Method and system for low-thrust spacecraft trajectory optimization based on hybrid expert model

Abstract

The application provides a small-thrust spacecraft trajectory optimization method and system based on a hybrid expert model, and relates to the technical field of spacecraft trajectory optimization. The application designs and implements an intelligent fusion prediction architecture based on a gating network and a hybrid expert model. The architecture solves the problems of insufficient generalization ability and precision decline of existing single models when facing diversified tasks. Each expert network is trained as a characteristic network for processing a specific type of small-thrust trajectory transfer trajectory. In a multi-target rendezvous task scenario, the hybrid expert model can autonomously fuse the prediction results of each expert, and show high-stable and high-precision prediction results on any type of small-thrust transfer orbit. The robustness and generalization performance of the system prediction are far superior to those of existing single models.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of spacecraft trajectory optimization, in particular to a small-thrust spacecraft trajectory optimization method and system based on a hybrid expert model. BACKGROUND

[0002] Small-thrust spacecraft trajectory optimization is one of the core technologies of deep space exploration and on-orbit service multi-target rendezvous complex task design. Traditional small-thrust trajectory optimization methods mainly include indirect methods based on variational methods and direct methods that discretize the problem. Both of them can obtain optimal solutions and near-optimal solutions, but the calculation process involves solving complex nonlinear optimal control problems, which has problems such as long calculation time and sensitivity to initial values, making it difficult to meet the needs of complex multi-target rendezvous trajectory optimization. In addition, when dealing with complex space task design, researchers often only focus on the optimal time or optimal fuel consumption of small-thrust transfer, and spacecraft control sequences are often used to establish constraint conditions or objective functions, which do not need to be accurately solved at the early stage of task design, which also highlights the need for more efficient optimization technology.

[0003] In view of the limitations of traditional methods, deep learning technology has been introduced into the field of small-thrust spacecraft trajectory optimization. Existing technologies train a deep neural network (DNN) to establish an end-to-end mapping from task initial state (spacecraft position and velocity), end state (spacecraft position and velocity) and other features to optimal solution (such as optimal flight time or optimal fuel consumption). That is, the purpose of trajectory optimization is to solve the optimal fuel consumption and flight time solution. The deep learning-based method replaces the traditional method and directly predicts the trajectory optimization result without iterative solution. This method converts the time-consuming iterative optimization process into network forward propagation calculation, greatly improving the calculation speed and providing the possibility of quickly obtaining the optimization result.

[0004] However, the single deep neural network model used in existing technologies has obvious limitations, the main limitations of which are as follows: poor generalization ability, difficult to accurately represent the feature diversity of small-thrust transfer trajectory features. Due to the significant differences in the internal dynamics of small-thrust spacecraft trajectories, such as orbit plane change maneuvers and orbit energy elevation maneuvers, their optimal thrust strategies and state evolution laws are different. A single model uses a set of fixed network parameters to optimize all types of trajectories, which can lead to a decrease in prediction accuracy when facing tasks with significant feature differences, making it difficult to guarantee prediction accuracy and robustness in a wide range of task spaces. SUMMARY

[0005] (I) Technical problems solved

[0006] In view of the deficiencies of the prior art, the application provides a small-thrust spacecraft trajectory optimization method and system based on a hybrid expert model, and solves the technical problem that a single deep neural network model in the prior art cannot accurately represent the characteristics of a small-thrust transfer trajectory.

[0007] (Two) Technical solutions

[0008] To achieve the above object, the application is implemented by the following technical solutions:

[0009] In a first aspect, the application provides a small-thrust spacecraft trajectory optimization method based on a hybrid expert model, comprising:

[0010] Randomly initializing a departure orbit and a target orbit of a small-thrust transfer, and constructing a dynamics model including constraint conditions and an objective function; substituting the departure orbit and the target orbit into the dynamics model, and solving a small-thrust trajectory by a direct method or an indirect method to obtain a plurality of trajectory data as an initial training set;

[0011] Constructing basic features and high-dimensional features for a small-thrust trajectory; taking the basic features and the high-dimensional features as clustering features, and performing trajectory clustering on the small-thrust initial training set to form K a plurality of small-thrust transfer trajectory data subsets;

[0012] For each of the K small-thrust transfer trajectory data subsets, an expert network oriented to small-thrust trajectory prediction is constructed; K optimizing the structure of the expert network to determine an optimal hyperparameter combination of each expert network;

[0013] Constructing and training a gating network, and obtaining a hybrid expert model by fusing the trained gating network and the trained K expert networks, wherein the hybrid expert model is used for optimizing a small-thrust trajectory of a spacecraft.

[0014] Preferably, the objective function includes a shortest flight time or a minimum negative value of an instantaneous mass of a spacecraft at the end of a small-thrust orbit transfer.

[0015] Preferably, the basic features include: a change amount of classical orbit elements , an improved equinox orbit element change amount , a position and velocity of a spacecraft in a Cartesian coordinate system , a position of the spacecraft in a spherical coordinate system , a coordinate in a cylindrical coordinate system , an initial mass of the spacecraft , a mass at arrival , and a flight time .

[0016] Preferably, the high-dimensional feature includes: orbital energy variation. Angular momentum change Angle between angular momentum vectors In-plane and out-of-plane maneuverability coefficients and orbital phase coupling characteristics .

[0017] Preferably, the basic features and high-dimensional features are used as clustering features to perform trajectory clustering on the initial training set with low thrust, forming... K A small subset of thrust transfer trajectory data, including:

[0018] Based on the task scenario, select basic features that are appropriate for the task scenario from the basic features;

[0019] High-dimensional features and selected basic features constitute clustering features;

[0020] Using the DBSCAN algorithm, clustering features are used as task characteristics to perform unsupervised clustering of low-thrust trajectory data in the low-thrust trajectory dataset, forming... K A small subset of thrust transfer trajectory data.

