A rapid sample generation method for intelligent optimization of solar sail transfer trajectories

Abstract

The present invention discloses a rapid sample generation method for intelligent optimization of solar sail transfer trajectories, comprising: setting relevant parameters under the mission scenario, including the solar sail light pressure characteristics, central celestial body parameters, and boundary conditions of the nominal trajectory; establishing a time-optimal transfer model; applying an indirect method to solve the nominal trajectory and its terminal state and terminal costate variables; applying random perturbations to the terminal costate variables and performing corrections on the perturbed costates according to time-optimality conditions; starting from the terminal state of the nominal trajectory, using the corrected terminal costate variables for backward integration to generate new time-optimal transfer trajectory data samples that meet the optimality conditions. By perturbing and correcting the terminal costates and combining them with backward generation technology, the present invention can quickly and cost-effectively generate large-scale, high-quality, time-optimal solar sail transfer trajectory datasets.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace technology, and specifically refers to a method for rapidly generating samples for intelligent optimization of solar sail transfer trajectories. Background Art

[0002] Solar sails utilize sunlight pressure for propulsion and require no fluid, making them particularly well-suited for deep-space missions requiring long-duration, multi-target exploration, such as asteroid exploration. The preliminary design phase of such missions requires rapid evaluation and screening of transfer trajectories among numerous potential targets, placing extremely high demands on the efficiency of trajectory optimization and generation. Traditional solar sail trajectory optimization methods, such as indirect and direct methods, can achieve optimal solutions, but the computational process is complex and time-consuming. Especially when generating thousands of optimal trajectories for multi-target mission planning or constructing machine learning datasets, the computational cost of repetitive solutions using traditional methods becomes prohibitively high, leading to low efficiency and a bottleneck in the rapid design of missions.

[0003] In recent years, the use of data-driven methods such as deep neural networks (DNNs) to predict flight times and achieve rapid trajectory design has become a research hotspot. Such methods rely on large-scale, high-quality training datasets. However, how to quickly and cost-effectively generate this training data, which contains a large number of optimal solar sail trajectories, is a core challenge of this technical approach. In existing technologies, the "backward generation" method provides a way to expand the sample: starting from the terminal state of a known optimal trajectory, new trajectory samples are generated by applying perturbations and performing backward integration. However, for solar sail problems with complex light pressure thrust models and strict optimality conditions, simply applying backward generation cannot guarantee that the newly generated trajectories still meet the optimality requirements of the original problem. This may result in a low-quality generated dataset, affecting the training effect and prediction accuracy of subsequent machine learning models. Summary of the Invention

[0004] In view of the shortcomings of the above-mentioned technologies, the present invention provides a method for rapid sample generation for intelligent optimization of solar sail transfer trajectories.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] The present invention provides a method for rapidly generating samples for intelligent optimization of solar sail transfer trajectories, comprising the following steps:

[0007] Step 1: Set the solar sail spacecraft and mission-related parameters;

[0008] Step 2: Construct a solar sail time optimal transfer model and use the indirect method to solve the nominal trajectory and its terminal state and terminal co-state variables;

[0009] Step 3: Apply random perturbations to the terminal co-state variables and perform terminal co-state correction based on the optimality condition;

[0010] Step 4: Perform backward integration from the terminal state of the nominal trajectory and use the modified terminal co-state variables to generate new time-optimal transfer trajectory data samples.

[0011] Furthermore, the step 1 specifically includes: setting parameters related to the solar sail spacecraft and mission.

[0012] Consider an ideal solar sail spacecraft, whose sail surface is a perfect reflective surface. The force generated by the solar radiation pressure (SRP) follow ,in is the solar radiation pressure, is the sail area, is the sail heel angle, is the unit vector of the sail's outward normal direction. Define the total mass of the spacecraft and sail mass to area ratio . Introducing the solar sail light pressure factor The acceleration generated by SRP is It can be expressed as:

[0013] (6);

[0014] Set the task to start from the initial state At the initial moment Departure and arrival at target state At the terminal moment The boundary conditions are set as follows:

[0015] (7);

[0016] Using the normalized unit system, the astronomical unit (AU) is selected as the distance unit. Year is the unit of time, at this time the solar gravitational constant In this normalized unit system, the SRP acceleration is expressed as:

[0017] (8);

[0018] Furthermore, step 2 specifically includes: constructing a solar sail time optimal transfer model and using an indirect method to solve the nominal trajectory and its terminal state and terminal co-state variables. In the normalized unit system, the spacecraft dynamic equation considering only the central gravity and SRP is:

[0019] (9);

[0020] The state vector is The control quantity is the sail attitude angle and clock angle , which together determine the sail surface normal vector In the heliocentric orbital coordinate system middle:

[0021] (10);

[0022] The time optimal control goal is to minimize the flight time According to the Pontryagin Maximum Principle (PMP), covariates are introduced ,in is an additional constant that helps numerical stability. Constructing the Hamiltonian

[0023] (11);

[0024] The co-state equation (Euler-Lagrange equation) is:

[0025] (12);

[0026] The optimal control law requires selecting the sail attitude angle So that the Hamiltonian function reaches its maximum value at every moment. This requires Direction and velocity co-state Direction There is a specific relationship. Specifically, the clock angle must satisfy ,in for Angle in the tangential-normal plane. Optimal sail heel angle and Inclination angle relative to radial direction Satisfies a specific piecewise function relationship:

[0027] (13);

[0028] At the same time, the optimal normal Need to meet

[0029] (14);

[0030] Due to the terminal time Free, terminal transversality conditions must be met .

[0031] The two-point boundary value problem (TPBVP) consisting of the state equation, co-state equation, boundary conditions, optimal control law and terminal transversal condition is solved by numerical methods (such as the shooting method) to obtain a nominal time optimal transfer trajectory and its terminal state. and the corresponding terminal co-state variables .

[0032] Furthermore, the step 3 specifically includes: applying random perturbations to the terminal co-state variables, and performing terminal co-state correction based on the optimality condition. Take the terminal co-state variables of the nominal solution obtained in step 2 . Set the disturbance range parameters . Generate a random perturbation vector , its components are The perturbation is applied to the nominal terminal co-state variable to obtain the terminal co-state variable after the initial perturbation. :

[0033] (15);

[0034] The key is to ensure that the new trajectory generated by backward integration strictly satisfies the terminal transversality condition of time optimal control. , the terminal co-state after the initial perturbation must be Perform correction calculation. This correction step is based on the Hamiltonian function expression and Constraints on The components are adjusted, and this process can be expressed as:

[0035] (16);

[0036] Through this key correction step, the corrected terminal co-state variables that finally meet the optimality conditions are obtained .

[0037] Furthermore, the step 4 specifically includes: performing backward integration from the terminal state of the nominal trajectory, and using the modified terminal co-state variables to generate new time-optimal transfer trajectory data samples. and the modified terminal co-state variable calculated in step 3 As at the terminal moment Using a high-precision numerical integrator, First, reversely integrate the state equation and the co-state equation along the time axis. At each time step of the reverse integration , the current sail attitude control value According to the current status Harmony The integration process continues until a preset initial moment is reached. Or meet other termination conditions. After the integration is completed, a new initial state is obtained The generated arrive The trajectory of Since its generation process follows the optimality principle and undergoes key terminal corrections, it constitutes a new time-optimal transfer trajectory data sample that meets the optimality conditions.

[0038] The beneficial effects of the present invention compared to the prior art are as follows: the data generation method is applicable to the problem of time-optimal solar sail transfer trajectory generation, and can generate a large-scale, high-quality solar sail trajectory data set that meets the optimality requirements in a short time at an extremely low computational cost; establish a time-optimal transfer model; apply an indirect method to obtain the nominal trajectory and its terminal state and terminal costate variables; apply random perturbations to the terminal costate variables, and perform corrections on the perturbed costates according to the time-optimality conditions; starting from the terminal state of the nominal trajectory, use the corrected terminal costate variables to perform backward integration to generate new time-optimal transfer trajectory data samples that meet the optimality conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0040] In order to facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and drawings. The contents mentioned in the embodiments are not intended to limit the present invention.

[0041] Reference Figure 1 As shown in FIG, a method for rapidly generating samples for intelligent optimization of solar sail transfer trajectories is described, and the steps are as follows:

[0042] 1) Set the solar sail spacecraft and mission-related parameters:

[0043] Define the ideal solar sail model and its light pressure characteristics, including key parameters such as the solar sail light pressure factor ; Set the sun as the central celestial body; specify the mission type as a time-optimal rendezvous mission and specify the initial state and the target terminal state Equal boundary conditions; normalized units are used to simplify calculations.

