Spacecraft small-thrust trajectory data generation method and system

Abstract

The application provides a spacecraft small-thrust trajectory data generation method and system, and relates to the technical field of trajectory data generation based on a deep neural network.A randomized data is input into a pre-established small-thrust trajectory optimization model for a spacecraft facing solar electric propulsion and a solution model for an optimal control problem, training data is solved, the training data is used as real trajectory data to train a generative adversarial network, a trajectory generator is obtained, and the trajectory generator is used to generate spacecraft small-thrust trajectory data.A small amount of randomly generated training data is used to train a generative model, after the training is completed, the same data distribution as the original small-thrust trajectory data can be generated at a high convergence rate, the data generation efficiency is greatly improved, and powerful high-quality training data guarantee is provided for small-thrust trajectory generation technology based on deep learning.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of trajectory data generation based on deep neural networks, in particular to a spacecraft small-thrust trajectory data generation method and system. BACKGROUND

[0002] The small-thrust trajectory optimization of a spacecraft is a complex optimization problem, which usually needs to solve an optimal control problem. Designing a continuous thrust trajectory that meets various constraints for a specific task (such as orbit transfer, rendezvous, constellation deployment, etc.) often involves long optimization calculations, with huge computational costs.

[0003] In recent years, artificial intelligence technologies such as deep learning have shown potential in trajectory design, such as treating trajectory design as a sequential decision problem and using reinforcement learning, or using deep learning models to directly predict the shortest time / fuel consumption of small-thrust trajectories, making complex multi-objective space mission design more efficient. However, deep learning methods require a large amount of training data, and for different task scenarios, spacecraft propulsion methods and dynamic constraints, high-quality small-thrust trajectory training data sets need to be generated efficiently. The traditional random method of generating data has low convergence rate, high computational cost, and problems such as solution uncertainty and resource waste, which greatly restricts the application of deep learning in continuous thrust trajectory optimization. The existing technical method basically adopts a random generation method based on Monte Carlo, the process mainly includes: first, for the task scenario, set the specific impulse, power, maximum thrust, spacecraft dry weight, propulsion method, etc. of the spacecraft. Then, randomly select the initial target position, end target position, flight time, spacecraft fuel mass, optimization target (shortest transfer time, minimum fuel consumption or multi-objective optimization), etc., and use the direct method or indirect method for solving, such as saving the small-thrust trajectory if there is a solution.

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

[0005] (I) Technical problems solved

[0006] In view of the deficiencies of the prior art, the present application provides a spacecraft small-thrust trajectory data generation method and system, which solves the technical problem of low convergence rate of the existing spacecraft small-thrust trajectory data generation method.

[0007] (II) Technical solutions

[0008] To achieve the above purpose, the present application is realized by the following technical solutions:

[0009] In a first aspect, the present application provides a spacecraft small-thrust trajectory data generation method, comprising:

[0010] Randomly set the spacecraft parameters, initial target position and velocity, and arrival target position and velocity, search for the minimum velocity increment under the double-pulse transfer orbit model, and the corresponding pulse orbit transfer time, randomly select the low-thrust transfer time according to the pulse orbit transfer time to obtain the orbit transfer time of the low-thrust spacecraft; randomly initialize the initial mass of the spacecraft to obtain the initial mass of the spacecraft;

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

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

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

[0014] The spacecraft state vector is represented as:

[0015]

[0016] where r = [r x ,r y ,r z ] is the position of the spacecraft 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 mass of the low-thrust spacecraft, m prop is the fuel weight of the spacecraft, and m wet is the wet mass of the spacecraft.

[0017] The low-thrust trajectory of the spacecraft is recursively calculated using the Sims-Flanagan method-based solar electric propulsion low-thrust trajectory state to obtain the position and velocity state of the spacecraft oriented to solar electric propulsion, and the update formulas for position, velocity, and mass;

[0018] The velocity update formula includes:

[0019] At each discrete control point i, assume that the size of Δv iThe pulse acceleration instantaneously acts on the control point i, and the unit vector control is adopted, and the control vector Δv i x y z is replaced by the unit control vector u = [u x , u y , u z ], wherein the unit range of [u x , u y , u z ] is [-1, 1]; thus, the spacecraft velocity at each moment is calculated by the following formula:

[0020]

[0021] After the velocity is updated, the spacecraft position is updated according to the orbit dynamics equation;

[0022] The mass update formula includes:

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

[0024]

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

[0026]

[0027] wherein μ is the gravitational constant; is the acceleration, and r is the Euclidean distance of the spacecraft from the sun; N seg is the number of trajectory discrete units, Δv max,i is the maximum velocity change that can be generated in the trajectory unit; the upper indexes "+" and "-" respectively represent the spacecraft after and before generating the pulse thrust; i is the forward recursion trajectory unit number, and j is the backward recursion trajectory unit number;

