Small-thrust spacecraft trajectory optimization method and system based on hybrid expert model

Abstract

The invention provides a low-thrust spacecraft trajectory optimization method and system based on a hybrid expert model, and relates to the technical field of spacecraft trajectory optimization. According to the invention, a set of intelligent fusion prediction architecture based on the gating network and the hybrid expert model is designed and realized. The architecture solves the problems that the generalization ability is insufficient and the precision is reduced when an existing single model faces diversified tasks. Each expert network is trained as a characteristic network for processing a special type of low-thrust trajectory transfer trajectory. In a scene requiring a multi-target rendezvous task, the hybrid expert model can autonomously fuse prediction results of all experts, a high-stability and high-precision prediction result is shown on any type of low-thrust transfer orbit, and the robustness and generalization performance of system prediction are far better than those of an existing single model.

Description

Technical Field

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

[0002] Spacecraft low-thrust trajectory optimization is one of the core technologies for the design of complex multi-target rendezvous missions for deep space exploration and on-orbit servicing. Traditional low-thrust trajectory optimization methods mainly include indirect methods based on the calculus of variations and direct methods that discretize the problem. These two methods can obtain optimal solutions and near-optimal solutions, but their calculation process involves solving complex nonlinear optimal control problems, which have problems such as long solution time and sensitivity to initial values, making it difficult to meet the requirements of complex multi-target rendezvous trajectory optimization. In addition, when dealing with complex space mission designs, researchers often only focus on the optimal time or optimal fuel consumption of low-thrust transfer. Spacecraft control sequences are often used to establish constraints or objective functions, and accurate solutions are usually not required in the early stages of mission design. This also highlights the need for more efficient optimization technologies.

[0003] Given the limitations of traditional methods, deep learning technology has been introduced to the field of low-thrust spacecraft trajectory optimization. Existing techniques train a deep neural network (DNN) to establish an end-to-end mapping from features such as the mission's initial state (spacecraft position and velocity) and final state (spacecraft position and velocity) to an optimal solution (such as optimal flight time or optimal fuel consumption). The goal of trajectory optimization is to find the optimal solution for fuel consumption and flight time. Deep learning-based methods replace traditional methods by directly predicting trajectory optimization results rather than iterating. This approach transforms the traditional, time-consuming iterative optimization process into a network forward propagation calculation, significantly improving computational speed and enabling rapid optimization results.

[0004] However, the single deep neural network model used in existing technologies has significant limitations, primarily due to its poor generalization ability and difficulty accurately characterizing the diverse characteristics of low-thrust transfer trajectories. Because the inherent dynamic characteristics of low-thrust spacecraft trajectories vary significantly, for example, maneuvers primarily focused on changing the orbital plane and those primarily focused on increasing orbital energy have different optimal thrust strategies and state evolution patterns. A single model optimizing all trajectory types with a fixed set of network parameters results in reduced prediction accuracy for missions with widely varying characteristics, making it difficult to ensure prediction accuracy and robustness across a wide range of missions. Summary of the Invention

[0005] (1) Technical problems solved In response to the shortcomings of the existing technology, the present invention provides a low-thrust spacecraft trajectory optimization method and system based on a hybrid expert model, which solves the technical problem that the single deep neural network model used in the existing technology is difficult to accurately characterize the characteristics of the small-thrust transfer trajectory with diverse features.

[0006] (2) Technical solution To achieve the above objectives, the present invention is implemented through the following technical solutions: In a first aspect, the present invention provides a low-thrust spacecraft trajectory optimization method based on a hybrid expert model, comprising: The starting and target trajectories for low-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 low-thrust trajectory is solved using direct or indirect methods to obtain several trajectory data as the initial training set. Construct basic features and high-dimensional features for small thrust trajectories; use basic features and high-dimensional features as clustering features to cluster the trajectories of the small thrust initial training set to form K A small subset of thrust transfer trajectory data; against K A small subset of thrust transfer trajectory data is constructed K Expert networks for low-thrust trajectory prediction; structural optimization of expert networks to determine the optimal hyperparameter combination for each expert network; Build and train the gated network by fusing the trained gated network with the trained K An expert network is constructed to obtain a hybrid expert model, which is used to optimize the low-thrust trajectory of the spacecraft.

[0007] Preferably, the objective function includes minimizing the negative value of the instantaneous mass of the spacecraft at the end of the low-thrust orbit transfer or minimizing the shortest flight time.

[0008] Preferably, the basic characteristics include: the variation of the number of classical orbital elements , Improve the change of the orbital elements of the vernal equinox , the position and velocity of the spacecraft in the Cartesian coordinate system , the position of the spacecraft in the spherical coordinate system , Coordinates in cylindrical coordinate system , spacecraft initial mass , quality upon arrival and flight time .

[0009] Preferably, the high-dimensional features include: orbital energy changes , angular momentum change 、Angular momentum vector angle , in-plane and out-of-plane maneuverability coefficients and orbital phase coupling characteristics .

[0010] Preferably, the basic features and high-dimensional features are used as clustering features to cluster the trajectory of the small thrust initial training set to form K A small subset of thrust transfer trajectory data, including: According to the task scenario, select basic features that are suitable for the task scenario from the basic features; High-dimensional features and selected basic features constitute clustering features; The DBSCAN algorithm is used to perform unsupervised clustering of the small thrust trajectory data in the small thrust trajectory dataset using clustering features as task characteristics to form K A small subset of thrust transfer trajectory data.

