A spacecraft orbit transfer control method and device suitable for a deep space ferry mission and a storage medium

Abstract

The present disclosure provides a spacecraft orbit transfer control method, device and storage medium suitable for deep space ferry mission, belonging to the field of spacecraft guidance and design. The method comprises: obtaining a dynamic model of a first spacecraft transferring from a first orbit to a second orbit; based on the dynamic model, an initial transfer orbit is obtained through a first homotopy parameter with energy optimization as the target; based on the initial transfer orbit, a target transfer orbit is obtained through a second homotopy parameter and a third homotopy parameter with fuel optimization as the target. The present disclosure provides an initial value guess for the fuel optimization problem by using the easily solvable energy optimization problem through the first homotopy parameter; through the synergistic effect of the second homotopy parameter and the third homotopy parameter, the target transfer orbit under the fuel optimization target is obtained, thereby reducing the sensitivity of the indirect method to the initial value and enhancing the convergence of the solution of the complex orbit transfer task.

Description

Technical Field

[0001] This disclosure relates to the field of spacecraft orbital dynamics and control technology, and in particular to a spacecraft orbital transfer control method, device and storage medium suitable for deep space shuttle missions. Background Technology

[0002] With the development of deep space exploration and space infrastructure construction, spacecraft orbit transfer missions (such as Earth orbit transfer, lunar-Earth transfer, and deep space resupply) are becoming increasingly frequent. In the resource-constrained space environment, designing a transfer orbit that minimizes fuel consumption (i.e., a fuel-optimal orbit) is crucial for improving spacecraft payload capacity and extending mission life.

[0003] For solving the problem of optimal fuel trajectories, existing technologies mainly employ direct and indirect methods. While direct methods eliminate the need to guess co-state variables lacking clear physical meaning, they often fail to strictly satisfy the optimality conditions for fuel optimization and are prone to getting trapped in local optima. Therefore, high-precision optimal fuel trajectories are mostly solved using indirect methods, based on Pontryagin's Minimum Principle (PMP), transforming the trajectory optimization problem into an analytical first-order necessary condition problem, ultimately reducing it to solving a two-point boundary value problem. However, when using indirect methods, co-state variables are extremely difficult to guess accurately. Since traditional target-spot methods for solving two-point boundary value problems are highly sensitive to initial conditions, this blindness in initial condition guessing is further amplified by the positive integration of the dynamic system, leading to computational divergence and difficulty in convergence when dealing with complex constraints or large-scale transfer tasks.

[0004] Therefore, designing a spacecraft orbit transfer control method with low dependence on initial conditions and strong convergence is of great engineering value for improving the planning efficiency and energy utilization of complex space missions. Summary of the Invention

[0005] In view of this, this disclosure aims to provide a spacecraft orbit transfer control method, device and storage medium suitable for deep space transfer missions, so as to improve the robustness of indirect methods to initial value guesses and enhance the convergence of solving complex orbit transfer missions.

[0006] Firstly, this disclosure provides a spacecraft orbital transfer control method suitable for deep space shuttle missions, including:

[0007] Obtain the dynamic model of the first spacecraft transferring from the first orbit to the second orbit;

[0008] Based on the aforementioned dynamic model, with energy optimization as the objective, the initial transfer trajectory is obtained through the first homotopy parameter.

[0009] Based on the initial transfer trajectory, with fuel optimization as the objective, the target transfer trajectory is obtained through the second and third homotopy parameters.

[0010] In some examples, obtaining the initial transfer trajectory based on the dynamic model, with energy optimization as the objective, through the first homotopy parameter, includes:

[0011] Construct a first homotopy equation. At the initial value of the first homotopy parameter, the value of the first homotopy equation corresponds to the number of orbital elements of the first orbit; at the final value of the first homotopy parameter, the value of the first homotopy equation corresponds to the number of orbital elements of the second orbit.

[0012] Based on the dynamic model, a cost function is set with the optimal energy as the performance index, terminal constraints are set according to the value of the first homotopy equation, and control variables are solved to obtain the initial transfer trajectory.

[0013] In some examples, obtaining the target transfer trajectory based on the initial transfer trajectory, with fuel optimization as the objective, using a second homotopy parameter and a third homotopy parameter, includes:

[0014] A second homotopy equation is constructed. At the initial value of the second homotopy parameter, the value of the second homotopy equation corresponds to the preset thrust amplitude. At the final value of the second homotopy parameter, the value of the second homotopy equation corresponds to the actual thrust amplitude.

[0015] A third homotopy equation is constructed. At the initial value of the third homotopy parameter, the value of the third homotopy equation corresponds to a cost function with energy optimization as the performance index. At the final value of the third homotopy parameter, the value of the third homotopy equation corresponds to a cost function with fuel optimization as the performance index.

[0016] Based on the dynamic model and the second homotopy equation, the cost function is set according to the value of the third homotopy equation, and the terminal constraint is set to the value of the first homotopy equation at the termination value of the first homotopy parameter. The control variables are solved using the initial transfer trajectory as the initial value for iteration to obtain the target transfer trajectory.

[0017] In some examples, the step of setting the cost function based on the dynamic model and the second homotopy equation, corresponding to the value of the third homotopy equation, setting the terminal constraint to the value of the first homotopy equation at the termination value of the first homotopy parameter, and solving the control variables with the initial transfer trajectory as the initial value for iteration to obtain the target transfer trajectory includes:

[0018] Based on the dynamic model and the second homotopy equation, the value of the third homotopy equation is set to the value at the initial value of the third homotopy parameter, and the terminal constraint is set to the value of the first homotopy equation at the termination value of the first homotopy parameter. The control variables are solved with the initial transfer trajectory as the initial value of the iteration to obtain the intermediate transfer trajectory.

[0019] Based on the dynamic model, the value of the second homotopy equation is set to the corresponding value at the termination value of the second homotopy parameter, the terminal constraint is set to the value of the first homotopy equation at the termination value of the first homotopy parameter, the cost function is set according to the value of the third homotopy equation, and the control variables are solved with the intermediate transfer trajectory as the initial value of the iteration to obtain the target transfer trajectory.

[0020] In some examples, when at least one of the first homotopy parameter, the second homotopy parameter, and the third homotopy parameter increases, the iteration step size corresponding to at least one of the first homotopy parameter, the second homotopy parameter, and the third homotopy parameter decreases.

[0021] In some examples, the first spacecraft includes an orbital transfer vehicle that does not carry a second spacecraft, or an orbital transfer vehicle that carries at least one second spacecraft.

[0022] In some examples, when the first spacecraft reaches the end of the second orbit, it releases the at least one second spacecraft and transmits the status information of the end of the second orbit to the at least one second spacecraft.

[0023] Secondly, this disclosure provides a spacecraft orbital transfer control device suitable for deep space shuttle missions, comprising:

[0024] Model building module: used to build a dynamic model of the first spacecraft transferring from the first orbit to the second orbit;

[0025] The first solution module communicates with the model building module and is configured to obtain the initial transfer trajectory based on the dynamic model, with energy optimization as the objective, through the first homotopy parameter.

[0026] The second solution module is communicatively connected to the first solution module and is configured to obtain the target transfer trajectory based on the initial transfer trajectory, with fuel optimization as the objective, through the second and third homotopy parameters.

[0027] Thirdly, this disclosure provides a computer storage medium storing at least one instruction for execution by a processor to implement the spacecraft orbit transfer control method as described in the first aspect and its examples. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of an orbital transfer scenario of a celestial body centered on the Earth, provided as an embodiment of the present disclosure.