[0021] Preferably, the step of optimizing the structure of the expert network to determine the optimal hyperparameter combination for each expert network includes:

[0022] The expert network parameters are optimized using a Bayesian optimizer to determine the hyperparameter configuration for each expert network, specifically including:

[0023] Construction phase:

[0024] Regarding the first k Hyperparameters to be optimized in an expert network and the range of values ​​for each of its hyperparameters Constructing the hyperparameter search space , This indicates the number of hyperparameters to be optimized. For indexing;

[0025] An evaluation function is constructed for a low-thrust trajectory optimization expert network to evaluate each set of sampled hyperparameters. The expression of the evaluation function includes:

[0026]

[0027] or,

[0028] in, These are the characteristic data of small thrust tests and the corresponding expert network prediction targets; Indicates the first k A network of experts; denotes the average relative error; denotes the root mean square error;

[0029] A Gaussian process model is constructed for sampling the optimal hyperparameter combination evaluation point in the search space of hyperparameters;

[0030] An acquisition function is constructed for calculating the next sampling point;

[0031] The deployment phase is executed:

[0032] The Bayesian optimizer checks the evaluation function of the expert network At the result of the initial hyperparameter sampling point , the Gaussian process model is initialized, the Gaussian process model is updated, and the posterior probability distribution of the evaluation function is obtained; the hyperparameter combination that maximizes the performance improvement of the acquisition function is searched , the expert network is constructed according to the structure parameters in , the training is performed according to the training parameters, and the true target function value is obtained, whether there is performance improvement is confirmed through the evaluation function of the expert network, and the optimal hyperparameter combination is updated ; the iterative optimization is continued until the preset evaluation step is reached, or the optimization is terminated in advance when the performance of the Gaussian process model is stagnant, and the optimal hyperparameter combination of each expert network is obtained.

[0033] Preferably, the constructed and trained gating network is fused with the trained K expert networks to obtain a hybrid expert model, including:

[0034] Gating network The output is layers containing outputs, and for a given input, the output is the weight , and after normalization, then:

[0035]

[0036] The expert model output prediction value is , and the final result of the gating network is weighted and fused according to the network allocation weight;

[0037] The training process of the gating network includes:

[0038] After freezing the weights and hyperparameters of the expert network neurons, the gating network parameters are trained and updated; the goal of training the gating network is to minimize the final prediction error of the entire expert hybrid model, and the loss function is the mean square error of the final prediction value output by the system and the true small thrust orbit transfer cost:

[0039]

[0040] in, The total loss of the system, ( ) is the mean square error function. For gated networks The generated first The weights of an expert network are parameters to be trained. For expert networks based on small thrust characteristics The output value; For small thrust trajectory The corresponding true value of the orbital maneuver cost;

[0041] During backpropagation in the training process, because all expert network parameters are frozen, gradient information is transmitted through... Transmitted to the gating network and update the network. The parameters are used to optimize the weights of the gating network for different low-thrust transfer trajectories.

[0042] Secondly, the present invention provides a trajectory optimization system for low-thrust spacecraft based on a hybrid expert model, comprising:

[0043] The training data generation module is used to randomly initialize the starting trajectory and target trajectory of the small thrust transfer, and construct a dynamic model including constraints and objective function; the starting trajectory and target trajectory are substituted into the dynamic model, and the small thrust trajectory is solved by direct or indirect methods to obtain a number of trajectory data as the initial training set;

[0044] The training data generation module is used to construct basic and high-dimensional features for low-thrust trajectories; using these basic and high-dimensional features as clustering features, it performs trajectory clustering on the initial low-thrust training set to form... K A small subset of thrust transfer trajectory data;

[0045] The expert network building module is used for... K A small subset of thrust transfer trajectory data is used to construct... K Expert networks for low-thrust trajectory prediction; structural optimization of the expert networks to determine the optimal hyperparameter combination for each expert network;

[0046] The hybrid expert model building module is used to build and train gating networks by fusing the trained gating network with the trained... K A hybrid expert model is obtained by using an expert network, which is used to optimize the low-thrust trajectory of a spacecraft.

[0047] In a third aspect, the present application provides a computer readable storage medium storing a computer program for small-thrust spacecraft trajectory optimization based on hybrid expert model, wherein the computer program causes a computer to perform the small-thrust spacecraft trajectory optimization based on hybrid expert model as described above.

[0048] In a fourth aspect, the present application provides an electronic device comprising:

[0049] one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the programs comprise a program for performing the small-thrust spacecraft trajectory optimization based on hybrid expert model as described above.

[0050] (Three) beneficial effects

[0051] The present application provides a small-thrust spacecraft trajectory optimization method and system based on a hybrid expert model. Compared with the prior art, the following beneficial effects are achieved:

[0052] The present application designs and implements an intelligent fusion prediction architecture based on a gating network and a hybrid expert model. The architecture solves the problem of insufficient generalization ability and precision decline of existing single global models when facing diversified tasks. Each expert network is trained to handle the characteristics of a specific type of small-thrust trajectory transfer trajectory. In multi-target rendezvous scenarios, the hybrid expert model can autonomously fuse the prediction results of each expert, and show high stability and high precision prediction results on any type of small-thrust transfer orbit. The robustness and generalization performance of the system prediction far exceed that of existing single models. BRIEF DESCRIPTION OF DRAWINGS

[0053] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0054] Figure 1 A block diagram of the small-thrust spacecraft trajectory optimization method based on hybrid expert model of the embodiments of the present application;

[0055] Figure 2 A flowchart of the small-thrust spacecraft trajectory optimization method based on hybrid expert model of the embodiments of the present application;

[0056] Figure 3 A schematic diagram of a multi-body rendezvous scenario;

[0057] Figure 4A comparison diagram of prediction effects of a single network and a hybrid expert network in a multi-body encounter mission. DETAILED DESCRIPTION

[0058] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application are described clearly and completely. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0059] The embodiments of the present application provide a small-thrust spacecraft trajectory optimization method and system based on a hybrid expert model, solve the technical problem that a single deep neural network model in the prior art cannot accurately represent the characteristics of small-thrust transfer trajectory features, and realize the technology of fusing multiple deep neural network models according to the characteristics of the input trajectory, which can improve the prediction accuracy of the optimal solution of the small-thrust trajectory in a multi-target task scenario.