[0028] and are respectively the spacecraft mass after and before the pulse thrust in the i th small thrust arc segment; and represent the spacecraft mass after and before the pulse thrust in the j th 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 j th control point; Δt LT is the orbit transfer time of the small thrust spacecraft; F max (r) is the maximum thrust that the spacecraft can generate in any direction when the Euclidean distance from the sun is r; ​​​The unit control amount of the i th unit;

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

[0030] Preferably, it further comprises:

[0031] The sampling of the spacecraft mass backward recursion method based on the omega equation optimizes the expression of the backward spacecraft mass recursion, and specifically:

[0032] The general form of backward recursion is given:

[0033]

[0034] To give the expression of , let:

[0035]

[0036] The original equation is reorganized into the omega function form to solve , and the method is as follows:

[0037]

[0038] Therefore, the backward recursion solving method of the variable maximum acceleration small thrust trajectory spacecraft mass facing 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 a constraint condition:

[0042] Where the objective function is to minimize fuel consumption, and its expression is as follows:

[0043] J = min (m fuel )

[0044] Where m fuel is the fuel consumption, and m fuel = m f -m i , where m f is the final mass of the spacecraft after passing through the small thrust orbit transfer, and m i is the initial mass of the spacecraft before transfer;

[0045] The constraint condition includes the spacecraft small thrust trajectory optimization equality constraint and inequality constraint, specifically:

[0046]

[0047]

[0048] where the upper indices fwd and bwd represent the forward and backward recursion respectively, and the lower index mp represents the matching point, respectively represent the spacecraft position equality constraints at the matching point, is the spacecraft velocity equality constraint, is the spacecraft mass equality constraint at the matching point;

[0049] The small-thrust trajectory solving inequality constraints are set as follows:

[0050]

[0051] m f ≥m dry (2)

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

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

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

[0055] The trajectory generator generates synthetic trajectory data using noise data as input; the trajectory discriminator is trained using an equal number of synthetic trajectory data and real trajectory data; and the trajectory discriminator evaluates the authenticity of the small-thrust transfer orbit data.

[0056] Preferably, the structure of the trajectory generator comprises L G layers of fully connected layers;

[0057] The trajectory discriminator comprises L D layers of fully connected layers.

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

[0059]

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

[0061]

[0062] In the formula:

[0063]

[0064] where x is real data, z is noise, is an interpolation point between synthetic low-thrust trajectory data and real trajectory data, and the λ term is a gradient penalty term, and λ is a penalty coefficient, is the L2 norm of the gradient vector of the trajectory discriminator at ; E x [D(x)] represents the real 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 real trajectory data x i input to the trajectory discriminator D; D(G(z i )) is random noise data z i synthetic trajectory data G(z i ) generated by the trajectory generator G input to the trajectory discriminator D; the gradient vector of the trajectory discriminator D at the interpolation point ; is the penalty term value of the interpolation point .

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

[0066] An initialization module is configured to randomly set spacecraft parameters, initial target position and velocity, and arrival target position and velocity, search for a minimum velocity increment under a double-impulse transfer orbit model, and obtain a corresponding impulse orbit transfer time, randomly select a low-thrust transfer time according to the impulse orbit transfer time, and obtain an orbit transfer time of a low-thrust spacecraft; and randomly initialize an initial mass of the spacecraft to obtain an initial mass of the spacecraft.

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

[0068] A trajectory generator training module is configured to train a generative adversarial network with the training data as real trajectory data, and obtain a trajectory generator, wherein the trajectory generator is configured to generate spacecraft low-thrust trajectory data.

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

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

[0071] one or more processors;

[0072] a 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, and the programs comprise a program for executing the spacecraft low-thrust trajectory data generation method as described above.

[0074] (III) Beneficial Effects

[0075] The present application provides a spacecraft low-thrust trajectory data generation method and system. Compared with the prior art, the following beneficial effects are achieved:

[0076] The present application obtains the minimum speed increment corresponding to the orbit transfer time under the double-pulse transfer orbit model by randomly setting the spacecraft parameters, the initial position and the position reaching the target, randomly selects the orbit transfer time according to the orbit transfer time to obtain the orbit transfer time of the low-thrust spacecraft, and obtains the initial position speed and the target position speed according to the initial position and the position reaching the target; the spacecraft mass initial value is randomly initialized to obtain the initial mass of the spacecraft; the initial position speed, the target position speed, the orbit transfer time and the initial mass of the spacecraft are substituted into the pre-established spacecraft low-thrust trajectory optimization model and optimal control problem solving model facing solar electric propulsion to obtain training data; the training data is used as real trajectory data to train a generative model to obtain a trajectory generator, which is used to generate spacecraft low-thrust trajectory data. The present application trains a generative model using a small amount of randomly generated training data, and after training, the same data distribution as the original low-thrust trajectory data can be generated at a high convergence rate, greatly improving the data generation efficiency and providing powerful high-quality training data support for low-thrust trajectory generation technology based on deep learning. BRIEF DESCRIPTION OF DRAWINGS

[0077] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments or prior art description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0078] Figure 1 A block diagram of a spacecraft small-thrust trajectory data generation method in an embodiment of the present application;