[0029] Figure 2 A block diagram illustrating a spacecraft orbital transfer control method suitable for deep space shuttle missions, provided as an embodiment of this disclosure;

[0030] Figure 3 A schematic diagram illustrating the solution steps of a spacecraft orbital transfer control method applicable to deep space shuttle missions, provided in an embodiment of this disclosure;

[0031] Figure 4 A schematic diagram illustrating another solution step of a spacecraft orbital transfer control method applicable to deep space shuttle missions, provided in an embodiment of this disclosure;

[0032] Figure 5 A schematic diagram of a spacecraft assembly provided in an embodiment of this disclosure;

[0033] Figure 6 A schematic diagram of a mission to explore the near-Earth asteroid Bennu provided as an embodiment of this disclosure;

[0034] Figure 7 A schematic diagram illustrating the angular variation of the thrust direction component in the orbital plane during the Bennu exploration mission, provided as an embodiment of this disclosure;

[0035] Figure 8 A schematic diagram illustrating the angular variation of the thrust component perpendicular to the orbital plane during the Bennu exploration mission, provided as an embodiment of this disclosure.

[0036] Figure 9 This is a schematic diagram of the transfer path during the orbit-ascending phase of the Bennu exploration mission provided in this embodiment of the disclosure;

[0037] Figure 10 A schematic diagram of the transfer path during the aerodynamic descent phase in the Bennu exploration mission provided in this embodiment of the disclosure;

[0038] Figure 11 A schematic diagram of a spacecraft orbital transfer control device suitable for deep space shuttle missions, provided as an embodiment of this disclosure;

[0039] Figure 12 A block diagram of a computing device for spacecraft orbit transfer control suitable for deep space shuttle missions, provided as an embodiment of this disclosure. Detailed Implementation

[0040] The technical solutions in the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings.

[0041] To enable those skilled in the art to more clearly understand the calculation formulas in the embodiments of this disclosure, the mathematical symbols used herein are explained as follows:

[0042] Vector representation: In this specification, if a variable symbol is indicated by a superscript arrow, it represents a vector. For example, Represents the velocity vector. This represents the position vector.

[0043] Scalar Notation: In this specification, if a variable symbol is not indicated by a superscript arrow, it represents a scalar. Typically, a scalar symbol represents the magnitude of its corresponding vector. For example, Represents velocity vector The length of the mold, Represents position vector The length of the module.

[0044] Please refer to Figure 1 The diagram illustrates an orbital transfer scenario centered on Earth 120. It includes two orbits orbiting Earth 120: orbit 140 and orbit 160. Spacecraft 170 can transfer from orbit 140 to orbit 160 via transfer trajectory 180, and from orbit 160 to orbit 140 via transfer trajectory 190.

[0045] In this disclosure, a spacecraft refers to any type of aircraft that operates in space according to the laws of celestial mechanics, performing specific tasks such as exploring, developing, and utilizing space and celestial bodies. This includes, but is not limited to: orbital transport spacecraft, such as Orbital Transfer Vehicles (OTVs, also known as Space Tugs or Deep Space Shuttles); exploration spacecraft, such as deep space probes, lunar probes, Mars probes, and asteroid probes; infrastructure spacecraft, such as artificial satellites (communication, navigation, and remote sensing satellites), space stations, cargo spacecraft, or manned spacecraft; and combined configurations: combinations formed by at least two of the above spacecraft through a docking mechanism, such as a combination of an OTV and a transported satellite. The orbital transfer control method described in this disclosure is applicable to any of the above-mentioned spacecraft. The first spacecraft and the second spacecraft mentioned in this disclosure can be understood as any of the above-mentioned spacecraft to perform an orbital transfer mission.

[0046] Please refer to Figure 2 The diagram illustrates a block diagram of a spacecraft orbital transfer control method for deep space shuttle missions, provided by an embodiment of this disclosure. The method includes:

[0047] Step S220: Obtain the dynamic model of the first spacecraft transferring from the first orbit to the second orbit.

[0048] It should be noted that the first orbit is the starting orbit for the orbital transfer, and the second orbit is the target orbit for the orbital transfer. The first and second orbits can belong to the same central celestial body, such as the transfer between Earth orbits, or they can cross different central celestial bodies, such as the transfer from Earth orbit to Moon orbit.

[0049] It should be noted that, for orbital transfers under the same central celestial body, this application does not limit the height (or semi-major axis) relationship between the first orbit and the second orbit, that is, it includes both orbital elevation (the first orbit is lower than the second orbit) and orbital descent (the first orbit is higher than the second orbit).

[0050] The dynamic model is used to characterize the iterative motion state of the first spacecraft during the transfer process. Specifically, the model can be expressed as a first-order differential equation of state variables with respect to transfer time, where the state variables can be characterized by position vectors, velocity vectors, and mass. It is understood that, depending on the chosen coordinate system (such as an inertial coordinate system or an orbital coordinate system), the state variables can include various combinations of parameters such as position and velocity; and the model is not limited to a continuous form, but can also encompass discretized differential expressions or incremental computational logic adapted for onboard computer processing.

[0051] It is understood that those skilled in the art can introduce more perturbation factors (such as J2 term perturbation, atmospheric drag, etc.) into the dynamic model according to actual task requirements, and such modifications do not depart from the core concept of the present invention.

[0052] Step S240: Based on the dynamic model, with energy optimization as the objective, obtain the initial transfer trajectory through the first homotopy parameter.

[0053] "Energy optimization" refers to minimizing the spacecraft's control energy consumption during orbit transfer as the optimization criterion. The optimal control problem corresponding to energy optimization has the characteristics of smooth solution and wide convergence region, which facilitates obtaining a feasible transfer orbit that satisfies the terminal constraints.

[0054] The "initial transfer trajectory" refers to the feasible transfer trajectory obtained in step S240. This transfer trajectory has the following characteristics: it aims for energy optimization, satisfies terminal constraints, and is easy to solve. This transfer trajectory is used to provide high-quality iterative initial values ​​for subsequent trajectory design.

[0055] In the above steps, the first homotopy parameter is introduced into the solution model, for example, by acting on the terminal constraints or dynamic equations, causing the complexity of the problem to gradually increase with the iteration of the first homotopy parameter. Using the solution corresponding to the value of the first homotopy parameter in the previous iteration as the initial value for the current iteration, the initial transfer trajectory is eventually obtained through continuous iteration of the first homotopy parameter.

[0056] Step S260: Based on the initial transfer trajectory, with fuel optimization as the objective, obtain the target transfer trajectory using the second homotopy parameter and the third homotopy parameter.

[0057] "Fuel optimization as the objective" refers to using the minimization of spacecraft control fuel consumption as the optimization criterion during orbital transfer. By directly using the minimization of thrust fuel consumption as the optimization criterion, payload capacity can be improved and mission life can be extended, which is particularly suitable for scenarios with high fuel efficiency requirements, such as low-thrust electric propulsion.

[0058] In this disclosure, the "target transfer orbit" is the fuel-optimal solution that meets the actual engineering needs, which can significantly reduce fuel consumption and improve the engineering feasibility and long-term operational capability of the orbit transfer mission.

[0059] In the above steps, the complex fuel optimization problem is decomposed into a series of continuous and easily convergent subproblems through the synergistic effect of the second and third homotopy parameters; the initial transfer trajectory obtained in step S240 is used as the initial value for iteration to gradually approximate the fuel optimization solution that meets the actual engineering requirements.

