Track transfer method and system under earth-moon three-body model based on deep neural network

Abstract

The invention discloses an orbit transfer method and system under an earth-moon three-body model based on a deep neural network, relates to the technical field of detector transfer design between earth-moon special orbits, and is used for solving the technical problem that the existing method cannot solve the problems of large calculation amount and long time consumption. According to the technical key points, the method comprises the steps of obtaining a transfer training data set between special orbits; constructing a deep neural network, and training the deep neural network according to the transfer training data set between the special orbits to obtain a trained deep neural network; and constructing a direct transfer optimization model between the special orbits of the earth-moon system, and carrying out iterative solution on the direct transfer optimization model by using a particle swarm algorithm and the trained deep neural network until an 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. According to the method, the optimal transfer pulse calculation and design between the special orbits of the earth-moon system are realized.

Description

Technical Field

[0001] The present invention relates to the technical field of designing 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 the only natural satellite of the Earth, the Moon has always been a hot topic in the field of deep space exploration. The demand for lunar resource exploration, verification of deep space probe communication capabilities, verification of deep space probe rendezvous and docking capabilities, and other tasks is increasing day by day, and the design of probe transfer orbits is one of the foundations for achieving the above goals. Among them, the special orbits of the Earth-Moon system such as the Halo orbit, NRHO orbit, and DRO provide convenience for the implementation of some space missions due to their special properties of spatial position and operation rules. How to quickly and efficiently complete the design of transfer orbits between special orbits has gradually 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 dynamics 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 dynamics model, the three-body problem has no analytical solution and the solution process relies on numerical integration. In view of the difficulty in solving the three-body problem and the large amount of calculation, the literature [1] proposed a quasi-linearization-local variational iteration method (QL-LVIM). Through the quasi-linearization idea, the nonlinear two-point boundary value problem is transformed into a series of initial value problems with a certain iteration 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 calculation efficiency depends on the initial estimated solution, which requires 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 of traditional numerical integration is heavily dependent on small integral steps and cannot meet the requirements of fast calculation of spacecraft on orbit. This algorithm can achieve large step-length high-speed calculation, 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 set and rational, the algorithm's large step-length 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 realized 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 transfer 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 a deep neural network, so as to solve the technical problems that the 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 under an Earth-Moon three-body model based on a deep neural network is proposed, comprising the following steps:

[0006] Step 1: Obtain a special track transfer training data set;

[0007] Step 2: construct a deep neural network and train the deep neural network according to the special 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 the trained deep neural network to iteratively solve the direct transfer optimization model 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.

[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 circular 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 of the starting orbit to any point of the target orbit, including position data and velocity data;

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

[0012] Step 13: Calculate the discrete data of the special orbit of the Earth-Moon system by traversal calculation method, and 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 minimization:

[0016] In the formula, ||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] In the formula, They respectively represent the off-orbit pulses leaving the starting orbit; They represent the pulses entering the target orbit; x c,i ,y c,i ,z c,iThey 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 of 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, They represent the three-axis velocities of the jth 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 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; 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 transfer training set between special orbits 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 plan as an output, wherein the optimal transfer plan 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 plan 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 iterating the above steps until the expected index or the maximum number of iterations is reached, and 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 an Earth-Moon three-body model is proposed, comprising:

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

[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 data set 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 use a particle swarm algorithm and a trained deep neural network to iteratively solve the optimization model 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.

[0026] Furthermore, the data acquisition module acquires the 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 circular 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 of the starting orbit to any point of the target orbit, including position data and velocity data;

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

[0029] Step 13: Calculate the discrete data of the special orbit of the Earth-Moon system by traversal calculation method, and 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 minimization:

[0033] In the formula, ||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] In the formula, They respectively represent the off-orbit pulses leaving the starting orbit; 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, They represent the three-axis velocities of the i-th data point of 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 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; 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 transfer training set between special orbits 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 plan as an output, wherein the optimal transfer plan 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 plan 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 iterating the above steps until the expected index or the maximum number of iterations is reached, and 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 an Earth-Moon three-body model based on a deep neural network. First, a special 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 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. It provides strong technical support for the rapid design of future lunar exploration mission orbits, 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 gives an algorithm for the transfer pulse scheme according to the state quantity of the transfer starting point, the state quantity of the transfer target point and the transfer time, which solves the problem that a large amount of computing resources are needed to solve the three-body Lambert problem using the traditional method; considering the strict requirements of the rapid design task on the solution efficiency, the computing power constraints of the onboard computer, etc., the present invention is based on the rapid design task requirements of the transfer orbit in the lunar exploration mission, and a certain degree of on-orbit real-time optimization requirements, using a calculation method with fast solution speed, small calculation amount and sufficiently high solution accuracy - a deep neural network (DNN) constructed based on deep learning; only enough training sets are needed to train the deep neural network to achieve the rapid calculation of the transfer orbit. The calculation method for the deep neural network used in the present invention for the transfer orbit design is optimized for the input and output respectively; wherein, the input is searched using intelligent algorithms such as particle swarm algorithm and genetic algorithm; the output optimization uses the deep neural network to solve the Lambert problem; the purpose of using less computing resources is achieved, and the transfer orbit between the special orbits of the earth and the moon is obtained under the premise of 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 rotation coordinate system of the center of mass of the earth-moon system in an embodiment of the present invention;

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

[0047] Figure 4 A schematic diagram of a libration point and a nearby special orbit in the earth-moon three-body system of the present invention;

[0048] Figure 5 is a mean square error variation curve diagram of the deep neural network training process in an embodiment of the present invention;

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

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

[0051] Figure 8 It is a comparison diagram of the evolution curve of iterative indicators solved by the embodiment of the present invention and the traditional sequential quadratic programming method and multi-point targeting method;

[0052] Fig. 9 This is an example diagram comparing the transfer orbits in the Earth-Moon system mass-center rotating coordinate system obtained by solving the embodiments 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 scheme of the present invention, exemplary implementations or embodiments of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described implementations or embodiments are only implementations or embodiments of a part of the present invention, not all of them. Based on the implementations or embodiments of the present invention, all other implementations or embodiments obtained by ordinary technicians in the field 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, such as Figure 1 As shown, the method comprises the following steps:

[0055] Step 1: Obtain a special track transfer training data set;

[0056] Step 2: construct a deep neural network and train the deep neural network according to the special 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 the trained deep neural network to iteratively solve the direct transfer optimization model 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.

[0058] The method starts with step one, in which a training data set for transfer between special orbits is obtained. Specifically, the training data set for transfer between special orbits is obtained according to the following process: first, the discrete data of the special orbit is calculated using a circular restricted three-body dynamics model; the discrete data of the special orbit is the transfer orbit data of different time lengths from any point of the starting orbit to any point of the target orbit, including position data and velocity data; then, the expected transfer time range is discretized to obtain a discrete transfer time; finally, the discrete data of the special orbit is calculated using a traversal calculation method to establish a training set for transfer between special orbits; the training set for transfer between special orbits includes a starting orbit data set and a target orbit data set. Specifically, the equation of the circular restricted three-body dynamics model (CRTBP model) is established in the Earth-Moon barycenter 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 calculated and saved to establish a special inter-orbit transfer data set, that is, a transfer training set between each orbit type is established; the starting orbit has p groups of data, the target orbit has q groups of data, and the time series has m groups of data, 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 the transfer orbit between the Earth-Moon special orbits, the relevant concepts are defined and the Earth-Moon mass center rotation coordinate system is established as follows:

[0060] Earth-Moon barycenter rotating coordinate system / reunion coordinate system: In the Earth-Moon three-body system, the 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 in 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] In the formula, x, y, z represent the position of the spacecraft in the three-body coordinate system; μ represents the mass ratio parameter of the two main celestial bodies; r1 and r2 represent the distances from the spacecraft to the two main celestial bodies. The initial orbit data set and the target orbit data set are obtained 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 of transfer time, T k Corresponding to a certain transfer time.