[0060] The technical solutions in the embodiments of the present application are as follows to solve the above technical problems:

[0061] Small-thrust spacecraft trajectories have diverse characteristics, and their internal dynamics are significantly different. For example, the optimal thrust strategy and state evolution law of the maneuver mainly changing the orbital plane are different from those of the maneuver mainly raising the orbital energy. A single deep neural network model uses a set of fixed network parameters to optimize all types of small-thrust trajectories, which reduces the prediction accuracy of the model when facing tasks with large feature differences. The model cannot guarantee the prediction accuracy and robustness in a wide task space. If an improvement measure is taken to establish a deep network for optimal solution prediction for each type of small-thrust transfer trajectory to overcome this problem, a large number of deep networks need to be established, which requires a large amount of data and consumes a large amount of computing resources. At the same time, the trained model is difficult to completely cover all types of small-thrust transfer orbits, and how to introduce a new deep model fusion mechanism is one of the difficulties in training a limited number of deep network prediction models.

[0062] To solve the above problems, the embodiments of the present application provide a small-thrust spacecraft trajectory optimization method based on a hybrid expert model, which can fuse multiple deep neural network models according to the characteristics of the input trajectory, and improve the prediction accuracy and robustness of the optimal solution of the small-thrust trajectory in a multi-target task scenario.

[0063] In order to better understand the above technical solutions, the above technical solutions will be described in detail in combination with the drawings in the specification and specific embodiments.

[0064] The embodiment of the application provides a small-thrust spacecraft trajectory optimization method based on a hybrid expert model, as shown in the figure, comprising: Figure 1

[0065] S1, randomly initializing a departure orbit and a target orbit of small-thrust transfer, constructing a dynamic model comprising constraint conditions and a target function; substituting the departure orbit and the target orbit into the dynamic model, solving the small-thrust trajectory through a direct method or an indirect method, and obtaining a plurality of trajectory data as an initial training set;

[0066] S2, constructing basic features and high-dimensional features for small-thrust trajectories; taking the basic features and the high-dimensional features as clustering features, performing trajectory clustering on the small-thrust initial training set, and forming K a small-thrust transfer trajectory data subset;

[0067] S3, for the K small-thrust transfer trajectory data subset, constructing K an expert network for small-thrust trajectory prediction; performing structure optimization on the expert network, and determining an optimal hyperparameter combination of each expert network;

[0068] S4, constructing and training a gating network, and obtaining a hybrid expert model by fusing the trained gating network and the trained K expert network, wherein the hybrid expert model is used for optimizing a small-thrust trajectory of a spacecraft.

[0069] The small-thrust spacecraft trajectory optimization method based on the hybrid expert model will be described in detail below with reference to the flowchart as shown in the figure: Figure 2

[0070] In an embodiment, S1, randomly initializing a departure orbit and a target orbit of small-thrust transfer, constructing a dynamic model comprising constraint conditions and a target function; substituting the departure orbit and the target orbit into the dynamic model, solving the small-thrust trajectory through a direct method or an indirect method, and obtaining a plurality of feasible trajectory data as an initial training set. The specific implementation process is as follows:

[0071] S101, initializing a small-thrust transfer departure orbit and a target orbit. Specifically, it comprises:

[0072] In order to obtain a uniformly distributed small-thrust trajectory data set and make the physical meaning of random initialization clear, the orbit elements are used to describe the departure and target orbits. The epoch time is set to , and the orbit elements of the small-thrust spacecraft departure target and arrival target are randomly generated by using the following formula:

[0073]

[0074] ​​

[0075]

[0076]

[0077]

[0078]

[0079] wherein, is the semi-major axis, is the eccentricity, is the orbital inclination, is the longitude of the ascending node, is the argument of perigee, is the true anomaly, is the semi-major axis variation coefficient, is the eccentricity variation coefficient, represents a random number function that takes a random number in the interval . According to the six elements of the orbit, the positions and velocities of the spacecraft at the initial time and the arrival time in the inertial system are obtained , and are represented as vectors .

[0080] S102, construct a dynamic model including constraint conditions and objective functions. Specifically as follows:

[0081] The state vector and dynamic equation of the small-thrust spacecraft in the Cartesian inertial coordinate system are established. Specifically, it includes:

[0082] The state vector is:

[0083]

[0084] wherein, is the position vector of the spacecraft at the time ; is the velocity vector of the spacecraft at the time ; is the instantaneous mass of the spacecraft at the time .

[0085] The dynamic equation is:

[0086]

[0087] wherein, , , is the rate of change of the position, velocity and mass of the spacecraft with time; is the central celestial body gravitational constant, ​The distance from the spacecraft to the center of mass of the central celestial body, The maximum thrust of the spacecraft, The control vector of the spacecraft in the Cartesian coordinate system at the moment, The control vector of the spacecraft in the Cartesian coordinate system at the moment, ; The specific impulse of the engine of the spacecraft, The standard gravity acceleration.

[0088] An optimization objective function of a low-thrust spacecraft transfer orbit is established.

[0089] The target function minimizes the negative value of the instantaneous mass of the spacecraft at the moment when the low-thrust orbit transfer ends:

[0090]

[0091] The boundary conditions are used as constraint conditions, wherein the initial conditions are:

[0092] , ,

[0093] The terminal conditions are:

[0094] ,

[0095] S103, substitute the departure orbit and the target orbit into the dynamic model, and solve the low-thrust trajectory by using a direct method or an indirect method. Specifically, the method comprises the following steps:

[0096] In the embodiment of the application, the low-thrust trajectory is solved by using a direct method or an indirect method, such as a pseudospectral method in the indirect method. The pseudospectral method will be described in detail as follows. The specific process is as follows:

[0097] First, the Legendre-Gauss-Lobatto (LGL) collocation method is used to discretize the dynamic equation, the number of nodes is , the node index is , and n and j are also indexes, . The time is normalized according to the following formula, and is represented by the variable :

[0098]

[0099] The low-thrust spacecraft dynamic equation can be expressed as: ​

[0100]

[0101] Then, the state variables and are fitted as follows using Lagrange interpolation:

[0102]

[0103] where is the basis function, and the interpolation basis function and its derivative are:

[0104]

[0105] The system equation discretized by the pseudospectral method can be expressed as:

[0106]

[0107] where is the differential matrix, is the Legendre polynomial degree.