[0060] The above technical solution provides a high-quality initial value guess for the fuel optimization problem by utilizing the easily solvable energy optimization problem, thereby significantly improving the efficiency of initial value solution. Through the synergistic effect of the second and third homotopy parameters, the target transfer trajectory under the fuel optimization objective is obtained, thereby improving the robustness of the indirect method to the initial value guess and enhancing the convergence of the solution for complex trajectory transfer tasks.

[0061] against Figure 2 In some possible implementations of the technical solution shown, the step of obtaining the initial transfer trajectory based on the dynamic model, with energy optimization as the objective, through the first homotopy parameter, includes:

[0062] Construct a first homotopy equation. At the initial value of the first homotopy parameter, the value of the first homotopy equation corresponds to the number of orbital elements of the first orbit; at the final value of the first homotopy parameter, the value of the first homotopy equation corresponds to the number of orbital elements of the second orbit.

[0063] Based on the dynamic model, a cost function is set with the optimal energy as the performance index, terminal constraints are set according to the value of the first homotopy equation, and control variables are solved to obtain the initial transfer trajectory.

[0064] For the example above, the dynamic model used to describe the first spacecraft, based on Newton's laws of motion and the law of universal gravitation, can be characterized as follows:

[0065]

[0066] in, For the state variables of the first spacecraft, The first-order differential of the state variables of the first spacecraft, i.e., the dynamic equation; For transfer time; This represents the position vector of the first spacecraft during the transfer process; This represents the velocity vector of the first spacecraft during the transfer process. This represents the mass of the first spacecraft during the transfer process, and its value can vary due to factors including fuel consumption. The gravitational constant of the central celestial body, The gravitational constant, The mass of the central celestial body; This represents the distance of the first spacecraft relative to the central celestial body. Let be the thrust coefficient of the first spacecraft, and have ; The thrust amplitude that the engine can provide; the actual thrust provided by the engine. Therefore, when At that time, the actual thrust provided by the engine is ;when At that time, the actual thrust provided by the engine is the maximum thrust it can provide; In the direction of thrust; For engine specific impulse; This is the standard gravitational acceleration at the Earth's surface.

[0067] In this disclosure, the initial values ​​of the first, second, and third homotopy parameters are set to 0, and the final values ​​of the first, second, and third homotopy parameters are set to 1. A homotopy parameter of 0 corresponds to the initial simplified problem (e.g., in the first homotopy equation, a parameter of 0 corresponds to the value of the first homotopy equation being the orbital element corresponding to the first orbital); a homotopy parameter of 1 corresponds to the target problem to be solved (e.g., in the first homotopy equation, a parameter of 1 corresponds to the value of the first homotopy equation being the orbital element corresponding to the second orbital). By iterating the homotopy parameter from 0 to 1, the complexity of the problem gradually increases, and finally, when the homotopy parameter converges to 1, the optimal solution to the target problem is obtained.

[0068] It should be noted that the initial value of homotopy parameter 0 and the final value of homotopy parameter 1 used in this disclosure are only exemplary values. Those skilled in the art may choose other values ​​according to the actual needs of the algorithm (such as iterating from 0 to 100, or from -1 to 1), which is still consistent with the inventive concept of this disclosure.

[0069] For the example above, by introducing a first homotopy parameter The first homotopy equation is constructed as follows:

[0070]

[0071] Among them, with Iterate from 0 to 1, and the value of the first homotopy equation gradually changes from the orbital element of the first orbital to the orbital element of the second orbital. Let be the value of the first homotopy equation, whose value varies with the first homotopy parameter. It changes with the changes; This represents the orbital elements corresponding to the first orbit; This represents the orbital elements corresponding to the second orbit.

[0072] Based on the value of the first homotopy equation during the iteration process, corresponding terminal constraints are set so that the first spacecraft reaches a state that satisfies the terminal constraints at the terminal time.

[0073] It should be noted that the orbital elements mentioned The parameter is a set of at least one of the following orbital parameters: semi-major axis, eccentricity, inclination, right ascension of the ascending node, argument of perigee, and true anomaly. Those skilled in the art can arbitrarily select and combine these parameters according to actual task requirements without inventive effort, and this still falls within the same inventive concept of this disclosure.

[0074] In the example above, using energy optimization as a performance metric could be achieved through the thrust coefficient. The square of the transfer time It can be represented in integral form, or it can be multiplied by a normalized weighting factor. This allows performance metrics to have more reasonable physical dimensions and numerical scales. In some examples, the cost function with energy optimization as the performance metric can be characterized as:

[0075]

[0076] in, This is the initial time; For terminal time, For transfer time.

[0077] Control variables are quantities that affect system behavior and can be directly manipulated, such as thrust magnitude and direction, pulse thrust, angle of attack, and roll angle. Those skilled in the art can arbitrarily select and combine them according to different mission requirements. In some examples of this disclosure, thrust magnitude and direction are used as control variables, and the control variables are solved based on the dynamic model, terminal constraints, and performance indicators.

[0078] In some examples, the solution process for the control variables in the above examples is as follows: based on the state variables of the first spacecraft. Introduce the corresponding costate variables Costate variables It is a set of state variables Introducing costate variables with the same dimensions of auxiliary variables. The core objective is to transform the originally complex dynamic optimization problem into a set of easily solvable two-point boundary value problems. Specifically, it describes the impact of state changes on the total cost through costate equations and directly determines the form of the optimal control law through the minimum condition. In some examples, the costate variables... It can be characterized as ,in It is related to the position vector The corresponding costate variable, It is related to the velocity vector The corresponding costate variable, Is related to quality The corresponding costate variables.

[0079] To derive the optimal control law (e.g., optimal thrust direction and optimal thrust coefficient), i.e., the optimal form of the control variables to be solved in the above example, the Hamiltonian function is introduced. The Hamiltonian function is a scalar function that couples the dynamic equations and performance indices through costate variables. Specifically, the Hamiltonian function can be characterized as:

[0080]

[0081] Separating the Hamiltonian function from the thrust direction The relevant items are Therefore, regarding the direction of thrust Minimizing the Hamiltonian function is equivalent to .because ,and ,in for and The angle between them, therefore the minimum value is at When obtained, that is, the optimal thrust direction is... The directions are opposite. Specifically, the optimal thrust direction. It can be characterized as:

[0082]

[0083] Based on obtaining the optimal thrust direction, Substituting the Hamiltonian function, the updated Hamiltonian function is:

[0084]

[0085] Because the expression of the last term in the above equation is... It is irrelevant, so it can be considered a constant term.

[0086] Define switch function The switching function is a scalar function constructed based on the Hamiltonian function, used to determine whether the optimal control quantity takes boundary values. By analyzing the zero-crossing points of the switching function, the engine start / stop timing can be determined. It is understood that the above expression of the switching function is merely an exemplary implementation of this disclosure. Based on this disclosure, those skilled in the art can adaptively adjust the specific form of the switching function according to actual task requirements (such as engine type, thrust constraint form, etc.) (e.g., introducing a smoothing factor or considering different thrust models).

[0087] Substitute the switching function and update the Hamiltonian function as follows:

[0088]

[0089] By finding the Hamiltonian function mentioned above... The partial derivatives yield:

[0090]

[0091] make This yields the result without considering boundary conditions (i.e. The optimal thrust coefficient under these conditions is:

[0092] Consider boundary conditions ,like ,but exist The value is monotonically decreasing within the range, and the minimum value is at this point. Obtained from; if ,but exist The value is monotonically increasing within the range, and the minimum value is at this point. Obtained from; if The minimum value is at The optimal thrust coefficient can be obtained from [the location]. Specifically, considering the boundary conditions, the optimal thrust coefficient can be characterized as:

[0093]

[0094] For the above example, please refer to Figure 3 It shows a schematic diagram of the solution steps of a spacecraft orbit transfer control method applicable to deep space shuttle missions provided in this disclosure.

