Low-thrust trajectory optimization method, detector and electronic equipment

Abstract

The invention discloses a low-thrust trajectory optimization method, a detector and electronic equipment, and the method comprises the steps: decoupling a coupling equation through employing an adjusted cross section condition, and enabling the detector to fly from a first orbit position to a target orbit according to the shortest time. The method comprises the steps that first state information of a first track position where a detector is located at the current moment is acquired, and second state information of the detector on a target track is determined; determining a constraint condition based on the second state information of the detector; determining a cross section condition according to the constraint condition; the cross section condition is adjusted, and the coefficient matrix of the adjusted cross section condition is reversible; determining the shortest time of the detector from the first track position to the target track according to the adjusted cross section condition, the constraint condition and the first state information of the detector; and determining a flight path of the detector from the first track position to the target track according to the first track position of the detector, the target track and the shortest time.

Description

Technical Field

[0001] The present application relates to the field of aerospace technology, and particularly to a small-thrust trajectory optimization method, a detector, and an electronic device. Background Art

[0002] In the process of detector trajectory optimization control, using a small thrust to propel the detector has the advantage of high specific impulse, and can effectively improve the payload ratio compared with chemical propulsion. Therefore, small-thrust propulsion detectors are increasingly widely used in deep space exploration missions.

[0003] Small-thrust trajectory optimization is usually solved by direct methods and indirect methods. The direct method usually uses the parameterization idea to convert the original infinite-dimensional optimization problem into a finite-dimensional optimization problem. Although it has strong adaptability to complex constraint conditions, it has a strong dependence on linear or nonlinear programming. Since the amount of calculation is related to the number of discrete nodes, the more the number of discrete nodes, the greater the amount of calculation, and finally the calculation time will be longer. The indirect method is usually based on the maximum principle, and the necessary conditions for optimality are derived analytically to convert the optimal control problem into a two-point boundary value problem, and then the shooting method is used to solve it. However, in the shooting method, multiple equations are coupled with each other, resulting in difficult convergence. Summary of the Invention

[0004] The present invention provides a small-thrust trajectory optimization method, a detector, and an electronic device, which decouple the coupled equations by using the adjusted transversality condition, so that the detector can fly from the first orbital position to the target orbit in the shortest time.

[0005] In a first aspect, a small-thrust trajectory optimization method provided by an embodiment of the present invention includes:

[0006] Obtain the first state information of the detector at the first orbital position at the current moment, and determine the second state information of the detector in the target orbit;

[0007] Determine the constraint conditions based on the second state information of the detector; and determine the transversality condition according to the constraint conditions; wherein, the terminal manifold of the constraint conditions is orthogonal to the terminal manifold of the transversality condition when the detector reaches the target orbit;

[0008] Adjust the transversality condition, wherein the coefficient matrix of the adjusted transversality condition is invertible;

[0009] Determine the shortest time for the detector to travel from the first orbital position to the target orbit according to the adjusted transversality condition, the constraint conditions, and the first state information of the detector;

[0010] Determine the flight trajectory of the detector from the first orbital position to the target orbit according to the first orbital position of the detector, the target orbit, and the shortest time.

[0011] Compared with the prior art, the small-thrust trajectory optimization method provided in this embodiment determines the constraint conditions by processing the second state information of the detector in the target orbit, and performs an invertible processing on the coefficient matrix of the transversality condition determined by using the constraint conditions, so that there is no coupling relationship in the adjusted transversality condition, which is an equation with independent relationships. Furthermore, the shortest time for the detector to fly from the first orbital position to the target orbit can be quickly determined by using the transversality condition with independent relationships, so that the detector flies from the first orbital position to the target orbit according to the flight trajectory determined by the shortest time.

[0012] As an optional implementation manner, the determining the shortest time for the detector to fly from the first orbital position to the target orbit according to the adjusted transversality condition, the constraint condition, and the first state information of the detector includes:

[0013] Determine the shooting equations according to the adjusted transversality condition and the constraint condition;

[0014] Input the co-state value corresponding to each specified parameter included in the first state information of the detector into the shooting equations to obtain the shortest time for the detector to fly from the first orbital position to the target orbit.

