Method, device, equipment and medium for solving spacecraft orbit rendezvous saddle point

Abstract

The present invention relates to a method, device, equipment and medium for solving a saddle point of a spacecraft orbit rendezvous. First, an aerospace dynamics model is constructed, and a spacecraft collision avoidance model is constructed according to the aerospace dynamics model; then, design variables are defined, and a co-state variable guessing initial value function is constructed according to the design variables; based on the spacecraft collision avoidance model, a particle swarm algorithm is used to optimize the co-state variable guessing initial value function, and the time optimal rendezvous trajectory of the first spacecraft when the second spacecraft is not maneuvering is obtained as the co-state variable at the initial moment; based on the gradient homology method, the thrust amplitude of the first spacecraft and the second spacecraft is gradually increased, and the co-state variable at the initial moment is used as the initial value, and the co-state variable is iteratively updated and solved, and the final spacecraft orbit rendezvous saddle point is solved. The present invention can quickly realize the saddle point solution of the spacecraft orbit rendezvous, and can significantly improve the control efficiency of the spacecraft.

Description

Technical Field

[0001] The present invention relates to the field of spacecraft control technology, and in particular to a method, device, equipment and medium for solving a spacecraft orbit rendezvous saddle point. Background Art

[0002] As space missions become increasingly complex, the mission environments faced by spacecraft are becoming more diverse. Spacecraft may encounter various emergencies. In this ever-changing environment, how to ensure the safety and reliability of spacecraft systems, avoid collisions or interference, and ensure their own safety has become one of the important issues in the field of space security.

[0003] The spacecraft orbit interaction problem is usually modeled as a differential game problem, in which each spacecraft maximizes its own objective. Compared with the unilateral optimal control problem, the orbit interaction problem is more difficult to solve. On the other hand, considering the high uncertainty of the space environment and the non-cooperation of the opponent, the orbit interaction problem has high requirements for real-time computing. A faster solution method can make the friendly spacecraft have stronger responsiveness in complex environments, thereby occupying an advantageous position in the orbit interaction scenario and protecting key satellites and space assets. Summary of the invention

[0004] Based on this, it is necessary to provide a two-layer solution architecture to address the above technical problems, which can more quickly solve the spacecraft orbit interaction problem by providing a spacecraft orbit rendezvous saddle point solution method, device, equipment and medium.

[0005] A method for solving a spacecraft orbit rendezvous saddle point, the method comprising:

[0006] constructing an aerospace dynamics model, and constructing a spacecraft collision avoidance model based on the aerospace dynamics model;

[0007] Define design variables, and then construct a co-state variable guessing initial value function according to the design variables;

[0008] Based on the spacecraft collision avoidance model, the particle swarm algorithm is used to optimize the initial value function of the co-state variable guessing, and the optimal rendezvous trajectory of the first spacecraft when the second spacecraft is not maneuvering is obtained as the co-state variable at the initial moment;

[0009] Based on the gradient homotopy method, the thrust amplitudes of the first spacecraft and the second spacecraft are gradually increased, the co-state variables at the initial moment are taken as initial values, the co-state variables are iteratively updated and solved, and the final spacecraft orbit rendezvous saddle point is solved.

[0010] A spacecraft orbit rendezvous saddle point solving device, the device comprising:

[0011] A model building module, used to build an aerospace dynamics model, and to build a spacecraft collision avoidance model based on the aerospace dynamics model;

[0012] The guessing initial value function building module is used to define the design variables and then build the co-state variable guessing initial value function according to the design variables;

[0013] An optimization module is used to optimize the co-state variable guessing initial value function based on the spacecraft collision avoidance model by using a particle swarm algorithm to obtain the optimal rendezvous trajectory of the first spacecraft as the initial co-state variable when the second spacecraft is not maneuvering;

[0014] The iterative update module is used to gradually increase the thrust amplitude of the first spacecraft and the second spacecraft based on the gradient homology method, take the co-state variables at the initial moment as initial values, iteratively update and solve the co-state variables, and solve the final spacecraft orbit rendezvous saddle point.

[0015] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the method for solving the spacecraft orbit rendezvous saddle point when executing the computer program.

[0016] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the method for solving the spacecraft orbit rendezvous saddle point.