[0011] Preferably, the structural optimization of the expert network to determine the optimal hyperparameter combination of each expert network includes: The expert network parameters are optimized using a Bayesian optimizer to determine the hyperparameter configuration of each expert network, including: Build phase: For the k Hyperparameters to be optimized for the expert network And the value range of each hyperparameter , construct hyperparameter search space , Indicates the number of hyperparameters to be optimized, is the index; Construct an evaluation function for the low-thrust orbit optimization expert network to evaluate each set of sampled hyperparameters. The expression of the evaluation function includes: or, in, They are small thrust test feature data and corresponding expert network prediction targets; Indicates the k a network of experts; represents the mean relative error; represents the root mean square error; Construct a Gaussian process model to sample the optimal hyperparameter combination evaluation points in the hyperparameter search space; Construct the acquisition expectation improvement function to calculate the next sampling point; Execute the deployment phase: Evaluation function of the Bayesian optimizer to test the expert network At the initial hyperparameter sampling point The result at , initializes the Gaussian process model, updates the Gaussian process model, and obtains the evaluation function The posterior probability distribution of ; Search for the hyperparameter combination that maximizes the performance improvement of the acquisition function ,in accordance with Build an expert network based on the structural parameters in the training parameters, perform training according to the training parameters, and obtain the true objective function value. Through the evaluation function of the expert network, confirm whether there is performance improvement and update the optimal hyperparameter combination. ; 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.

[0012] Preferably, the construction and training of the gated network is performed by fusing the trained gated network with the trained K expert networks, and obtain a hybrid expert model, including: Gated Network The output contains Output Layer, for a given input, the output is the weight , normalized, then: The output prediction value of the expert model is ,The final result of the gating network is weighted fused according to the network allocation weight; The training process of the gating network includes: After freezing the weights and hyperparameters of the expert network neurons, we start training and updating the parameters of the gating network. The goal of training the gating network is to minimize the final prediction error of the entire expert mixture model. The loss function is is the mean square error between the final predicted value output by the system and the actual low-thrust orbit transfer cost: in, is the total loss of the system, ( ) is the mean square error function, Foreground Gated Network The generated The weight of an expert network is a parameter to be trained; For expert networks based on small thrust characteristics The output value of Small thrust trajectory The corresponding true value of the orbital maneuvering cost; During the back propagation process during training, because all expert network parameters are frozen, the gradient information is passed through Pass to the gating network , and update the network Parameters are used to optimize the gating network weights for different low-thrust transfer orbits.

[0013] In a second aspect, the present invention provides a low-thrust spacecraft trajectory optimization system based on a hybrid expert model, comprising: The training data generation module is used to randomly initialize the starting and target trajectories for low-thrust transfer and construct a dynamic model including constraints and objective functions. The starting and target trajectories are substituted into the dynamic model and the low-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 features and high-dimensional features for small thrust trajectories; the basic features and high-dimensional features are used as clustering features to cluster the trajectories of the small thrust initial training set to form K A small subset of thrust transfer trajectory data; Expert network building blocks for K A small subset of thrust transfer trajectory data is constructed K Expert networks for low-thrust trajectory prediction; structural optimization of expert networks to determine the optimal hyperparameter combination for each expert network; The hybrid expert model building module is used to build and train the gating network by fusing the trained gating network and the trained K An expert network is constructed to obtain a hybrid expert model, which is used to optimize the low-thrust trajectory of the spacecraft.

[0014] In a third aspect, the present invention provides a computer-readable storage medium storing a computer program for optimizing the trajectory of a low-thrust spacecraft based on a hybrid expert model, wherein the computer program enables a computer to execute the low-thrust spacecraft trajectory optimization method based on a hybrid expert model as described above.

[0015] In a fourth aspect, the present invention provides an electronic device, comprising: One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, the programs including instructions for executing the low-thrust spacecraft trajectory optimization method based on the hybrid expert model as described above.

[0016] (3) Beneficial effects The present invention provides a low-thrust spacecraft trajectory optimization method and system based on a hybrid expert model. Compared with the existing technology, it has the following advantages: This paper designs and implements an intelligent fusion prediction architecture based on a gated network and a hybrid expert model. This architecture addresses the issues of insufficient generalization and reduced accuracy of existing single global models when faced with diverse tasks. Each expert network is trained to handle a specific type of low-thrust transfer trajectory. In scenarios requiring multi-target rendezvous missions, the hybrid expert model can autonomously fuse the predictions of each expert, demonstrating highly stable and high-precision predictions for any type of low-thrust transfer trajectory. The robustness and generalization performance of the system's predictions far exceed those of existing single models. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0018] Figure 1 A block diagram of a low-thrust spacecraft trajectory optimization method based on a hybrid expert model according to an embodiment of the present invention; Figure 2 This is a flow chart of a low-thrust spacecraft trajectory optimization method based on a hybrid expert model according to an embodiment of the present invention; Figure 3 This is a schematic diagram of a multi-celestial body encounter scenario; Figure 4 Schematic diagram comparing the prediction effects of a single network and a hybrid expert network in a multi-celestial body rendezvous mission. DETAILED DESCRIPTION

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0020] The embodiments of the present application provide a low-thrust spacecraft trajectory optimization method and system based on a hybrid expert model, which solves the technical problem that the single deep neural network model used in the prior art is difficult to accurately characterize the characteristics of the low-thrust transfer trajectory with diverse features. It realizes a technology that can fuse multiple deep neural network models according to the characteristics of the input trajectory, and can improve the prediction accuracy of the optimal solution of the low-thrust trajectory in multi-target mission scenarios.

