm, a Lambert problem under the corresponding three-body dynamics model is constructed. Then, the trained deep neural network is used to solve it and the transfer pulse is obtained. The sum of the transfer pulse sizes is used as the particle swarm optimization indicator.

[0106] Design an optimization model for direct transfer between special orbits of the Earth-Moon system based on deep neural networks;

[0107] The particle swarm algorithm is used to optimize the input, and the trained deep neural network is used to optimize the output.

[0108] Using the particle swarm algorithm, the search space is set to discrete transfer starting orbit data, discrete target orbit data, and discrete transfer time. After setting the number of particles and the number of iterations, the search results of each particle in each round of search are used to obtain the combination of transfer starting point, transfer target point, and transfer time, and the three-body Lambert problem, that is, the output optimization problem, is established in turn.

[0109] The only remaining free variable in the output optimization problem is the six-dimensional pulse sequence Δv. Based on the states of the transfer start and destination points and the transfer time obtained from the input optimization, the pulse sequence Δv is obtained by solving the three-body Lambert problem using a trained deep neural network.

[0110] The particle swarm algorithm calculates its performance based on the pulses generated by the deep neural network. This performance is then fed back into the input optimization problem. The algorithm then uses the optimization mechanism to reselect points and iterates until the desired performance or the maximum number of iterations is reached. The algorithm then outputs a performance iteration curve and discrete transfer orbit data. Ultimately, the optimal transfer pulse between specific orbits in the Earth-Moon system is obtained.

[0111] Another embodiment of the present invention provides an orbit transfer system based on a deep neural network in an Earth-Moon three-body model, the system comprising:

[0112] a data acquisition module configured to acquire a special inter-track transfer training dataset;

[0113] A neural network training module is configured to construct a deep neural network and train the deep neural network according to the special inter-track transfer training dataset to obtain a trained deep neural network;

[0114] The model solving module is configured to construct an optimization model for direct transfer between special orbits of the Earth-Moon system, and iteratively solve the direct transfer optimization model using a particle swarm algorithm and a trained deep neural network until the desired index or the maximum number of iterations is reached, thereby obtaining an iterative index curve and a transfer orbit under the Earth-Moon three-body model.

[0115] In this embodiment, preferably, the data acquisition module acquires the special track transfer training data set including:

[0116] Step 11: Calculate and obtain discrete data of a special orbit of the Earth-Moon system using a circularly restricted three-body dynamics model; the discrete data of the special orbit of the Earth-Moon system is transfer orbit data of different time lengths from any point in the starting orbit to any point in the target orbit, including position data and velocity data;

[0117] Step 1 and 2: Discretize the expected transfer time range to obtain discrete transfer time;

[0118] Step 13: Calculate the discrete data of the special orbits of the Earth-Moon system using a traversal calculation method to establish a special orbit transfer training set; the special orbit transfer training set includes a starting orbit data set and a target orbit data set.

[0119] Furthermore, the direct transfer optimization model between special orbits of the Earth-Moon system in the model solving module includes an upper optimization model and a lower optimization model; wherein,

[0120] The upper optimization model is:

[0121] The objective function is to minimize the pulse J1: Energy J2 is minimized:

[0122] Constraints:

[0123] Where J1 represents the pulse optimization; J2 represents the energy optimization; ||Δv i ||2 represents the amplitude of the i-th pulse; n is the number of pulses.

[0124] The lower layer optimization model is:

[0125]

[0126] Constraints:

[0127] Where, They represent the off-orbit pulses that leave the starting orbit; They represent the pulses entering the target orbit; x c,i ,y c,i ,z c,i Respectively represent the three-axis coordinates of the i-th data point of the starting track, They represent the three-axis velocities of the i-th data point on the starting track; x t,j ,y t,j ,z t,j Represent the three-axis coordinates of the j-th data point of the target track, They represent the three-axis velocities of the jth data point on the target track, t k represents the kth data point of the transfer time; i represents the position of the transfer starting point in the starting trajectory data, j represents the position of the transfer target point in the target trajectory, k represents the position of the transfer time in the transfer time series, p represents the total number of starting trajectory data points, q represents the total number of target trajectory data points, and m represents the total number of transfer time data points; DNN represents the trained deep neural network.

[0128] The technical effects of the present invention are further verified through experiments.

[0129] The experiment used the transfer of the Halo orbit around the L1 point and the Halo orbit around the L2 point in the Earth-Moon three-body dynamics model as an example to simulate and verify the technical effect of the present invention. The present invention is applicable to multi-pulse transfer between orbits. This example uses a two-pulse direct transfer as an example. The relevant parameters are set as shown in Table 1 below:

[0130] Table 1 Simulation parameters

[0131]

[0132] Other parameter values ​​of the intelligent algorithm are shown in Table 2 below.

[0133] Table 2 Particle swarm optimization algorithm parameters

[0134]

[0135] In order to verify the effect and computational efficiency of the present invention, the same starting orbit and target orbit are selected, the parameters of the upper particle swarm algorithm remain unchanged, and the lower layer uses the sequential quadratic programming method and the multi-point shooting method to solve the Lambert problem, and the calculation time and the pulse size obtained by the solution are statistically analyzed. The comparison results are shown in Table 3. Figure 8 、 Figure 9 shown.