[0079] Figure 2 A flowchart of the training phase and the application phase of the generative adversarial network;

[0080] Figure 3 A schematic diagram of the small-thrust trajectory state of the solar electric propulsion based on the Sims-Flanagan method for recursively generating the small-thrust trajectory of a spacecraft;

[0081] Figure 4 A schematic diagram of the training loss curve of the generative adversarial network;

[0082] Figure 5 A schematic diagram of the convergence rate curve of the thrust trajectory feature trajectory generator;

[0083] Figure 6 A schematic diagram of the comparison between the synthesized trajectory data features and the real trajectory features. DETAILED DESCRIPTION

[0084] To make the objectives, technical solutions, and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application are described clearly and completely. Obviously, the described embodiments are some embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

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

[0086] The technical solutions in the embodiments of the present application are as follows to solve the above technical problems:

[0087] Deep learning and other artificial intelligence technologies have shown potential in the field of trajectory design. However, deep learning methods require a large amount of training data, and obtaining a large amount of continuous thrust trajectory training data faces the following difficulties:

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

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

[0090] (3) Scene diversity leads to explosive data demand: In the face of different propulsion systems (such as different specific impulse, maximum thrust), task objects (such as different initial orbits and target orbits), and various task scenarios (such as flyby tasks, rendezvous tasks, flying, landing or other special tasks), each combination needs to generate a corresponding data set. It is a very time-consuming and resource-intensive task to build a large amount of training data for each specific task scenario and parameter combination.

[0091] The existing technical method basically adopts a Monte Carlo-based random generation method to obtain training data, as follows: first, set the spacecraft specific impulse, power, maximum thrust, spacecraft dry weight, propulsion mode, etc. for the task scenario. Then, randomly select the initial target position, end target position, flight time, spacecraft fuel mass, optimization target (shortest transfer time, minimum fuel consumption or multi-objective optimization), etc., and use the direct method or indirect method for solving, such as saving the small thrust trajectory control amount if there is a solution. In some scenarios, the convergence rate of the solution is less than 10% when randomly initialized. Some studies use restrictions on the differences between certain orbital elements between the targets to improve the convergence rate, such as limiting the inclination difference, eccentricity difference, etc. This improves the convergence rate to some extent, but the overall convergence rate is still low, and this problem has not been fundamentally solved; at the same time, this method directly affects the generalization ability of the trained continuous thrust trajectory model, and when encountering a large inclination difference or a large eccentricity difference, 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 bottlenecks of traditional data acquisition methods and provide sufficient training support for deep learning-based rapid orbit design. The embodiment of the present application proposes to use a generative neural network technology to solve this problem. Based on the spacecraft small thrust trajectory generation technology of the generative adversarial network, a small amount of randomly generated original data is used to train the generative model, and after training, the same data distribution as the original small thrust trajectory data can be generated with a high convergence rate, greatly improving the data generation efficiency and providing powerful high-quality training data guarantee for deep learning-based small thrust trajectory generation technology.

[0093] In order to better understand the above technical solutions, the above technical solutions will be described in detail below in conjunction with the drawings and specific embodiments of the specification.

[0094] The embodiment of the present application provides a spacecraft small thrust trajectory data generation method, as shown in Figure 1As shown, it includes:

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

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

[0097] S3. Train a generative adversarial network using training data as real trajectory data to obtain a trajectory generator, which is used to generate spacecraft low-thrust trajectory data.

[0098] The embodiments of the present invention utilize a small amount of randomly generated training data to train a generative model. After training, the model can generate the same data distribution as the original small thrust trajectory data with a high convergence rate, which greatly improves the data generation efficiency and provides a strong guarantee of high-quality training data for the small thrust trajectory generation technology based on deep learning.

[0099] The following is combined with Figure 2 The schematic diagrams illustrating the training and application phases of the generative adversarial network illustrate the embodiments of the present invention in detail:

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

[0101] Step S1 specifically includes:

[0102] S101. Randomly select small celestial bodies A1 and A2, and define the task time period [T]. start ,T end In this embodiment of the invention, a mission time period [2460676.5, 2475286.5] (January 1, 2025 to January 1, 2065) is defined. Simultaneously, the initial target position velocity and the velocity upon reaching the target position are determined by: based on two randomly selected small celestial bodies, a random mission start time is assigned, and the ephemeris of 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 velocity upon reaching the target position is calculated based on the end time. In the aerospace field, low thrust refers to an engine with a thrust of less than 30 kN.

[0103] S102, randomly selecting a small-thrust transfer task initial time t i ∈[T start ,T end ], flight time TOF0, establishing a double-pulse orbit transfer model, obtaining the total velocity increment Δv = lambert(A1, A2, t i , TOF0) under the double-pulse thrust by solving the Lambert equation. In the embodiment of the present application, the flight time TOF0 = 15 days.