[0021] The technical solution in the embodiments of the present application is to solve the above technical problems, and the overall idea is as follows: Low-thrust spacecraft trajectories have diverse characteristics, and their inherent dynamic characteristics vary significantly. For example, the optimal thrust strategies and state evolution patterns differ between maneuvers primarily focused on changing the orbital plane and those primarily focused on increasing orbital energy. A single deep neural network model uses a fixed set of network parameters to optimize all types of low-thrust trajectories, resulting in reduced prediction accuracy for missions with significantly different characteristics. This model struggles to maintain prediction accuracy and robustness across a wide range of missions. To overcome this problem, the improvement measure of establishing a deep network for optimal solution prediction for each type of low-thrust transfer trajectory requires the establishment of a large number of deep networks, requiring massive amounts of data and consuming significant computing resources. Furthermore, it is difficult to fully cover all types of low-thrust transfer trajectories with a trained model. Introducing new deep model fusion mechanisms and training a limited number of deep network prediction models are key challenges.

[0022] To solve the above problems, an embodiment of the present invention provides a low-thrust spacecraft trajectory optimization method based on a hybrid expert model. This method can integrate the technologies and corresponding systems of multiple deep neural network models according to the characteristics of the input trajectory, and can improve the prediction accuracy and robustness of the optimal solution for the low-thrust trajectory in multi-objective mission scenarios.

[0023] In order to better understand the above technical solution, the above technical solution will be described in detail below with reference to the accompanying drawings and specific implementation methods.

[0024] The embodiment of the present invention provides a low-thrust spacecraft trajectory optimization method based on a hybrid expert model. Figure 1 Shown, including: S1. Randomly initialize the starting and target trajectories for low-thrust transfer and construct a dynamic model including constraints and objective functions. Substitute the starting and target trajectories into the dynamic model and solve the low-thrust trajectory using direct or indirect methods to obtain several trajectory data as the initial training set. S2. Construct basic features and high-dimensional features for small thrust trajectories; use basic features and high-dimensional features as clustering features to cluster the trajectories of the small thrust initial training set to form K A small subset of thrust transfer trajectory data; S3, for K A small subset of thrust transfer trajectory data is constructed K Expert networks for low-thrust trajectory prediction; structural optimization of expert networks to determine the optimal hyperparameter combination for each expert network; S4, build and train the gated network, by integrating the trained gated network and the trained K An expert network is constructed to obtain a hybrid expert model, which is used to optimize the low-thrust trajectory of the spacecraft.

[0025] The following is combined with Figure 2 The flowchart shown in the figure explains in detail the low-thrust spacecraft trajectory optimization method based on the hybrid expert model: In one embodiment, S1 randomly initializes the starting and target trajectories for low-thrust transfer, constructs a dynamic model including constraints and objective functions, substitutes the starting and target trajectories into the dynamic model, solves the low-thrust trajectory using direct or indirect methods, and obtains several feasible trajectory data as the initial training set. The specific implementation process is as follows: S101: Initialize the low-thrust transfer departure orbit and target orbit. Specifically include: In order to obtain a uniformly distributed small thrust trajectory dataset and make the physical meaning of random initialization clear, orbital elements are used to describe the departure and target orbits. The epoch time is set to , use the following formula to randomly generate the orbital elements of the departure target and arrival target of the low-thrust spacecraft: in, is the semi-major axis, is the eccentricity, is the orbital inclination, is the right ascension of the ascending node, is the perigee depression angle, is the true anomaly angle, is the coefficient of variation of the semi-major axis, is the coefficient of eccentricity variation, Representatives in A random number function that takes a random number within the interval. The position of the spacecraft at the initial time and arrival time in the inertial system is obtained based on the six orbital numbers. ,speed , and expressed as a vector .

[0026] S102: Construct a dynamic model including constraints and objective functions. The details are as follows: Establish the state vector and dynamic equations of the low-thrust aircraft in the Cartesian inertial coordinate system. Specifically include: State vector for: in, For spacecraft in Position vector at the moment; For spacecraft in Velocity vector at time instant; For spacecraft in The instantaneous quality of the moment.

[0027] The kinetic equation is: in, , , is the rate of change of the aircraft's position, velocity, and mass over time; is the gravitational constant of the central celestial body, The distance from the spacecraft to the center of mass of the central celestial body, is the maximum thrust of the spacecraft, For spacecraft in The control vector in the Cartesian coordinate system at any time ; is the spacecraft engine specific impulse, is the standard acceleration due to gravity.

[0028] Establish the low-thrust spacecraft transfer orbit optimization objective function. Specifically include The objective function minimizes the end time of low-thrust orbit transfer The negative value of the instantaneous mass of the aircraft: The boundary conditions are used as constraints, where the initial conditions are: , , The terminal conditions are: , S103: Substitute the departure trajectory and target trajectory into the dynamics model and solve the low-thrust trajectory using a direct or indirect method. Specifically, In the embodiment of the present invention, the low-thrust trajectory is solved by a direct method or an indirect method, such as the pseudo-spectral method in the indirect method. The pseudo-spectral method is described in detail below. The specific process is as follows: First, the Legendre-Gauss-Lobatto (LGL) collocation method is used to discretize the dynamic equations. The number of nodes is , the node index is ,at the same time, n and j Also for index, According to the following formula, time Normalize and use variables express: The dynamic equation of the low-thrust aircraft can be expressed as: Then, Lagrange interpolation is used to calculate the state variables and The fitting is performed as follows: in, is the basis function, the interpolation basis function and its derivative results are: Then the system equation discretized by pseudo-spectral method can be expressed as: in, for Differentiation matrix, is the degree of the Legendre polynomial.