[0108] The fuel objective function discretized by the pseudospectral method is:

[0109]

[0110] The above process can be solved by the GPOPS solver to obtain the optimal trajectory.

[0111] Through the above method, a large amount of trajectory data is obtained as an initial training set.

[0112] In an embodiment, S2, the basic features and high-dimensional features of the small-thrust trajectory are constructed; the basic features and high-dimensional features are used as clustering features to perform trajectory clustering on the small-thrust initial training set to form K small-thrust transfer trajectory data subsets. The specific implementation process is as follows:

[0113] S201, according to the small-thrust trajectory data in the initial training set, the basic features of the small-thrust trajectory are constructed. Specifically, it includes:

[0114] The basic feature data of the small-thrust trajectory includes each feature data in the feasible trajectory data in the initial training set, specifically including: the classical orbit root change amount , the improved equinox orbit root change amount , the position and velocity of the spacecraft in the Cartesian coordinate system , the position of the spacecraft in the spherical coordinate system , the coordinates in the cylindrical coordinate system , etc. The corresponding ephemeris change amount can be calculated by the following formula 、 、 、 、 . Details are as follows:

[0115]

[0116] Note that the variable contains a positive or negative sign at this time, which contains small thrust trajectory transfer information, such as: inclination change in classical orbit elements If it is negative, it means that it is transferred from a low-inclination orbit to a high-inclination orbit, and vice versa if the inclination change If it is positive, it means that it is transferred from a high-inclination orbit to a low-inclination orbit.

[0117] At the same time, the initial mass of the spacecraft , the mass at the time of arrival , the flight time , etc. are set as small-thrust trajectory basic characteristic data.

[0118] S202, according to the small-thrust orbit basic characteristic data, construct high-dimensional features. Including:

[0119] The high-dimensional features include:

[0120] The two-pulse maneuver orbit velocity increment Can be calculated by solving Lambert's equation; the change in orbital energy is: ( ) The change in angular momentum is: ( ) .

[0121] The angle between the angular momentum vectors can be calculated by taking the dot product of the launch orbit angular momentum And the angular momentum of the target orbit :

[0122]

[0123] The in-plane and out-of-plane maneuver coefficients are used to describe whether the transfer orbit is mainly in the form of ascending and descending orbits in the orbital plane or mainly in the form of large-inclination orbit plane out-of-plane maneuver:

[0124]

[0125] Where, is the semi-major axis change before and after the orbit transfer, is the semi-major axis of the launch orbit, is the eccentricity change. For example The larger, the more obvious the inclination maneuver of the orbit, and vice versa.

[0126] Orbit phase coupling feature For non-circular orbit transfer, the departure and arrival phase greatly affect the orbit maneuver cost. The orbit phase coupling feature couples the change of orbit shape and the change of phase, and identifies the phase-sensitive orbit transfer (for example, using the low-speed area near the apogee to perform efficient plane maneuver).

[0127]

[0128] S203, using high-dimensional features and basic features as clustering features, trajectory clustering is performed on the initial training set to form a small-thrust transfer trajectory data subset. Specifically, it includes:

[0129] The DBSCAN algorithm is used to perform unsupervised clustering on the small-thrust trajectory data in the small-thrust trajectory data set. The purpose is to automatically divide a large number of heterogeneous trajectory data into several clusters with clear task characteristics according to their inherent physical and geometric similarity. According to the above description, the clustering features of any trajectory can be described as:

[0130]

[0131] It should be noted that in the specific implementation process, the basic features contained in the clustering features can be adjusted according to the actual situation, for example, 3 can be selected, or 4 can be selected. Can choose , or not .

[0132] The small-thrust trajectory data is z-score standardized, and the distance between any two small-thrust trajectories A and B is The Euclidean distance between two points, that is:

[0133]

[0134] Among them, the characteristics constructed by the embodiment of the application enable the clustering algorithm to perform unsupervised clustering on transfer trajectories with spatial similarity other than typical large inclination maneuvers, ascending and descending orbit maneuvers. For example, two trajectories that are If one is a pure inclination change and the other is accompanied by a large Ω change, the difference in dimension will significantly increase, so that they can be correctly identified as two different tasks in clustering. The introduction of high-dimensional features makes the Euclidean distance have physical connotation.

[0135] For a small-thrust trajectory, calculate the Euclidean distance between other trajectory features and the trajectory features, and count the center with a radius of the number of trajectories contained in the hypersphere of the trajectory A, such as no less than a threshold , the trajectory A is taken as a core point, and the density directness of the corresponding trajectory and the core point is determined.

[0136] By starting from any unvisited core point, DBSCAN can automatically and robustly find clusters of arbitrary shape in the data, and identify the singular trajectories in the sparse region that do not belong to any cluster as noise, thereby completing intelligent and adaptive clustering of complex low-thrust trajectory tasks, and obtaining K low-thrust transfer trajectory data subsets.

[0137] In an embodiment, S3, for K low-thrust transfer trajectory data subsets, constructs K expert networks for low-thrust trajectory prediction; and performs structural optimization on the expert networks to determine the optimal hyperparameter combination of each expert network. The specific implementation process is as follows:

[0138] For each low-thrust trajectory feature data set, an expert network is constructed. The base network of each expert network is constructed by a fully connected network, and the initial network contains hidden layers, each layer contains neurons, and the activation function is .

[0139] In the optimization training process, the expert network for low-thrust trajectory prediction is trained through each low-thrust trajectory data subset . Each expert network predicts the optimal low-thrust orbit trajectory and transfer cost (for example: time, fuel, energy) according to the input low-thrust orbit maneuver features.

[0140] The trajectory features for low-thrust orbit transfer cost prediction are as follows:

[0141]

[0142] The input feature data of the expert network includes basic features and high-dimensional features, wherein the basic features include: the change amount of the classical orbit element , the change amount of the improved equinox orbit element , the initial mass of the spacecraft , the flight time , the high-dimensional features: the orbit velocity increment of the double-impulse maneuver , the change of the orbit energy is ; the change of the angular momentum is .

[0143] The label data in the expert network training process is the final mass of the spacecraft after the low-thrust orbit transfer is completed Of course, in the specific implementation process, the time optimization can also be considered, and the shortest flight time is taken as the optimization target, and accordingly, the shortest flight time is taken as the tag data.