[0015] This embodiment uses the transversality condition without coupling relationship after adjustment to determine the shooting equations, so that the shortest time for the detector to fly from the first orbital position to the target orbit can be quickly determined according to the shooting equations.

[0016] As an optional implementation manner, determine the co-state value corresponding to each specified parameter included in the first state information of the detector in the following way:

[0017] Randomly generate the first co-state value corresponding to the first specified parameter included in the first state information of the detector, and randomly generate the first transfer time for the detector to fly from the first orbital position to the target orbit; wherein, the first specified parameter is the position information or velocity value of the detector on the first orbit at the current moment;

[0018] Based on the first co-state value and the first transfer time, determine the co-state value corresponding to each specified parameter when the Hamiltonian function takes the minimum value, wherein the independent variable parameters of the Hamiltonian function include the azimuth angle of the pre-set detector thrust acceleration.

[0019] In this embodiment, by presetting the azimuth angle of the detector thrust acceleration, the co-state value corresponding to each specified parameter included in the first state information can be accurately determined according to the Hamiltonian function preset according to the azimuth angle.

[0020] As an alternative implementation, after randomly generating the first co-state value corresponding to the first specified parameter included in the first state information of the detector and randomly generating the first transfer time of the detector from the first orbital position to the target orbit, the method further includes:

[0021] Adjust the first co-state value and the first transfer time respectively according to the azimuth angle of the detector thrust acceleration;

[0022] The determining, based on the first co-state value and the first transfer time, of the co-state value corresponding to each specified parameter when the Hamiltonian function of the detector takes the minimum value includes:

[0023] Based on the adjusted first co-state value and the adjusted first transfer time, determine the co-state value corresponding to each specified parameter when the Hamiltonian function of the detector takes the minimum value.

[0024] In this embodiment, by further adjusting the first co-state value and the first transfer time according to the azimuth angle of the detector thrust acceleration, the Hamiltonian function preset according to the azimuth angle can more accurately determine the co-state value corresponding to each specified parameter included in the first state information.

[0025] As an alternative implementation, the method further includes:

[0026] If the shortest time cannot be determined by inputting the co-state value corresponding to each specified parameter into the shooting equations, re-execute the steps of randomly generating the first co-state value corresponding to the first specified parameter included in the first state information of the detector and randomly generating the first transfer time of the detector from the first orbital position to the target orbit;

[0027] Based on the newly determined first co-state value and the newly determined first transfer time, re-determine the new co-state value corresponding to each specified parameter when the Hamiltonian function of the detector takes the minimum value.

[0028] In this embodiment, when the shortest time cannot be determined, that is, when the shooting equations have no solution, the first co-state value corresponding to the first specified parameter and the first transfer time can be reset, and the new co-state value corresponding to each specified parameter can be re-determined by using the new first co-state value and the new first transfer time, so as to re-determine the shortest time by using the new co-state value.

[0029] As an alternative embodiment, when the target orbit is an elliptical orbit, the co-state values corresponding to each specified parameter included in the first state information of the detector are determined in the following manner:

[0030] Determine a circular orbit associated with the target orbit, and determine the co-state values corresponding to each specified parameter included in the first state information of the detector in the case of the circular orbit;

[0031] Respectively use each co-state value in the case of the circular orbit as the initial co-state value corresponding to each specified parameter in the case of the elliptical orbit;

[0032] Based on the initial co-state values corresponding to each specified parameter in the case of the elliptical orbit, determine the co-state values corresponding to each specified parameter in the case of the elliptical orbit.

[0033] This embodiment takes into account that when the target orbit is a circular orbit, it is possible to more simply and quickly determine the co-state value corresponding to each specified parameter compared to when the target orbit is an elliptical orbit. Therefore, when designing the target orbit as an elliptical orbit, it is possible to first determine the circular orbit associated with the elliptical orbit, and then use the co-state value corresponding to each specified parameter in the case of the circular orbit as the initial co-state value corresponding to each specified parameter in the case of the elliptical orbit, thereby more quickly determining the co-state value corresponding to each specified parameter in the case of the elliptical orbit.

[0034] As an alternative embodiment, after determining the flight trajectory of the detector from the first orbital position to the target orbit, the method further includes:

[0035] Control the detector to fly from the first orbital position to the target orbit along the flight trajectory by applying a set initial velocity and a set acceleration; the set initial velocity and the set acceleration are both determined according to the shortest time and the flight distance represented by the flight trajectory.