[0095] against Figure 2 In some possible examples of the technical solution, when the first homotopy parameter increases, the iteration step size corresponding to the first homotopy parameter decreases.

[0096] Step S341: Initial state for solving the problem, take... , .

[0097] in Let be the number of iterations. In the initial state, since... Therefore, there is ,and When the homotopy parameter is zero, the terminal constraint corresponds to the first orbital element, at which point the spacecraft only needs to maintain its original orbit.

[0098] Step S342: Take .

[0099] in The iteration step size is variable. In the initial stage of the iteration ( When the size is small, a larger step size is used for rapid advancement to improve computational efficiency; as the size increases... As the initial value increases, the solution becomes more sensitive to the initial value. At this point, reducing the step size avoids iterative divergence caused by an excessively large step size. This step size control strategy optimizes the allocation of computational resources and improves the robustness and applicability of the control method while ensuring solution accuracy.

[0100] Step S343: Update the current terminal constraints as follows: .

[0101] In step S343, a homotopy parameter is introduced. The terminal constraints are iterated, and in each iteration, the terminal constraints are gradually adjusted, thereby resolving the original terminal constraints that were difficult to solve directly. With known initial terminal constraints Smooth connection.

[0102] Step S344: Place the first The solution of the nth iteration is used as the first... The guessed value for the next iteration.

[0103] In step S344, the homotopy parameter from the previous iteration is used... The converged solution (including the state trajectory, initial values ​​of costate variables, and control law) is used as the current iteration parameter. The initial guess values ​​are fully utilized, taking full advantage of the high similarity between the solution spaces of adjacent subproblems, thereby significantly improving the iteration convergence speed and numerical stability, and avoiding solution divergence caused by parameter mutations.

[0104] Step S345: Check whether the current terminal constraints are met. If the conditions are met, proceed to step S346; if the conditions are not met, proceed to step S347.

[0105] In step S345, it is checked whether the terminal state obtained in the current iteration meets the preset terminal constraint tolerance. If it does, it indicates that the solution result of the current iteration has successfully converged and can proceed to the next step to update the homotopy parameter (step S346); if it does not meet, it is necessary to continue to adjust the guessed value (such as the guessed value of the costate variable) under the current homotopy parameter, i.e., step S347.

[0106] Step S346: Check Should it be increased to 1? If so... If the judgment condition is met, proceed to step S349; if If the judgment condition is not met, proceed to step S348.

[0107] In step S346, by checking Has the value been incremented to the termination value of 1 to determine if the homotopy process is complete? This indicates that the terminal constraints have changed from the initial state. Complete iteration to the target state The current solution result is the solution to the target problem, and we can proceed to the result output step S349; if If so, proceed to step S348 to continue increasing the homotopy parameter and solve the next parameter subproblem until it finally converges to the solution of the target problem.

[0108] Step S347: Adjust the guessed value, and then proceed to step S345.

[0109] In step S347, if the current guess value cannot meet the terminal constraint accuracy, the guess value needs to be adjusted. Specifically, the guess value (e.g., initial value of the costate variable) can be corrected based on the sensitivity information of the deviation to the guess value (e.g., estimated using Newton's method or gradient method), thereby generating a set of updated guess values ​​that are closer to the optimal solution. After adjustment, step S345 is executed to re-detect, iterating repeatedly until the current... The solution converges downwards, ensuring that an accurate solution is obtained before proceeding to the next solution iteration.

[0110] Step S348: Let Then, step S342 is executed.

[0111] In step S348, after obtaining an exact solution that satisfies the current terminal constraints, the next iteration process begins to update the terminal constraints, thereby further approximating the target problem. Then, step S342 is executed, and the currently obtained exact solution is used as a guess for the next iteration.

[0112] Step S349: Obtain the initial transfer orbit.

[0113] In step S349, an initial transfer trajectory satisfying the energy-optimal performance index and terminal constraints from the first trajectory to the second trajectory was successfully obtained. This included the complete state variable change process and co-state variable change process, as well as the change process of thrust amplitude and thrust direction. This can serve as an accurate initial guess for subsequent optimization problems (such as optimizing the thrust model to the actual thrust constraint model).

[0114] Through the above technical solution, the terminal constraint conditions were continuously iterated, so that the initial transfer trajectory could satisfy the terminal constraint conditions, thereby improving the convergence region of the solution.

[0115] against Figure 2 In some possible implementations of the technical solution shown, the step of obtaining the target transfer orbit based on the initial transfer orbit, with fuel optimization as the objective, through the second and third homotopy parameters, includes:

[0116] A second homotopy equation is constructed. At the initial value of the second homotopy parameter, the value of the second homotopy equation corresponds to the preset thrust amplitude. At the final value of the second homotopy parameter, the value of the second homotopy equation corresponds to the actual thrust amplitude.

[0117] A third homotopy equation is constructed. At the initial value of the third homotopy parameter, the value of the third homotopy equation corresponds to the cost function with energy optimization as the performance index. At the final value of the third homotopy parameter, the value of the third homotopy equation corresponds to the cost function with fuel optimization as the performance index.

[0118] Based on the dynamic model and the second homotopy equation, the cost function is set according to the value of the third homotopy equation, and the terminal constraint is set to the value of the first homotopy equation at the termination value of the first homotopy parameter. The control variables are solved with the initial transfer trajectory as the initial value for iteration to obtain the target transfer trajectory.

[0119] For the above example, in some possible implementations, the step of setting the cost function based on the dynamic model and the second homotopy equation, corresponding to the value of the third homotopy equation, setting the terminal constraint to the value of the first homotopy equation at the termination value of the first homotopy parameter, and solving the control variables with the initial transfer trajectory as the initial value for iteration to obtain the target transfer trajectory includes:

[0120] Based on the dynamic model and the second homotopy equation, the value of the third homotopy equation is set to the value at the initial value of the third homotopy parameter, and the terminal constraint is set to the value of the first homotopy equation at the termination value of the first homotopy parameter. The control variables are solved with the initial transfer trajectory as the initial value of the iteration to obtain the intermediate transfer trajectory.

[0121] Based on the dynamic model, the value of the second homotopy equation is set to the corresponding value at the termination value of the second homotopy parameter, the terminal constraint is set to the value of the first homotopy equation at the termination value of the first homotopy parameter, the cost function is set according to the value of the third homotopy equation, and the control variables are solved with the intermediate transfer trajectory as the initial value of the iteration to obtain the target transfer trajectory.

[0122] In the above example, the actual constrained thrust amplitude model refers to the model of the maximum thrust value that the engine can provide; the preset thrust amplitude model refers to the idealized thrust model that is set in advance for the convenience of numerical solution. The thrust amplitude in this model can be much larger than the actual constrained thrust amplitude (for example, it can be set to 10 times, 100 times or more of the actual maximum thrust amplitude as needed). However, other forms of preset thrust models can also be selected as the starting point of the second homotopy parameter according to the characteristics of the actual problem, such as simplified dynamic model, infinitesimal thrust model, etc., so that the solution of the subproblem in the iteration process of the second homotopy parameter satisfies feasibility and convergence.