[0144] Since different expert networks learn different small-thrust trajectory feature network structures (such as network depth, width, layer type, activation function, etc.) and training parameters required for the network structure and the training parameters are quite different, parameter optimization must be performed for each expert network. In the embodiment of the present application, in order to cope with the huge search space and various types of optimizable parameters (continuous, integer, and category), the expert network parameters are optimized by a Bayesian optimizer. The structure of each expert network and the training related hyperparameter configuration are determined. Bayesian optimization is a sequence-based optimization technique that can intelligently configure parameters to find the optimal solution in the fewest steps based on the training history. The steps of constructing and using the Bayesian optimizer for the small-thrust orbit optimization expert network are as follows:

[0145] Construction stage:

[0146] First, the hyperparameter search space to be optimized is constructed: for the first k expert network to be optimized and the value range of each hyperparameter , the hyperparameter search space is constructed, represents the number of hyperparameters to be optimized, is the index, and the hyperparameters include all parameters.

[0147] Second, the evaluation function of the small-thrust orbit optimization expert network is constructed: for each set of sampled hyperparameters, an expert network is constructed for testing, and the optimization target of the hyperparameters is the average relative error ( MRE ) or the root mean square error ( RMSE ). The essence of hyperparameter optimization is to find the configuration that can minimize the objective function. The evaluation function of the expert network is as follows:

[0148]

[0149] wherein are the small-thrust test feature data and the corresponding expert network prediction target, respectively. To ensure randomness of the test, the test set is not selected from a fixed set but is randomly selected from a larger test data pool each time.

[0150] Third, the surrogate model is constructed to sample the optimal hyperparameter combination evaluation point in the search space of the hyperparameters. The embodiment of the present application adopts a Gaussian process model. The Gaussian process can predict the performance of unknown points based on existing observation points and give the uncertainty of the prediction.

[0151] Finally, the acquisition function is constructed. This embodiment of the invention uses the Expected Improvement (EI) function. It utilizes the predicted mean and uncertainty of the surrogate model to calculate how much improvement is expected compared to the current optimal solution when sampling again at a certain point.

[0152] Execution and deployment phase:

[0153] Bayesian optimizer tests the evaluation function of expert network At the initial hyperparameter sampling point The results are processed, the Gaussian process model is initialized, the GP model is updated, and the evaluation function is obtained. The posterior probability distribution. Searching for hyperparameter combinations that maximize the performance improvement of the acquisition function. ,in accordance with The structural parameters are used to construct an expert network, which is then trained based on the training parameters. The true objective function value is obtained, and the evaluation function of the expert network is used to confirm whether there is a performance improvement, and the optimal hyperparameter combination is updated. The optimization process continues iteratively until a preset number of evaluation steps is reached, or the optimization is terminated early when the model performance stagnates, thereby obtaining the optimal hyperparameter combination for each expert network.

[0154] In one embodiment, S4, construct and train a gating network, by fusing the trained gating network with the trained... K A hybrid expert model is obtained by using multiple expert networks. The specific implementation process is as follows:

[0155] This step involves designing a gating network, adjusting the prediction proportions of each expert network through network weights, and designing an expert network evolution strategy. Details are as follows:

[0156] The gating network receives the same input as the expert network. For high-dimensional features of low-thrust trajectories, the gating network determines the proportion of predictions from each expert network that are adopted. The output contains Each output A layer, for a given input, outputs weights. After normalization, we get:

[0157]

[0158] The expert model outputs the predicted value. The final result of the gated network is weighted and fused according to the weights assigned to the network.

[0159] The training process for the gating network is as follows:

[0160] A phased, constrained training strategy is adopted.

[0161] The expert network trained in step S3 is functionally preserved by freezing the weights of the expert network neurons. The expert network is only used as an evaluator for the weight allocation of the gating network, and the weights are not updated during backpropagation.

[0162] After freezing the weights and hyperparameters of the expert network neurons, training and updating the gating network parameters begins. The goal of training the gating network is to minimize the final prediction error of the entire expert mixture model, with the loss function... The mean squared error between the final predicted value output by the system and the actual cost of the low-thrust trajectory transfer:

[0163]

[0164] in, The total loss of the system, ( ) is the mean square error function. For gated networks The generated first The weights of an expert network are parameters to be trained. For expert networks based on small thrust characteristics The output value; For small thrust trajectory The actual value of the corresponding orbital maneuver cost.

[0165] During backpropagation in the training process, because all expert network parameters are frozen, gradient information is transmitted through... Transmitted to the gating network and update the network. The parameters are used to optimize the weights of the gating network for different low-thrust transfer trajectories.

[0166] Because the training and update process requires frequent freezing and updating of network parameters, resulting in high computational costs, real-time update methods are not suitable. In practice, end-to-end network fine-tuning is only performed when a sufficient amount of update data is collected and the triggering conditions are met. During the processing of batches of small-thrust trajectory training data, the loss in the expert network's prediction of the current batch of data is recorded. Simultaneously, a sampled dataset is obtained from the low-thrust trajectory database, and the loss of the current expert network on the sampled dataset is calculated. .like Calculate the rate of increase in prediction error:

[0167]

[0168] If the ratio Above the threshold If the difference is large, it is considered that the new data contains a small-thrust orbit maneuver type. The online learning process is triggered, the new and old data are mixed, the data are re-clustered and fused, the specific expert network weight is unfrozen and trained, and the network parameters are updated. If the degree of decline is low, end-to-end fine-tuning update is adopted, that is, the expert network is not retrained separately using a large amount of data, but end-to-end training is performed on the batch data, and the network parameters are fine-tuned using a small amount of data.

[0169] The effectiveness of the embodiment of the application is verified by specific data as follows:

[0170] 1. Small-thrust trajectory data generation. According to step S1, a small-thrust transfer task is simulated by randomly initializing a “departure orbit-target orbit” pair, wherein the semi-major axis a is , the eccentricity e is , the orbit inclination i is , the range is 0-0.5, the orbit inclination i is , the range is 0-30°, the ascending node right ascension Ω is , the perigee pitch angle ω is , and the true anomaly f is , which is randomly taken.