[0017] The above-mentioned method, device, equipment and medium for solving the spacecraft orbit rendezvous saddle point first constructs an aerospace dynamics model, and constructs a spacecraft collision avoidance model based on the aerospace dynamics model; then defines design variables, and constructs a co-state variable guessing initial value function based on the design variables; based on the spacecraft collision avoidance model, a particle swarm algorithm is used to optimize the co-state variable guessing initial value function, and the time-optimal rendezvous trajectory of the first spacecraft when the second spacecraft is not maneuvering is obtained as the co-state variable at the initial moment; based on the gradient homology method, the thrust amplitudes of the first spacecraft and the second spacecraft are gradually increased, and the co-state variables at the initial moment are used as the initial values, and the co-state variables are iteratively updated and solved to solve the final spacecraft orbit rendezvous saddle point.

[0018] The present invention adopts a two-layer solution architecture of particle swarm algorithm and gradient homotopy method. First, the co-state variables at the initial moment are solved based on the particle swarm algorithm and used as the initial value. Then, the differential game saddle point is iteratively generated based on the gradient homotopy method. The saddle point solution of spacecraft orbital rendezvous can be realized quickly, which can significantly improve the control efficiency of the spacecraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0020] Figure 1 A schematic diagram of a process for solving a spacecraft orbit rendezvous saddle point in one embodiment;

[0021] Figure 2 A schematic diagram of trajectories of a first spacecraft and a second spacecraft in a spacecraft orbit rendezvous in one embodiment;

[0022] Figure 3 Schematic diagram of a curve showing a change in the number of orbital elements of the vernal equinox of a first spacecraft and a second spacecraft in a spacecraft orbit rendezvous in another embodiment; wherein (a) is a schematic diagram showing a curve showing a change in the semi-diameter, (b) is a schematic diagram showing a curve showing a change in the true longitude, (c) is a schematic diagram showing a curve showing a change in the number of elements f, (d) is a schematic diagram showing a curve showing a change in the number of elements g, (e) is a schematic diagram showing a curve showing a change in the number of elements h, and (f) is a schematic diagram showing a curve showing a change in the number of elements k;

[0023] Figure 4 It is a structural block diagram of a spacecraft orbit rendezvous saddle point solving device in one embodiment;

[0024] Figure 5 FIG. 4 is a diagram showing the internal structure of a computer device in one embodiment.

[0025] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0027] The following will describe the implementation of the present invention in detail with reference to the accompanying drawings in the embodiment diagram of the present invention.

[0028] In one embodiment, Figure 1 As shown, a method for solving a spacecraft orbit rendezvous saddle point is provided, comprising the following steps:

[0029] Step 101, constructing an aerospace dynamics model, and constructing a spacecraft collision avoidance model based on the aerospace dynamics model.

[0030] It can be understood that the aerospace dynamics model is mainly used to describe the motion behavior of spacecraft in space and understand the trajectory of the spacecraft. Then, based on the aerospace dynamics model, the collision probability and avoidance strategy are further considered to construct a spacecraft collision avoidance model.

[0031] Step 102, define the design variables, and then construct a co-state variable guessing initial value function according to the design variables.

[0032] It can be understood that by defining the design variables in advance and then constructing the co-state variable guessing initial value function based on the design variables, the co-state variable guessing initial value of the first spacecraft and the co-state variable guessing initial value of the second spacecraft meet certain conditions, thereby reducing the search space when the particle swarm algorithm is used for subsequent optimization.

[0033] Step 103, based on the spacecraft collision avoidance model, a particle swarm algorithm is used to optimize the initial value function of the co-state variable guessing, and the optimal rendezvous trajectory of the first spacecraft when the second spacecraft is not maneuvering is obtained as the co-state variable at the initial moment.

[0034] The first spacecraft is a spacecraft that may collide, and the second spacecraft is a spacecraft that needs to avoid collision.

[0035] It can be understood that after constructing the initial value function of the co-state variable guessing, the particle swarm optimization (PSO) algorithm is used to solve the saddle point, which involves the optimization solution of the design variables, and the goal is to find the optimal solution based on satisfying the set conditions.

[0036] Furthermore, in order to reduce the search space, the second spacecraft is assumed to be in a non-maneuvering state, and then the particle swarm algorithm is used for optimization to obtain the optimal rendezvous trajectory of the first spacecraft, which is then regarded as the initial moment co-state variable as the initial value of step 104, and the time optimal rendezvous trajectory of the first spacecraft with the second spacecraft when the second spacecraft is maneuvering is solved, and it is used as the initial moment co-state variable.

