Spacecraft low-thrust trajectory data generation method and system

Abstract

The invention provides a spacecraft low-thrust trajectory data generation method and system, and relates to the technical field of trajectory data generation based on a deep neural network. The method comprises the following steps: inputting randomized data into a pre-established solar electric propulsion-oriented spacecraft low-thrust trajectory optimization model and an optimal control problem solving model, solving to obtain training data, taking the training data as real trajectory data to train a generative adversarial network to obtain a trajectory generator, and calculating the optimal control problem of the solar electric propulsion-oriented spacecraft low-thrust trajectory optimization model. And the trajectory generator is used for generating spacecraft low-thrust trajectory data. According to the method, the generative model is trained by using a small amount of randomly generated training data, and data distribution which is the same as original low-thrust trajectory data can be generated at a relatively high convergence rate after training is finished, so that the data generation efficiency is greatly improved, and powerful high-quality training data guarantee is provided for a low-thrust trajectory generation technology based on deep learning.

Description

Technical Field

[0001] The present invention relates to the technical field of trajectory data generation based on deep neural networks, and in particular to a method and system for generating low-thrust trajectory data for spacecraft. Background Art

[0002] Optimizing low-thrust spacecraft trajectories is a complex optimization problem, often requiring solving an optimal control problem. Designing continuous thrust trajectories that meet various constraints for specific missions (such as orbit transfer, rendezvous, and constellation deployment) often involves lengthy optimization calculations and incurs significant computational costs.

[0003] In recent years, artificial intelligence technologies such as deep learning have demonstrated potential in trajectory design. For example, by formulating trajectory design as a sequential decision-making problem and employing reinforcement learning, or by using deep learning models to directly predict the minimum time and fuel consumption of low-thrust trajectories, these methods have made the design of complex, multi-objective space missions more efficient. However, deep learning methods require a large amount of training data. Efficiently generating high-quality low-thrust trajectory training datasets for diverse mission scenarios, spacecraft propulsion methods, and dynamic constraints is crucial. Traditional random data generation methods suffer from low convergence rates, high computational costs, solution uncertainty, and resource waste, significantly limiting the application of deep learning in continuous thrust trajectory optimization. Existing approaches generally employ Monte Carlo-based random generation methods. The process involves: first, setting the spacecraft specific impulse, power, maximum thrust, dry weight, and propulsion method for the mission scenario. Then, the initial target position, final target position, flight time, spacecraft fuel mass, and optimization objective (minimum transfer time, minimum fuel consumption, or multi-objective optimization) are randomly selected. A direct or indirect method is used to solve the problem, and if a solution exists, the low-thrust trajectory is saved.

[0004] However, the overall convergence rate of the Monte Carlo-based random generation method is still low. Summary of the Invention

[0005] (1) Technical problems solved

[0006] In view of the shortcomings of the existing technology, the present invention provides a method and system for generating spacecraft low-thrust trajectory data, which solves the technical problem of low convergence rate of the existing spacecraft low-thrust trajectory data generation method.

[0007] (2) Technical solution

[0008] To achieve the above objectives, the present invention is implemented through the following technical solutions:

[0009] In a first aspect, the present invention provides a method for generating low-thrust trajectory data for a spacecraft, comprising:

[0010] The spacecraft parameters, initial target position velocity, and arrival target position velocity are randomly set. The minimum velocity increment and the corresponding pulse orbit transfer time under the dual-pulse transfer orbit model are searched and obtained. The low-thrust transfer time is randomly selected based on the pulse orbit transfer time to obtain the orbit transfer time of the low-thrust spacecraft. The initial value of the spacecraft mass is randomly initialized to obtain the initial mass of the spacecraft.

[0011] Substitute the initial position velocity, target position velocity, orbit transfer time, and initial mass of the spacecraft into a pre-established low-thrust trajectory optimization model and optimal control problem solving model for solar electric propulsion to obtain training data.

[0012] The training data is used as real trajectory data to train a generative adversarial network to obtain a trajectory generator, which is used to generate low-thrust trajectory data of a spacecraft.

[0013] Preferably, the pre-established low-thrust trajectory optimization model for a spacecraft oriented to solar electric propulsion includes a spacecraft state vector, position and velocity state quantities of the spacecraft oriented to solar electric propulsion, and update formulas for position, velocity, and mass;

[0014] Among them, the spacecraft state vector is expressed as:

[0015]

[0016] Where r = [r x ,r y ,r z ] is the spacecraft position in the inertial coordinate system, v=[v x ,v y ,v z ] is the velocity vector of the spacecraft in the inertial coordinate system, m=m wet =m dry +m prop , m dry is the dry weight of the low-thrust spacecraft, m prop is the weight of spacecraft fuel, m wet is the spacecraft wet weight;

[0017] The low-thrust trajectory state of solar electric propulsion based on the Sims-Flanagan method is used to recursively infer the low-thrust trajectory of the spacecraft, and the spacecraft position and velocity state quantities for solar electric propulsion, as well as the update formulas for position, velocity, and mass, are obtained.

[0018] The velocity update formula includes:

[0019] At each discrete control point i, assuming the size is Δv iThe pulse acceleration acts on the control point i instantly, and the unit vector control is adopted. The control vector Δv i =[Δv x ,Δv y ,Δv z ] is replaced by the unit control vector u=[u x ,u y ,u z ], where [u x ,u y ,u z ] has a unit range of [-1,1]; therefore, the spacecraft speed at each moment is calculated by the following formula:

[0020]

[0021] After the velocity is updated, the spacecraft position is updated based on the orbital dynamics equations;

[0022] The quality update formula includes:

[0023] The recursive expression of the forward spacecraft mass is as follows:

[0024]

[0025] The expression for the backward spacecraft mass recursion is as follows:

[0026]

[0027] Where μ is the gravitational constant; is the acceleration, r is the Euclidean distance between the spacecraft and the sun; N seg is the number of discrete units of the trajectory, Δv max,i is the maximum velocity change that can be generated in this trajectory unit; the “+” and “-” superscripts represent the spacecraft before and after the generation of pulse thrust, respectively; i is the forward recursive trajectory unit number, and j is the backward recursive trajectory unit number;

[0028] and are the spacecraft masses after and before the pulse thrust is generated in the i-th small thrust arc segment; and represents the mass of the spacecraft before and after the pulse thrust in the jth arc segment of the backward recursion; v e is the effective exhaust velocity; Δv j is the spacecraft velocity increment generated by the pulse engine at the jth control point; Δt LT is the orbit transfer time of the low-thrust spacecraft; F max (r) is the maximum thrust that the spacecraft can generate in any direction when the spacecraft is at a Euclidean distance r from the sun; is the unit control quantity of the i-th unit;

[0029] Parameters with subscripts x, y, and z represent the components of the corresponding parameters in the three directions in the inertial system.