[0029] The fuel objective function after the pseudo-spectral method is discretized is: The above process can use the GPOPS solver to solve the optimal trajectory.

[0030] Through the above method, a large amount of trajectory data is obtained as the initial training set.

[0031] In one embodiment, S2, construct basic features and high-dimensional features for small thrust trajectories; use basic features and high-dimensional features as clustering features to cluster the trajectories of the small thrust initial training set to form K A small subset of thrust transfer trajectory data. The specific implementation process is as follows: S201: Based on the low-thrust trajectory data in the initial training set, construct the basic features of the low-thrust trajectory. Specifically, it includes: The basic feature data of the low-thrust trajectory includes the various feature data in the feasible trajectory data in the initial training set, specifically including: the change in the number of classical orbital elements , improve the change of the orbital elements of the vernal equinox , the position and velocity of the spacecraft in the Cartesian coordinate system , the position of the spacecraft in the spherical coordinate system , coordinates in cylindrical coordinate system The corresponding ephemeris change can be calculated by the following formula: 、 、 、 、 The details are as follows: Note that this variable contains positive and negative signs, which contains small thrust trajectory transfer information, such as the orbital inclination change in the classical orbital elements. If it is a negative number, it means that the orbit is shifting from a low-inclination orbit to a high-inclination orbit. If it is a positive number, it means a shift from a high-inclination orbit to a low-inclination orbit.

[0032] At the same time, the initial mass of the spacecraft , quality upon arrival , flight time etc. are set as the basic characteristic data of small thrust trajectory.

[0033] S202: Construct high-dimensional features based on the low-thrust orbit basic feature data. This includes: High-dimensional features include: Double-pulse maneuver orbital velocity increment It can be obtained by solving the Lambert equation; the orbital energy change is: ( ) ; The change in angular momentum is: ( ) .

[0034] The angle of the angular momentum vector can be obtained by calculating the angular momentum of the starting orbit and the target orbital angular momentum The dot product of: The in-plane maneuver coefficient is used to describe whether the transfer orbit is mainly ascending and descending in the orbital plane or mainly out-of-plane maneuvers in a high-inclination orbit: in, The change of the semi-major axis before and after the track change, is the semi-major axis of the departure orbit, is the eccentricity change. If the value is larger, the orbital inclination maneuvering will be more obvious, otherwise the orbital maneuvering within the plane of the orbit will be the main method.

[0035] Orbital phase coupling characteristics For non-circular orbit transfers, the departure and arrival phases significantly influence the orbital maneuver cost. The orbital phase coupling feature couples orbital shape changes with phase changes to identify phase-sensitive orbit transfers (e.g., utilizing the low-speed region near apogee for efficient planar maneuvers).

[0036] S203, using high-dimensional features and basic features as clustering features, clustering the trajectories of the initial training set to form a small thrust transfer trajectory data subset. Specifically including: The DBSCAN algorithm is used to perform unsupervised clustering of the low-thrust trajectory data in the low-thrust trajectory dataset. The goal is to automatically divide the massive, heterogeneous trajectory data into several clusters with clear mission characteristics based on their inherent physical and geometric similarities. Based on the above description, the clustering characteristics of any trajectory can be described as: It should be noted that, in the specific implementation process, the basic features included in the clustering feature can be adjusted according to the actual situation. For example, 3 or 4 can be selected. You can also choose not to .

[0037] The small thrust trajectory data is z-score normalized, and the distance between any two small thrust trajectories A and B is is the Euclidean distance between two points, that is: Among them, the embodiment of the present invention is constructed The clustering algorithm can perform unsupervised clustering of transfer trajectories with spatial similarity other than typical large-angle maneuvers, ascending and descending orbit maneuvers. If one of the trajectories is a pure inclination change and the other is accompanied by a huge Δ Ω changes, they are The difference in dimensions will increase significantly, and thus they will be correctly identified as two different tasks in clustering. The introduction of high-dimensional features gives the Euclidean distance a physical connotation.

[0038] For a small thrust trajectory, calculate the Euclidean distance between other trajectory features and this trajectory feature, and count the number of small thrust trajectory features with it as the center and radius as The number of trajectories contained in the hypersphere is not less than the threshold , then take trajectory A as the core point, and the corresponding trajectory is directly connected to the core point density.

[0039] By starting from any unvisited core point and continuously searching for all density-reachable samples and grouping them into a cluster, DBSCAN can automatically and robustly discover clusters of any shape in the data, while identifying singular trajectories in sparse areas that do not belong to any cluster as noise, thereby completing the intelligent and adaptive clustering of complex small-thrust trajectory tasks. K A small subset of thrust transfer trajectory data.

[0040] In one embodiment, S3, for K A small subset of thrust transfer trajectory data is constructed K An expert network for low-thrust trajectory prediction is developed; the structure of the expert network is optimized to determine the optimal hyperparameter combination for each expert network. The specific implementation process is as follows: For each low-thrust trajectory feature dataset, an expert network is constructed. The basic network of each expert network is constructed by a fully connected network. The initial network contains hidden layers, each containing neurons, and the activation function is .