[0044] 2) Construct a solar sail time-optimal transfer model and use the indirect method to solve the nominal trajectory and its terminal state and terminal co-state variables:

[0045] Establish the normalized dynamic equations of the solar sail under the influence of central gravity and light pressure; based on the goal of minimizing flight time, apply the Pontryagin Maximum Principle (PMP) to construct a Hamiltonian system for the time optimal control problem, including the state equation, co-state equation, optimal control law (determining the sail attitude) and terminal transversality condition. ; Using the indirect method, by numerically solving this two-point boundary value problem (TPBVP), a benchmark (nominal) time-optimal transfer trajectory and its corresponding terminal co-state variables are obtained. .

[0046] 3) Apply random perturbations to the terminal co-state variables and perform terminal co-state correction based on the optimality condition:

[0047] Select the terminal co-state variables of the nominal solution obtained in step 2 ; Apply a range-controlled random perturbation to it , and obtain the terminal co-state after the initial perturbation ; To ensure that the generated trajectory strictly meets the terminal cross-section condition required by time optimality , according to the Hamiltonian function expression and this constraint, Perform necessary correction calculations to obtain the corrected terminal co-state variables that ultimately meet the optimality conditions .

[0048] 4) Perform backward integration from the terminal state of the nominal trajectory and use the modified terminal co-state variables to generate new time-optimal transfer trajectory data samples:

[0049] The known target end state and the modified terminal co-state variables obtained in step 3 As a terminal moment The boundary conditions of At the beginning, a high-precision numerical integrator is used to reversely integrate the state equation and the co-state equation; during the integration process, the sail attitude is determined in real time according to the current state and co-state through the optimal control law; reverse integration is performed to a certain initial moment , get the new initial state corresponding to the trajectory ; Record this including the new initial state, original terminal state and flight time The time optimal (or nearly optimal) trajectory is taken as a data sample.

[0050] The following is an example of the optimal rendezvous trajectory between the Earth and the asteroid Apophis:

[0051] Step 1: Set the parameters of the solar sail spacecraft and mission. First, in this problem, the mission scenario is set as a solar sail spacecraft starting from near the Earth orbit and performing a time-optimal rendezvous with the near-Earth asteroid Apophis. The ideal solar sail model is used, and its key characteristic parameters are determined by the solar sail light pressure factor. Definition, where is the solar sail surface mass ratio. The sun is the central gravitational body. The normalized unit system (distance unit AU, time unit Year, the solar gravitational constant The goal of time-optimal control is to minimize the total flight time from departure near the Earth to rendezvous with Apophis. .

[0052] Step 2: Construct the solar sail time optimal transfer model and use the indirect method to solve the nominal trajectory and its terminal state and terminal co-state variables.

[0053] In the normalized unit system, the spacecraft dynamic equation considering only the central gravity and SRP is:

[0054] (17);

[0055] The state vector is The control quantity is the sail attitude angle and clock angle , which together determine the sail surface normal vector In the heliocentric orbital coordinate system middle:

[0056] (18);

[0057] The time optimal control goal is to minimize the flight time According to the Pontryagin Maximum Principle (PMP), covariates are introduced ,in is an additional constant that helps numerical stability. Constructing the Hamiltonian

[0058] (19);

[0059] The co-state equation (Euler-Lagrange equation) is:

[0060] (20);

[0061] The optimal control law requires selecting the sail attitude angle So that the Hamiltonian function reaches its maximum value at every moment. This requires Direction and velocity co-state Direction There is a specific relationship. Specifically, the clock angle must satisfy ,in for Angle in the tangential-normal plane. Optimal sail heel angle and Inclination angle relative to radial direction Satisfies a specific piecewise function relationship:

[0062] (twenty one);

[0063] At the same time, the optimal normal Need to meet

[0064] (twenty two);

[0065] Due to the terminal time Free, terminal transversality conditions must be met .

[0066] Combining the boundary conditions of Earth departure and Apophis arrival, as well as the terminal transversality condition, a two-point boundary value problem (TPBVP) is constructed. By numerically solving this TPBVP, a nominal time optimal transfer trajectory from Earth to Apophis is obtained. The flight time of this nominal solution is calculated to be approximately 233 days. At the same time, the solution process obtains the trajectory at the nominal arrival time. The terminal state (i.e. the state of Apophis at that moment) and the corresponding terminal costate variable .

[0067] Step 3: Apply random perturbations to the terminal co-state variables and perform terminal co-state correction based on the optimality condition.