[0036] In this embodiment, after determining the flight trajectory, the set initial velocity and the set acceleration can be calculated through the determined shortest time and the flight distance determined according to the flight trajectory, and then fly according to the set initial velocity, the set acceleration, and the flight trajectory, so that the detector can accurately fly to the target orbit.

[0037] In a second aspect, a detector provided by an embodiment of the present invention includes a thruster and a controller, wherein:

[0038] The controller is configured to perform the following steps:

[0039] Obtain the first state information of the detector at the current moment at the first orbital position, and determine the second state information of the detector on the target orbit;

[0040] Determine the constraint conditions based on the second state information of the detector; and determine the transversality conditions according to the constraint conditions; wherein, the terminal manifolds of the constraint conditions are orthogonal to the terminal manifolds of the transversality conditions when the detector reaches the target orbit;

[0041] Adjust the transversality conditions, wherein the coefficient matrix of the adjusted transversality conditions is invertible;

[0042] Determine the shortest time for the detector to move from the first orbital position to the target orbit according to the adjusted transversality conditions, the constraint conditions, and the first state information of the detector;

[0043] Determine the flight trajectory of the detector from the first orbital position to the target orbit according to the first orbital position of the detector, the target orbit, and the shortest time.

[0044] In a third aspect, an embodiment of the present invention further provides an electronic device, which includes a processor and a memory. The memory is used to store a program executable by the processor, and the processor is used to read the program in the memory and execute the following steps:

[0045] Obtain the first state information of the detector at the current moment at the first orbital position, and determine the second state information of the detector on the target orbit;

[0046] Determine the constraint conditions based on the second state information of the detector; and determine the transversality conditions according to the constraint conditions; wherein, the terminal manifolds of the constraint conditions are orthogonal to the terminal manifolds of the transversality conditions when the detector reaches the target orbit;

[0047] Adjust the transversality conditions, wherein the coefficient matrix of the adjusted transversality conditions is invertible;

[0048] Determine the shortest time for the detector to move from the first orbital position to the target orbit according to the adjusted transversality conditions, the constraint conditions, and the first state information of the detector;

[0049] Determine the flight trajectory of the detector from the first orbital position to the target orbit according to the first orbital position of the detector, the target orbit, and the shortest time.

[0050] In a fourth aspect, an embodiment of the present invention further provides a small-thrust trajectory optimization device, and the device includes:

[0051] An acquisition module, configured to acquire first state information of the detector at a first orbital position at the current moment, and determine second state information of the detector in a target orbit;

[0052] A determination module, configured to determine a constraint condition based on the second state information of the detector; and determine a transversality condition according to the constraint condition; wherein, when the detector reaches the target orbit, a terminal manifold of the constraint condition is orthogonal to a terminal manifold of the transversality condition;

[0053] An adjustment module, configured to adjust the transversality condition, wherein a coefficient matrix of the adjusted transversality condition is invertible;

[0054] A time calculation module, configured to determine the shortest time for the detector to move from the first orbital position to the target orbit according to the adjusted transversality condition, the constraint condition, and the first state information of the detector;

[0055] A flight trajectory determination module, configured to determine a flight trajectory of the detector from the first orbital position to the target orbit according to the first orbital position of the detector, the target orbit, and the shortest time.

[0056] In a fifth aspect, an embodiment of the present invention further provides a computer storage medium, on which a computer program is stored, and when the program is executed by a processor, it is used to implement the steps of the method described in any one of the first aspects above.

[0057] In a sixth aspect, the present application provides a computer program product, which includes: computer program code, and when the computer program code runs on a computer, it causes the computer to execute the method described in any one of the first aspects.

[0058] These aspects or other aspects of the present application will be more clearly understood in the following description of the embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings without creative efforts based on these drawings.