[0069] The circular restricted three-body problem dynamics model has five libration points, also called equilibrium points. There are also many special periodic solutions around the libration points and the main celestial body, which constitute the special periodic orbits and quasi-periodic orbits in the three-body model. Figure 4 The main special orbits are drawn in the figure, namely the large-value 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, which can be expressed by the following matrix:

[0071]

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

[0073] Considering that the transfer starting track has p discrete points, the target track has q discrete points, and the transfer time has m discrete points, we can construct p×q×m sets of training data sets 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 numbers of the starting orbit, target orbit and transfer time discrete point, respectively, and x c,i ,y c,i ,zc,i They 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 of the starting track respectively;

[0077] 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, They represent the three-axis velocities of the jth data point of the target track, t k Represents the kth discrete point of the 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] Among them, 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 the deep neural network is trained according to 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 the network is 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] The 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 speed of the starting point of the starting orbit transfer, the 6-dimensional variables of the three-axis position and speed 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. Depending on the complexity of the problem, the number of layers can be appropriately increased or decreased. 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 of the three-axis off-orbit pulse at the transfer starting point, and a 3-dimensional variable of 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, and a heavier penalty is imposed on larger errors to achieve a smaller allowable error and make the output accuracy of the model higher. 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 MaxEpochs for model training is set to 30, that is, the model uses the training set for 30 complete learnings; 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-batch 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'piecewise constant strategy 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, that 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, that is, after each of these iterations, 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 will be 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, step three is executed. In step three, an optimization model for direct transfer between special orbits of the Earth-Moon system is constructed: the direct transfer optimization model is iteratively solved 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 the iterative index curve and the transfer orbit under the Earth-Moon three-body model are obtained.

[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 iteratively solve until the expected index or the maximum number of iterations is reached, and an iterative index curve and a transfer trajectory under a three-body model are obtained; specifically, the following steps are used: using a 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 expected index or the maximum number of iterations is reached, and outputting an iterative index evolution curve and a transfer trajectory, such as Figure 6 , Figure 7 shown.

[0097] Then, the particle swarm optimization method is selected, and the transfer starting point, transfer target point and transfer time are used as the search volume. The corresponding three-body Lambert problem is established, and the deep neural network is used to solve the three-body Lambert problem. The transfer pulse and transfer trajectory data are output, and the optimization index of the particle swarm optimization is constructed using the transfer pulse; specifically, it includes:

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

[0099] Use the trained deep neural network to solve the pulse problem of the output quantity, take the input quantity as the known quantity, solve to obtain the corresponding pulse sequence, and use the pulse size or the amount of energy consumed (expressed as the sum of squares of pulses) as the optimization index;

[0100] The indicators are fed back to the particle swarm optimization input optimization problem, the transfer starting point, transfer target point and transfer time are searched again, and the pulse problem is solved using a deep neural network; the above steps are repeated repeatedly, and the indicators obtained in each round are compared to obtain the optimal transfer pulse and transfer orbit data.

[0101] According to the above method of this embodiment, the optimization problem is iteratively solved based on the particle swarm algorithm and the deep neural network algorithm until the expected 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, the corresponding Lambert problem under the three-body dynamics model is constructed respectively, and then the trained deep neural network is used to solve it to obtain the transfer pulse, and the sum of the transfer pulse sizes is used as the particle swarm algorithm 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 free variable left in the output optimization problem is the 6-dimensional pulse sequence Δv. Based on the states of the transfer start point and transfer target point and the transfer time obtained by the input optimization, the three-body Lambert problem is solved through the trained deep neural network to obtain the pulse sequence Δv.

[0110] The particle swarm algorithm is used to calculate the index of the pulses solved by the deep neural network, and the index is fed back to the input optimization problem. The particle swarm algorithm optimization mechanism is used to reselect points, and the iteration is repeated until the expected index or the maximum number of iterations is reached. The index iteration curve and discrete transfer orbit data are output. Finally, the optimal transfer pulse between special orbits of the Earth-Moon system is obtained.

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

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

[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 data set 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 use a particle swarm algorithm and a trained deep neural network to iteratively solve the optimization model 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.

[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 circular 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 of the starting orbit to any point of the target orbit, including position data and velocity data;

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

[0118] Step 13: Calculate the discrete data of the special orbit of the Earth-Moon system by traversal calculation method, and 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 minimization:

[0122] Constraints:

[0123] Where J1 represents the pulse optimum; J2 represents the energy optimum; ||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] In the formula, They respectively represent the off-orbit pulses leaving the starting orbit; 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, They represent the three-axis velocities of the i-th data point of 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, They represent the three-axis velocities of the jth 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 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; DNN represents the trained deep neural network.

[0128] The technical effect of the present invention is further verified through experiments.

[0129] The experiment takes 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 takes two-pulse direct transfer as an example, and the relevant parameters are selected and 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 calculation 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 , Fig. 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 the MATLAB version is 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 method, and it has obvious advantages in the rapid design of transfer trajectories.