[0030] Preferably, it also includes:

[0031] The spacecraft mass backward recursion method based on the Omega equation is sampled and the expression of the backward spacecraft mass recursion is optimized, specifically:

[0032] This gives the general form of the backward recursion:

[0033]

[0034] To give The expression of , let:

[0035]

[0036] Reorganize the original equation into the form of Omega function To solve, the method is as follows:

[0037]

[0038] Therefore, the backward recursive solution to the mass of the spacecraft with variable maximum acceleration and low thrust trajectory for solar electric propulsion is as follows:

[0039]

[0040] Where w0 is the Omega function.

[0041] Preferably, the pre-established optimal control problem solving model includes an objective function and constraints:

[0042] Among them, the objective function is to minimize fuel consumption, which is expressed as follows:

[0043] J=min(m fuel )

[0044] Among them, m fuel is the fuel consumption, m fuel =m f -m i , where m f is the final mass of the spacecraft after the low-thrust orbit transfer, m i is the initial mass of the spacecraft before transfer;

[0045] The constraints include equality constraints and inequality constraints for spacecraft low-thrust trajectory optimization, specifically:

[0046]

[0047]

[0048] Among them, the superscripts fwd and bwd represent forward recursion and backward recursion respectively, and the subscript mp represents the matching point. Respectively represent the spacecraft position equality constraints at the matching points, is the spacecraft velocity equation constraint, is the mass equality constraint of the spacecraft at the matching point;

[0049] The inequality constraints for solving the small thrust trajectory are set up as follows:

[0050]

[0051] m f ≥m dry (2)

[0052] Inequality constraint (1) indicates that at any control point, the modulus of the unit control quantity is less than 1, that is, the acceleration generated by the spacecraft for any trajectory unit is less than the ratio of its maximum thrust to the mass of the spacecraft at that moment; Inequality constraint (2) indicates that the final mass of the spacecraft at the end of the orbit transfer must be greater than the dry weight of the spacecraft m dry .

[0053] Preferably, the training of the generative adversarial network using the training data as the real trajectory data includes:

[0054] The generative adversarial network consists of a trajectory generator and a trajectory discriminator;

[0055] The trajectory generator uses noise data as input to generate synthetic trajectory data; the trajectory discriminator is trained using an equal amount of synthetic trajectory data and real trajectory data; the trajectory discriminator evaluates the authenticity of the low-thrust transfer trajectory data.

[0056] Preferably, the structure of the trajectory generator includes L G Layer fully connected layer;

[0057] The trajectory discriminator includes L D Layer fully connected layer.

[0058] Preferably, the trajectory discriminator loss function is calculated as follows:

[0059]

[0060] The trajectory generator loss function is calculated as follows:

[0061]

[0062] Where:

[0063]

[0064] Among them, x is the real data, z is the noise, is the interpolation point between the synthetic low-thrust trajectory data and the real trajectory data, the term with λ is the gradient penalty term, and λ is the penalty coefficient. For the trajectory discriminator The L2 norm of the gradient vector at E x [D(x)] represents the true trajectory expectation, E z [D(G(z))] represents the generated trajectory expectation, represents the trajectory discriminator expectation; N b is the batch size; D(x i ) is the real trajectory data x i The value input to the trajectory discriminator D; D(G(z i )) is the random noise data z i The trajectory generator G generates synthetic trajectory data G(z i )The value input to the trajectory discriminator D; Trajectory discriminator D at the interpolation point The gradient vector at ; Interpolation point The penalty value of .

[0065] In a second aspect, the present invention provides a spacecraft low-thrust trajectory data generation system, comprising:

[0066] The initialization module is used to randomly set the spacecraft parameters, the initial target position velocity, and the arrival target position velocity, search for the minimum velocity increment under the dual-pulse transfer orbit model, and the corresponding pulse orbit transfer time. Based on the pulse orbit transfer time, the low-thrust transfer time is randomly selected to obtain the orbit transfer time of the low-thrust spacecraft; the initial value of the spacecraft mass is randomly initialized to obtain the initial spacecraft mass;

[0067] A training data acquisition module is used to substitute the initial position velocity, target position velocity, orbit transfer time, and initial mass of the spacecraft into a pre-established low-thrust trajectory optimization model and optimal control problem solving model for solar electric propulsion to obtain training data.

[0068] The trajectory generator training module is used to train a generative adversarial network using the training data as real trajectory data to obtain a trajectory generator, which is used to generate low-thrust trajectory data for spacecraft.

[0069] In a third aspect, the present invention provides a storage medium storing a computer program for generating low-thrust trajectory data for a spacecraft, wherein the computer program enables a computer to execute the method for generating low-thrust trajectory data for a spacecraft as described above.

[0070] In a third aspect, the present invention provides an electronic device, comprising:

[0071] one or more processors;

[0072] Memory; and

[0073] 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 instructions for executing the method for generating low-thrust trajectory data for a spacecraft as described above.