[0060] Figure 1 It is a flowchart of an implementation of a small-thrust trajectory optimization method provided by an embodiment of the present invention;

[0061] Figure 2 It is a flowchart of an implementation of determining the co-state value corresponding to each specified parameter included in the first state information of the detector provided by an embodiment of the present invention;

[0062] Figure 3 Another implementation flowchart for determining the co-state value corresponding to each specified parameter included in the first state information of the detector provided by the embodiments of the present invention;

[0063] Figure 4 Another implementation flowchart for determining the co-state value corresponding to each specified parameter included in the first state information of the detector provided by the embodiments of the present invention;

[0064] Figure 5 An implementation flowchart for determining the co-state value corresponding to each specified parameter included in the first state information of the detector when the target orbit is an elliptical orbit provided by the embodiments of the present invention;

[0065] Figure 6a A schematic diagram of the flight trajectory and thrust acceleration direction of the detector in the case where the target orbit is a circular orbit provided by the embodiments of the present invention;

[0066] Figure 6b A schematic diagram of the flight trajectory and thrust acceleration direction of the detector in the case where the target orbit is an elliptical orbit provided by the embodiments of the present invention;

[0067] Figure 7 A schematic diagram of a detector provided by the embodiments of the present invention;

[0068] Figure 8 A schematic diagram of an electronic device provided by the embodiments of the present invention;

[0069] Figure 9 A schematic diagram of a small thrust trajectory optimization device provided by the embodiments of the present invention. Detailed implementation manners

[0070] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0071] In the embodiments of the present invention, the term "and / or" describes the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, and B exists alone. The character " / " generally represents an "or" relationship between the associated objects before and after.

[0072] The application scenarios described in the embodiments of the present invention are for more clearly illustrating the technical solutions of the embodiments of the present invention, and do not constitute a limitation on the technical solutions provided by the embodiments of the present invention. Those of ordinary skill in the art can know that with the emergence of new application scenarios, the technical solutions provided by the embodiments of the present invention are also applicable to similar technical problems. Among them, in the description of the present invention, unless otherwise specified, the meaning of "a plurality" is two or more.

[0073] Before introducing the trajectory optimization method provided by the embodiments of the present application, for the convenience of understanding, first, the technical background of the embodiments of the present application will be introduced in detail below.

[0074] Space probe: Also known as a space detector, deep space detector or cosmic detector, it is an unmanned spacecraft for exploring celestial bodies and space beyond the moon and is the main tool for space exploration. It is divided into lunar probes, planetary and interplanetary probes, small body probes, etc. according to the objects of exploration.

[0075] In the process of optimizing the trajectory control of a detector, the use of a small thrust to propel the detector has the advantage of high specific impulse, and can effectively improve the payload ratio compared with chemical propulsion. Therefore, small-thrust propelled detectors are increasingly widely used in deep space exploration missions.

[0076] Small-thrust trajectory optimization usually uses direct methods and indirect methods for solution. The direct method usually uses the parameterization idea to convert the original infinite-dimensional optimization problem into a finite-dimensional optimization problem. Although it has strong adaptability to complex constraint conditions, it has a strong dependence on linear or nonlinear programming. Since the amount of calculation is related to the number of discrete nodes, the more the number of discrete nodes, the greater the amount of calculation, and finally the calculation time will also be longer. The indirect method is usually based on the maximum principle, and the necessary conditions for optimality are derived analytically to convert the optimal control problem into a two-point boundary value problem, and then the shooting method is used for solution. However, in the shooting method, multiple equations are coupled with each other, resulting in difficult convergence.

[0077] To solve the above technical problems, this embodiment proposes a small-thrust trajectory optimization method. By processing the second state information of the detector in the target orbit to determine the constraint conditions, and performing an invertible processing on the coefficient matrix of the transversality condition determined by the constraint conditions, the adjusted transversality condition has no coupling relationship and is an equation with an independent relationship. Furthermore, the shortest time for the detector to move from the first orbital position to the target orbit can be quickly determined using the transversality condition with an independent relationship, so that the detector flies from the first orbital position to the target orbit along the flight trajectory determined by the shortest time.

[0078] As Figure 1 shown, this embodiment provides a small-thrust trajectory optimization method, and the specific implementation steps of this method are as follows:

[0079] S101. Obtain the first state information of the detector at the first orbital position at the current moment, and determine the second state information of the detector in the target orbit.

[0080] Exemplarily, the target orbit can be a circular orbit or an elliptical orbit. The first state information of the detector at the first orbital position may at least include position information, velocity value, etc. The second state information of the detector in the target orbit may at least include the semi-major axis a, eccentricity e, orbital inclination i, right ascension of the ascending node Ω, argument of perigee ω, etc. Here, the true anomaly of the detector reaching the target orbit is free. For example, Table 1 shows the orbital elements of the first orbit and the target orbit.