[0123] In the example above, a second homotopy parameter is introduced. The second homotopy equation is constructed as follows:

[0124]

[0125] Among them, with Iterates from 0 to 1, gradually changing the thrust model from the preset thrust amplitude model to the actual constrained thrust amplitude model. Let be the value of the second homotopy equation, whose value varies with the second homotopy parameter. It changes with the changes; For the preset thrust amplitude model; This is the actual constrained thrust amplitude model.

[0126] In the example above, a third homotopy parameter is introduced. The third homotopy equation is constructed as follows:

[0127]

[0128] Among them, with Iterate from 0 to 1, and the performance index gradually changes from energy optimal to fuel optimal.

[0129] In some examples, the solution process for the control variables in the above examples is as follows:

[0130] Based on the introduction of the second and third homotopy equations, the Hamiltonian function can be expressed as:

[0131]

[0132] Based on the form of the Hamiltonian function, the second homotopy parameter... The introduction of this only changes the magnitude range of the thrust model, without altering the structure of the thrust-direction-related terms in the Hamiltonian function. Therefore, regardless of Regardless of the value, the optimal thrust direction is always with The directions are opposite. Simultaneously, this property ensures the consistency of the thrust direction of the transfer trajectory obtained by applying the trajectory transfer control method of this disclosure, guaranteeing the continuity of the homotopy path. Specifically, in the above example, the optimal thrust direction can still be characterized as:

[0133]

[0134] Based on obtaining the optimal thrust direction, Substituting the Hamiltonian function, the updated Hamiltonian function is:

[0135] Substitute the switching function and update the Hamiltonian function as follows:

[0136]

[0137] The constant term is a term that is independent of the control variable.

[0138] By finding the Hamiltonian function mentioned above... The partial derivatives yield:

[0139]

[0140] make This yields the result without considering boundary conditions (i.e. The optimal thrust coefficient under these conditions is:

[0141] Consider boundary conditions ,like ,but exist The value is monotonically decreasing within the range, and the minimum value is at this point. Obtained from; if ,but exist The value is monotonically increasing within the range, and the minimum value is at this point. Obtained from; if The minimum value is at This is obtained from [the source]. Specifically, the optimal thrust coefficient can be characterized as:

[0142]

[0143] For the above example, please refer to Figure 4 This diagram illustrates another solution step of a spacecraft orbital transfer control method for deep space shuttle missions provided in this disclosure.

[0144] Step S461: Take , , The transfer trajectory at this point is equal to the initial transfer trajectory obtained in step S240.

[0145] In step S461, by... and Simultaneously set to 0, construct a solution state equivalent to step S240, thereby using the initial transfer trajectory obtained in S240 as the precise starting point for subsequent optimization.

[0146] Step S462: Fix ,Pick .

[0147] In step S462, while still maintaining energy optimization as the performance metric, the second homotopy parameter is... According to the preset step size The thrust amplitude is increased incrementally, thus iterating the thrust model from a preset thrust amplitude model to an actual constrained thrust amplitude model. This is achieved by fixing... This ensures that only changes in the thrust model are considered at the current stage, without introducing changes in performance indicators, thus decoupling the multi-parameter coupled problem into a single-parameter iterative problem.

[0148] Step S463: Place the first The solution of the nth iteration is used as the first... The guessed value for the next iteration.

[0149] In step S463, after obtaining the exact solution under the current thrust model, the next iteration process is entered to update the thrust model, thereby getting closer to the target problem, and the currently obtained exact solution is used as the guess value for the next iteration.

[0150] Step S464: Check if the current terminal constraints are met. If the conditions are met, proceed to step S466; if the conditions are not met, proceed to step S465.

[0151] In step S464, it is checked whether the terminal state obtained in the current iteration satisfies the terminal constraint tolerance. If it does, it indicates that the solution result of the current iteration has successfully converged, and the next step can be performed. Check if it increases to 1 (step S466); if not, then in the current... Continue to adjust the guessed values ​​(such as the guessed values ​​of costate variables) under numerical conditions, i.e., step S465.

[0152] Step S465: Adjust the guessed value, and then proceed to step S464.

[0153] In step S465, if the current guess value cannot meet the terminal constraint tolerance, the guess value needs to be adjusted. Specifically, the guess value (e.g., initial value of the costate variable) can be corrected based on the sensitivity information of the deviation magnitude to the guess value (e.g., estimated using Newton's method or gradient method), thereby generating a set of updated guess values ​​that are closer to the optimal solution. After adjustment, step S464 is executed to re-check, iterating repeatedly until the current value meets the requirements. Numerical convergence ensures that an accurate solution is obtained before proceeding to the next solution iteration.

[0154] Step S466: Check Increase to 1. If the condition is met, proceed to step S468; if the condition is not met, proceed to step S467.

[0155] In step S466, by checking Has the value been incremented to the termination value of 1 to determine if the homotopy process is complete? This indicates that the thrust model has iterated from the preset thrust amplitude model to the actual constrained thrust amplitude model, and the current solution result is the solution to the target problem. The process can proceed to the result output step S468. If so, proceed to step S467 to continue increasing the homotopy parameter and solve the next parameter subproblem until the solution to the target problem is finally converged.

[0156] Step S467: Let Then proceed to step S462.

[0157] In step S467, after obtaining the exact solution under the current thrust model, the next iteration process is initiated to update the thrust model, thereby further approximating the target problem. Subsequently, step S462 is executed, and the currently obtained exact solution is used as the guess value for the next iteration.

[0158] Step S468: Obtain the intermediate transfer orbit.

[0159] In step S469, an intermediate transfer trajectory from the first trajectory to the second trajectory that satisfies the energy-optimal performance index and terminal constraints, as well as the actual thrust constraints, was successfully obtained. This included the complete state variable change process and co-state variable change process, as well as the change process of thrust amplitude and thrust direction, which can serve as an accurate initial guess for subsequent optimization problems (such as optimizing the performance index as fuel-optimal).

[0160] Step S469: Take , , The transfer trajectory at this point is equal to the transfer trajectory obtained in step S468.

[0161] In step S469, by Set to 0, and Set to 1 to construct a solution state equivalent to step S469, thereby using the intermediate transition path obtained in S469 as the precise starting point for subsequent optimization.

[0162] Step S470: Fix ,Pick .

[0163] In step S462, while maintaining the thrust model as the actual constrained thrust model, the third homotopy parameter is... According to the preset step size The performance index is increased incrementally, thus iterating from energy optimal to fuel optimal.

[0164] Step S471: Place the first The solution of the nth iteration is used as the first... The guessed value for the next iteration.

[0165] In step S471, after obtaining the exact solution under the current performance index, the next iteration process is entered to update the performance index, thereby getting closer to the target problem, and the currently obtained exact solution is used as the guess value for the next iteration.

[0166] Step S472: Check if the current terminal constraints are met. If the conditions are met, proceed to step S474; if the conditions are not met, proceed to step S473.

[0167] In step S464, it is checked whether the terminal state obtained in the current iteration satisfies the terminal constraint tolerance. If it does, it indicates that the solution result of the current iteration has successfully converged, and the next step can be performed. Check whether the value increases to 1 (step S474); if not, then in the current... Continue to adjust the guessed values ​​(such as the guessed values ​​of costate variables) under numerical conditions, i.e., step S473.

[0168] Step S473: Adjust the guessed value, and then proceed to step S472.