[0074] (3) Beneficial effects

[0075] The present invention provides a method and system for generating low-thrust trajectory data for spacecraft. Compared with the existing technology, it has the following advantages:

[0076] The present invention randomly sets spacecraft parameters, initial position, and target position to obtain the orbit transfer time corresponding to the minimum velocity increment under a dual-pulse transfer orbit model. Based on the orbit transfer time, the low-thrust transfer time is randomly assigned a value to obtain the orbit transfer time of the low-thrust spacecraft. The initial position velocity and target position velocity are then obtained based on the mission initial position and target position. The initial value of the spacecraft mass is randomly initialized to obtain the spacecraft initial mass. The initial position velocity, target position velocity, orbit transfer time, and spacecraft initial mass are substituted into a pre-established low-thrust trajectory optimization model and optimal control problem-solving model for solar electric propulsion to obtain training data. The training data is used as real trajectory data to train a generative adversarial network to obtain a trajectory generator, which is used to generate low-thrust trajectory data for the spacecraft. The present invention uses a small amount of randomly generated training data to train a generative model. After training, the model can generate data with a high convergence rate that is identical to the original low-thrust trajectory data, greatly improving data generation efficiency and providing a strong guarantee for high-quality training data for low-thrust trajectory generation technology based on deep learning. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] 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.

[0078] Figure 1 This is a block diagram of a method for generating low-thrust trajectory data for a spacecraft according to an embodiment of the present invention;

[0079] Figure 2 Flowchart of the training and application phases of the generative adversarial network;

[0080] Figure 3 This is a schematic diagram of using the solar electric propulsion low-thrust trajectory state based on the Sims-Flanagan method to recursively deduce the spacecraft low-thrust trajectory;

[0081] Figure 4 A diagram showing the loss curve for training a generative adversarial network.

[0082] Figure 5 This is a schematic diagram of the convergence rate curve of the thrust trajectory characteristic trajectory generator;

[0083] Figure 6 Schematic diagram for comparing the characteristics of synthetic trajectory data and real trajectory characteristics. DETAILED DESCRIPTION

[0084] 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.

[0085] The embodiments of the present application provide a method and system for generating low-thrust trajectory data for spacecraft, thereby solving the technical problem of low convergence rate of existing methods for generating low-thrust trajectory data for spacecraft, providing efficient data generation technology for deep learning-based trajectory optimization in multiple scenarios, and providing strong support for the application of various types of deep learning in low-thrust trajectory optimization.

[0086] The technical solution in the embodiments of the present application is to solve the above technical problems, and the overall idea is as follows:

[0087] Artificial intelligence technologies such as deep learning have shown potential in trajectory design. However, deep learning methods require a large amount of training data. Obtaining massive amounts of continuous thrust trajectory training data faces the following difficulties:

[0088] (1) High computational cost: Whether using direct or indirect methods, the process of solving the optimal trajectory is itself a computationally intensive task and takes a lot of time. If more complex multi-body problems or those involving multiple constraints are considered, the design difficulty and computational cost will be further increased.

[0089] (2) Solution uncertainty and resource waste: Before solving the optimal control problem, it is often impossible to determine whether the currently set transfer trajectory has a feasible solution. A large amount of computing resources and time may be wasted trying to solve transfer trajectories that are actually infeasible.

[0090] (3) Scenario diversity leads to an explosion in data requirements: Faced with different propulsion systems (e.g., different specific impulses and maximum thrusts), mission objectives (e.g., different initial and target orbits), and diverse mission scenarios (e.g., flyby missions, rendezvous missions, accompanying missions, landing missions, or other special missions), each combination requires the generation of a corresponding dataset. Building massive amounts of training data for each specific mission scenario and parameter combination is extremely time-consuming and resource-intensive.

[0091] Existing methods typically use a Monte Carlo-based random generation method to obtain training data. Specifically, the spacecraft specific impulse, power, maximum thrust, dry weight, and propulsion method are set for the mission scenario. Then, the initial target position, final target position, flight time, spacecraft fuel mass, and optimization objective (such as minimum transfer time, minimum fuel consumption, or multi-objective optimization) are randomly selected. A direct or indirect method is used to solve the problem. If a solution exists, the low-thrust trajectory control variable is retained. In some scenarios, the convergence rate of the solution using random initialization is less than 10%. Some studies have improved the convergence rate by limiting the differences between certain orbital elements between the targets, such as those in orbital inclination or eccentricity. This has improved the convergence rate to some extent, but the overall convergence rate remains low, and the problem has not been fundamentally resolved. Furthermore, this approach directly results in poor generalization of the trained continuous thrust orbit model. For scenarios with large differences in orbital inclination or eccentricity, it may not be able to output a good solution.

[0092] Therefore, there is an urgent need for a method that can efficiently generate continuous thrust trajectory data to overcome the bottleneck of traditional data acquisition methods and provide sufficient training support for rapid orbit design based on deep learning. The embodiment of the present invention proposes to use generative neural network technology to solve this problem. The spacecraft low-thrust trajectory generation technology based on generative adversarial networks uses a small amount of randomly generated raw data to train the generative model. After training, it can generate data distribution identical to the original low-thrust trajectory data with a high convergence rate, greatly improving the data generation efficiency and providing a strong guarantee of high-quality training data for the low-thrust trajectory generation technology based on deep learning.

[0093] 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.

[0094] The embodiment of the present invention provides a method for generating low-thrust trajectory data of a spacecraft, such as Figure 1Shown, including:

[0095] S1. Randomly set the spacecraft parameters, initial target position velocity, and arrival target position velocity, search for the minimum velocity increment under the dual-pulse transfer orbit model, and the corresponding pulse orbit transfer time. Randomly select the low-thrust transfer time based on the pulse orbit transfer time to obtain the orbit transfer time of the low-thrust spacecraft; randomly initialize the initial value of the spacecraft mass to obtain the spacecraft initial mass;

[0096] S2. Substituting the initial position velocity, target position velocity, orbit transfer time of the low-thrust spacecraft, and initial mass of the spacecraft into a pre-established low-thrust trajectory optimization model and optimal control problem solving model for solar electric propulsion to obtain training data;

[0097] S3. Using the training data as real trajectory data to train a generative adversarial network to obtain a trajectory generator, wherein the trajectory generator is used to generate low-thrust trajectory data of the spacecraft.