[0081] Table 1

[0082]

[0083] S102. Determine the constraint conditions based on the second state information of the detector; and determine the transversality conditions according to the constraint conditions; wherein, the terminal manifolds of the constraint conditions and the transversality conditions are orthogonal when the detector reaches the target orbit.

[0084] In some embodiments, it is defined that the position vector of the detector is represented by r, the velocity vector is represented by v, and the unit vector direction of the thrust acceleration is represented by u (the vectors are all described in the J2000 inertial system). The maximum thrust acceleration is represented by Γ max and the thrust acceleration ratio is represented by κ, and κ ∈ [0,1]. Assume that the current moment of the detector is represented by t0, and the moment when the detector reaches the target orbit is represented by t f Then t0 = 0, and t f is free.

[0085] Under the Cartesian coordinate system, create an optimal model for the minimum-time low-thrust trajectory. Specifically, it includes: the minimum-time control problem is represented by the following Formula One, Formula Two, Formula Three, and Formula Four:

[0086]

[0087] g f = g(r f , v f ) = 0 Formula Four

[0088] Among them, J represents the time optimization parameter. Equation (2) is the constructed kinetic model, Equation (3) is the constraint condition determined based on the first state information of the detector, and Equation (4) is the constraint condition determined based on the second state information of the detector. μ represents the gravitational constant of the central celestial body, r = ||r|| represents the distance between the detector and the central celestial body, r0 represents the position vector of the detector in the first orbit, v0 represents the velocity vector of the detector at the position in the first orbit, r f represents the position vector of the detector reaching the target orbit, and v f represents the velocity vector of the detector reaching the target orbit.

[0089] Since the position of the detector reaching the target orbit is free, the constraint condition of the detector in the target orbit can be described by the orbital elements (such as semi-major axis a f , eccentricity e f , orbital inclination i f , right ascension of the ascending node Ω f , argument of perigee ω f ) in the second state information. For the orbital transfer problem of the detector, the constraint condition of the target orbit (i.e., Equation (4)) can be expressed by the five constraint equations in Equation (5) below:

[0090]

[0091] Among them, h f represents the angular momentum of the target orbit, i h represents the unit vector of the angular momentum of the target orbit, which is a constant value. n represents the unit vector of the intersection line of the orbital plane and the inertial reference plane. g f,1 represents the constraint equation for the angular momentum of the target orbit, g f,2 represents the constraint equation for the mechanical energy of the target orbit, g f,3 represents the position constraint equation for the detector reaching the target orbit, g f,4 represents the velocity constraint equation for the detector reaching the target orbit, g f,5 represents the constraint equation for the direction of the eccentricity vector. And, h f , i h , e f , n are respectively represented by the corresponding equations in Equation (6) below:

[0092]

[0093] Here, considering that in the case of a circular target orbit, the circular orbit can be represented by the angular momentum vector and the orbital radius, so g f,2 and g f,5 can be simplified by Equation (7) below:

[0094]

[0095] Assume that the co - state variables of position and velocity are represented by λ r and λ v respectively. Then, according to Formula One and Formula Two, the Hamiltonian function can be determined to be represented by Formula Eight:

[0096]

[0097] Therefore, the co - state variable equations of position and velocity can be represented by Formula Nine:

[0098]

[0099] According to the maximum principle, the minimum - time control problem is equivalent to the problem of minimizing the Hamiltonian function, that is, minimizing Therefore, the magnitude and direction of the thrust acceleration are represented by Formula Ten:

[0100]

[0101] It can be seen from Formula Ten that the direction of the thrust acceleration is opposite to the direction of the co - state variable of velocity, and in order to ensure the shortest time for the detector to reach the target orbit, the thrust acceleration always maintains the maximum value.

[0102] Since the terminal manifold of the constraint condition is orthogonal to the terminal manifold of the transversality condition when the detector reaches the target orbit, the transversality condition can be represented by Formula Eleven:

[0103]

[0104] where And the coefficient matrix G(x f ) is represented by Formula Twelve:

[0105]

[0106] The expressions of each term in the coefficient matrix G(x f ) are respectively:

[0107]

[0108] where, [r f × and [v f × represent the cross - product matrices of r f and v f respectively.