[0139] It should be noted that the transfer trajectory curve obtained by the present invention is a preliminary design of the spacecraft before the actual flight mission, and is only applicable to the Earth-Moon three-body dynamics model. These trajectories can be used as nominal trajectories in actual control. When used specifically, mid-course corrections need to be made according to the actual flight situation.

[0140] Although the present invention has been described according to a limited number of embodiments, it will be apparent to those skilled in the art, with the benefit of the above description, that other embodiments can be envisioned within the scope of the invention thus described. The disclosure of the present invention is intended to be illustrative, not restrictive, and the scope of the present invention 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 track transfer training data set; Step 2: construct a deep neural network and train the deep neural network according to the special 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 use the particle swarm algorithm and the trained deep neural network to iteratively solve the direct transfer optimization model 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.

2. The orbit transfer method based on deep neural network under the Earth-Moon three-body model according to claim 1 is characterized in that: 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 circular 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 of the starting orbit to any point of the target orbit, including position data and velocity data; Step 1 and 2: discretize the expected transfer time range to obtain a discrete transfer time; Step 13: Calculate the discrete data of the special orbit of the Earth-Moon system by traversal calculation method, and 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.

3. The orbit transfer method based on deep neural network under the Earth-Moon three-body model according to claim 2 is characterized in that: 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 minimization: In the formula, ||Δv i ||2 represents the amplitude of the i-th pulse; n is the number of pulses; The lower layer optimization model is: Constraints: In the formula, They respectively represent the off-orbit pulses leaving the starting orbit; 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, They represent the three-axis velocities of the i-th data point of 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, They represent the three-axis velocities of the jth 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 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; DNN represents the trained deep neural network.

4. The orbit transfer method based on deep neural network under the Earth-Moon three-body model according to claim 3 is characterized in that: The iterative solution of the direct transfer optimization model based on the particle swarm algorithm and the trained deep neural network includes: taking the transfer training set between special orbits and the discrete transfer time as search conditions, optimizing and solving the upper optimization model by using the particle swarm algorithm, and calculating the optimal transfer plan as an output, wherein the optimal transfer plan 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 optimization model, inputting the optimal transfer plan output by the upper 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 optimization model, reselecting the point by using the particle swarm algorithm, and iterating the above steps until the expected index or the maximum number of iterations is reached, and obtaining the iterative index curve and the transfer orbit under the Earth-Moon three-body model.

5. The orbit transfer system under 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 data set; 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 data set to obtain a trained deep neural network; The model solving module is configured to construct an optimization model for direct transfer between special orbits of the Earth-Moon system, and use a particle swarm algorithm and a trained deep neural network to iteratively solve the optimization model 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.

6. The orbit transfer system based on deep neural network under the Earth-Moon three-body model according to claim 5 is characterized in that: 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 circular 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 of the starting orbit to any point of the target orbit, including position data and velocity data; Step 1 and 2: discretize the expected transfer time range to obtain a discrete transfer time; Step 13: Calculate the discrete data of the special orbit of the Earth-Moon system by traversal calculation method, and 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.

7. The orbit transfer system based on deep neural network under the Earth-Moon three-body model according to claim 6 is characterized in that: 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 minimization: In the formula, ||Δv i ||2 represents the amplitude of the i-th pulse; n is the number of pulses; The lower layer optimization model is: Constraints: In the formula, They respectively represent the off-orbit pulses leaving the starting orbit; 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, They represent the three-axis velocities of the i-th data point of 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, They represent the three-axis velocities of the jth 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 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; DNN represents the trained deep neural network.

8. The orbit transfer system based on deep neural network under the Earth-Moon three-body model according to claim 7 is characterized in that: The iterative solution of the direct transfer optimization model based on the particle swarm algorithm and the trained deep neural network includes: taking the transfer training set between special orbits and the discrete transfer time as search conditions, optimizing and solving the upper optimization model by using the particle swarm algorithm, and calculating the optimal transfer plan as an output, wherein the optimal transfer plan 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 optimization model, inputting the optimal transfer plan output by the upper 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 optimization model, reselecting the point by using the particle swarm algorithm, and iterating the above steps until the expected index or the maximum number of iterations is reached, and obtaining the iterative index curve and the transfer orbit under the Earth-Moon three-body model.

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