[0098] The embodiment of the present invention uses a small amount of randomly generated training data to train the generative model. After training, it can generate data distribution identical to the original low-thrust trajectory data with a high convergence rate, greatly improving the data generation efficiency and providing a strong guarantee for high-quality training data for the low-thrust trajectory generation technology based on deep learning.

[0099] The following combination Figure 2 The schematic diagram of the training phase and application phase of the generative adversarial network shown in FIG. 1 is used to describe the embodiment of the present invention in detail:

[0100] In this embodiment of the present invention, before executing step S1, a low-thrust trajectory optimization mission scenario for a near-Earth asteroid exploration mission is established, and 30,000 asteroids with public ephemeris are selected as a target dataset.

[0101] Step S1 specifically includes:

[0102] S101, randomly select small celestial bodies A1, A2, define the mission time period [T start ,T end In this embodiment of the present invention, the mission time period [2460676.5, 2475286.5] (January 1, 2025 to January 1, 2065) is defined. At the same time, the initial target position velocity and the target position velocity are calculated based on two randomly selected small celestial bodies, a random mission start time is given, and the ephemeris of the small celestial body A1 at the mission start time is calculated as the initial position velocity of the low-thrust spacecraft; then, by trying different flight times, the mission end time can be obtained, and the target position velocity is calculated based on the end time. Low thrust in the aerospace field refers to an engine with a thrust of less than 30kN.

[0103] S102, randomly select the initial time t of the small thrust transfer task i ∈[T start ,T end ], time of flight TOF0, establish a dual-pulse orbit transfer model, and solve the Lambert equation to obtain the total velocity increment Δv under dual-pulse thrust at time of flight TOF0 = lambert(A1, A2, t i In the embodiment of the present invention, the time of flight TOF0=15 days.

[0104] S103. Repeat step S102 to perform a variable step search on the time of flight TOF0, and try to search at TOF0 (the range is (TOF0-h0, TOF0+h0), where h0 is the initial search step, and the embodiment of the present invention is set to h0=5 days). The direction of the next search and the new step size are determined according to the changing trend of Δv. If Δv becomes smaller, the step size is increased (the embodiment of the present invention is set to 1.2h0). If Δv becomes larger, the step size is reduced (the embodiment of the present invention is set to 0.8h0). In this way, the orbit corresponding to the minimum velocity increment under the double-pulse transfer orbit model and the pulse orbit transfer time Δt are obtained. impls .

[0105] S104, based on the obtained Δt impls Randomly select the value of the small thrust transfer time in the interval: Δt LT ∈[a1·Δt impls ,a2·Δt impls ], a1 and a2 are the lower and upper limit coefficients of the transfer trajectory time, which are adjusted according to engineering experience, Δt LT is the orbit transfer time of a low-thrust spacecraft.

[0106] At the same time, the initial value of the spacecraft mass needs to be randomly initialized in the interval m0∈[m dry ,m max In the embodiment of the present invention, Δt LT ∈[1.2·Δt impls ,min{2Δt impls ,700}],m0∈[1200kg,3000kg]. That is, the dry weight of the low-thrust spacecraft is m dry =1200kg, spacecraft wet mass m wet The maximum is 3000kg, so the weight of the spacecraft fuel is m prop The maximum is 1800kg.

[0107] Step S2 specifically includes:

[0108] In the embodiment of the present invention, the low-thrust trajectory optimization model for a spacecraft for solar electric propulsion consists of a spacecraft state vector, the position and velocity state quantities of the spacecraft for solar electric propulsion, and the update formulas for position, velocity, and mass. The establishment process is as follows:

[0109] In the embodiment of the present invention, the solar electric propulsion low thrust trajectory state based on the Sims-Flanagan method is used to recursively infer the spacecraft low thrust trajectory, as shown in the schematic diagram. Figure 3 shown.

[0110] The spacecraft state vector can be expressed as:

[0111] s=[rvm]

[0112] Where r = [r x ,r y ,r z ],v=[v x ,v y ,v z ] is the spacecraft position and velocity vector in the inertial coordinate system, m=m wet =m dry +m prop . m dry is the dry weight of the low-thrust spacecraft, m prop is the weight of spacecraft fuel, m wet is the wet mass of the spacecraft.

[0113] According to the low-thrust trajectory state of solar electric propulsion based on the Sims-Flanagan method, the bidirectional recursion of the spacecraft state is performed to obtain the spacecraft state at each discrete moment. At each discrete control point i, assuming the size is Δv i The pulse acceleration acts on the control point i instantly. In order to increase the robustness of the solver, unit vector control is adopted, and the control vector Δv i =[Δv x ,Δv y ,Δv z ] is replaced by the unit control vector u=[u x ,u y ,u z ], where [u x ,u y ,u z The unit range of ] is [-1,1]. Therefore, the spacecraft speed at each moment is calculated by the following formula:

[0114]

[0115] Among them, N seg is the number of discrete units of the trajectory (i.e., the number of segments of the trajectory, in the embodiment of the present invention, Nseg The initial value of Δv is set to 20), max,i is the maximum velocity change that can be generated in this trajectory unit. As the spacecraft fuel is continuously consumed, the mass of the spacecraft gradually decreases, so Δv max,i The values ​​are different in different trajectory segments. The “+” and “-” superscripts represent the state before and after the spacecraft generates impulse thrust, respectively. The + direction is always relative to the forward recursive direction of the spacecraft state. i is the forward recursive trajectory unit number, and j is the backward recursive trajectory unit number.

[0116] The recursive calculation of the spacecraft position and velocity can be obtained from the spacecraft dynamics equations:

[0117]

[0118] Where μ is the gravitational constant, is the acceleration. Expanding the above formula, we can obtain the expression of the spacecraft position and velocity state quantity X for solar electric propulsion as follows:

[0119]

[0120] in, is the velocity vector, is the acceleration vector;

[0121] For the above dynamic equations, the Kepler two-body model is used for calculation in the rapid search stage. In engineering application scenarios, factors such as complex perturbations can be considered, and the Runge-Kutta-Fehlberg (RKF78) method is used for recursion to obtain better results.