[0169] In step S473, if the current guess value cannot meet the terminal constraint tolerance, the guess value needs to be adjusted. Specifically, the guess value (e.g., initial value of the costate variable) can be corrected based on the sensitivity information of the deviation magnitude to the guess value (e.g., estimated using Newton's method or gradient method), thereby generating a set of updated guess values ​​that are closer to the optimal solution. After adjustment, step S472 is executed to re-check, iterating repeatedly until the current value meets the requirements. Numerical convergence ensures that an accurate solution is obtained before proceeding to the next solution iteration.

[0170] Step S474: Inspection Increase to 1. If the condition is met, proceed to step S476; if the condition is not met, proceed to step S475.

[0171] In step S474, by checking Has the value been incremented to the termination value of 1 to determine if the homotopy process is complete? This indicates that the performance index has iterated from energy optimal to fuel optimal, and the current solution result is the solution to the target problem. We can proceed to the result output step S476; if If so, proceed to step S475 to continue increasing the homotopy parameter and solve the next parameter subproblem until the solution to the target problem is finally converged.

[0172] Step S475: Let Then, step S470 is executed.

[0173] In step S475, after obtaining the exact solution under the current performance metric, the next iteration process is initiated to update the performance metric, thereby further approximating the target problem. Subsequently, step S470 is executed, and the currently obtained exact solution is used as the guess value for the next iteration.

[0174] Step S476: Obtain the target transfer trajectory.

[0175] In step S476, the optimal fuel transfer trajectory from the first trajectory to the second trajectory, which satisfies the optimal energy performance index, the terminal constraint condition, and the actual thrust constraint, is successfully obtained, i.e., the target transfer trajectory.

[0176] Second homotopy parameter and third homotopy parameter During the iteration process, the following iteration step size control strategy can also be adopted: when the value of any parameter increases, the iteration step size corresponding to that parameter decreases accordingly. This strategy can effectively cope with the convergence difficulties caused by the enhancement of nonlinearity in the later stages of iteration, and ensure the stability of the control method throughout the entire iteration path.

[0177] It should be noted that the first homotopy equation, the second homotopy equation, and the third homotopy equation are completely independent of specific solvers (such as the target shooting method, the collocation method, etc.). The selection of the solver at each solution path point is a common method in this field, and those skilled in the art can arbitrarily replace it without any creative effort.

[0178] Through the above technical solutions, the embodiments of this disclosure achieve the following beneficial effects:

[0179] By iterating the second homotopy parameter, the transfer trajectory can meet the actual thrust constraints.

[0180] By iterating the third homotopy parameter, the transfer trajectory can smoothly iterate from energy optimal to fuel optimal, thus improving the continuity of the solution to the fuel optimal problem.

[0181] The above homotopy iteration strategy achieves efficient collaborative solving of multiple parameters, significantly improving the solution efficiency.

[0182] In embodiments of this disclosure, the first spacecraft docks with at least one second spacecraft to form a combined assembly; the combined assembly performs the orbital transfer control method described in this disclosure.

[0183] Through coordinated execution by the combined spacecraft, the first and second spacecraft were able to share resources such as propellant and computing resources, further improving the energy efficiency and mission planning capabilities of the orbital transfer mission.

[0184] For the example above, please refer to Figure 5This disclosure provides a schematic diagram of a spacecraft assembly. The assembly includes an orbital transfer vehicle 510 and a second spacecraft assembly 520 connected to the orbital transfer vehicle 510. The second spacecraft assembly 520 may include one or more second spacecraft (e.g., second spacecraft-1 to second spacecraft-N). The connection between the orbital transfer vehicle 510 and the second spacecraft assembly 520 can be any form known to those skilled in the art, including but not limited to: physical connection (achieved through mechanical gripping, electromagnetic adsorption, locking docking, friction connection, or physical bolting); non-physical connection (achieved through formation flying, position holding, etc.); and a connection medium that can include physical connection components or achieve logical connection solely through control commands or data synchronization.

[0185] In some possible examples of the above technical solutions, the first spacecraft releases the second spacecraft at a release point and transmits the status information of the release point to the second spacecraft; wherein, the status information serves as input parameters for the second spacecraft to perform subsequent tasks.

[0186] Next, please refer to Figure 6 It illustrates a mission diagram for exploring the near-Earth asteroid Bennu, as provided in the above example, to illustrate in detail the application of the control methods described in this disclosure in a practical engineering scenario. Figure 6 It includes: an orbit transfer vehicle 601, a small satellite 602, and two orbits centered on Earth 120, namely a low Earth orbit (LEO) 670 and a preset high orbit 680; a phase 610 for launching the small satellite to the low Earth orbit 670; a combination 603 formed by combining the orbit transfer vehicle and the small satellite; a phase 630 for the orbit transfer vehicle carrying the small satellite to ascend to orbit; a phase 640 for releasing the small satellite 602 at a preset release point; a phase 650 for the released small satellite to conduct deep space exploration; and a phase 660 for the orbit transfer vehicle to aerodynamically assist in descending to orbit.

[0187] The mission involves a coordinated system consisting of an orbital transfer vehicle 601 and a small satellite 602 (Class A, i.e., an artificial satellite with a mass of less than 1000 kg). The orbital transfer vehicle 601 has a mass of 500 kg, is equipped with an electric propulsion system with a thrust of 1 N, and a specific impulse of 2500 s; the small satellite 602 to be transported has a mass of about 100 kg. The mission requires the orbital transfer vehicle 601 to deliver the small satellite 602 to a predetermined release point. Subsequently, the orbital transfer vehicle 601 returns to low Earth orbit 670, and the small satellite 602 autonomously travels to Bennu to complete further deep space exploration.

[0188] During the orbit ascent phase 630, the orbit transfer method described in this disclosure is used for efficient and accurate planning. A low Earth orbit 670 is designated as the first orbit, and a pre-defined high Earth orbit 680 is designated as the second orbit. First, with energy optimization as the objective, the initial transfer orbit is solved using a first homotopy parameter. Second, based on the initial transfer orbit, a second and third homotopy parameter are introduced to solve for the fuel-optimal transfer orbit that satisfies the thrust constraint amplitude.

[0189] To illustrate the effectiveness and feasibility of the orbital transfer control method described in this disclosure, please refer to... Figures 7 to 9 The figure shows the numerical simulation verification results for the above example. Figures 7 to 9 Together, they demonstrate that the orbital transfer control method described in this disclosure can generate a feasible, smooth, and practically constrained optimal fuel transfer orbit.

[0190] For the example above, please refer to Figure 7 This diagram illustrates the angular variation of the thrust direction component in the orbital plane during the Bennu exploration mission, as provided in this embodiment of the present disclosure. The horizontal axis represents the transfer time in days; the vertical axis represents the thrust angle. (Yaw angle), in degrees (°). Please refer to... Figure 8 This diagram illustrates the angular variation of the thrust direction perpendicular to the orbital plane during the Bennu exploration mission, as provided in this embodiment of the present disclosure. The horizontal axis represents the transfer time in days, and the vertical axis represents the thrust angle. (Pitch angle), in degrees (°). From Figure 7 and Figure 8 It can be seen that the thrust direction changes smoothly and continuously without obvious abrupt changes, which demonstrates that the orbital transfer control method described in this disclosure has good practicality and avoids frequent engine start-ups and shutdowns or drastic attitude adjustments.