[0104] S103, repeating step S102, performing variable step search on the flight time TOF0, trying to search at TOF0 (range (TOF0-h0, TOF0+h0), wherein h0 is an initial search step, and the embodiment of the present application sets h0 = 5 days), determining the direction and new step of the next search according to the change trend of Δv, if Δv becomes smaller, increasing the step (the embodiment of the present application sets 1.2h0), if Δv becomes larger, decreasing the step (the embodiment of the present application sets 0.8h0), thereby obtaining the minimum velocity increment corresponding to the orbit and the impulse orbit transfer time Δt impls under the double-pulse transfer orbit model.

[0105] S104, randomly selecting a small-thrust transfer time according to the obtained Δt impls , interval: Δt LT ∈[a1·Δt impls ,a2·Δt impls ], a1 and a2 are the lower limit coefficient and the upper limit coefficient of the transfer trajectory time, which are adjusted according to engineering experience, and Δt LT is the orbit transfer time of the small-thrust spacecraft.

[0106] Meanwhile, the initial value of the spacecraft mass also needs to be randomly initialized, interval: m0∈[m dry ,m max ]. In the embodiment of the present application, Δt LT ∈[1.2·Δt impls ,min{2Δt impls ,700}], m0∈[1200kg, 3000kg]. That is, the dry weight of the small-thrust spacecraft is m dry = 1200kg, the maximum wet weight of the spacecraft is m wet = 3000kg, and the maximum fuel weight of the spacecraft is m prop = 1800kg.

[0107] Step S2 specifically comprises:

[0108] In the embodiment of the present application, the small-thrust trajectory optimization model of the solar-electric propulsion spacecraft is composed of the spacecraft state vector, the position and velocity state of the solar-electric propulsion spacecraft, and the position, velocity and mass update formula, and the establishment process is as follows:

[0109] In the embodiment of the present application, the small-thrust trajectory state of the solar-electric propulsion based on the Sims-Flanagan method is used to recursively calculate the small-thrust trajectory of the spacecraft, and a schematic diagram is shown in Figure 3

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

[0111] s=[r v m]

[0112] Wherein, r=[r x ,r y ,r z ], v=[v x ,v y ,v z ] are the position and velocity vectors of the spacecraft in the inertial coordinate system, and m=m wet =m dry +m prop . m dry is the dry weight of the small-thrust spacecraft, m prop is the fuel weight of the spacecraft, and m wet is the wet weight of the spacecraft.

[0113] According to the small-thrust trajectory state of the solar-electric propulsion based on the Sims-Flanagan method, the two-way recursion of the spacecraft state is performed to obtain the spacecraft state at each discrete time. At each discrete control point i, it is assumed that a pulse acceleration of size Δv i acts instantaneously on the control point i. In order to increase the robustness of the solver, unit vector control is used, 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 ], wherein the unit range of [u x ,u y ,u z ] is [-1, 1]. Thus, the spacecraft velocity at each time is calculated by the following formula:

[0114]

[0115] Wherein, N seg is the number of trajectory discrete units (i.e. the number of trajectory segments, in the embodiment of the present application N​seg The initial value of Δv is set to 20. max,i The initial value of Δv is set to 20. max,i The values of Δv in different trajectory segments are not the same. The "+" and "-" superscripts respectively represent the state of the spacecraft after and before the spacecraft generates the impulse thrust, the "+" direction is always forward relative to the forward recursion direction of the state of the spacecraft, i is the sequence number of the forward recursion trajectory unit, and j is the sequence number of the backward recursion trajectory unit.

[0116] The recursion of the position and velocity of the spacecraft can be obtained from the spacecraft dynamics equation:

[0117]

[0118] where μ is the gravitational constant, is the acceleration. Expanding the above equation, the expression of the position and velocity state quantity X of the spacecraft facing solar energy electric propulsion can be specifically obtained as follows:

[0119]

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

[0121] The above dynamics equation, the Kepler two-body model is used for calculation in the fast search stage, and in the engineering application scene, complex perturbation factors can be considered, and the Runge-Kutta-Fehlberg (RKF78) method is used for recursion, so that better results can be obtained.

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

[0123]

[0124] where the "+" and "-" superscripts represent the mass of the spacecraft after and before the impulse thrust is generated, and the "+" is relative to the positive direction of the recursion of the state of the spacecraft. v e is the effective exhaust velocity, v e = I sp · g0, I sp is the engine specific impulse, g0 is the gravitational acceleration (in the embodiment of the present application, the engine specific impulse I sp = 4000 s, g0 = 9.80665e-3 km / s 2 , the effective exhaust velocity v e = I sp · g0 = 39.2266 km / s, Δv iThe spacecraft velocity increment produced by the impulse engine at the ith control point. In the forward recursion, Δv i The spacecraft mass, the maximum thrust of the spacecraft determine, calculated by the following formula:

[0125]

[0126] Where, Δv max,i The maximum velocity increment that can be produced by the ith unit, The unit control amount of the ith unit, F max The maximum thrust that the spacecraft can produce in any direction. Δt LT The orbit transfer time of the small-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. r is the Euclidean distance between the spacecraft and the sun. In the embodiment of the present application, η = 0.6, P0 is set to 40kW, 1 AU = 149597870.7km, so the maximum thrust of the spacecraft at 1 AU is F max (1AU) = 1.2237N.