[0122] The spacecraft mass update is calculated using the Tsiolkovsky rocket equation:

[0123]

[0124] The + / - subscripts represent the mass of the spacecraft before and after the impulse thrust is generated, and the “+” is relative to the positive direction of the spacecraft state recursion. e is the effective exhaust velocity, v e =I sp g0, I sp is the engine specific impulse, g0 is the acceleration due to gravity (in the embodiment of the present invention, the engine specific impulse is sp =4000s, g0=9.80665e-3km / s 2 , effective exhaust velocity v e =I sp g0 = 39.2266 km / s, Δv iis the spacecraft velocity increment generated by the pulse engine at the i-th control point. In the forward recursion, Δv i It is determined by the spacecraft mass and the maximum thrust of the spacecraft and is calculated by the following formula:

[0125]

[0126] Where Δv max,i is the maximum velocity increment that can be generated in the i-th unit, is the unit control quantity of the i-th unit, F max Δt is the maximum thrust that the spacecraft can generate in any direction. LT is the orbit transfer time of a low-thrust spacecraft. In the solar electric propulsion scenario, the maximum thrust is not a fixed value, which can be expressed as

[0127]

[0128] Where η is the energy conversion efficiency of the solar electric propulsion system, P0 is the solar power obtained by the spacecraft at 1 AU, and r is the Euclidean distance between the spacecraft and the sun. In the embodiment of the present invention, η = 0.6, P0 is set to 40kW, and 1 AU = 149597870.7 km. Therefore, the maximum thrust of the spacecraft at 1 AU is F max (1AU)=1.2237N.

[0129] The forward rocket equation for spacecraft mass is recursively calculated as follows:

[0130]

[0131] in, and are the spacecraft masses after and before the pulse thrust is generated in the i-th small thrust arc segment, respectively. It should be noted that the model used in this embodiment of the present invention is closer to engineering practice, and the model is a model with variable maximum thrust and variable acceleration. The backward spacecraft mass is recursively deduced as follows:

[0132]

[0133] in, and Represents the mass of the spacecraft after and before the pulse thrust in the j-th arc segment of the backward recursion.

[0134] However, the above expression of the backward spacecraft mass recursion ignores Δv j It's actually about In order to obtain a more accurate analytical expression for a transcendental function, an embodiment of the present invention provides a spacecraft mass backward recursion method based on the Omega equation, which is specifically designed for trajectory calculation of small-thrust spacecraft with variable acceleration.

[0135] First, we give the general form of backward recursion:

[0136]

[0137] To give The expression of , let:

[0138]

[0139] Reorganize the original equation into the form of Omega function To solve, the method is as follows:

[0140]

[0141] in, is an Omega function. Therefore, the backward recursive solution to the mass of a spacecraft with a variable maximum acceleration and low thrust trajectory for solar electric propulsion is as follows:

[0142]

[0143] The Omega function can be solved by a variety of professional tools, thereby obtaining the spacecraft mass under the condition of maximum thrust time-varying conditions and performing backward recursion.

[0144] The pre-established optimal control problem solving model includes the objective function and constraints:

[0145] The constraints include equality constraints and inequality constraints for spacecraft low-thrust trajectory optimization.

[0146] like Figure 3 As shown in the forward and backward recursion, the spacecraft state at the matching point must be continuous, thus establishing the small thrust trajectory optimization equation constraint:

[0147]

[0148] Among them, the superscripts fwd and bwd represent forward recursion and backward recursion respectively, and the subscript mp represents the matching point. Respectively represent the spacecraft position equality constraints at the matching points, is the spacecraft velocity equation constraint, is the mass equality constraint for the spacecraft at the matching point. This equality constraint ensures that the forward and backward recursive positions, velocities, and masses of the spacecraft at the matching point are strictly equal. Parameters with subscripts x, y, and z denote their components in the three directions of the inertial frame.

[0149] The inequality constraints for solving the small thrust trajectory are set up as follows:

[0150]

[0151] m f ≥m dry

[0152] Inequality constraint 1 indicates that at any control point, the modulus of the unit control quantity is less than 1, that is, the acceleration generated by the spacecraft in any trajectory unit is less than the ratio of its maximum thrust to the mass of the spacecraft at that moment; Inequality constraint 2 indicates that the final mass of the spacecraft at the end of the orbit transfer must be greater than the dry weight m of the spacecraft. dry From the above, the small thrust trajectory optimization problem for solar electric propulsion is transformed into a large-scale nonlinear programming problem. The improved problem model can improve the accuracy of the solution. The optimization goal is to minimize fuel consumption. The objective function is as follows:

[0153] J=min(m fuel )

[0154] Among them, m fuel is the fuel consumption, m fuel =m f -m i , where m f is the final mass of the spacecraft after the low-thrust orbit transfer, m i is the initial mass of the spacecraft before transfer. The solar electric propulsion low-thrust trajectory optimization problem is thus transformed into a large-scale nonlinear programming problem. The improved problem model improves solution accuracy, with the optimization objective being to minimize fuel consumption. This problem can be solved using open-source or commercial tools such as IPOPT, SNOPT, and MATLAB (fmincon function).

[0155] The initial and target position and velocity information, the low-thrust spacecraft's orbit transfer time, and the spacecraft's initial mass are substituted into the pre-established low-thrust spacecraft trajectory optimization model and optimal control problem solving model for solar electric propulsion. The specific process of solving the training data is as follows:

[0156] S201: Calculate the trajectory between the low-thrust trajectory control points using the Kepler two-body model. Random initial values ​​are used for the unit pulse amplitude and direction, and a nonlinear solver is used to solve the problem. If convergence is achieved, proceed to step S202. If convergence is not achieved after a preset number of random initial values ​​(set to 5 in this embodiment), the transfer trajectory is stored in the infeasible trajectory database and the process returns to step S1 to re-initialize.