[0191] For the example above, Figure 9 This diagram illustrates the transfer path during the orbital ascent phase of the Bennu exploration mission, as provided in this embodiment of the disclosure. In the diagram: the "Starting Point" marker indicates the initial position where the spacecraft begins its orbital transfer, corresponding to a specific point on the first orbit; the "Arrival Point" marker indicates the final position where the spacecraft completes its orbital transfer, corresponding to a specific point on the second orbit; the solid curve represents the complete transfer trajectory of the spacecraft; the units of the X, Y, and Z axes in the diagram are astronomical units (AU, approximately equal to the average distance from the Earth to the Sun). As can be seen from the diagram, the transfer trajectory is smooth and continuous, and accurately meets the terminal constraints, achieving precise orbital transfer control.

[0192] In the release phase 640, the small satellite 602 is released at a predetermined release point. After the assembly reaches the predetermined release point, the orbital transfer vehicle 601 releases the small satellite 602 it carries and transmits the precise state parameters of the release point (including the release point's position, release velocity, epoch time, etc.) to the small satellite 602. In the deep space exploration phase 650, the released small satellite autonomously conducts a deep space exploration mission to Bennu based on the received state parameters of the release point and information such as ephemeris data. Since the release point of this disclosure is predetermined based on the small satellite's subsequent mission to Bennu, its orbital constraints are considered in the orbital transfer design, enabling the small satellite to start from an efficient initial state and carry out a deep space exploration mission.

[0193] In the aerodynamically assisted descent phase 660 of the orbit transfer vehicle 601, the orbit transfer control method of this disclosure is combined with the aerodynamically assisted descent technology to dissipate orbital energy using atmospheric drag. The basic principle of the aerodynamically assisted descent technology is that when the vehicle returns from a preset high orbit 680 to a low Earth orbit 670, by precisely controlling the reentry attitude and angle of attack, the vehicle experiences controllable aerodynamic drag during atmospheric reentry, thereby converting some of the orbital kinetic energy into heat energy dissipation, achieving the goal of reducing orbital altitude without consuming propellant. Compared with traditional pure thrust descent, aerodynamically assisted descent can significantly save fuel consumption and extend the vehicle's on-orbit lifespan. In the orbital design of this phase, aerodynamic terms need to be introduced into the dynamic equations, specifically the influence of drag acceleration and lift acceleration on the velocity vector, the magnitude of which can depend on factors including atmospheric density, vehicle aerodynamic shape, angle of attack, and flight Mach number. To address the potential for multiple atmospheric crossings during the return trajectory, a dynamic discretization strategy can be implemented within the optimization framework. This involves densifying the discrete nodes in the near-Earth segment (within the atmosphere) to improve the solution accuracy for the aerodynamic action phase, while appropriately sparsening the nodes in the far-Earth segment (outside the atmosphere) to reduce computational burden. This aerodynamically assisted trajectory design enables efficient and economical trajectory descent operations, providing support for the spacecraft's subsequent standby and mission expansion.

[0194] Please refer to Figure 10 , Figure 10 This diagram illustrates the transfer path during the aerodynamically assisted orbit descent phase of the Bennu exploration mission, as provided in this embodiment of the disclosure. Figure 10 In the figure, the solid line represents the aerodynamically assisted descent trajectory, the dotted line represents the preset high orbit of 680°, and the dashed line represents the low Earth orbit of 670°. As can be seen from the figure, the orbit transfer control method described in this disclosure, by incorporating aerodynamic terms into the dynamic equations, can achieve joint optimization of engine thrust and aerodynamic forces. This effectively reduces fuel consumption and shortens the transfer trajectory while still generating a smooth and continuous transfer trajectory, demonstrating good robustness and engineering applicability.

[0195] Based on the same inventive concept, please refer to Figure 11 This disclosure presents a schematic diagram of a spacecraft orbit transfer control device suitable for deep space shuttle missions. The spacecraft orbit transfer control device 1100 includes:

[0196] Model building module 1110: Used to build a dynamic model of the first spacecraft transferring from the first orbit to the second orbit;

[0197] First solution module 1120: used to communicate with the model building module 1110, and configured to obtain the initial transfer trajectory based on the dynamic model, with energy optimization as the objective, through the first homotopy parameter;

[0198] The second solution module 1130 is used to communicate with the first solution module 1120 and is configured to obtain the target transfer trajectory based on the initial transfer trajectory, with fuel optimization as the objective, through the second homotopy parameter and the third homotopy parameter.

[0199] In some examples, the first solver module 1120 is configured to: construct a first homotopy equation, wherein at the initial value of the first homotopy parameter, the value of the first homotopy equation corresponds to the number of orbital elements of the first orbit; and at the final value of the first homotopy parameter, the value of the first homotopy equation corresponds to the number of orbital elements of the second orbit.

[0200] Based on the dynamic model, a cost function is set with the optimal energy as the performance index, terminal constraints are set according to the value of the first homotopy equation, and control variables are solved to obtain the initial transfer trajectory.

[0201] In some examples, the second solver module 1130 is configured to: construct a second homotopy equation, wherein at the initial value of the second homotopy parameter, the value of the second homotopy equation corresponds to a preset thrust amplitude; and at the final value of the second homotopy parameter, the value of the second homotopy equation corresponds to the actual thrust amplitude.

[0202] A third homotopy equation is constructed. At the initial value of the third homotopy parameter, the value of the third homotopy equation corresponds to the cost function with energy optimization as the performance index. At the final value of the third homotopy parameter, the value of the third homotopy equation corresponds to the cost function with fuel optimization as the performance index.

[0203] Based on the dynamic model and the second homotopy equation, the cost function is set according to the value of the third homotopy equation, and the terminal constraint is set to the value of the first homotopy equation at the termination value of the first homotopy parameter. The control variables are solved with the initial transfer trajectory as the initial value for iteration to obtain the target transfer trajectory.

[0204] In some examples, the second solver module 1130 is configured to: based on the dynamic model and the second homotopy equation, set the value of the third homotopy equation to the value at the initial value of the third homotopy parameter, set the terminal constraint to the value of the first homotopy equation at the termination value of the first homotopy parameter, solve the control variables with the initial transfer trajectory as the initial value of the iteration, and obtain the intermediate transfer trajectory;

[0205] Based on the dynamic model, the value of the second homotopy equation is set to the corresponding value at the termination value of the second homotopy parameter, the terminal constraint is set to the value of the first homotopy equation at the termination value of the first homotopy parameter, the cost function is set according to the value of the third homotopy equation, and the control variables are solved with the intermediate transfer trajectory as the initial value of the iteration to obtain the target transfer trajectory.

[0206] Please refer to Figure 12 Based on the same inventive concept, this disclosure also discloses a block diagram of a computing device for spacecraft orbit transfer control suitable for deep space shuttle missions. In some examples, the computing device 1200 can be at least one of devices such as a smartphone, smartwatch, desktop computer, laptop, virtual reality terminal, augmented reality terminal, wireless terminal, and laptop computer. The computing device 1200 has communication functions and can access wired or wireless networks. The computing device 1200 can refer to one of multiple terminals, and those skilled in the art will understand that the number of such terminals can be more or less. In some examples, the computing device 1200 can receive data based on the accessed wired or wireless network. It is understood that the computing device 1200 undertakes the calculation and processing work of the technical solution of this disclosure, and this disclosure does not limit this aspect.

[0207] like Figure 12 As shown, the computing device in this application may include one or more of the following components: processor 1210 and memory 1220.

