Sample rapid generation method for intelligent optimization of solar sail transfer trajectory

Abstract

The invention discloses a rapid sample generation method for intelligent optimization of a solar sail transfer trajectory, and the method comprises the steps: setting related parameters in a task scene, including solar sail light pressure characteristics, central celestial body parameters and boundary conditions of a nominal trajectory; establishing a time optimal transfer model; solving by applying an indirect method to obtain a nominal trajectory and a tail end state and a tail end co-state variable thereof; random disturbance is applied to the tail end co-state variable, and the disturbed co-state is corrected according to the time optimality condition; and starting from the tail end state of the nominal trajectory, performing backward integration by using the corrected tail end co-state variable to generate a new time optimal transfer trajectory data sample meeting the optimality condition. According to the method, a large-scale and high-quality time optimal solar sail transfer trajectory data set can be quickly generated at low cost by disturbing and correcting the end co-state and combining a backward generation technology.

Description

Technical Field

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

[0002] Solar sails use solar radiation pressure for propulsion without the need for propellant, and are particularly suitable for deep space missions such as asteroid exploration that require long-term flight and multi-target detection. In the preliminary design stage of such missions, it is necessary to quickly evaluate and screen transfer trajectories among numerous potential targets, and there are extremely high requirements for the efficiency of trajectory optimization and generation. Traditional solar sail trajectory optimization methods, such as indirect methods and direct methods, although able to obtain optimal solutions, have complex and time-consuming calculation processes. Especially when thousands of optimal trajectories need to be generated for multi-target mission planning or constructing machine learning data sets, the computational cost of repeated solutions by traditional methods becomes extremely high and the efficiency is low, becoming a bottleneck restricting the rapid design of missions.

[0003] In recent years, data-driven methods such as deep neural networks (DNNs) have become a research hotspot for predicting flight time and achieving rapid trajectory design. Such methods rely on large-scale and high-quality training data sets. However, how to quickly and low-costly generate these training data containing a large number of optimal solar sail trajectories is the core challenge of this technical route. In the prior art, the "backward generation" method provides an idea for expanding samples: starting from the end 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 radiation pressure thrust models and strict optimality conditions, simply applying backward generation is difficult to ensure that the newly generated trajectories still meet the optimality requirements of the original problem, which may lead to low quality of the generated data set and affect the training effect and prediction accuracy of subsequent machine learning models. Summary of the Invention

[0004] Aiming at the deficiencies in the above technologies, the present invention provides a method for quickly generating samples for intelligent optimization of solar sail transfer trajectories.

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

[0006] A method for quickly generating samples for intelligent optimization of solar sail transfer trajectories according to the present invention comprises the following steps:

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

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

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

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

[0011] Furthermore, the specific content of Step 1 includes: setting the parameters related to the solar sail spacecraft and the mission.

[0012] Considering an ideal solar sail spacecraft with a perfect reflective sail surface. At a distance from the sun the force generated by solar radiation pressure (SRP) follows where is the solar radiation pressure, is the sail area, is the sail inclination angle, is the unit vector in the direction of the outer normal of the sail surface. Define the total mass of the spacecraft and the ratio of sail mass to area Introduce the solar sail light pressure factor Then the acceleration generated by SRP can be expressed as:

[0013] (6);

[0014] Set the mission as a rendezvous mission starting from the initial state at the initial time and reaching the target state at the terminal time The boundary conditions are set as:

[0015] (7);

[0016] Adopt the normalized unit system, select the astronomical unit (AU) as the distance unit, and the year as the time unit. At this time, the solar gravitational constant In this normalized unit system, the SRP acceleration is expressed as:

[0017] (8);

[0018] Furthermore, the specific content of Step 2 includes: constructing a solar sail time-optimal transfer model and using the indirect method to solve the nominal trajectory, its end state, and end co-state variables. In the normalized unit system, the spacecraft dynamics equation considering only the central gravitational force and SRP is:

[0019] (9);

[0020] where the state vector is The control variable is the sail attitude angle and the clock angle , which jointly determine the sail normal vector . In the heliocentric orbital coordinate system :

[0021] (10);

[0022] The time-optimal control objective is to minimize the flight time . According to the Pontryagin's maximum principle (PMP), a co-state variable is introduced, where is an additional constant that helps with numerical stability. The Hamiltonian function

[0023] (11);

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

[0025] (12);

[0026] The optimal control law requires selecting the sail attitude angle such that the Hamiltonian function reaches its maximum value at each moment. This requires to have a specific relationship with the direction of the velocity co-state . Specifically, the clock angle needs to satisfy , where is the angle of in the tangential-normal plane. The optimal sail inclination angle and the inclination angle of relative to the radial direction satisfy a specific piecewise function relationship:

[0027] (13);

[0028] Meanwhile, the optimal normal needs to satisfy

[0029] (14);

[0030] Since the terminal time is free, the terminal transversality condition must be satisfied.