[0157] S202. If a converged low-thrust trajectory is obtained in step S201, an optimization model with more trajectory segments is established. The trajectory recursion between the low-thrust control points is numerically recursively calculated using the RKF78 method to obtain a more accurate solution. The transfer trajectory is stored in the feasible trajectory database as training data for the generative adversarial model.

[0158] Step S3 specifically includes:

[0159] Incorporating generative adversarial thinking, a generative adversarial network model is constructed and trained to obtain a trajectory generator. This generates low-thrust trajectory data features that approximate the distribution of the original low-thrust trajectory data at a high convergence rate. This embodiment of the present invention is specifically designed and optimized for the low-thrust trajectory generation problem.

[0160] The generative adversarial network (GAN) designed in this embodiment of the present invention includes a trajectory generator and a trajectory discriminator. A GAN is a deep neural network whose architecture consists of two deep neural networks: a trajectory generator and a trajectory discriminator, which compete with each other during training.

[0161] The overall goal of training the trajectory generator is to obtain a trajectory generator that only generates feasible low-thrust transfer features for spacecraft, thereby addressing the low convergence rate of trajectory data acquisition in existing technologies. Spacecraft low-thrust orbit transfer features include the spacecraft's initial mass, final mass, flight time, and the positions, velocities, or six-element numbers of the two target celestial bodies.

[0162] The trajectory generator uses the noisy data as input to generate synthetic low-thrust transfer trajectory feature data. The trajectory discriminator is trained using an equal amount of synthetic trajectory data and real trajectory data. The trajectory discriminator evaluates the authenticity of the low-thrust transfer trajectory data.

[0163] The trajectory generator network G has an input capacity of N input ×N b Gaussian noise vector, N input is the noise dimension, N b is the training data batch size, and the trajectory generator network G consists of L G layers of fully connected layers, each layer contains neurons, of which the dropout layer is designed with a dropout rate of The activation function is Leaky Relu or Relu, and the network learning rate is η G , the learning rate decay period is The learning rate decay rate is Low thrust trajectory data F generated by the trajectory generator GEN ={m i ,tof,m f,COE,MEE,PV}. In the implementation of the present invention, N input =100, N b =300, the trajectory generator network G consists of 20 fully connected layers, each layer contains 200 neurons, with a dropout rate of 0.5, an activation function of ReLU, and a network learning rate of 2.5×10 -4 , the learning rate decay cycle is 200 epochs, and the learning rate decay rate is 0.05.

[0164] The input of trajectory discriminator D is equal amounts of synthetic small thrust transfer data and real small thrust transfer data. D layers of fully connected layers, each layer contains neurons, the activation function is Relu, and the network learning rate is η D In the implementation of the present invention, the trajectory discriminator D consists of 4 fully connected layers, each layer contains 400 neurons, the activation function is ReLU, and the network learning rate is 1×10 -4 .

[0165] To prevent gradient vanishing and improve training stability, the embodiment of the present invention designs a Wasserstein loss function with gradient penalty to replace the conventional log-likelihood loss. The trajectory discriminator loss function is calculated as follows:

[0166]

[0167] Among them, x is the real data, z is the noise, is the interpolation point between the synthetic low-thrust trajectory data and the real trajectory data, the term with λ is the gradient penalty term, and λ is the penalty coefficient (in the embodiment of the present invention, λ=10), For the trajectory discriminator The L2 norm of the gradient vector at .

[0168] The trajectory generator loss function is calculated as follows:

[0169]

[0170] During the training process, Gaussian noise is generated and sampled as the input of the trajectory generator, and synthetic trajectory data is obtained through the trajectory generator. At this time, the synthetic trajectory data and the real trajectory data are input into the trajectory discriminator, and the trajectory discriminator is allowed to classify the real and synthetic data, calculate the loss function and gradient, and use the Adam algorithm to update the parameters of the trajectory discriminator. After that, the trajectory generator is trained. Sampling from the noise sample again, input into the trajectory generator to generate new data again, the newly generated data is input into the trajectory discriminator for identification, and the parameters of the trajectory generator are updated based on the error fed back to the trajectory discriminator by the trajectory discriminator. This is repeated iteratively, and the parameters of the trajectory generator and the trajectory discriminator are continuously adjusted. The generative adversarial network is trained until the trajectory generator generates synthetic low-thrust transfer trajectory data that the trajectory discriminator cannot distinguish between true and false. This shows that the low-thrust transfer features generated by the trajectory generator have the same distribution as the real features. In the implementation process, the Mini-Batch training method is adopted to randomly sort the training data obtained in step three and sort them according to the batch size N. b The data is divided into batches and then input into the deep network in sequence. Then the true trajectory expectation E x , generate trajectory expectation E z , trajectory discriminator expectation The average value of the batch data is obtained using the following formula:

[0171]

[0172] Among them, N b is the batch size, D(x i ) is the real trajectory data x i The value input to the trajectory discriminator D, D(G(z i )) is the random noise data z i The trajectory generator G generates synthetic trajectory data G(z i ) is the value input to the trajectory discriminator D, Trajectory discriminator D at the interpolation point The gradient vector at , Interpolation point The penalty value of .

[0173] The generator and discriminator loss functions during training are as follows Figure 4 shown.

[0174] In order to evaluate the network training, the scoring Rank of the trajectory generator and trajectory discriminator is introduced in each round of training iteration. G and Rank D , evaluate whether the capabilities of the two deep neural networks are balanced. For a batch of trajectory data, Randk G and Rank DThe design is as follows:

[0175]

[0176] The trajectory discriminator always outputs the probability that the low-thrust trajectory feature is true. and are the probabilities of synthetic low-thrust trajectory data and real trajectory data being judged as true, Rank G is the mean probability of the synthetic trajectory data being judged as true, Rank D It represents the mean probability that the trajectory discriminator can correctly identify the synthetic and real trajectories. G and Rank D The Rank G and Rank D Both are close to 0.5, indicating that the two network capabilities are balanced. G and Rank D 0.4 and 0.6 respectively.