[0208] Optionally, the processor 1210 connects various parts within the computing device using various interfaces and lines. It executes various functions and processes data by running or executing instructions, programs, code sets, or instruction sets stored in the memory 1220, and by calling data stored in the memory 1220. Optionally, the processor 1210 can be implemented using at least one hardware form of Digital Signal Processing (DSP), Field-Programmable Gate Array (FPGA), or Programmable Logic Array (PLA). The processor 1210 can integrate one or more of the following: Central Processing Unit (CPU), Graphics Processing Unit (GPU), Neural-network Processing Unit (NPU), and baseband chip. Specifically, the CPU primarily handles the operating system, user interface, and applications; the GPU is responsible for rendering and drawing the content displayed on the touchscreen; the NPU implements artificial intelligence (AI) functions; and the baseband chip handles wireless communication. It is understandable that the aforementioned baseband chip may not be integrated into the processor 1210, but may be implemented using a separate chip.

[0209] The memory 1220 may include random access memory (RAM) or read-only memory (ROM). Optionally, the memory 1220 may include a non-transitory computer-readable storage medium. The memory 1220 may be used to store instructions, programs, code, code sets, or instruction sets. The memory 1220 may include a program storage area and a data storage area, wherein the program storage area may store instructions for implementing an operating system, instructions for at least one function (such as touch function, sound playback function, image playback function, etc.), instructions for implementing the various method embodiments described above, etc.; the data storage area may store data created according to the use of the computing device, etc.

[0210] In addition, those skilled in the art will understand that the structure of the computing device shown in the above figures does not constitute a limitation on the computing device. The computing device may include more or fewer components than shown, or combine certain components, or have different component arrangements. For example, the computing device may also include a display screen, camera assembly, microphone, speaker, radio frequency circuit, input unit, sensors (such as accelerometer, angular velocity sensor, light sensor, etc.), audio circuit, WiFi module, power supply, Bluetooth module, etc., which will not be described in detail here.

[0211] This application also provides a computer-readable storage medium storing at least one instruction that is executed by a processor to implement the orbital transfer control method described in the above embodiments.

[0212] This application also provides a computer program product, which includes computer instructions stored in a computer-readable storage medium; a processor of a computing device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computing device to perform the orbital transfer control method described in the above embodiments.

[0213] Those skilled in the art will recognize that the functions described in the embodiments of this application in one or more of the above examples can be implemented using hardware, software, firmware, or any combination thereof. When implemented using software, these functions can be stored in a computer-readable medium or transmitted as one or more instructions or code on a computer-readable medium. Computer-readable media include computer storage media and communication media, wherein communication media include any medium that facilitates the transfer of a computer program from one place to another. Storage media can be any available medium that can be accessed by a general-purpose or special-purpose computer.

[0214] It should be noted that the technical solutions described in the embodiments of this disclosure can be combined arbitrarily without conflict.

[0215] The above description is merely a specific embodiment of this disclosure, but the scope of protection of this disclosure is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this disclosure should be included within the scope of protection of this disclosure. Therefore, the scope of protection of this disclosure should be determined by the scope of the claims.

Claims

1. A spacecraft orbital transfer control method suitable for deep space shuttle missions, characterized in that, include: Obtain the dynamic model of the first spacecraft transferring from the first orbit to the second orbit; Based on the aforementioned dynamic model, with energy optimization as the objective, the terminal constraint conditions are iterated using the first homotopy parameter to obtain the initial transfer trajectory. Based on the initial transfer trajectory, with fuel optimization as the objective, the thrust model is iterated using the second homotopy parameter, and the performance index is iterated using the third homotopy parameter to obtain the target transfer trajectory.

2. The method according to claim 1, characterized in that, The process of obtaining the initial transfer trajectory based on the dynamic model, with energy optimization as the objective, through the first homotopy parameter, includes: Construct a first homotopy equation. At the initial value of the first homotopy parameter, the value of the first homotopy equation corresponds to the number of orbital elements of the first orbit; at the final value of the first homotopy parameter, the value of the first homotopy equation corresponds to the number of orbital elements of the second orbit. Based on the dynamic model, a cost function is set with the optimal energy as the performance index, terminal constraints are set according to the value of the first homotopy equation, and control variables are solved to obtain the initial transfer trajectory.

3. The method according to claim 2, characterized in that, The step of obtaining the target transfer trajectory based on the initial transfer trajectory, with fuel optimization as the objective, through the second and third homotopy parameters, includes: A second homotopy equation is constructed. At the initial value of the second homotopy parameter, the value of the second homotopy equation corresponds to the preset thrust amplitude. At the final value of the second homotopy parameter, the value of the second homotopy equation corresponds to the actual thrust amplitude. A third homotopy equation is constructed. At the initial value of the third homotopy parameter, the value of the third homotopy equation corresponds to a cost function with energy optimization as the performance index; at the final value of the third homotopy parameter, the value of the third homotopy equation corresponds to a cost function with fuel optimization as the performance index. Based on the dynamic model and the second homotopy equation, the cost function is set according to the value of the third homotopy equation, and the terminal constraint condition is set to the value of the first homotopy equation at the termination value of the first homotopy parameter. The control variables are solved with the initial transfer trajectory as the initial value for iteration to obtain the target transfer trajectory.

4. The method according to claim 3, characterized in that... Based on the dynamic model and the second homotopy equation, a cost function is set according to the value of the third homotopy equation, and the terminal constraint is set to the value of the first homotopy equation at the termination value of the first homotopy parameter. The control variables are solved using the initial transfer trajectory as the initial value for iteration to obtain the target transfer trajectory, including: Based on the dynamic model and the second homotopy equation, the value of the third homotopy equation is set to the value at the initial value of the third homotopy parameter, and the terminal constraint condition is set to the value of the first homotopy equation at the termination value of the first homotopy parameter. The control variables are solved using the initial transfer trajectory as the initial value of the iteration to obtain the intermediate transfer trajectory. Based on the dynamic model, the value of the second homotopy equation is set to the value at the termination value of the second homotopy parameter, the terminal constraint condition is set to the value of the first homotopy equation at the termination value of the first homotopy parameter, the cost function is set according to the value of the third homotopy equation, and the control variables are solved with the intermediate transfer trajectory as the initial value of the iteration to obtain the target transfer trajectory.

5. The method according to claim 1, characterized in that, When at least one of the first homotopy parameter, the second homotopy parameter, and the third homotopy parameter increases, the iteration step size corresponding to that parameter decreases.

6. The method according to claim 1, characterized in that, The first spacecraft includes an orbital transfer vehicle that does not carry a second spacecraft, or an orbital transfer vehicle that carries at least one second spacecraft.

7. The method according to claim 6, characterized in that, When the first spacecraft includes an orbital transfer vehicle carrying at least one second spacecraft, the method further includes: When the first spacecraft reaches the end of the second orbit, it releases the at least one second spacecraft and transmits the status information of the end of the second orbit to the at least one second spacecraft.

8. A spacecraft orbital transfer control device suitable for deep space shuttle missions, characterized in that, include: Model building module: used to build a dynamic model of the first spacecraft transferring from the first orbit to the second orbit; The first solution module is communicatively connected to the model building module and is configured to iterate the terminal constraints based on the dynamic model with energy optimization as the objective, using the first homotopy parameter to obtain the initial transfer trajectory. The second solution module is communicatively connected to the first solution module and is configured to iterate the thrust model using a second homotopy parameter and the performance index using a third homotopy parameter based on the initial transfer trajectory, with fuel optimization as the objective, in order to obtain the target transfer trajectory.

9. A computer storage medium, characterized in that, The computer storage medium stores at least one instruction, which is executed by a processor to implement the method as described in any one of claims 1 to 7.

Images