[0041] During the optimization training process, each small thrust trajectory data subset , trains expert networks for low-thrust trajectory prediction. Each expert network predicts the optimal low-thrust trajectory and transfer cost (e.g., time, fuel, energy) based on the input low-thrust orbital maneuver characteristics.

[0042] The trajectory characteristics for low-thrust orbit transfer cost prediction are as follows: The input feature data of the expert network includes basic features and high-dimensional features, among which the basic features include: the variation of the number of classical orbital elements , improve the change of the orbital elements of the vernal equinox , the initial mass of the aircraft , flight time , high-dimensional features: double-pulse maneuver orbital velocity increment , the orbital energy changes to ; The change in angular momentum is .

[0043] The label data during the expert network training process is the final mass of the spacecraft after the corresponding low-thrust orbit transfer. Of course, in the specific implementation process, time optimization can also be considered, and the shortest flight time can be used as the optimization target. Accordingly, the shortest flight time can be used as the label data.

[0044] Since different expert networks require different network structures (such as network depth, width, type of layer, activation function, etc.) and training parameters for learning different low-thrust trajectory characteristics, parameter optimization must be performed for each expert network. In an embodiment of the present invention, in order to cope with the huge search space and various types of optimizable parameters (continuous, integer, categorical), the expert network parameters are optimized by a Bayesian optimizer. This is to determine the structure of each expert network and the configuration of training-related hyperparameters. Bayesian optimization is a sequence-based optimization technology that can find the optimal solution in the fewest steps based on training history and through intelligent parameter configuration. The steps for constructing and using the Bayesian optimizer for the low-thrust trajectory optimization expert network are as follows: Build phase: First, construct the hyperparameter search space to be optimized: k Hyperparameters to be optimized for the expert network And the value range of each hyperparameter , construct hyperparameter search space , Indicates the number of hyperparameters to be optimized, is the index, and hyperparameters include all parameters.

[0045] Secondly, 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 target of its hyperparameter optimization is the mean relative error ( MRE ) or the root mean square error ( RMSE The essence of hyperparameter optimization is to find the configuration that minimizes the objective function. The evaluation function of the expert network is as follows: in, are the small thrust test feature data and the corresponding expert network prediction target. To ensure the randomness of the test, the test set Instead of selecting a fixed set, each time a random sample is drawn from a larger test data pool.

[0046] Next, a proxy model is constructed to sample the optimal hyperparameter combination evaluation points in the hyperparameter search space. This embodiment of the present invention utilizes a Gaussian process model. This Gaussian process can predict the performance of unknown points based on existing observations and provide the uncertainty of the prediction.

[0047] Finally, a collection function is constructed. This is the expected improvement (EI) function in this embodiment of the present invention. It uses the predicted mean and uncertainty of the surrogate model to calculate the expected improvement over the current optimal solution for the next sampling at a certain point.

[0048] Execute the deployment phase: Evaluation function of the Bayesian optimizer to test the expert network At the initial hyperparameter sampling point The result at , initializes the Gaussian process model, updates the GP model, and obtains the evaluation function The posterior probability distribution of . Search for the hyperparameter combination that maximizes the performance improvement of the acquisition function ,in accordance with Build an expert network based on the structural parameters in the training parameters, perform training according to the training parameters, and obtain the true objective function value. Through the evaluation function of the expert network, confirm whether there is performance improvement and update the optimal hyperparameter combination. . Continuous iterative optimization until the 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.

[0049] In one embodiment, S4, construct and train a gating network, by fusing the trained gating network and the trained K An expert network is constructed to obtain a hybrid expert model. The specific implementation process is as follows: This step designs a gating network, adjusts the prediction ratio of each expert network through network weights, and designs an expert network evolution strategy. The details are as follows: The gating network has the same input as the expert network. For the high-dimensional features of the small thrust trajectory, the gating network determines the proportion of the prediction values ​​of each expert network. The output contains Output Layer, for a given input, the output is the weight , normalized, then: The output prediction value of the expert model is ,The final result of the gating network is weighted fused according to the network allocation weight.

[0050] The training process of the gating network is as follows: A phased, constrained training strategy was adopted.

[0051] The function of the expert network trained in step S3 is preserved, and the weights of the expert network neurons are frozen. The expert network is only used as an evaluator for the weight distribution of the gating network, and the weights are not updated during back propagation.

[0052] After freezing the weights and hyperparameters of the expert network neurons, we start training and updating the parameters of the gating network. The goal of training the gating network is to minimize the final prediction error of the entire expert mixture model, the loss function is the mean square error between the final predicted value output by the system and the actual low-thrust orbit transfer cost: in, is the total loss of the system, ( ) is the mean square error function, Foreground Gated Network The generated The weight of an expert network is a parameter to be trained; For expert networks based on small thrust characteristics The output value of Small thrust trajectory The corresponding true value of the orbital maneuvering cost.

[0053] During the back propagation process during training, because all expert network parameters are frozen, the gradient information is passed through Pass to the gating network , and update the network Parameters are used to optimize the gating network weights for different low-thrust transfer orbits.