[0177] The trajectory generator network can directly generate synthetic trajectories that are consistent with the distribution of real feasible low-thrust trajectory data from noise. During the training process, the convergence rate gradually increases and eventually reaches about 90% (see Figure 5 ), and the trajectory generator synthetic data is basically consistent with the real data distribution (see Figure 6 ), which greatly improves the data generation efficiency while ensuring the integrity of the generated data set.

[0178] The trained trajectory generator network is used as a trajectory generator to generate spacecraft low-thrust trajectory data based on Gaussian noise.

[0179] An embodiment of the present invention further provides a spacecraft low-thrust trajectory data generation system, comprising:

[0180] The initialization module is used to randomly set the spacecraft parameters, the initial target position velocity, and the arrival target position velocity, search for the minimum velocity increment under the dual-pulse transfer orbit model, and the corresponding pulse orbit transfer time. Based on the pulse orbit transfer time, the low-thrust transfer time is randomly selected to obtain the orbit transfer time of the low-thrust spacecraft; the initial value of the spacecraft mass is randomly initialized to obtain the initial spacecraft mass;

[0181] A training data acquisition module is used to substitute the initial position velocity, target position velocity, orbit transfer time, and initial mass of the spacecraft into a pre-established low-thrust trajectory optimization model and optimal control problem solving model for solar electric propulsion to obtain training data.

[0182] The trajectory generator training module is used to train a generative adversarial network using the training data as real trajectory data to obtain a trajectory generator, which is used to generate low-thrust trajectory data for spacecraft.

[0183] An embodiment of the present invention further provides a computer-readable storage medium storing a computer program for generating low-thrust trajectory data for a spacecraft, wherein the computer program enables a computer to execute the method for generating low-thrust trajectory data for a spacecraft as described above.

[0184] 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 spacecraft low-thrust trajectory data generation method as described above.

[0185] It is understandable that the spacecraft low-thrust trajectory data generation system, storage medium and electronic device provided in the embodiments of the present invention correspond to the above-mentioned spacecraft low-thrust trajectory data generation method. The explanations, examples, beneficial effects and other parts of the relevant contents can refer to the corresponding contents in the spacecraft low-thrust trajectory data generation method, and will not be repeated here.

[0186] In summary, compared with the existing technology, the present invention has the following beneficial effects:

[0187] 1. The embodiment of the present invention uses a small amount of randomly generated training data to train the generative model. After training, it can generate data distribution identical to the original low-thrust trajectory data with a high convergence rate, greatly improving the data generation efficiency and providing a strong guarantee for high-quality training data for the low-thrust trajectory generation technology based on deep learning.

[0188] 2. This embodiment, targeting low-thrust trajectory data generation scenarios, innovatively proposes generative adversarial networks (GANs) to accelerate spacecraft low-thrust data generation. Through extensive experiments, the architectures of the trajectory generator network and the trajectory discriminator are optimized, balancing the capabilities of the two networks. A loss function and network evaluation metrics are designed, along with a specific network training strategy and process, ensuring network convergence and preventing mode collapse.

[0189] 3. The embodiment of the present invention aims at the optimization problem of small inference trajectories with time-varying maximum thrust (time-varying maximum acceleration of control points) such as solar electric propulsion, and improves the backward recursion method of spacecraft mass by using the Omega equation. Without significantly increasing the computational complexity, the problem of coupling between the spacecraft recursive mass and the exponential term of the rocket equation during the backward recursion of the spacecraft mass is solved, thereby improving the accuracy of the analytical model.

[0190] 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.

[0191] 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 method for generating low-thrust trajectory data of a spacecraft, characterized in that: include: The spacecraft parameters, initial target position velocity, and arrival target position velocity are randomly set. The minimum velocity increment and the corresponding pulse orbit transfer time under the dual-pulse transfer orbit model are searched and obtained. The low-thrust transfer time is randomly selected based on the pulse orbit transfer time to obtain the orbit transfer time of the low-thrust spacecraft. The initial value of the spacecraft mass is randomly initialized to obtain the initial mass of the spacecraft. Substitute the initial position velocity, target position velocity, orbit transfer time, and initial mass of the spacecraft into a pre-established low-thrust trajectory optimization model and optimal control problem solving model for solar electric propulsion to obtain training data. The training data is used as real trajectory data to train a generative adversarial network to obtain a trajectory generator, which is used to generate low-thrust trajectory data of a spacecraft.

2. The method for generating low-thrust trajectory data of a spacecraft according to claim 1, wherein: The pre-established low-thrust trajectory optimization model for a spacecraft oriented to solar electric propulsion includes a spacecraft state vector, spacecraft position and velocity state quantities oriented to solar electric propulsion, and update formulas for position, velocity, and mass; Among them, the spacecraft state vector is expressed as: s=[rvm] Where r = [r x ,r y ,r z ] is the spacecraft position in the inertial coordinate system, v=[v x ,v y ,v z ] is the velocity vector of the spacecraft in the inertial coordinate system, m=m wet =m dry +m prop , m dry is the dry weight of the low-thrust spacecraft, m prop is the weight of spacecraft fuel, m wet is the spacecraft wet weight; The low-thrust trajectory state of solar electric propulsion based on the Sims-Flanagan method is used to recursively infer the low-thrust trajectory of the spacecraft, and the spacecraft position and velocity state quantities for solar electric propulsion, as well as the update formulas for position, velocity, and mass, are obtained. The velocity update formula includes: At each discrete control point i, assuming the size is Δv i The pulse acceleration acts on the control point i instantly, and the unit vector control is adopted. The control vector Δv i =[Δv x ,Δv y ,Δv z ] is replaced by the unit control vector u=[u x ,u y ,u z ], where [u x ,u y ,u z ] has a unit range of [-1,1]; therefore, the spacecraft speed at each moment is calculated by the following formula: After the velocity is updated, the spacecraft position is updated based on the orbital dynamics equations; The quality update formula includes: The recursive expression of the forward spacecraft mass is as follows: The expression for the backward spacecraft mass recursion is as follows: Where μ is the gravitational constant; is the acceleration, r is the Euclidean distance between the spacecraft and the sun; N seg is the number of discrete units of the trajectory, Δv max,i is the maximum velocity change that can be generated in this trajectory unit; the "+" and "-" superscripts represent the spacecraft before and after the generation of pulse thrust, respectively; i is the forward recursive trajectory unit number, and j is the backward recursive trajectory unit number; and are the spacecraft masses after and before the pulse thrust is generated in the i-th small thrust arc segment; and represents the mass of the spacecraft before and after the pulse thrust in the jth arc segment of the backward recursion; v e is the effective exhaust velocity; Δv j is the spacecraft velocity increment generated by the pulse engine at the jth control point; Δt LT is the orbit transfer time of the low-thrust spacecraft; F max (r) is the maximum thrust that the spacecraft can generate in any direction when the spacecraft is at a Euclidean distance r from the sun; is the unit control quantity of the nth unit; Parameters with subscripts x, y, and z represent the components of the corresponding parameters in the three directions in the inertial system.