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

[0130]

[0131] Where, And The spacecraft mass after and before the impulse thrust in the ith small-thrust arc segment. It should be noted here that the model used in the embodiment of the present application is more close to the engineering practice, and the model is a maximum thrust that is not fixed, and the acceleration is not fixed. The backward spacecraft mass recursion is as follows:

[0132]

[0133] Where, And Represent the spacecraft mass after and before the impulse thrust in the jth arc segment of the backward recursion.

[0134] But the expression of the above backward spacecraft mass recursion ignores Δv j In fact, it is a transcendental function about In order to obtain a more accurate analytical expression, the embodiment of the present application provides a spacecraft mass backward recursion method based on omega equation, which is specially designed for small-thrust spacecraft trajectory calculation with variable acceleration.

[0135] Firstly, the general form of backward recursion is given as:

[0136]

[0137] To give the expression of , let:

[0138]

[0139] Reorganize the original equation, and arrange it into the form of omega function , the method is as follows:

[0140]

[0141] where is the omega function. Thus, the backward recursion of spacecraft mass for solar electric propulsion variable maximum acceleration small thrust trajectory is as follows:

[0142]

[0143] The omega function can be solved by various professional tools, thus obtaining the spacecraft mass backward recursion under the condition of maximum thrust time-varying.

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

[0145] The constraint conditions include small thrust trajectory optimization equality constraints and inequality constraints of spacecraft.

[0146] As shown in Figure 3 , in the forward-backward recursion, the spacecraft state at the matching point (Match Point) must be continuous, thus the small thrust trajectory optimization equality constraint condition can be established:

[0147]

[0148] where the superscripts fwd and bwd represent forward recursion and backward recursion respectively, the subscript mp represents the matching point, represents the spacecraft position equality constraint at the matching point, is the spacecraft velocity equality constraint, is the mass equality constraint of the spacecraft at the matching point. The equality constraint ensures that the position, velocity and mass of the spacecraft in forward and backward recursion are strictly equal at the matching point. The parameters with subscripts x, y and z represent the components of the corresponding parameters in the inertial system in three directions.

[0149] The small thrust trajectory solving inequality constraint is set as follows:

[0150]

[0151] m f ≥m dry

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

[0153] J = min (m fuel )

[0154] Wherein, m fuel is the fuel consumption, m fuel = m f -m i , wherein m f is the final mass of the spacecraft after the small-thrust orbit transfer, and m i is the initial mass of the spacecraft before the transfer. Accordingly, the solar electric propulsion small-thrust trajectory optimization problem is converted into a large-scale nonlinear programming problem, and the improved problem model can improve the accuracy of the solution, and the optimization objective is to minimize fuel consumption. The problem can be solved by IPOPT, SNOPT, MATLAB (fmincon function) and other open source or commercial tools.

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

[0156] S201, the Kepler two-body model is used to calculate the orbit between the small-thrust trajectory control points. The unit pulse amplitude and direction use random initial values, and a nonlinear solver is used for solving. If it converges, step S202 is performed, and if the random initial value still does not converge for a preset number of times (5 times in the embodiment of the present application), the transfer orbit is stored in the infeasible trajectory database, and the initialization process is re-executed.

[0157] S202, if the small-thrust trajectory obtained in step S201 converges, more optimization models of the trajectory segment are established, the orbit recursion between the small-thrust control points is numerically recursively calculated by using the RKF78 method to obtain a higher-precision solution, and the transfer orbit is stored in a feasible trajectory database as training data of the generative adversarial model.

[0158] Step S3 specifically includes:

[0159] In combination with the generative adversarial idea, a generative adversarial network model is constructed and trained to obtain a trajectory generator to generate small-thrust trajectory data features that are similar to the original small-thrust trajectory data distribution at a high convergence rate. The embodiment of the present application is specially designed and optimized for small-thrust trajectory generation.

[0160] The generative adversarial network designed in the embodiment of the present application includes a trajectory generator and a trajectory discriminator. The generative adversarial network is a deep neural network, and its architecture includes two deep neural networks, a trajectory generator and a trajectory discriminator, which are mutually opposed in the training process.

[0161] The overall goal of training the trajectory generator is to obtain a trajectory generator that only generates feasible spacecraft small-thrust transfer features to solve the low convergence rate problem of obtaining trajectory data in the prior art. The spacecraft small-thrust orbit transfer features include the initial mass of the spacecraft, the final mass, the flight time, the positions of the two target celestial bodies, the velocities or the six elements, etc.

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

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

[0164] The trajectory discriminator D input is an equal number of synthetic small-thrust transfer data and real small-thrust transfer data. The trajectory discriminator D is composed of L D layers of fully connected layers, each layer containing neurons, with an activation function of Relu, and a network learning rate of η D In the embodiment of the present application, the trajectory discriminator D is composed of 4 layers of fully connected layers, each layer containing 400 neurons, with an activation function of Relu, and a network learning rate of 1 x 10 -4 .