[0054] Since the training and update process requires frequent freezing of the network and updating of network parameters, the computational cost is high, so the real-time update method is not suitable. In the application process, only when a considerable amount of update data is collected and the trigger conditions are met, the network end-to-end fine-tuning is performed. When processing batch small thrust trajectory training data, the loss of the expert network prediction of the current batch data is recorded. At the same time, a sample data set is obtained from the small thrust trajectory database, and the loss of the current expert network on the sample data set is calculated. .like , calculate the forecast error increase rate: If the ratio Above threshold If the decrease is small, the new data is considered to contain a significantly different, low-thrust orbital maneuver type. This triggers the online learning process, mixing the new and old data, re-clustering and fusing the data, unfreezing and training the specific expert network weights, and updating the network parameters. If the decrease is small, end-to-end fine-tuning is used. This means that instead of retraining the expert network using a large amount of data, the network parameters are fine-tuned using batch data and a small amount of data.

[0055] The effectiveness of the embodiment of the present invention is verified by specific data below: 1. Generate low-thrust trajectory data. According to step S1, randomly initialize the "departure orbit-target orbit" pair to simulate the low-thrust transfer mission, where the semi-major axis The value range is , orbital eccentricity The range is 0-0.5, orbital inclination The value range is 0-30°, the right ascension of the ascending node , is the perigee depression angle , is the true anomaly angle exist Random value.

[0056] 2. For randomly generated tasks, the pseudo-spectral method is used to solve the fuel optimization problem. Assume that the central celestial body is the sun and the gravitational constant is , the initial mass of the spacecraft is , of which the dry weight is , using small thrust mode, the maximum thrust is , the engine specific impulse is The flight time is randomly selected in the range of [30,6*365] days.

[0057] 3. Model the trajectory optimization problem. Construct the corresponding constraints and optimization objectives. In this example, the optimization objective is fuel optimization. Use software such as GPOPS-II to solve the problem. If a converged solution exists, save the following low-thrust transfer trajectory information: mission start time, end time, spacecraft orbit at start time, possible spacecraft orbit at end time, spacecraft mass at start time, spacecraft mass at interpretation time, and the pulse thrust velocity increment required for the transfer. Save at least 200,000 sets of feasible trajectory data as the initial training set.

[0058] 4. After obtaining the initial training set, construct clustering features: in, is the initial mass of the aircraft, is the change in the number of classical orbital elements, To improve the change of the orbital elements of the vernal equinox, is the double-pulse maneuver orbital velocity increment, The orbital energy change is, the angular momentum change is, is the angle between the angular momentum vectors, is the in-plane and out-of-plane maneuver coefficient, is the orbit phase coupling feature. All features are Z-score normalized. Run DBSCAN clustering to obtain a small thrust transfer trajectory subset. , and the noisy dataset .

[0059] The amount of data in the verification process is large. Calculate the density direct point threshold, is the dimension of the small inference trajectory data used for clustering. The radius is Setting k -Distance method to obtaink After the distance graph data point, the best value is obtained by calculating the inflection point of the L-shaped curve. The inflection point represents the boundary from the sparse trajectory data noise area to the dense trajectory data cluster area. Finally, several small thrust trajectory data clusters are formed: In the embodiment, a total of 5 low-thrust trajectory training data subsets are obtained, and each core point represents a typical feasible low-thrust trajectory transfer domain. The cluster data may represent: starting from GTO, the inclination angle is reduced by about 10 degrees, and the perigee is raised. The low-thrust orbit transfer; orbit climbing / energy-dominated low-thrust transfer ( Larger, Smaller); large plane maneuver-dominated transfer ( Larger); orbital shape / phase-dominated transfer ( Larger). Among them, Noise points represent atypical low-thrust transfer trajectories. For example, for an extremely high-inclination orbital transfer, if the phase angle, flight time, and spacecraft mass coincidentally meet specific initial conditions, a feasible trajectory solution that satisfies all constraints exists. However, the characteristics of such low-thrust trajectories are sparsely distributed. Noise datasets can also be interpreted as low-thrust transfer trajectories without distinct features. In this project, a separate expert network for noise data is not designed. Instead, a general trajectory expert network is obtained from the entire data set to process data classified as noise.

[0060] 5. For the established small thrust data set , construct the Bayesian optimization hyperparameter space. The parameters to be optimized include feature combination, number of network layers , the number of neurons Activation function ; Learning rate ; Exponential decay rate hyperparameter of first-order moment estimate ; Exponential decay rate hyperparameters for second-order moment estimates wait.

[0061] 6. Construction and training of hybrid expert model based on gated network. The gated network is set as follows: [12,16,5] fully connected layers, with the last layer being a Softmax output layer. During the training of the gated network, the output of the multi-expert network trained in step 6 is used, and the weights are adjusted by the output layer of the gated network. The final output is the weighted sum of each expert. The loss function is calculated and the gating network parameters are updated. During the updating process, the parameters of the five expert networks are frozen and unchanged. The Adam optimizer is used to train the gating network.