[0109] Here, considering the case where the target orbit is a circular orbit, and ​​It can be simplified by the following formula XIII:

[0110]

[0111] After determining the transverse condition in step S102, considering the mutual coupling relationship among multiple equations during the shortest-time calculation process according to the transverse condition expressed by formula XI, the transverse condition expressed by formula XI can be processed by the augmented matrix inverse transformation method. Specifically, continue to execute step S103 to adjust the transverse condition, where the coefficient matrix of the adjusted transverse condition is invertible.

[0112] Exemplarily, augment the coefficient matrix G(x f ) into a 6×6 square matrix, then the new coefficient matrix can be expressed as where l is a column vector of undetermined constant values. This is only an example to illustrate the calculation method of the invertible coefficient matrix, and various invertible processing methods such as the adjoint matrix method and the elementary row transformation method can also be used.

[0113] After adjusting the transverse condition, continue to execute step S104. According to the adjusted transverse condition, constraint condition, and the first state information of the detector, determine the shortest time for the detector to move from the first orbital position to the target orbit. Then execute step S105. According to the first orbital position, target orbit, and shortest time of the detector, determine the flight trajectory of the detector from the first orbital position to the target orbit.

[0114] In some embodiments, step S104 specifically includes: according to the adjusted transverse condition and constraint condition, determine the shooting equations, and then input the co-state value corresponding to each specified parameter included in the first state information of the detector into the shooting equations to obtain the shortest time for the detector to move from the first orbital position to the target orbit.

[0115] For example, for the case where the detector reaches the target orbital position freely and with the shortest time, the Hamiltonian function satisfies In addition to adjusting the coefficient matrix, the adjusted transverse condition can also augment η into a 6×1 matrix, that is Therefore, the adjusted transverse condition can be expressed by formula XIV:

[0116]

[0117] By selecting an appropriate column vector l such that is invertible, then is equivalent to Therefore can be regarded as the adjusted transverse condition. That is, the shooting equations determined according to the equivalent condition of the adjusted transverse condition, the constraint condition, and the Hamiltonian function in the case of the shortest time are as follows:

[0118]

[0119] After determining the shooting equations, input the co-state values corresponding to each specified parameter included in the first state information of the detector into the shooting equations, and the shortest time for the detector to move from the first orbital position to the target orbit can be obtained by using the Newton iteration method.

[0120] In some embodiments, as Figure 2 shown, the co-state values corresponding to each specified parameter included in the first state information of the detector can be determined by the following method:

[0121] S201, randomly generate the first co-state value corresponding to the first specified parameter included in the first state information of the detector, and randomly generate the first transfer time for the detector to move from the first orbital position to the target orbit; wherein, the first specified parameter is the position information or velocity value of the detector on the first orbit at the current moment.

[0122] S202, based on the first co-state value and the first transfer time, determine the co-state values corresponding to each specified parameter when the Hamiltonian function takes the minimum value, wherein the independent variable parameters of the Hamiltonian function include the azimuth angles of the preset detector thrust acceleration.

[0123] Exemplarily, for the Hamiltonian function represented by Equation VIII, the following Equation XVI can be obtained by using the extreme value condition:

[0124]

[0125] wherein, p represents the order of the derivative with respect to time. For example, p = 1 is the first-order extreme value condition, and u = [u1, u2, u3] T represents the direction vector of the detector thrust acceleration. Assuming that the azimuth angles of the detector thrust acceleration are α and β, then the direction vector of the detector thrust acceleration can be expressed as:

[0126] u = [cosαcosβ, sinαcosβ, sinβ] T

[0127] Assuming ν = [α, β] T , then the time-optimal problem can be transformed into At this time, the Hamiltonian function can be expressed by Equation XVII:

[0128]

[0129] If λ v = [λ v1 , λ v2 , λ v3 ​T , Then, according to Formula XVI, it can be known that:

[0130]

[0131]

[0132] wherein,

[0133] g1(α,β) = [-sinαcosβ cosαcosβ 0] T

[0134] g2(α,β) = [-cosαsinβ -sinαsinβ cosβ] T

[0135]

[0136] In addition, for the calculation process of the shortest time, there is H(t)≡0, then the following Formula XX can be obtained:

[0137]

[0138] According to Formula XVIII, Formula XIX and Formula XX, the following system of equations can be constructed:

[0139]

[0140] It can be known from the above Formula XXI that according to the first co-state value corresponding to the first specified parameter included in the first state information of the randomly generated detector, the co-state values corresponding to the other specified parameters of the detector when the Hamiltonian function takes the minimum value can be obtained.