[0037] Step 104, based on the gradient homology method, gradually increase the thrust amplitude of the first spacecraft and the second spacecraft, take the initial co-state variables as initial values, iteratively update and solve the co-state variables, and solve the final spacecraft orbit rendezvous saddle point.

[0038] It can be understood that the gradient homotopy method combines the advantages of homotopy transformation and gradient descent, and can effectively solve large-scale, complex nonlinear equations. By combining the particle swarm algorithm with the gradient homotopy method, the orbital rendezvous saddle point of the spacecraft can be obtained in a short time with very low computational cost, significantly improving the control efficiency of the spacecraft and achieving safe and accurate rendezvous and docking.

[0039] In the above-mentioned method for solving the spacecraft orbit rendezvous saddle point, firstly, an aerospace dynamics model is constructed, and a spacecraft collision avoidance model is constructed based on the aerospace dynamics model; then, design variables are defined, and a co-state variable guessing initial value function is constructed based on the design variables; based on the spacecraft collision avoidance model, a particle swarm algorithm is used to optimize the co-state variable guessing initial value function, and the time-optimal rendezvous trajectory of the first spacecraft when the second spacecraft is not maneuvering is obtained as the co-state variable at the initial moment; based on the gradient homology method, the thrust amplitudes of the first spacecraft and the second spacecraft are gradually increased, and the co-state variables at the initial moment are taken as the initial values, and the co-state variables are iteratively updated and solved to solve the final spacecraft orbit rendezvous saddle point.

[0040] The present invention adopts a two-layer solution architecture of particle swarm algorithm and gradient homotopy method. First, the co-state variables at the initial moment are solved based on the particle swarm algorithm and used as the initial value. Then, the differential game saddle point is iteratively generated based on the gradient homotopy method. The saddle point solution of spacecraft orbital rendezvous can be realized quickly, which can significantly improve the control efficiency of the spacecraft.

[0041] In one embodiment, constructing an aerospace dynamics model includes:

[0042] Gets the improved equinox orbital roots.

[0043] A space dynamics model is constructed based on the engine thrust, engine jet speed, spacecraft mass and improved equinox orbit elements.

[0044] Specifically, the improved expression of the orbital elements of the vernal equinox is:

[0045] ;

[0046] In the formula, Represents the improved six numbers of the vernal equinox, among which, represents the semi-diameter, , , , Indicates the number of roots, Indicates true longitude; represents the semi-major axis; represents eccentricity; Indicates the inclination angle; represents the right ascension of the ascending node; represents the argument of perigee; represents the vector transpose of the corresponding state variable, where Represents a corresponding state variable that can be replaced.

[0047] The aerospace dynamics model is constructed based on the engine thrust, the engine jet speed, the mass of the spacecraft and the improved vernal equinox orbit elements. The expression is:

[0048] ;

[0049] ;

[0050] In the formula, Indicates the engine thrust; represents the mass of the spacecraft; Indicates the engine jet speed; represents the transformation matrix when the improved vernal equinox orbit elements are used as the state vector; represents the direction vector of the engine thrust; represents the gravitational vector; represents the first-order time derivative of the corresponding state variable, where Represents a corresponding state variable that can be replaced.

[0051] in, For 6 3 matrix, For 6 A column vector of 1, For 3 1 column vector, the expression is:

[0052] ;

[0053] ;

[0054] ;

[0055] In the formula, represents the Earth's gravitational constant; represents the semi-diameter of the orbital root of the vernal equinox; Indicates the true longitude in the orbital root of the vernal equinox; represents the yaw angle; Indicates the pitch angle.

[0056] In one embodiment, a spacecraft collision avoidance model is constructed based on an aerospace dynamics model, including:

[0057] The objective function and the terminal condition are determined according to the first spacecraft objective and the second spacecraft objective.

[0058] Construct the Hamiltonian function.

[0059] The thrust direction unit vector equation, thrust amplitude equation, switching function equation and differential game co-state equation of the first spacecraft and the second spacecraft are defined.

[0060] According to the optimal control strategy, based on the objective function, terminal conditions and Hamiltonian function, a spacecraft collision avoidance model is constructed through the thrust direction unit vector equation, thrust amplitude equation, switch function equation and differential game co-state equation of the first spacecraft and the second spacecraft.