[0165] To prevent gradient disappearance and improve training stability, the Wasserstein loss function with gradient penalty designed in the embodiment of the present application replaces the conventional log-likelihood loss. The trajectory discriminator loss function is calculated as follows:

[0166]

[0167] Where x is the real data, z is the noise, is the interpolation point between the synthetic small-thrust trajectory data and the real trajectory data, the λ term is the gradient penalty term, and λ is the penalty coefficient (in the embodiment of the present application, λ = 10), is the L2 norm of the gradient vector of the trajectory discriminator at .

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

[0169]

[0170] During training, Gaussian noise is generated and sampled as input to the trajectory generator, which then generates synthetic trajectory data. This synthetic and real trajectory data are then fed into a trajectory discriminator to classify the real and synthetic data, calculate the loss function and gradient, and update the discriminator's parameters using the Adam algorithm. The trajectory generator is then trained again. Noise samples are sampled again and fed into the trajectory generator to generate new data. This newly generated data is then fed into the discriminator for identification, and the discriminator's parameters are updated based on the error feedback. This process is iterated repeatedly, continuously adjusting the parameters of the trajectory generator and discriminator. The generative adversarial network is trained until the trajectory generator generates synthetic low-thrust transfer trajectory data that the trajectory discriminator cannot distinguish between real and fake data. This indicates that the low-thrust transfer features generated by the trajectory generator have the same distribution as the real features. In implementation, a Mini-Batch training method is used. The training data obtained in step three is randomly sorted and divided into batches of size N. b The data is segmented into batches and sequentially input into the deep network. The expected true trajectory E is then calculated. x Generate trajectory expectation E z The trajectory discriminator expects The average value of the batch data is obtained using the following formula:

[0171]

[0172] Where, N b D(x) represents the batch size. i (x) represents the actual trajectory data. i The value input into the trajectory discriminator D, D(G(z) i )) represents random noise data z i Synthetic trajectory data G(z) is generated using trajectory generator G. i The value input into trajectory discriminator D, Trajectory discriminator D at interpolation point The gradient vector at that point, interpolation point The penalty value.

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

[0174] To evaluate the network training performance, a ranking system (Rank) is introduced for the trajectory generator and trajectory discriminator during each training iteration. G and Rank D To evaluate whether the capabilities of the two deep neural networks are balanced. For a specific batch of trajectory data, Randk... G and Rank DThe design is as follows:

[0175]

[0176] The trajectory discriminator always outputs the probability that the small-thrust trajectory feature is true, and respectively, the probability that the synthesized small-thrust trajectory data and the real trajectory data are judged to be true, Rank G is the mean value of the probability that the synthesized trajectory data is judged to be true, Rank D represents the mean value of the probability that the trajectory discriminator can correctly identify the synthesized and real trajectory. In the training, Rank G and Rank D will tend to be flat, Rank G and Rank D are close to 0.5, indicating that the capabilities of the two networks are balanced. In the embodiment of the application, Rank G and Rank D are 0.4 and 0.6 respectively.

[0177] The trajectory generator network can directly generate synthesized trajectories consistent with the distribution of real feasible small-thrust trajectory data from noise. In the training process, the convergence rate gradually increases, and finally reaches about 90% (see Figure 5 ), and the distribution of the trajectory generator synthesized data is basically consistent with the real data (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 small-thrust trajectory data of a spacecraft according to Gaussian noise.

[0179] The embodiment of the application also provides a small-thrust trajectory data generation system for a spacecraft, comprising:

[0180] An initialization module is configured to randomly set the parameters of the spacecraft, the initial target position and velocity, and the arrival target position and velocity, search for the minimum velocity increment under the double-impulse transfer orbit model, and the corresponding impulse orbit transfer time, randomly select the small-thrust transfer time according to the impulse orbit transfer time, and obtain the orbit transfer time of the small-thrust spacecraft; and randomly initialize the initial mass of the spacecraft to obtain the initial mass of the spacecraft.

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

[0182] A trajectory generator training module is configured to train the generative adversarial network with the training data as real trajectory data to obtain a trajectory generator configured to generate small-thrust trajectory data of a spacecraft.

[0183] The embodiment of the present application also provides a computer readable storage medium storing a computer program for generating small-thrust trajectory data of a spacecraft, wherein the computer program causes a computer to perform the method for generating small-thrust trajectory data of a spacecraft.

[0184] The embodiment of the present application also provides an electronic device including one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the programs include a program for performing the method for generating small-thrust trajectory data of a spacecraft.

[0185] It can be understood that the small-thrust trajectory data generation system, the storage medium and the electronic device provided by the embodiment of the present application correspond to the method for generating small-thrust trajectory data of a spacecraft, and the related content explanation, examples, advantages and the like can refer to the corresponding content in the method for generating small-thrust trajectory data of a spacecraft, which will not be described here.