[0062] 7. Construct a multi-target intersection scenario and compare the difference in prediction results between the hybrid expert model of the embodiment of the present invention and the conventional single network. Figure 3 In the multi-target rendezvous scenario shown, the spacecraft departs from the Earth with an initial mass of 2800 kg, a specific impulse of 4000 s, and a maximum thrust of 300 , visit multiple space targets, and return to Earth. The target orbit parameters are shown in Table 1: Table 1 Target orbit parameters In the design of multi-celestial body rendezvous missions, there is a cumulative error in spacecraft mass, that is, the error in spacecraft fuel consumption at the previous moment will be reflected in the initial value of the spacecraft mass during the next stage of transfer, and will be cascaded and amplified in the multi-target rendezvous visit sequence. In this example, a total of 5 space targets were visited and returned to the Earth, involving a total of six low-thrust transfer orbits. The average relative error of the spacecraft mass prediction for the six missions decreased from 7.7% to 2.1%. After the last low-thrust orbit transfer before returning to the Earth, the cumulative relative error of the spacecraft mass prediction decreased from 16.6% to 3.7%. For detailed information, see Figure 4 It can be seen that the hybrid expert network system model effectively improves the prediction accuracy in complex multi-celestial body rendezvous missions.

[0063] An embodiment of the present invention provides a low-thrust spacecraft trajectory optimization system based on a hybrid expert model, comprising: The training data generation module is used to randomly initialize the starting and target trajectories for low-thrust transfer and construct a dynamic model including constraints and objective functions. The starting and target trajectories are substituted into the dynamic model and the low-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 features and high-dimensional features for small thrust trajectories; the basic features and high-dimensional features are used as clustering features to cluster the trajectories of the small thrust initial training set to form K A small subset of thrust transfer trajectory data; Expert network building blocks for K A small subset of thrust transfer trajectory data is constructed K Expert networks for low-thrust trajectory prediction; structural optimization of expert networks to determine the optimal hyperparameter combination for each expert network; The hybrid expert model building module is used to build and train the gating network by fusing the trained gating network and the trained K An expert network is constructed to obtain a hybrid expert model, which is used to optimize the low-thrust trajectory of the spacecraft.

[0064] An embodiment of the present invention also provides a computer-readable storage medium storing a computer program for optimizing the trajectory of a low-thrust spacecraft based on a hybrid expert model, wherein the computer program enables a computer to execute the low-thrust spacecraft trajectory optimization method based on a hybrid expert model as described above.

[0065] An embodiment of the present invention also provides an electronic device, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and the programs include a method for executing the low-thrust spacecraft trajectory optimization method based on the hybrid expert model as described above.

[0066] In summary, compared with the existing technology, the present invention has the following beneficial effects: 1. This embodiment of the present invention significantly improves the prediction accuracy and generalization performance of low-thrust trajectory optimization by designing a hybrid expert prediction architecture based on gated network control. Specifically, this embodiment of the present invention designs and implements an intelligent fusion prediction architecture based on gated networks and hybrid expert models. This architecture addresses the problems of insufficient generalization and reduced accuracy of existing single models when faced with diverse tasks. In this embodiment of the present invention, each expert network is trained to handle a specific type of low-thrust trajectory transfer trajectory. Due to the high correlation of their training data, the optimal network structure and hyperparameters inevitably differ. The parallel Bayesian optimization algorithm introduced in this invention optimizes the expert network structure and training parameters, enabling the expert network to learn deeper and more detailed nonlinear mapping relationships than a single model. For example, an expert may have strong predictive ability for the coupling relationship between orbit phase and thrust direction, which is difficult for a single model to account for. The innovative introduction of the gated network implements a dynamic fusion mechanism, ensuring that the system's final output is always dominated by the most relevant expert, effectively improving the prediction accuracy of this embodiment of the present invention. In mission scenarios requiring multi-target rendezvous, the hybrid expert model can autonomously fuse the prediction results of each expert, and demonstrate highly stable and high-precision prediction results on any type of low-thrust transfer orbit. The robustness and generalization performance of the system's prediction far exceed those of existing single models.

[0067] 2. This embodiment of the present invention achieves effective decoupling and dimensionality reduction of complex optimization problems by constructing a low-thrust trajectory clustering technique based on unsupervised clustering, laying the foundation for high-precision prediction. Specifically, this embodiment of the present invention innovatively proposes and applies a DBSCAN-based high-dimensional feature space clustering technique for low-thrust trajectories, shifting the paradigm for problem solving. Through feature engineering, a high-dimensional feature space is innovatively constructed that reflects trajectory physical properties, including orbital geometry changes, dynamic energy, in-plane maneuvering ratios, and phase coupling characteristics. Leveraging the density-based clustering properties of the DBSCAN algorithm, this embodiment of the present invention automatically discovers natural communities in high-dimensional data without requiring a pre-set number of categories. This decomposes a complex, high-dimensional, nonlinear global optimization problem into several relatively simple subproblems with highly consistent internal features. For example, all "high-inclination, low-energy" in-plane maneuvering tasks are grouped into one category, while all "high-energy, nearly coplanar" orbit climb tasks are grouped into another. This divide-and-conquer strategy reduces the learning complexity of subsequent individual expert networks.

[0068] 3. The DBSCAN-based trajectory clustering strategy designed in this embodiment of the present invention can identify clusters of arbitrary shapes and effectively identify noise points—atypical low-thrust trajectories that do not fit into any mainstream categories. It also uses a universal model to process these points, significantly enhancing the robustness of the entire system. Ultimately, this intelligent clustering based on physical properties provides a dedicated training set for each subsequent expert network, laying a solid foundation for the implementation of hybrid expert models.

[0069] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply the existence of any such actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or device comprising the element.