[0171] 2. The pseudo-spectral method is used to solve the fuel optimal problem for the randomly generated task. It is assumed that the central celestial body is the sun, the gravitational constant is , the initial mass of the spacecraft is , wherein the dry weight is , the small-thrust mode is adopted, the maximum thrust is , the engine specific impulse is , and the flight time is randomly selected in the range of [30, 6*365] days.

[0172] 3. Trajectory optimization problem modeling. The corresponding constraints and optimization objectives are constructed, and the fuel optimization is the optimization objective in this example. GPOPS-II and other software are used for solving, and if there is a convergent solution, the following small-thrust transfer orbit information is saved: task start time, end time, spacecraft orbit at the start time, spacecraft orbit at the end time, spacecraft mass at the start time, spacecraft mass at the interpretation time, impulse thrust velocity increment required for transfer, and at least 200,000 groups of feasible trajectory data are saved as an initial training set.

[0173] 4. After obtaining the initial training set, the clustering features are constructed:

[0174]

[0175] , wherein is the initial mass of the spacecraft, is the classical orbit root change amount, ​To improve the variation of equinox orbit elements, To improve the variation of equinox orbit elements, To improve the variation of equinox orbit elements, To improve the variation of equinox orbit elements, To improve the variation of equinox orbit elements, To improve the variation of equinox orbit elements. All features are standardized by Z-score. Run DBSCAN clustering to obtain small-thrust transfer trajectory subsets , and noise data sets .

[0176] The data volume in this verification process is large, and the density direct point threshold is calculated, The small-thrust trajectory data dimension used for clustering is Set the radius to k - distance method to obtain k After obtaining the distance map data points, the best value is obtained by calculating the L-shaped curve inflection point. The inflection point represents the demarcation line from the sparse trajectory data noise area to the dense trajectory data cluster area. Finally, several small-thrust trajectory data clusters are formed:

[0177]

[0178] In the embodiment, 5 small-thrust trajectory training data subsets are obtained, and each core point represents a typical feasible small-thrust trajectory transfer domain. Cluster data may represent: small-thrust orbit transfer starting from GTO, inclination reduced by about 10°, perigee raised; orbit climbing / energy dominant small-thrust transfer ( greater, smaller); large-plane maneuver dominant transfer ( greater); orbit shape / phase dominant transfer ( greater). Among them, Noise points represent atypical small-thrust transfer trajectories. For example, an orbit transfer with a super-large inclination, when the phase angle, flight time, spacecraft mass, and other numerical values satisfy the specific initial conditions, there exists a feasible trajectory solution that satisfies all constraints, but the characteristic distribution of such small-thrust trajectories is relatively sparse. The noise data set can also be explained as a small-thrust transfer trajectory without obvious features. In engineering, a noise data expert network is not designed separately, and a general trajectory expert network is obtained using all data to process data divided into noise.

[0179] 5. For the small-thrust data set established, a Bayesian optimization hyperparameter space is constructed. The parameters to be optimized include feature combination, network layer number , and neuron number ; activation function ; learning rate ; exponential decay rate hyperparameter for first moment estimate ; exponential decay rate hyperparameter for second moment estimate , etc.

[0180] 6. Hybrid expert model construction and training based on gating network. The gating network is set as follows: [12, 16, 5] fully connected layer group, and the last layer is a Softmax output layer. In the training process of the gating network, the output of the multi-expert network trained in step 6 is taken, the weight is regulated by the output layer of the gating network, and the final output is the weighted sum of each expert . The loss function is calculated therefrom, and the gating network parameters are updated. In the updating process, the parameters of the five expert networks are frozen and unchanged, and the Adam optimizer is used to train the gating network.

[0181] 7. Multi-target rendezvous scenarios are constructed, and the differences in prediction results between the hybrid expert model of the embodiment of the application and the conventional single network are compared. The multi-target rendezvous scenario is designed as shown in Figure 3 . The spacecraft is launched from the Earth, the initial mass is 2800 kg, the specific impulse is 4000 s, the maximum thrust is 300 , visits multiple space targets, and returns to the Earth. The target orbit parameters are shown in Table 1:

[0182] Table 1 Target Orbit Parameters

[0183]

[0184] In the multi-body rendezvous mission design, the spacecraft mass has cumulative errors, that is, the spacecraft fuel consumption error at the previous time will be reflected in the initial value of the spacecraft mass in the next stage transfer, and will be propagated and amplified in the multi-target rendezvous access sequence. In this example, a total of 5 space targets are visited, and the spacecraft returns to the Earth, involving six low-thrust transfer orbits. The average relative error of the spacecraft mass prediction of the six tasks decreases from 7.7% to 2.1%, and after the last low-thrust orbit transfer to return to the Earth, the cumulative spacecraft mass prediction relative error decreases from 16.6% to 3.7%. See Figure 4 for specific information. It can be seen that the hybrid expert network system model effectively improves the prediction accuracy in complex multi-body rendezvous tasks.

[0185] The embodiment of the application provides a low-thrust spacecraft trajectory optimization system based on a hybrid expert model, which comprises:

[0186] The training data generation module is configured to randomly initialize a departure orbit and a target orbit of small-thrust transfer, and construct a dynamic model including constraint conditions and an objective function; the departure orbit and the target orbit are substituted into the dynamic model, and a small-thrust trajectory is solved by a direct method or an indirect method to obtain a plurality of trajectory data as an initial training set;

[0187] The training data generation module is configured to construct basic features and high-dimensional features for the small-thrust trajectory; the basic features and the high-dimensional features are used as clustering features to perform trajectory clustering on the small-thrust initial training set, and form K a plurality of small-thrust transfer trajectory data subsets;

[0188] The expert network construction module is configured to construct K a plurality of small-thrust transfer trajectory data subsets, and construct K an expert network for small-thrust trajectory prediction; the expert network is subjected to structure optimization to determine an optimal hyperparameter combination of each expert network;

[0189] The hybrid expert model construction module is configured to construct and train a gating network, and obtain a hybrid expert model by fusing the trained gating network and the trained K a plurality of expert networks, the hybrid expert model being used for optimizing a small-thrust trajectory of a spacecraft.