[0186] In summary, compared with the prior art, the embodiment of the present application has the following advantages:

[0187] 1. The embodiment of the present application trains the generative model with a small amount of randomly generated training data, and after training, the same data distribution as the original small-thrust trajectory data can be generated with a high convergence rate, which greatly improves the data generation efficiency and provides strong high-quality training data guarantee for the small-thrust trajectory generation technology based on deep learning.

[0188] 2. The embodiment is directed to the small-thrust trajectory data generation scene, and the generative adversarial network technology is innovatively proposed to accelerate the small-thrust data generation of the spacecraft. Through a large number of experiments, the trajectory generator network and the trajectory discriminator structure are optimized, the capabilities of the two networks are balanced, the loss function and the network evaluation index are designed, and the specific network training strategy and process are given, which guarantees the convergence of the network and prevents the pattern collapse problem.

[0189] 3. The embodiment of the present application is directed to the small-thrust trajectory optimization problem of the solar electric propulsion with the maximum time-varying thrust (maximum acceleration time-varying control point), and the spacecraft mass backward recursion method is improved by using the omega equation. Without significantly increasing the calculation complexity, the problem of coupling between the spacecraft recursion mass and the rocket equation exponential term in the spacecraft mass backward recursion process is solved, and the accuracy of the analytical model is improved.

[0190] It is to be noted that, in the present text, relational terms such as first and second and the like can be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises", "comprising", or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can also include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by "comprises... a" does not, without more constraints, exclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element.

[0191] The above embodiments are only used to illustrate the technical solutions of the present application, rather than limit the present application; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for generating small-thrust trajectory data for a spacecraft, the method comprising: The method comprises the following steps: Randomly setting a spacecraft parameter, an initial target position and velocity, and a target position and velocity, searching for a minimum velocity increment under a double-pulse transfer orbit model, and corresponding pulse orbit transfer time, randomly setting a small-thrust transfer time according to the pulse orbit transfer time to obtain an orbit transfer time of a small-thrust spacecraft; and randomly initializing an initial mass of the spacecraft to obtain an initial mass of the spacecraft; The initial position and velocity, the target position and velocity, the orbit transfer time, and the initial mass of the spacecraft are substituted into a pre-established small-thrust trajectory optimization model and an optimal control problem solving model of the spacecraft facing 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, and the trajectory generator is used to generate small-thrust trajectory data of the spacecraft; The pre-established small-thrust trajectory optimization model of the spacecraft facing solar electric propulsion comprises a spacecraft state vector, a position and velocity state of the spacecraft facing solar electric propulsion, and update formulas of the position, velocity, and mass; The pre-established optimal control problem solving model comprises a target function and constraint conditions: The target function is to minimize fuel consumption, and the expression is as follows: wherein is the fuel consumption, wherein is the final mass of the spacecraft after the low-thrust orbit transfer, is the initial mass of the spacecraft before the transfer; The constraint conditions comprise small-thrust trajectory optimization equality constraints and inequality constraints of the spacecraft.

2. The spacecraft low-thrust trajectory data generation method of claim 1, wherein, The spacecraft state vector is expressed as: wherein, is the spacecraft position in an inertial coordinate system, is the spacecraft velocity vector in an inertial coordinate system, , is the dry mass of the small thrust spacecraft, is the fuel weight of the spacecraft, is the wet mass of the spacecraft; The small-thrust trajectory state of the solar electric propulsion based on the Sims-Flanagan method is used to recursively calculate the small-thrust trajectory of the spacecraft to obtain the position and velocity state of the spacecraft facing solar electric propulsion, and the update formulas of the position, velocity, and mass; The velocity update formula comprises: At each discrete control point , assuming an impulsive acceleration of magnitude acts at control point , with unit vector control, the control vector is replaced by the unit control vector , where has a unit range of [-1,1]; thus, the spacecraft velocity at each time instant is calculated by After the velocity is updated, the position of the spacecraft is updated according to an orbit dynamics equation; The mass update formula comprises: The expression of the forward mass recursion of the spacecraft is as follows: The expression of the backward mass recursion of the spacecraft is as follows: wherein, G is the gravitational constant; a is the acceleration, r is the Euclidean distance between the spacecraft and the sun; N is the number of trajectory discrete units, is the maximum change of velocity that can be produced in the trajectory unit; the upper indices "+" and "-" indicate respectively after and before the spacecraft produces the impulse thrust; is the forward recursion trajectory unit number, is the backward recursion trajectory unit number; and are the spacecraft mass after and before the impulse thrust generation in the th small thrust arc segment, respectively; and represent the spacecraft mass after and before the impulse thrust generation in the th arc segment of the backward recursion; is the effective exhaust velocity; is the spacecraft velocity increment generated by the impulse engine at the th control point; is the orbital transfer time of the small thrust spacecraft; is the maximum thrust that the spacecraft can generate in any direction when at a Euclidean distance of r from the Sun; is the unit control amount of the th unit; Parameters with subscripts x, y, z The parameters with subscripts all represent the components of the corresponding parameter in the three directions of the inertial frame.