[0068] The terminal costate variables of the Earth-Apophis nominal optimal trajectory obtained in step 2 As a basis. Apply random perturbations to the terminal co-state variables and perform terminal co-state correction based on the optimality condition. Take the terminal co-state variables of the nominal solution obtained in step 2 . Set the disturbance range parameters . Generate a random perturbation vector , its components are The perturbation is applied to the nominal terminal co-state variable to obtain the terminal co-state variable after the initial perturbation. :

[0069] (twenty three);

[0070] The key is to ensure that the new trajectory generated by backward integration strictly satisfies the terminal transversality condition of time optimal control. , the terminal co-state after the initial perturbation must be Perform correction calculation. This correction step is based on the Hamiltonian function expression and Constraints on The components are adjusted, and this process can be expressed as:

[0071] (twenty four);

[0072] Through this key correction step, the corrected terminal co-state variables that finally meet the optimality conditions are obtained .

[0073] Step 4: Perform backward integration from the terminal state of the nominal trajectory and use the modified terminal co-state variables to generate new time-optimal transfer trajectory data samples.

[0074] Apophis at the nominal arrival time Status and the modified terminal co-state variables obtained in step 3 As a terminal moment The boundary conditions of At the beginning, a high-precision numerical integrator is used to reversely integrate the state equation and the co-state equation; during the integration process, the sail attitude is determined in real time according to the current state and co-state through the optimal control law; reverse integration is performed to a certain initial moment , get the new initial state corresponding to the trajectory ; Record this including the new initial state, original terminal state and flight time The optimal (or nearly optimal) trajectory in time is used as a data sample. By repeating this step, the dataset can be effectively expanded to 128,000 samples. The entire expansion process takes only about 1 minute.

[0075] It can be seen from the above embodiments that the method proposed in the present invention can generate a large-scale, high-quality, time-optimal solar sail transfer trajectory dataset quickly and at low cost based on a nominal optimal solution by perturbing and correcting the terminal costate and combining it with backward generation technology.

[0076] The present invention has many specific application paths. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principles of the present invention. These improvements should also be considered as the scope of protection of the present invention.

Claims

1. A method for rapid sample generation for intelligent optimization of solar sail transfer trajectories, characterized in that: include: Step 1: Set the solar sail spacecraft and mission-related parameters; Step 2: Construct a solar sail time-optimal transfer model and use the indirect method to solve the nominal trajectory and its terminal state and terminal co-state variables; Step 3: Apply random perturbations to the terminal co-state variables and perform terminal co-state correction based on the optimality condition; Step 4: Perform backward integration from the terminal state of the nominal trajectory and use the modified terminal co-state variables to generate new time-optimal transfer trajectory data samples; In step 2, constructing the solar sail time optimal transfer model includes: establishing the dynamic equation under the action of the central gravitational field and solar light pressure: （1）； Among them, r and v are the spacecraft position and velocity vectors respectively, represents the distance between the solar sail and the sun, is the solar sail light pressure factor, is the sail inclination angle, n is the sail surface normal vector; Use the indirect method to solve the nominal trajectory, apply the Pontryagin maximum principle, and construct the Hamiltonian function: （2）； in, , , is a co-variable; Derive the co-state equation: （3）； in, , , To simplify the formula, represents the Hamiltonian function; The optimal control law selects the sail attitude angle so that the Hamiltonian function Reaching the maximum value at each moment; including clock angles satisfying ,in for Angle in the tangential-normal plane; optimal sail heel angle and Inclination angle relative to radial direction Satisfies the following piecewise function relationship: （4）； At the same time, the optimal sail surface normal vector satisfy: （5）； Due to the terminal time Free, meeting the terminal transversality condition ; By numerically solving the two-point boundary value problem consisting of the state equation, co-state equation, boundary conditions, optimal control law and terminal transversal conditions, a nominal time optimal transfer trajectory and its terminal state are obtained. and the corresponding terminal co-state variables ,in, express The terminal value of In step 3, performing the terminal co-state correction based on the time optimality condition includes: applying random perturbations to The initial perturbation terminal costate obtained after Perform correction calculation to obtain the corrected terminal co-state variable , which ensures the use of the modified terminal covariate variables The calculated Hamiltonian at the terminal time Satisfy the time-optimal cross-section condition .

2. The method for rapid sample generation according to claim 1, characterized in that: In step 4, performing backward integration includes: The terminal state and the modified terminal costate variable As a terminal moment Boundary conditions; From the terminal moment Start the reverse numerical integration of the state equation and the co-state equation. During the integration process, the optimal sail attitude control at each time point is determined by the optimal control law based on the current state and co-state. Integrate to the initial moment Get a new initial state ; Repeat steps 3 and 4 to generate a large number of samples.

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