[0190] The embodiment of the present application also provides a computer readable storage medium storing a computer program for small-thrust spacecraft trajectory optimization based on a hybrid expert model, wherein the computer program causes a computer to execute the small-thrust spacecraft trajectory optimization method based on the hybrid expert model.

[0191] The embodiment of the present application also provides an electronic device, including one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the program includes a small-thrust spacecraft trajectory optimization method based on a hybrid expert model.

[0192] Compared with the prior art, the embodiment of the present application has the following beneficial effects:

[0193] 1. The embodiment of the present application improves the prediction accuracy and generalization performance of small-thrust trajectory optimization by designing a hybrid expert prediction architecture based on gated network regulation. In detail, the embodiment of the present application designs and implements an intelligent fusion prediction architecture based on gated network and hybrid expert model. The architecture solves the problem of insufficient generalization ability and precision decline of existing single model when facing diversified tasks. In the embodiment of the present application, each expert network is trained to process the characteristics of a special small-thrust trajectory transfer trajectory. Due to the high correlation of its training data, the optimal network structure and hyperparameters must differ. The parallel Bayesian optimization algorithm introduced in the present application optimizes the expert network structure and training parameters, and the expert network can learn more in-depth and detailed nonlinear mapping relationships than single models. For example, a certain expert may have strong prediction ability for the coupling relationship between orbit phase and thrust direction, which is difficult for single models to consider. By innovatively introducing a gating network, a dynamic fusion mechanism is realized, ensuring that the final output of the system is always dominated by the most relevant expert, effectively improving the prediction accuracy of the embodiment of the present application. In the multi-target rendezvous task scenario, the hybrid expert model can autonomously fuse the prediction results of each expert, and show high stability and high precision prediction results on any type of small-thrust transfer trajectory. The robustness and generalization performance of the system prediction far exceed that of existing single models.

[0194] 2. The embodiment of the present application realizes effective decoupling and dimensionality reduction of complex optimization problems by constructing a small-thrust trajectory clustering technology based on unsupervised clustering, laying a foundation for high-precision prediction. In detail, the embodiment of the present application innovatively proposes and applies a small-thrust trajectory high-dimensional feature space clustering technology based on DBSCAN, changing the problem solving paradigm. Through feature engineering, a high-dimensional feature space reflecting the physical properties of the trajectory is innovatively constructed, including orbit geometric changes, dynamic energy, in-plane and out-of-plane maneuver ratio, and phase coupling characteristics. Using the density-based clustering characteristics of the DBSCAN algorithm, the embodiment of the present application can automatically discover natural communities in high-dimensional data without pre-setting the number of categories. The complex high-dimensional nonlinear global optimization problem is decomposed into several relatively simple sub-problems with highly consistent internal characteristics; for example, all "large inclination, low energy" plane maneuver tasks are classified into one category, and all "high energy, near coplanar" orbit climbing tasks are classified into another category. Using the divide-and-conquer strategy, the learning difficulty of the subsequent single expert network is reduced.

[0195] 3、The track clustering strategy based on DBSCAN designed in the embodiment of the application can identify clusters of arbitrary shapes, and can effectively identify noise points, i.e., atypical small-thrust track not belonging to any mainstream category, and process by using a general model, thereby significantly enhancing the robustness of the entire system. Ultimately, the intelligent clustering based on physical characteristics provides a dedicated training set for each subsequent expert network, and provides a solid foundation for the implementation of a hybrid expert model.

[0196] It should be noted that the relational terms herein such as first and second and the like are used solely to distinguish one entity or action from another, without necessarily requiring or implying any such actual relationship or order between such entities or actions. Moreover, the terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element preceded by "comprises... a" does not, without more constraints, foreclose the existence of additional identical elements in the process, method, article, or apparatus that comprises the recited element.

[0197] The above embodiments are only used to illustrate the technical solutions of the present application, rather than limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacements for some technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A trajectory optimization method for low-thrust spacecraft based on a hybrid expert model, characterized in that, include: The starting and target trajectories for the small thrust transfer are randomly initialized, and a dynamic model including constraints and objective functions is constructed. The starting and target trajectories are substituted into the dynamic model, and the small thrust trajectory is solved by direct or indirect methods to obtain several trajectory data as an initial training set. Construct basic and high-dimensional features for low-thrust trajectories; use these features as clustering features to perform trajectory clustering on the initial low-thrust training set, forming... K A small subset of thrust transfer trajectory data; against K A small subset of thrust transfer trajectory data is used to construct... K Expert networks for low-thrust trajectory prediction; structural optimization of the expert networks to determine the optimal hyperparameter combination for each expert network; Construct and train a gating network, and then fuse the trained gating network with the trained... K A hybrid expert model is obtained by using an expert network, which is used to optimize the low-thrust trajectory of a spacecraft. The process of optimizing the expert network structure to determine the optimal hyperparameter combination for each expert network includes: The expert network parameters are optimized using a Bayesian optimizer to determine the hyperparameter configuration for each expert network, specifically including: Construction phase: Regarding the first k Hyperparameters to be optimized in an expert network and the range of values ​​for each of its hyperparameters Constructing the hyperparameter search space , This indicates the number of hyperparameters to be optimized. For indexing; An evaluation function is constructed for a low-thrust trajectory optimization expert network to evaluate each set of sampled hyperparameters. The expression of the evaluation function includes: or, in, These are the characteristic data of small thrust tests and the corresponding expert network prediction targets; Indicates the first k A network of experts; Indicates the average relative error; Indicates the root mean square error; A Gaussian process model is constructed to sample the optimal hyperparameter combination evaluation point in the hyperparameter search space; Construct a sampling expectation boost function to calculate the next sampling point; Execution and deployment phase: Bayesian optimizer tests the evaluation function of expert network At the initial hyperparameter sampling point The results are processed, and the Gaussian process model is initialized, updated, and the evaluation function is obtained. The posterior probability distribution; searching for hyperparameter combinations that maximize the performance improvement of the acquisition function. ,in accordance with The structural parameters are used to construct an expert network, which is then trained based on the training parameters. The true objective function value is obtained, and the evaluation function of the expert network is used to confirm whether there is a performance improvement, and the optimal hyperparameter combination is updated. ; Continue iterative optimization until the preset number of evaluation steps is reached, or terminate the optimization early when the performance of the Gaussian process model stagnates, to obtain the optimal hyperparameter combination for each expert network.