[0070] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A low-thrust spacecraft trajectory optimization method based on a hybrid expert model, characterized in that: include: The starting and target trajectories for low-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 low-thrust trajectory is solved using direct or indirect methods to obtain several trajectory data as the initial training set. Construct basic features and high-dimensional features for small thrust trajectories; use basic features and high-dimensional features as clustering features to cluster the trajectories of the small thrust initial training set to form K A small subset of thrust transfer trajectory data; against K A small subset of thrust transfer trajectory data is constructed K Expert networks for low-thrust trajectory prediction; structural optimization of expert networks to determine the optimal hyperparameter combination for each expert network; Build and train the gated network by fusing the trained gated network with the trained K An expert network is constructed to obtain a hybrid expert model, which is used to optimize the low-thrust trajectory of the spacecraft.

2. The low-thrust spacecraft trajectory optimization method based on the hybrid expert model according to 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 orbit transfer.

3. The low-thrust spacecraft trajectory optimization method based on a hybrid expert model according to claim 1, characterized in that: The basic characteristics include: the variation of the number of classical orbital elements , Improve the change of the orbital elements of the vernal equinox , the position and velocity of the spacecraft in the Cartesian coordinate system , the position of the spacecraft in the spherical coordinate system , Coordinates in cylindrical coordinate system , spacecraft initial mass , quality upon arrival and flight time .

4. The low-thrust spacecraft trajectory optimization method based on a hybrid expert model according to claim 3, characterized in that: The high-dimensional features include: orbital energy changes , angular momentum change 、Angular momentum vector angle , in-plane and out-of-plane maneuverability coefficients and orbital phase coupling characteristics .

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

6. The low-thrust spacecraft trajectory optimization method based on a hybrid expert model according to any one of claims 1 to 5, characterized in that: The structural optimization of the expert network to determine the optimal hyperparameter combination of each expert network includes: The expert network parameters are optimized using a Bayesian optimizer to determine the hyperparameter configuration of each expert network, including: Build phase: For the k Hyperparameters to be optimized for the expert network And the value range of each hyperparameter , construct hyperparameter search space , Indicates the number of hyperparameters to be optimized, is the index; Construct an evaluation function for the low-thrust orbit optimization expert network to evaluate each set of sampled hyperparameters. The expression of the evaluation function includes: or, in, They are small thrust test feature data and corresponding expert network prediction targets; Indicates the k a network of experts; represents the mean relative error; represents the root mean square error; Construct a Gaussian process model to sample the optimal hyperparameter combination evaluation points in the hyperparameter search space; Construct the acquisition expectation improvement function to calculate the next sampling point; Execute the deployment phase: Evaluation function of the Bayesian optimizer to test the expert network At the initial hyperparameter sampling point The result at , initializes the Gaussian process model, updates the Gaussian process model, and obtains the evaluation function The posterior probability distribution of ; Search for the hyperparameter combination that maximizes the performance improvement of the acquisition function ,in accordance with Build an expert network based on the structural parameters in the training parameters, perform training according to the training parameters, and obtain the true objective function value. Through the evaluation function of the expert network, confirm whether there is performance improvement and update the optimal hyperparameter combination. ; 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.

7. The low-thrust spacecraft trajectory optimization method based on a hybrid expert model according to any one of claims 1 to 5, characterized in that: The gated network is constructed and trained by fusing the trained gated network and the trained K expert networks, and obtain a hybrid expert model, including: Gated Network The output contains Output Layer, for a given input, the output is the weight , normalized, then: The output prediction value of the expert model is ,The final result of the gating network is weighted fused according to the network allocation weight; The training process of the gating network includes: After freezing the weights and hyperparameters of the expert network neurons, we start training and updating the parameters of the gating network. The goal of training the gating network is to minimize the final prediction error of the entire expert mixture model. The loss function is is the mean square error between the final predicted value output by the system and the actual low-thrust orbit transfer cost: in, is the total loss of the system, ( ) is the mean square error function, Foreground Gated Network The generated The weight of an expert network is a parameter to be trained; For expert networks based on small thrust characteristics The output value of Small thrust trajectory The corresponding true value of the orbital maneuvering cost; During the back propagation process during training, because all expert network parameters are frozen, the gradient information is passed through Pass to the gating network , and update the network Parameters are used to optimize the gating network weights for different low-thrust transfer orbits.

8. A low-thrust spacecraft trajectory optimization system based on a hybrid expert model, characterized in that: include: The training data generation module is used to randomly initialize the starting and target trajectories for low-thrust transfer and construct a dynamic model including constraints and objective functions. The starting and target trajectories are substituted into the dynamic model and the low-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 features and high-dimensional features for small thrust trajectories; the basic features and high-dimensional features are used as clustering features to cluster the trajectories of the small thrust initial training set to form K A small subset of thrust transfer trajectory data; Expert network building blocks for K A small subset of thrust transfer trajectory data is constructed K Expert networks for low-thrust trajectory prediction; structural optimization of expert networks to determine the optimal hyperparameter combination for each expert network; The hybrid expert model building module is used to build and train the gating network by fusing the trained gating network and the trained K An expert network is constructed to obtain a hybrid expert model, which is used to optimize the low-thrust trajectory of the spacecraft.

9. A computer-readable storage medium, characterized in that It stores a computer program for low-thrust spacecraft trajectory optimization based on a hybrid expert model, wherein the computer program enables 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 7.

10. 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 are configured to be executed by the one or more processors, and the programs include a method for executing the low-thrust spacecraft trajectory optimization method based on a hybrid expert model as described in any one of claims 1 to 7.

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