[0061] Specifically, the first spacecraft goal is to minimize the rendezvous time, and the second spacecraft goal is to maximize the rendezvous time. Therefore, the objective function and terminal condition are:

[0062] ;

[0063] ;

[0064] In the formula, represents the objective function of the first spacecraft; represents the objective function of the second spacecraft; Indicates the relative motion state of the first spacecraft; represents the relative motion state of the second spacecraft, Indicates the terminal rendezvous time.

[0065] Construct the Hamiltonian function, the expression is:

[0066] ;

[0067] In the formula, Indicates the number of orbital elements The corresponding covariate is 6 1 column vector, the expression is: ; represents the quality co-state variable; represents the multiplier used for normalization; The Hamiltonian function representing the first spacecraft; represents the Hamiltonian function of the second spacecraft; represents the co-state variables of the first spacecraft; represents the co-state variable of the second spacecraft; represents the derivative of the relative motion state vector of the first spacecraft; represents the derivative of the relative motion state vector of the second spacecraft; represents the vector transpose of the corresponding state variable, where Represents a corresponding state variable that can be replaced.

[0068] According to the minimum principle, the thrust direction unit vector equation of the first spacecraft and the second spacecraft is expressed as:

[0069] ;

[0070] In the formula, a direction vector representing the thrust of the first spacecraft engine; a direction vector representing the thrust of the second spacecraft engine; represents the transformation matrix of the first spacecraft; Indicates the number of orbital elements of the first spacecraft at the vernal equinox The corresponding co-variables; represents the transformation matrix of the second spacecraft; Indicates the number of the second spacecraft's equinox orbital elements The corresponding covariate.

[0071] The thrust amplitude equation is expressed as:

[0072] ;

[0073] In the formula, Indicates the thrust magnitude of the first spacecraft; represents the switching function of the first spacecraft; represents the thrust magnitude of the second spacecraft; represents the switching function of the second spacecraft.

[0074] The switch function equation is: (direction and size of on / off switch)

[0075] ;

[0076] In the formula, represents the mass co-state variable of the first spacecraft; represents the mass co-state variable of the second spacecraft; represents the jet speed of the first spacecraft; represents the jet speed of the second spacecraft;

[0077] The co-state equation expression of the differential game is:

[0078] ;

[0079] ;

[0080] The transversality condition for the differential game is:

[0081] ;

[0082] According to the optimal control theory, the target shooting equation of the differential game is constructed, and the expression is:

[0083] ;

[0084] In order to further speed up the convergence of the solution, the shooting equation is simplified and the normalization condition is introduced:

[0085] ;

[0086] The normalized co-state equation satisfies .

[0087] Then the simplified differential game shooting equation is the final spacecraft collision avoidance model, expressed as:

[0088] ;

[0089] In the formula, represents the shooting function; Represents the initial co-state variables of the spacecraft when the engine is turned on; The first spacecraft The relative motion state when Indicates that the second spacecraft is The relative motion state when The first spacecraft The orbital element covariate at ; Indicates that the second spacecraft is The orbital element covariate at ; The first spacecraft The quality covariate variable at ; Indicates that the second spacecraft is The quality covariate variable at ; Indicates that the spacecraft is Time optimal control function when ; Indicates the normalization of the corresponding state variables, where Represents a corresponding state variable that can be replaced.

[0090] In one embodiment, design variables are defined, and then a co-state variable guessing initial value function is constructed according to the design variables, including:

[0091] Define the design variables as:

[0092] ;

[0093] According to the design variables, a co-state variable guessing initial value function is constructed, and the expression is:

[0094] ;

[0095] In the formula, Indicates the estimated value of the terminal rendezvous time; are five angular parameters without physical meaning; Represents the guessed initial value of the co-state variable at the initial moment of the first spacecraft; Represents the guessed initial value of the co-state variable at the initial moment of the second spacecraft.

[0096] Specifically, it can be known from the spacecraft collision avoidance model that , considering the orbital dynamics, we know , combined with the spacecraft collision avoidance model, it is pointed out In order to reduce the search space, the initial guess value of the co-state variable is defined as and , and the guessed initial value satisfies and two conditions, and by defining the design variables, that is, by defining five angle parameters without physical meaning To meet these two conditions in advance, the co-state variable guessing initial value function is constructed, and the particle swarm algorithm is used to solve the saddle point containing these six design variables.