2. The trajectory optimization method for low-thrust spacecraft based on a hybrid expert model as described in claim 1, characterized in that, The objective function includes minimizing the shortest flight time or minimizing the negative value of the instantaneous mass of the spacecraft at the end of the low-thrust orbital transfer.

3. The trajectory optimization method for low-thrust spacecraft based on a hybrid expert model as described in claim 1, characterized in that, The fundamental features include: the variation of classical orbital elements. Improved change in orbital elements at the vernal equinox The spacecraft's position and velocity in the Cartesian coordinate system The position of the spacecraft in spherical coordinates Coordinates in cylindrical coordinate system Initial mass of spacecraft Quality upon arrival and flight time .

4. The trajectory optimization method for low-thrust spacecraft based on a hybrid expert model as described in claim 3, characterized in that, The high-dimensional features include: orbital energy variation. Angular momentum change Angle between angular momentum vectors In-plane and out-of-plane maneuverability coefficients and orbital phase coupling characteristics .

5. The trajectory optimization method for low-thrust spacecraft based on a hybrid expert model as described in claim 4, characterized in that, The method uses basic features and high-dimensional features as clustering features. Trajectory clustering is performed on the initial training set with low thrust to form K A small subset of thrust transfer trajectory data, including: Based on the task scenario, select basic features that are appropriate for the task scenario from the basic features; High-dimensional features and selected basic features constitute clustering features; Using the DBSCAN algorithm, clustering features are used as task characteristics to perform unsupervised clustering of low-thrust trajectory data in the low-thrust trajectory dataset, forming... K A small subset of thrust transfer trajectory data.

6. The trajectory optimization method for low-thrust spacecraft based on a hybrid expert model as described in any one of claims 1 to 5, characterized in that, The construction and training of the gating network involves fusing the pre-trained gating network with the pre-trained... K A network of experts is used to obtain a hybrid expert model, including: Gated networks The output contains Each output A layer, for a given input, outputs weights. After normalization, we get: The expert model outputs the predicted value. The final results of the gated network are weighted and fused according to the network's assigned weights; The training process of a gating network includes: After freezing the weights and hyperparameters of the expert network neurons, training and updating the gating network parameters begins. The goal of training the gating network is to minimize the final prediction error of the entire expert mixture model, with the loss function... The mean squared error between the final predicted value output by the system and the actual cost of the low-thrust trajectory transfer: in, The total loss of the system, ( ) is the mean square error function. For gated networks The generated first The weights of an expert network are parameters to be trained. For expert networks based on small thrust characteristics The output value; For small thrust trajectory The corresponding true value of the orbital maneuver cost; During backpropagation in the training process, because all expert network parameters are frozen, gradient information is transmitted through... Transmitted to the gating network and update the network. The parameters are used to optimize the weights of the gating network for different low-thrust transfer trajectories.

7. A trajectory optimization system for low-thrust spacecraft based on a hybrid expert model, characterized in that, include: The training data generation module is used to randomly initialize the starting trajectory and target trajectory of the small thrust transfer, and construct a dynamic model including constraints and objective function; the starting trajectory and target trajectory are substituted into the dynamic model, and the small thrust trajectory is solved by direct or indirect methods to obtain a number of trajectory data as the initial training set; The training data generation module is used to construct basic and high-dimensional features for low-thrust trajectories; using these basic and high-dimensional features as clustering features, it performs trajectory clustering on the initial low-thrust training set to form... K A small subset of thrust transfer trajectory data; The expert network building module is used for... K A small subset of thrust transfer trajectory data is used to construct... K Expert networks for low-thrust trajectory prediction; structural optimization of the expert networks to determine the optimal hyperparameter combination for each expert network; The hybrid expert model building module is used to build and train gating networks by fusing the trained gating network with the trained... K A hybrid expert model is obtained by using an expert network, which is used to optimize the low-thrust trajectory of a spacecraft. The process of optimizing the expert network structure to determine the optimal hyperparameter combination for each expert network includes: The expert network parameters are optimized using a Bayesian optimizer to determine the hyperparameter configuration for each expert network, specifically including: Construction phase: Regarding the first k Hyperparameters to be optimized in an expert network and the range of values ​​for each of its hyperparameters Constructing the hyperparameter search space , This indicates the number of hyperparameters to be optimized. For indexing; An evaluation function is constructed for a low-thrust trajectory optimization expert network to evaluate each set of sampled hyperparameters. The expression of the evaluation function includes: or, in, These are the characteristic data of small thrust tests and the corresponding expert network prediction targets; Indicates the first k A network of experts; Indicates the average relative error; Indicates the root mean square error; A Gaussian process model is constructed to sample the optimal hyperparameter combination evaluation point in the hyperparameter search space; Construct a sampling expectation boost function to calculate the next sampling point; Execution and deployment phase: Bayesian optimizer tests the evaluation function of expert network At the initial hyperparameter sampling point The results are processed, and the Gaussian process model is initialized, updated, and the evaluation function is obtained. The posterior probability distribution; searching for hyperparameter combinations that maximize the performance improvement of the acquisition function. ,in accordance with The structural parameters are used to construct an expert network, which is then trained based on the training parameters. The true objective function value is obtained, and the evaluation function of the expert network is used to confirm whether there is a performance improvement, and the optimal hyperparameter combination is updated. ; Continue iterative optimization until the preset number of evaluation steps is reached, or terminate the optimization early when the performance of the Gaussian process model stagnates, to obtain the optimal hyperparameter combination for each expert network.

8. A computer-readable storage medium, characterized in that, It stores a computer program for optimizing the trajectory of a low-thrust spacecraft based on a hybrid expert model, wherein the computer program causes a computer to execute the low-thrust spacecraft trajectory optimization method based on a hybrid expert model as described in any one of claims 1 to 6.

9. An electronic device, characterized in that, include: One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs including methods for performing low-thrust spacecraft trajectory optimization based on a hybrid expert model as described in any one of claims 1 to 6.

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