[0031] Solve the two-point boundary value problem (TPBVP) composed of the state equation, co-state equation, boundary conditions, optimal control law, and terminal transversality condition through 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, step 3 specifically includes: applying a random perturbation to the terminal co - state variables and performing terminal co - state correction based on the optimality conditions. Take the terminal co - state variables of the nominal solution obtained in step 2 . Set the perturbation range parameter . Generate a random perturbation vector , whose components are uniformly distributed within the interval. Apply this perturbation to the nominal terminal co - state variables to obtain the preliminarily perturbed terminal co - state variables :

[0033] (15);

[0034] The key lies in that to ensure that the new trajectory generated by backward integration strictly satisfies the terminal transversality condition of time - optimal control , it is necessary to perform a correction calculation on the preliminarily perturbed terminal co - state . This correction step is based on the Hamiltonian function expression and constraints, and adjust the components of . This process can be expressed as:

[0035] (16);

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

[0037] Furthermore, step 4 specifically includes: performing backward integration from the terminal state of the nominal trajectory and using the corrected terminal co - state variables to generate new time - optimal transfer trajectory data samples. Take the known terminal state of the target celestial body and the corrected terminal co - state variables calculated in step 3 as the boundary conditions at the terminal time . Use a high - precision numerical integrator to integrate the state equation and the co - state equation backward along the time axis starting from . At each time step of the backward integration, the current sail attitude control quantity is determined in real - time according to the current state and the co - state through the optimal control law. The integration process continues until a preset initial time is reached or other termination conditions are met. After the integration ends, a new initial state is obtained. The resulting one from to trajectory, whose flight time is . Since its generation process follows the optimality principle and undergoes critical terminal corrections, it constitutes a new data sample of the time-optimal transfer trajectory that meets the optimality conditions.

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

[0039] Figure 1 is a schematic flow chart of the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] For the convenience of those skilled in the art, the present invention will be further described below in conjunction with embodiments and the accompanying drawings. The content mentioned in the embodiments does not limit the present invention.

[0041] Referring to Figure 1 shown, a method for quickly generating samples for intelligent optimization of solar sail transfer trajectories is as follows:

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

[0043] Define the ideal solar sail model and its light pressure action characteristics, including key parameters such as the solar sail light pressure factor ; Set the sun as the central celestial body; clarify that the mission type is a time-optimal rendezvous mission, and specify the initial state and the target terminal state and other boundary conditions; adopt a normalized unit system to simplify the calculation.

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

[0045] Establish the normalized dynamic equation of the solar sail under the action of central gravity and light pressure; based on the goal of minimizing the flight time, apply the Pontryagin maximum principle (PMP) to construct the Hamiltonian system of the time-optimal control problem, including the state equation, the co-state equation, the optimal control law (determine the sail attitude), and the terminal transversality condition ; Using the indirect method, solve this two-point boundary value problem (TPBVP) numerically to obtain a reference (nominal) time-optimal transfer trajectory and its corresponding terminal co-state variables. .

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

[0047] Select the terminal co-state variables of the nominal solution obtained in step 2 ; Apply a randomly perturbed within a controlled range to obtain the preliminarily perturbed terminal co-state ; To ensure that the generated trajectory strictly satisfies the terminal transversality condition required for time optimality , based on the Hamiltonian function expression and this constraint condition, perform necessary correction calculations to obtain the corrected terminal co-state variables that finally satisfy the optimality conditions .

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

[0049] Take the known target terminal state and the corrected terminal co-state variables obtained in step 3 as the boundary conditions at the terminal time ; Starting from , use a high-precision numerical integrator to integrate the state equation and co-state equation backward; During the integration process, determine the sail attitude in real time through the optimal control law according to the current state and co-state; Integrate backward to an initial time to obtain the new initial state corresponding to this trajectory; Record this time-optimal (or near-optimal) trajectory including the new initial state, the original terminal state, and the flight time as a data sample.

[0050] The following takes the time-optimal rendezvous trajectory between the Earth and the Apophis asteroid as an example for illustration:

[0051] Step 1. Set the parameters related to the solar sail spacecraft and the mission. First, in this problem, the mission scenario is set as a solar sail spacecraft starting from near the Earth's orbit and performing a time-optimal rendezvous with the near-Earth asteroid Apophis. An ideal solar sail model is adopted, and its key characteristic parameters are defined by the solar sail radiation pressure factor , where is the mass per unit area of the solar sail. The sun is the central gravitational body. The normalized unit system is adopted (distance unit AU, time unit Year, solar gravitational constant ). The objective of time-optimal control is to minimize the total flight time from near the Earth to rendezvous with Apophis .