[0097] In one embodiment, based on the spacecraft collision avoidance model, a particle swarm algorithm is used to optimize the initial value function of the co-state variable guessing, and the optimal rendezvous trajectory of the first spacecraft when the second spacecraft is not maneuvering is obtained as the co-state variable at the initial moment, including:

[0098] Determine the search space of design variables as:

[0099] ;

[0100] ;

[0101] The objective function of the particle swarm algorithm is constructed as:

[0102] ;

[0103] In the formula, Represents the shooting function The square of the modulus.

[0104] Based on the objective function of the particle swarm algorithm and the search space of the design variables, the initial value function of the co-state variable guessing is optimized to obtain the time-optimal rendezvous trajectory of the first spacecraft to the second spacecraft when the second spacecraft is not maneuvering, which is used as the co-state variable at the initial moment.

[0105] In one embodiment, based on the gradient homotopy method, the thrust amplitudes of the first spacecraft and the second spacecraft are gradually increased, the initial co-state variables are used as initial values, the co-state variables are iteratively updated and solved, and the final spacecraft orbit rendezvous saddle point is solved, including:

[0106] Establishing homotopy parameters , to adjust the thrust amplitude of the first spacecraft and the second spacecraft, the expression is:

[0107] ;

[0108] The feasible homotopy target point is expressed as:

[0109] ;

[0110] Then, the initial value of the co-state variable is taken as the initial value, and the co-state variable is iteratively updated and solved. During the iterative update process, the true value of the co-state variable of the previous time is taken as the initial value of the current co-state variable guess; or

[0111] Get the true values ​​of the co-state variables of the previous two times, and use the gradient descent method to calculate the initial value of the co-state variable guess for the current time; until the final spacecraft orbit rendezvous saddle point is solved;

[0112] Among them, the true value of the previous co-state variable is used as the initial value of the current co-state variable guess, and the expression is:

[0113] ;

[0114] Get the true values ​​of the previous two co-state variables, and use the gradient descent method to calculate the initial value of the current co-state variable guess. The expression is:

[0115] ;

[0116] In the formula, represents the first spacecraft thrust; represents the second spacecraft thrust; Indicates The homotopy parameter at the iteration time; Indicates the maximum number of iterations of the gradient homotopy method; Indicates The homotopy parameter at the iteration The corresponding initial moment co-state variable truth value; Indicates The homotopy parameter at the iteration The guessed initial value of the co-state variable at the corresponding initial moment.

[0117] It is worth mentioning that The initial value of the co-state variable is guessed, that is, the co-state variable at the initial moment is provided by the particle swarm algorithm optimization, and the rest The initial value guess is provided by the real value obtained by the previous calculation.

[0118] The initial value guessing of the homotopy process specifically includes two calculation methods. One is to use the true value of the co-state variable of the previous time as the initial value of the current co-state variable guessing. The advantage of this method is that the calculation is simple and easy to understand; the other is to rely on the true value of the co-state variable of the previous two times, and use the gradient descent method to calculate the initial value of the current co-state variable guessing. The advantage of this method is that it introduces gradient information and can iteratively update the parameters in the opposite direction of the objective function gradient, gradually approaching the local minimum of the function. When implemented, the guessed initial value of the first method is first used to solve, and when the first method does not converge, the second method is used to provide the initial value. By combining the particle swarm algorithm with the gradient homotopy method, the spacecraft orbit rendezvous saddle point can be quickly solved, with stronger real-time performance, so that decisions can be made quickly and the orbit can be adjusted to achieve safe and accurate rendezvous and docking.

[0119] In one of the embodiments, in order to verify the effectiveness of the method proposed in the present invention, an example is provided below for explanation.

[0120] Assume that the initial mass of the two spacecraft is 1000 kg, the jet speed of the engine is 3 km / s, and the length, time and mass are respectively given by the radius of the earth (Re = 6378.137 km), ( ) and initial mass (m0 = 1000 kg) for normalization. The settings of the particle swarm algorithm include the maximum number of iterations = 100, the population size is S = 30. Terminal game time The range is from 0 to 180 minutes, and the maximum number of targeting function calls in MinPack is set to 1000.

[0121] This example needs to calculate the orbital rendezvous saddle point of the two spacecraft. The thrust of the first spacecraft is 68.6 N, and the thrust of the second spacecraft is 34.3 N. The orbital elements of the second spacecraft at the initial time of the mission are shown in Table 1, and the relative motion state of the first spacecraft is shown in Table 2.