3. The method for generating spacecraft low-thrust trajectory data according to claim 1 according to claim 2, wherein: Also includes: The spacecraft mass backward recursion method based on the Omega equation is sampled and the expression of the backward spacecraft mass recursion is optimized, specifically: This gives the general form of the backward recursion: To give The expression of , let: Reorganize the original equation into the form of Omega function To solve, the method is as follows: Therefore, the backward recursive solution to the mass of the spacecraft with variable maximum acceleration and low thrust trajectory for solar electric propulsion is as follows: in, is the Omega function.

4. The method for generating low-thrust trajectory data of a spacecraft according to claim 1, wherein: The pre-established optimal control problem solving model includes an objective function and constraints: Among them, the objective function is to minimize fuel consumption, which is expressed as follows: J=min(m fuel ) Among them, m fuel is the fuel consumption, m fuel =m f -m i , where m f is the final mass of the spacecraft after the low-thrust orbit transfer, m i is the initial mass of the spacecraft before transfer; The constraints include equality constraints and inequality constraints for spacecraft low-thrust trajectory optimization, specifically: Among them, the superscripts fwd and bwd represent forward recursion and backward recursion respectively, and the subscript mp represents the matching point. Respectively represent the spacecraft position equality constraints at the matching points, is the spacecraft velocity equation constraint, is the mass equality constraint of the spacecraft at the matching point; The inequality constraints for solving the small thrust trajectory are set up as follows: m f ≥m dry (2) Inequality constraint (1) indicates that at any control point, the modulus of the unit control quantity is less than 1, that is, the acceleration generated by the spacecraft for any trajectory unit is less than the ratio of its maximum thrust to the mass of the spacecraft at that moment; Inequality constraint (2) indicates that the final mass of the spacecraft at the end of the orbit transfer must be greater than the dry weight of the spacecraft m dry .

5. The method for generating low-thrust trajectory data of a spacecraft according to any one of claims 1 to 4, characterized in that: The method of training a generative adversarial network using the training data as real trajectory data includes: The generative adversarial network consists of a trajectory generator and a trajectory discriminator; The trajectory generator uses noise data as input to generate synthetic trajectory data; the trajectory discriminator is trained using an equal amount of synthetic trajectory data and real trajectory data; the trajectory discriminator evaluates the authenticity of the low-thrust transfer trajectory data.

6. The method for generating low-thrust trajectory data of a spacecraft according to claim 5, wherein: The structure of the trajectory generator includes L G Layer fully connected layer; The trajectory discriminator includes L D Layer fully connected layer.

7. The method for generating low-thrust trajectory data of a spacecraft according to claim 5, wherein: The trajectory discriminator loss function is calculated as follows: The trajectory generator loss function is calculated as follows: Where: Among them, x is the real data, z is the noise, is the interpolation point between the synthetic low-thrust trajectory data and the real trajectory data, the term with λ is the gradient penalty term, and λ is the penalty coefficient. For the trajectory discriminator The L2 norm of the gradient vector at E x [D(x)] represents the true trajectory expectation, E z [D(G(z))] represents the generated trajectory expectation, represents the trajectory discriminator expectation; N b is the batch size; D(x i ) is the real trajectory data x i The value input to the trajectory discriminator D; D(G(z i )) is the random noise data z i The trajectory generator G generates synthetic trajectory data G(z i )The value input to the trajectory discriminator D; Trajectory discriminator D at the interpolation point The gradient vector at ; Interpolation point The penalty value of .

8. A spacecraft low-thrust trajectory data generation system, characterized in that: include: The initialization module is used to randomly set the spacecraft parameters, the initial target position velocity, and the arrival target position velocity, search for the minimum velocity increment under the dual-pulse transfer orbit model, and the corresponding pulse orbit transfer time. Based on the pulse orbit transfer time, the low-thrust transfer time is randomly selected to obtain the orbit transfer time of the low-thrust spacecraft; the initial value of the spacecraft mass is randomly initialized to obtain the initial spacecraft mass; A training data acquisition module is used to substitute the initial position velocity, target position velocity, orbit transfer time, and spacecraft initial mass into a pre-established spacecraft low-thrust trajectory optimization model and optimal control problem solving model for solar electric propulsion to obtain training data; The trajectory generator training module is used to train a generative adversarial network using the training data as real trajectory data to obtain a trajectory generator, which is used to generate low-thrust trajectory data for spacecraft.

9. A storage medium, characterized in that: It stores a computer program for generating spacecraft low-thrust trajectory data, wherein the computer program enables a computer to execute the spacecraft low-thrust trajectory data generating method according to any one of claims 1 to 7.

10. An electronic device, characterized in that: include: one or more processors; Memory; as well as 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 a method for executing the spacecraft low-thrust trajectory data generation method according to any one of claims 1 to 7.

Images