[0136] Table 3 Comparison of calculation results between the method of the present invention and the traditional method

[0137]

[0138] The experimental verification is based on the AMD Ryzen 5900X platform, using 12-core parallel computing and MATLAB version R2018b. From the comparative data in Table 4, it can be seen that the transfer pulse obtained by the method of the present invention is slightly better than the multi-point shooting method, but worse than the sequential quadratic programming method. Figure 8 It can be seen that the method of the present invention can achieve computational convergence within a shorter number of iteration steps. Considering that the calculation time is much shorter than that of the sequential quadratic programming method and the multi-point shooting method, the comprehensive computational efficiency of the method of the present invention is far superior to that of the traditional methods, and it has obvious advantages in the rapid design of transfer trajectories.

[0139] It should be noted that the transfer trajectory curves obtained in this paper are preliminary designs made before the actual flight mission of the spacecraft. They are only applicable to the Earth-Moon three-body dynamic model. These trajectories can be used as nominal trajectories in actual control. During specific use, mid-course corrections are required based on actual flight conditions.

[0140] Although the present invention has been described with respect to a limited number of embodiments, it will be readily apparent to those skilled in the art, having benefit of the foregoing description, that other embodiments are contemplated within the scope of the invention thus described. This disclosure is intended to be illustrative, not restrictive, of the scope of the invention, which is defined by the appended claims.

[0141] The documents cited in the present invention are as follows:

[0142] [1] Feng Haoyang, Yue Xiaokui, Wang Xuechuan. A new solution to the perturbed Lambert problem with large-scale convergence: quasi-linearization-local variational iteration method[J]. Acta Aeronautica Sinica, 2021.

[0143] [2] Zhang Zhe, Dai Honghua, Feng Haoyang, et al. Fast numerical calculation method for orbital dynamics equations with initial value constraints and two-point boundary value constraints [J]. Chinese Journal of Mechanics, 2022.

[0144] [3] Sánchez-Sánchez C, Izzo D. Real-time optimal control via deep neural networks: study on landing problems[J]. Journal of Guidance, Control, and Dynamics, 2018.

[0145] [4]Cheng L, Wang Z, Jiang F, et al. Real-time optimal control for spacecraft orbit transfer via multiscaledeep neural networks [J]. IEEE Transactions on Aerospace and Electronic Systems, 2018.

Claims

1. The orbit transfer method based on deep neural network under the Earth-Moon three-body model is characterized by: The following steps are involved: Step 1: Obtain a special inter-track transfer training dataset; Step 2: construct a deep neural network and train the deep neural network based on the special inter-track transfer training data set to obtain a trained deep neural network; Step 3: Construct an optimization model for direct transfer between special orbits of the Earth-Moon system, and iteratively solve the model using a particle swarm optimization algorithm and a trained deep neural network until the desired index or the maximum number of iterations is reached, thereby obtaining an iterative index curve and the transfer orbit under the Earth-Moon three-body model. The specific steps of step one include: Step 11: Calculate and obtain discrete data of a special orbit of the Earth-Moon system using a circularly restricted three-body dynamics model; the discrete data of the special orbit of the Earth-Moon system is transfer orbit data of different time lengths from any point in the starting orbit to any point in the target orbit, including position data and velocity data; Step 1 and 2: Discretize the expected transfer time range to obtain discrete transfer time; Step 13: Calculate the discrete data of the special orbit of the Earth-Moon system using a traversal calculation method to establish a special orbit transfer training set; the special orbit transfer training set includes a starting orbit data set and a target orbit data set; The direct transfer optimization model between special orbits of the Earth-Moon system described in step 3 includes an upper optimization model and a lower optimization model; wherein, The upper optimization model is: The objective function is to minimize the pulse J1: Energy J2 is minimized: Where, ||Δv i ||2 represents the amplitude of the i-th pulse; n is the number of pulses; The lower layer optimization model is: [Δx c ,Δy c ,Δz c ,Δx t ,Δy t ,Δz t ] ijk =DNN(x c,i ,y c,i ,z c,i ,x c,i ,y c,i ,z c,i ,x t,j ,y t,j ,z t,j ,x t,j ,y t,j ,z t,j ,t k ) Constraints: Where Δx c ,Δy c ,Δz c They represent the off-orbit pulses that leave the starting orbit; Δx t ,Δy t ,Δz t They represent the pulses entering the target orbit; x c,i ,y c,i ,z c,i They represent the three-axis coordinates of the i-th data point of the starting track, x c,i ,y c,i ,z c,i They represent the three-axis velocities of the i-th data point on the starting track; x t,j ,y t,j ,z t,j They represent the three-axis coordinates of the j-th data point of the target track, x t,j ,y t,j ,z t,j They represent the three-axis velocities of the j-th data point of the target track, t k represents the kth data point of the transfer time; i represents the position of the transfer starting point in the starting trajectory data, j represents the position of the transfer target point in the target trajectory, k represents the position of the transfer time in the transfer time series, p represents the total number of starting trajectory data points, q represents the total number of target trajectory data points, and m represents the total number of transfer time data points; DNN represents the trained deep neural network; The iterative solution of the direct transfer optimization model based on the particle swarm algorithm and the trained deep neural network includes: taking the special inter-orbit transfer training set and the discrete transfer time as search conditions, optimizing and solving the upper-level optimization model using the particle swarm algorithm, and calculating the optimal transfer scheme as the output, wherein the optimal transfer scheme includes a combination of the transfer starting point position and speed, the transfer target point position and speed, and the transfer time; for the lower-level optimization model, inputting the optimal transfer scheme output by the upper-level optimization model into the trained deep neural network to obtain a corresponding pulse sequence, and calculating the corresponding index; wherein the corresponding index is the transfer orbit data, the size of the transfer pulse or the amount of energy consumed; feeding the corresponding index back to the upper-level optimization model, reselecting the point using the particle swarm algorithm, and iterating the above steps until the expected index or the maximum number of iterations is reached, thereby obtaining an iterative index curve and the transfer orbit under the Earth-Moon three-body model.