[0122] Table 1 The orbital elements of the second spacecraft at the initial moment

[0123]

[0124] Table 2 Relative motion state of the first spacecraft at the initial moment

[0125]

[0126] Before calculating the spacecraft orbit rendezvous saddle point, it is necessary to calculate the time-optimal low-thrust rendezvous orbit of the first spacecraft with respect to the second spacecraft assuming that the second spacecraft does not maneuver.

[0127] Set the homotopy initial state and homotopy parameters , the thrust of the first and second spacecraft is reduced at the same time. At this time, the thrust of the first spacecraft is 34.3 N, the thrust of the second spacecraft is 0 N, the calculated rendezvous time is 58.783 minutes, and the co-state variable size of the first spacecraft at the initial moment is as follows:

[0128] ;

[0129] The homology method proposed in this paper is used to iteratively solve the co-state variables. The corresponding initial value of the pursuit spacecraft co-state variable is guessed as:

[0130] ;

[0131] When the iteration reaches the homotopy parameter At this time, the thrust of the first spacecraft is 68.6 N, and the thrust of the second spacecraft is 34.3 N. The calculated rendezvous time is 57.607 minutes. The co-state variables of the first spacecraft and the second spacecraft at the initial moment are as follows:

[0132] ;

[0133] The trajectory of the orbital rendezvous between the first spacecraft and the second spacecraft is as follows Figure 2 As shown in Figure 1, the first spacecraft is moving towards the second spacecraft. The curve of the orbital elements at the vernal equinox is as follows: Figure 3 As shown, all the roots are exactly the same at the termination time, and the first spacecraft successfully rendezvoused with the second spacecraft.

[0134] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0135] In one embodiment, Figure 4 As shown, a spacecraft orbit rendezvous saddle point solving device is provided, comprising: a model building module 201, a guessing initial value function building module 202, an optimization module 203 and an iterative update module 204, wherein:

[0136] The model building module 201 is used to build an aerospace dynamics model, and to build a spacecraft collision avoidance model based on the aerospace dynamics model.

[0137] The initial value guessing function building module 202 is used to define design variables and then build a co-state variable initial value guessing function according to the design variables.

[0138] The optimization module 203 is used to optimize the initial value function of the co-state variable guessing based on the spacecraft collision avoidance model by using a particle swarm algorithm to obtain the optimal rendezvous trajectory of the first spacecraft as the initial co-state variable when the second spacecraft is not maneuvering.

[0139] The iterative update module 204 is used to gradually increase the thrust amplitude of the first spacecraft and the second spacecraft based on the gradient homology method, take the initial co-state variables as initial values, iteratively update and solve the co-state variables, and solve the final spacecraft orbit rendezvous saddle point.

[0140] For the specific definition of the spacecraft orbit rendezvous saddle point solving device, please refer to the definition of the spacecraft orbit rendezvous saddle point solving method mentioned above, which will not be repeated here. Each module in the above-mentioned spacecraft orbit rendezvous saddle point solving device can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0141] In one embodiment, a computer device is provided. The computer device may be a server, and its internal structure diagram may be as follows: Figure 5 As shown. The computer device includes a processor, a memory, a network interface and a database connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store spacecraft orbit rendezvous saddle point solution data. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a spacecraft orbit rendezvous saddle point solution method is implemented.

[0142] Those skilled in the art will understand that Figure 5 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present invention, and does not constitute a limitation on the computer device to which the solution of the present invention is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0143] In one embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the computer program, the following steps are implemented:

[0144] Step 101, constructing an aerospace dynamics model, and constructing a spacecraft collision avoidance model based on the aerospace dynamics model.

[0145] Step 102, define the design variables, and then construct a co-state variable guessing initial value function according to the design variables.

[0146] Step 103, based on the spacecraft collision avoidance model, a particle swarm algorithm is used to optimize the initial value function of the co-state variable guessing, and the optimal rendezvous trajectory of the first spacecraft when the second spacecraft is not maneuvering is obtained as the co-state variable at the initial moment.

[0147] Step 104, based on the gradient homology method, gradually increase the thrust amplitude of the first spacecraft and the second spacecraft, take the initial co-state variables as initial values, iteratively update and solve the co-state variables, and solve the final spacecraft orbit rendezvous saddle point.

[0148] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, the following steps are implemented:

[0149] Step 101, constructing an aerospace dynamics model, and constructing a spacecraft collision avoidance model based on the aerospace dynamics model.

[0150] Step 102, define the design variables, and then construct a co-state variable guessing initial value function according to the design variables.