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

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

[0054] (17);

[0055] where the state vector is . The control variables are the sail attitude angle and the clock angle , which together determine the sail normal vector . In the heliocentric orbital coordinate system :

[0056] (18);

[0057] The time-optimal control objective is to minimize the flight time . According to the Pontryagin maximum principle (PMP), co-state variables are introduced, where is an additional constant that helps with numerical stability. The Hamiltonian function is constructed

[0058] (19);

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

[0060] (20);

[0061] The optimal control law requires selecting the sail attitude angle such that the Hamiltonian function reaches its maximum value at each moment. This requires to have a specific relationship with the direction of the velocity co-state . Specifically, the clock angle needs to satisfy , where is the angle of in the tangential-normal plane. The optimal sail inclination and the inclination of relative to the radial direction satisfy a specific piecewise function relationship:[[]]

[0062] (21);

[0063] Meanwhile, the optimal normal vector needs to satisfy

[0064] (22);

[0065] Since the terminal time is free, the terminal transversality condition .

[0066] Combining the boundary conditions for the Earth departure and Apophis arrival and the terminal transversality condition forms a two-point boundary value problem (TPBVP). By numerically solving this TPBVP, a nominal time-optimal transfer trajectory from the Earth to Apophis is obtained. The flight time of this nominal solution is calculated to be approximately 233 days. Meanwhile, the end state at the nominal arrival time of this trajectory (i.e., the state of Apophis at that time) and the corresponding end co-state variables .

[0067] Step 3. Apply a random perturbation to the end co-state variables and perform end co-state correction based on the optimality conditions.

[0068] Based on the end co-state variables of the nominal optimal trajectory from the Earth to Apophis obtained in Step 2. Apply a random perturbation to the end co-state variables and perform end co-state correction based on the optimality conditions. Take the end co-state variables of the nominal solution obtained in Step 2. Set the perturbation range parameter . Generate a random perturbation vector whose components are uniformly distributed within the interval. Apply this perturbation to the nominal end co-state variables to obtain the preliminarily perturbed end co-state variables

[0069] (23);

[0070] The key is that to ensure that the new trajectory generated by backward integration strictly satisfies the terminal transversality condition of the time-optimal control, it is necessary to perform a correction calculation on the preliminarily perturbed end co-state . This correction step is based on the Hamiltonian function expressions and constraints to adjust the components of , and this process can be expressed as:

[0071] (24);

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

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

[0074] Take the state of Apophis at the nominal arrival time and the corrected terminal co-state variables obtained in Step 3 as the boundary conditions at the terminal time ; starting from , use a high-precision numerical integrator to integrate the state equation and the co-state equation backward; during the integration process, determine the sail attitude in real time through the optimal control law according to the current state and co-state; integrate backward to an initial time to obtain the new initial state corresponding to this trajectory; record this time-optimal (or near-optimal) trajectory including the new initial state, the original terminal state, and the flight time as a data sample. By repeating this step, the dataset can be effectively amplified to 128,000 samples, and the entire amplification process only takes about 1 minute.

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

[0076] The specific application ways of the present invention are numerous. The above description is only the preferred implementation manner of the present invention. It should be noted that for those of ordinary skill in the art in this technical field, several improvements can be made without departing from the principle of the present invention, and these improvements should also be regarded as the protection scope 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 the optimal time transfer model of the solar sail and use the indirect method to solve the nominal trajectory and its terminal state and terminal co-state variables; Step 3: applying random disturbances to the terminal co-state variables and performing 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.

2. The method for rapid sample generation according to claim 1, characterized in that: In step 2, constructing the optimal time transfer model of the solar sail includes: establishing the dynamic equation under the action of the central gravitational field and the solar light pressure: （1）； Where r and v are the spacecraft position and velocity vectors, respectively. is 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 every moment; including the clock angle satisfying ,in for Angle in the tangential-normal plane; optimum 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, satisfying 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 condition, a nominal time optimal transfer trajectory and its terminal state are obtained. and the corresponding terminal covariate ;in, express The end value of .

3. The method for rapid sample generation according to claim 1, characterized in that: In step 3, performing terminal co-state correction based on the time optimality condition includes: applying random disturbance to The initial perturbation terminal costate obtained after Perform correction calculation to obtain the corrected terminal co-state variable , which ensures that the modified terminal costate variables are used The calculated Hamiltonian at the terminal time Satisfy the time-optimal cross-section condition .

4. 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 of From the terminal moment Start reverse numerical integration of state equations and co-state equations. During the integration process, the optimal sail attitude control at each time point is determined according to the current state and co-state through the optimal control law; Integrate to the initial time Get a new initial state ; Repeat steps 3 and 4 to generate a large number of samples.

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