2. The orbit transfer system based on the Earth-Moon three-body model based on deep neural network is characterized by: include: a data acquisition module configured to acquire a special inter-track transfer training dataset; A neural network training module is configured to construct a deep neural network and train the deep neural network according to the special inter-track transfer training dataset to obtain a trained deep neural network; a model solving module configured to construct an optimization model for direct transfer between special orbits of the Earth-Moon system, and iteratively solve the optimization model using a particle swarm optimization algorithm and a trained deep neural network until a desired index or a maximum number of iterations is reached, thereby obtaining an iterative index curve and a transfer orbit under the Earth-Moon three-body model; The data acquisition module acquires a special track transfer training data set including: Step 11: Calculate and obtain discrete data of a special orbit of the Earth-Moon system using a circularly restricted three-body dynamics model; the discrete data of the special orbit of the Earth-Moon system is transfer orbit data of different time lengths from any point in the starting orbit to any point in the target orbit, including position data and velocity data; Step 1 and 2: Discretize the expected transfer time range to obtain discrete transfer time; Step 13: Calculate the discrete data of the special orbit of the Earth-Moon system using a traversal calculation method to establish a special orbit transfer training set; the special orbit transfer training set includes a starting orbit data set and a target orbit data set; The direct transfer optimization model between special orbits of the Earth-Moon system in the model solving module includes an upper optimization model and a lower optimization model; wherein, The upper optimization model is: The objective function is to minimize the pulse J1: Energy J2 is minimized: Where, ||Δv i ||2 represents the amplitude of the i-th pulse; n is the number of pulses; The lower layer optimization model is: [Δx c ,Δy c ,Δz c ,Δx t ,Δy t ,Δz t ] ijk =DNN(x c,i ,y c,i ,z c,i ,x c,i ,y c,i ,z c,i ,x t,j ,y t,j ,z t,j ,x t,j ,y t,j ,z t,j ,t k ) Constraints: Where Δx c ,Δy c ,Δz c They represent the off-orbit pulses that leave the starting orbit; Δx t ,Δy t ,Δz t They represent the pulses entering the target orbit; x c,i ,y c,i ,z c,i They represent the three-axis coordinates of the i-th data point of the starting track, x c,i ,y c,i ,z c,i They represent the three-axis velocities of the i-th data point on the starting track; x t,j ,y t,j ,z t,j They represent the three-axis coordinates of the j-th data point of the target track, x t,j ,y t,j ,z t,j They represent the three-axis velocities of the j-th data point of the target track, t k represents the kth data point of the transfer time; i represents the position of the transfer starting point in the starting trajectory data, j represents the position of the transfer target point in the target trajectory, k represents the position of the transfer time in the transfer time series, p represents the total number of starting trajectory data points, q represents the total number of target trajectory data points, and m represents the total number of transfer time data points; DNN represents the trained deep neural network; The iterative solution of the direct transfer optimization model based on the particle swarm algorithm and the trained deep neural network includes: taking the special inter-orbit transfer training set and the discrete transfer time as search conditions, optimizing and solving the upper-level optimization model using the particle swarm algorithm, and calculating the optimal transfer scheme as the output, wherein the optimal transfer scheme includes a combination of the transfer starting point position and speed, the transfer target point position and speed, and the transfer time; for the lower-level optimization model, inputting the optimal transfer scheme output by the upper-level optimization model into the trained deep neural network to obtain a corresponding pulse sequence, and calculating the corresponding index; wherein the corresponding index is the transfer orbit data, the size of the transfer pulse or the amount of energy consumed; feeding the corresponding index back to the upper-level optimization model, reselecting the point using the particle swarm algorithm, and iterating the above steps until the expected index or the maximum number of iterations is reached, thereby obtaining an iterative index curve and the transfer orbit under the Earth-Moon three-body model.

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