3. The spacecraft low-thrust trajectory data generation method of claim 2, wherein, Further comprising: The mass backward recursion method of the spacecraft based on the omega equation is sampled, and the expression of the backward mass recursion of the spacecraft is optimized, and the specific expression is as follows: The general form of the backward recursion is given as follows: To give an expression for the expression Let: The original equation is reorganized and arranged into an omega function form Solving the equation is as follows: Therefore, the backward recursion solving method of the mass of the small-thrust trajectory spacecraft facing solar electric propulsion with variable maximum acceleration is as follows: wherein is the Omega function.

4. The small-thrust trajectory data generation method of the spacecraft according to claim 1, wherein The small-thrust trajectory optimization equality constraint of the spacecraft is specifically as follows: where the upper indices and represent forward and backward recursion, respectively, and the lower index represents the matching point, , , denote the spacecraft position equality constraint at the matching point, , , is the spacecraft velocity equality constraint, is the spacecraft mass equality constraint at the matching point; The inequality constraint of the small-thrust trajectory solving is set as follows: （1） （2） Inequality constraint (1) means that the module of any control point and unit control amount is less than 1, i.e. the acceleration generated by the spacecraft for any trajectory unit is less than the ratio of the maximum thrust and the mass of the spacecraft at the moment; inequality constraint (2) means that the final mass of the spacecraft at the end of the orbit transfer must be greater than the dry mass of the spacecraft .

5. The method of claim 1-4, wherein, The training of the generative adversarial network with the training data as the real trajectory data comprises the following steps: The generative adversarial network comprises 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 number of synthetic trajectory data and real trajectory data; and the trajectory discriminator evaluates the authenticity of the small-thrust transfer orbit data.

6. The small-thrust trajectory data generation method of the spacecraft according to claim 5, wherein The structure of the trajectory generator comprises layer fully connected layer; The trajectory discriminator comprises layer fully connected layer.

7. The spacecraft low-thrust trajectory data generation method of claim 5, wherein, The trajectory discriminator loss function is calculated as follows: The trajectory generator loss function is calculated as follows: In the formula: wherein, is real data, is noise, is an interpolation point between synthetic low-thrust trajectory data and real trajectory data, with is a gradient penalty term, and λ is a penalty coefficient, is the L2-norm of the gradient vector of the trajectory discriminator at ; denotes the real trajectory expectation, denotes the generated trajectory expectation, denotes the trajectory discriminator expectation; is the batch size; is the real trajectory data input to the trajectory discriminator ; is random noise data generated by the trajectory generator to generate synthetic trajectory data input to the trajectory discriminator ; the trajectory discriminator at the interpolation point ; is the penalty term value at the interpolation point .

8. A spacecraft small thrust trajectory data generation system, characterized by, Further comprising: An initialization module is configured to randomly set a spacecraft parameter, an initial target position and velocity, and an arrival target position and velocity, search for a minimum velocity increment under a double-pulse transfer orbit model, and obtain a corresponding pulse orbit transfer time, randomly select a small-thrust transfer time according to the pulse orbit transfer time, and obtain an orbit transfer time of a small-thrust spacecraft; and randomly initialize an initial mass of the spacecraft to obtain an initial mass of the spacecraft; A training data acquisition module is configured to input the initial position and velocity, the target position and velocity, the orbit transfer time, and the initial mass of the spacecraft into a pre-established small-thrust trajectory optimization model and an optimal control problem solving model for a spacecraft with solar electric propulsion, and solve the training data; A trajectory generator training module is configured to train a generative adversarial network with the training data as real trajectory data, and obtain a trajectory generator configured to generate small-thrust trajectory data of the spacecraft. The pre-established small-thrust trajectory optimization model for the spacecraft with solar electric propulsion includes a spacecraft state vector, a position and velocity state of the spacecraft with solar electric propulsion, and update formulas of the position, the velocity, and the mass. The pre-established optimal control problem solving model includes an objective function and constraint conditions. The objective function is to minimize fuel consumption, and is expressed as follows: wherein is the fuel consumption, wherein is the final mass of the spacecraft after the low-thrust orbit transfer, is the initial mass of the spacecraft before the transfer; The constraint conditions include small-thrust trajectory optimization equality constraints and inequality constraints of the spacecraft.

9. A storage medium, characterized by The computer program for generating small-thrust trajectory data of the spacecraft is stored in the memory, and the computer program is configured to enable the computer to execute the small-thrust trajectory data generation method of any one of claims 1-7.

10. An electronic device, comprising: The computer program for generating small-thrust trajectory data of the spacecraft is stored in the memory, and the computer program is configured to enable the computer to execute the small-thrust trajectory data generation method of any one of claims 1-7. The computer program for generating small-thrust trajectory data of the spacecraft is stored in the memory, and the computer program is configured to enable the computer to execute the small-thrust trajectory data generation method of any one of claims 1-7. The computer program for generating small-thrust trajectory data of the spacecraft is stored in the memory, and the computer program is configured to enable the computer to execute the small-thrust trajectory data generation method of any one of claims 1-7. ​ ​

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