[0151] Step 103, based on the spacecraft collision avoidance model, a particle swarm algorithm is used to optimize the initial value function of the co-state variable guessing, and the optimal rendezvous trajectory of the first spacecraft when the second spacecraft is not maneuvering is obtained as the co-state variable at the initial moment.

[0152] Step 104, based on the gradient homology method, gradually increase the thrust amplitude of the first spacecraft and the second spacecraft, take the initial co-state variables as initial values, iteratively update and solve the co-state variables, and solve the final spacecraft orbit rendezvous saddle point.

[0153] A person of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment method can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided by the present invention can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0154] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0155] The above-mentioned embodiments only express several implementation modes of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention. It should be pointed out that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the attached claims.

Claims

1. A method for solving a spacecraft orbit rendezvous saddle point, characterized in that: The method comprises: constructing an aerospace dynamics model, and constructing a spacecraft collision avoidance model based on the aerospace dynamics model; Define design variables, and then construct a co-state variable guessing initial value function according to the design variables; Based on the spacecraft collision avoidance model, the particle swarm algorithm is used to optimize the initial value function of the co-state variable guessing, and the optimal rendezvous trajectory of the first spacecraft when the second spacecraft is not maneuvering is obtained as the co-state variable at the initial moment; Based on the gradient homotopy method, the thrust amplitudes of the first spacecraft and the second spacecraft are gradually increased, the co-state variables at the initial moment are taken as initial values, the co-state variables are iteratively updated and solved, and the final spacecraft orbit rendezvous saddle point is solved; Based on the gradient homotopy method, the thrust amplitudes of the first spacecraft and the second spacecraft are gradually increased, the co-state variables at the initial moment are taken as initial values, the co-state variables are iteratively updated and solved, and the final spacecraft orbit rendezvous saddle point is solved, including: Establishing homotopy parameters , to adjust the thrust amplitude of the first spacecraft and the second spacecraft, the expression is: ； The feasible homotopy target point is expressed as: ； Then, the co-state variable at the initial moment is taken as the initial value, and the co-state variable is iteratively updated to solve, and during the iterative updating process, the true value of the co-state variable at the last time is taken as the initial value of the co-state variable guessed at the current time; or Get the true values ​​of the co-state variables of the previous two times, and use the gradient descent method to calculate the initial value of the co-state variable guess for the current time; until the final spacecraft orbit rendezvous saddle point is solved; Among them, the true value of the previous co-state variable is used as the initial value of the current co-state variable guess, and the expression is: ； Get the true values ​​of the previous two co-state variables, and use the gradient descent method to calculate the initial value of the current co-state variable guess. The expression is: ； In the formula, represents the first spacecraft thrust; represents the second spacecraft thrust; Indicates Homotopy parameters at the iteration; Indicates the maximum number of iterations of the gradient homotopy method; Indicates The homotopy parameter at the iteration The corresponding initial moment co-state variable truth value; Indicates The homotopy parameter at the iteration The guessed initial value of the co-state variable at the corresponding initial moment.

2. The method for solving the spacecraft orbit rendezvous saddle point according to claim 1, characterized in that: Build aerospace dynamics models, including: Get the improved equinox orbital elements; The aerospace dynamics model is constructed based on the engine thrust, the engine jet speed, the mass of the spacecraft and the improved vernal equinox orbit elements; The aerospace dynamics model expression is: ； ； In the formula, Indicates the engine thrust; represents the mass of the spacecraft; Indicates the engine jet speed; represents the transformation matrix when the improved vernal equinox orbit elements are used as the state vector; represents the direction vector of the engine thrust; represents the gravitational vector; represents the first-order time derivative of the corresponding state variable, where Represents a corresponding state variable that can be replaced.

3. The method for solving the spacecraft orbit rendezvous saddle point according to claim 2, characterized in that: A spacecraft collision avoidance model is constructed according to the aerospace dynamics model, including: Determine an objective function and a terminal condition according to the first spacecraft objective and the second spacecraft objective; Construct Hamiltonian function; Define the thrust direction unit vector equation, thrust amplitude equation, switching function equation and differential game co-state equation of the first spacecraft and the second spacecraft; According to the optimal control strategy, based on the objective function, terminal conditions and Hamiltonian function, a spacecraft collision avoidance model is constructed through the thrust direction unit vector equation, thrust amplitude equation, switch function equation and differential game co-state equation of the first spacecraft and the second spacecraft.

4. The method for solving the spacecraft orbit rendezvous saddle point according to claim 3, characterized in that: The spacecraft collision avoidance model expression is: ； In the formula, represents the shooting function; Represents the initial co-state variables of the spacecraft when the engine is turned on; The first spacecraft The relative motion state at the time; Indicates that the second spacecraft is relative motion state when The first spacecraft The orbital element covariate at ; Indicates that the second spacecraft is The orbital element covariate at ; Indicates the normalization of the corresponding state variables, where Represents a corresponding state variable that can be replaced.

5. The method for solving the spacecraft orbit rendezvous saddle point according to claim 3, characterized in that: Define the design variables, and then construct a co-state variable guessing initial value function according to the design variables, including: Define the design variables as: ； According to the design variables, a co-state variable guessing initial value function is constructed, and the expression is: ； In the formula, Indicates the estimated value of the terminal rendezvous time; are five angular parameters without physical meaning; Represents the guessed initial value of the co-state variable at the initial moment of the first spacecraft; Represents the guessed initial value of the co-state variable at the initial moment of the second spacecraft.

6. The method for solving the spacecraft orbit rendezvous saddle point according to claim 5, characterized in that: Based on the spacecraft collision avoidance model, the particle swarm algorithm is used to optimize the initial value function of the co-state variable guessing, and the optimal rendezvous trajectory of the first spacecraft when the second spacecraft is not maneuvering is obtained as the co-state variable at the initial moment, including: Determine the search space of design variables as: ； ； The objective function of the particle swarm algorithm is constructed as: ； In the formula, Represents the shooting function The square of the modulus of Based on the objective function of the particle swarm algorithm and the search space of the design variables, the initial value function of the co-state variable guessing is optimized to obtain the time-optimal rendezvous trajectory of the first spacecraft to the second spacecraft when the second spacecraft is not maneuvering, which is used as the co-state variable at the initial moment.

7. A spacecraft orbit rendezvous saddle point solving device, characterized in that: The device comprises: A model building module, used to build an aerospace dynamics model, and to build a spacecraft collision avoidance model based on the aerospace dynamics model; The initial value guessing function building module is used to define the design variables and then build the initial value guessing function of the co-state variables according to the design variables; An optimization module is used to optimize the co-state variable guessing initial value function based on the spacecraft collision avoidance model by using a particle swarm algorithm to obtain the optimal rendezvous trajectory of the first spacecraft as the initial co-state variable when the second spacecraft is not maneuvering; An iterative update module is used to gradually increase the thrust amplitude of the first spacecraft and the second spacecraft based on a gradient homotopy method, take the co-state variables at the initial moment as initial values, iteratively update and solve the co-state variables, and solve the final spacecraft orbit rendezvous saddle point; In the iterative update module, based on the gradient homotopy method, the thrust amplitudes of the first spacecraft and the second spacecraft are gradually increased, the co-state variables at the initial moment are taken as initial values, the co-state variables are iteratively updated and solved, and the final spacecraft orbit rendezvous saddle point is solved, including: Establishing homotopy parameters , to adjust the thrust amplitude of the first spacecraft and the second spacecraft, the expression is: ； The feasible homotopy target point is expressed as: ； Then, the co-state variable at the initial moment is taken as the initial value, and the co-state variable is iteratively updated to solve, and during the iterative updating process, the true value of the co-state variable at the last time is taken as the initial value of the co-state variable guessed at the current time; or Get the true values ​​of the co-state variables of the previous two times, and use the gradient descent method to calculate the initial value of the co-state variable guess for the current time; until the final spacecraft orbit rendezvous saddle point is solved; Among them, the true value of the previous co-state variable is used as the initial value of the current co-state variable guess, and the expression is: ； Get the true values ​​of the previous two co-state variables, and use the gradient descent method to calculate the initial value of the current co-state variable guess. The expression is: ； In the formula, represents the first spacecraft thrust; represents the second spacecraft thrust; Indicates Homotopy parameters at the iteration; Indicates the maximum number of iterations of the gradient homotopy method; Indicates The homotopy parameter at the iteration The corresponding initial moment co-state variable truth value; Indicates The homotopy parameter at the iteration The guessed initial value of the co-state variable at the corresponding initial moment.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method for solving the spacecraft orbit rendezvous saddle point according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for solving the spacecraft orbit rendezvous saddle point according to any one of claims 1 to 6 are implemented.

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