[0141] In some embodiments, as Figure 3 shown, after step S201, step S203 can also be continued to adjust the first co-state value and the first transfer time respectively according to the azimuth angle of the detector thrust acceleration. Then step S202 can continue to execute according to step S204 to determine the co-state values corresponding to each specified parameter of the detector when the Hamiltonian function takes the minimum value based on the adjusted first co-state value and the adjusted first transfer time.

[0142] Exemplarily, assume that the azimuth angle of the detector thrust acceleration is α and β , the first co-state value is x, and the first transfer time is t. Then according to the azimuth angle α and β of the detector thrust acceleration, the adjusted first co-state value is x1, and the adjusted first transfer time is t1.

[0143] In some embodiments, as Figure 4 shown, after step S204, step S205 can be continued to solve the shooting equations using the Newton iteration method, and step S206 to determine whether the solution is successful. If so, step S207 is continued to determine the shortest time; if not, return to execute step S201. That is, if the adjoint state values corresponding to each specified parameter are input into the shooting equations and the shortest time cannot be determined, the step of randomly generating the first adjoint state value corresponding to the first specified parameter included in the first state information of the detector is re-executed, and the step of randomly generating the first transfer time of the detector from the first orbital position to the target orbit is re-executed. Then, based on the re-determined first adjoint state value and the re-determined first transfer time, the new adjoint state values corresponding to each specified parameter of the detector when the Hamiltonian function takes the minimum value are re-determined.

[0144] In some embodiments, considering that the target orbit is a circular orbit, compared with the case where the target orbit is an elliptical orbit, the adjoint state values corresponding to each specified parameter can be determined more simply and quickly. Therefore, when designing the target orbit to be an elliptical orbit, the circular orbit associated with the elliptical orbit can be determined first, and then the adjoint state values corresponding to each specified parameter in the case of the circular orbit are used as the initial adjoint state values corresponding to each specified parameter in the case of the elliptical orbit, so as to more quickly determine the adjoint state values corresponding to each specified parameter in the case of the elliptical orbit.

[0145] Specifically, as Figure 5 shown, when the target orbit is an elliptical orbit, the adjoint state values corresponding to each specified parameter included in the first state information of the detector are determined by the following method:

[0146] S501, determine the circular orbit associated with the target orbit, and determine the adjoint state values corresponding to each specified parameter included in the first state information of the detector in the case of the circular orbit;

[0147] For example, determine the associated circular orbit with the semi-major axis of the elliptical orbit as the radius. Here, the specific determination method of the adjoint state values corresponding to each specified parameter included in the first state information of the detector in the case of the circular orbit can refer to the above description and will not be elaborated here.

[0148] S502, use each adjoint state value in the case of the circular orbit as the initial adjoint state value corresponding to each specified parameter in the case of the elliptical orbit;

[0149] S503, based on the initial adjoint state values corresponding to each specified parameter in the case of the elliptical orbit, determine the adjoint state values corresponding to each specified parameter in the case of the elliptical orbit.

[0150] Similarly, the co-state values corresponding to each specified parameter in the case of an elliptical orbit can be determined with reference to the above description, which will not be elaborated here.

[0151] In some embodiments, after determining the flight trajectory of the detector from the first orbital position to the target orbit in step S105, the detector can also be controlled to fly from the first orbital position to the target orbit along the flight trajectory by applying a set initial velocity and a set acceleration, where the set initial velocity and the set acceleration are both determined according to the shortest time and the flight distance represented by the flight trajectory. Additionally, the direction of the set acceleration can also be determined.

[0152] In some embodiments, before solving the shortest time process, the first state information and the second state information collected are first normalized. Assuming that the heliocentric gravitational constant μ after normalization is 1.32712440018E+20 m 3 / s 2 , the heliocentric distance LU after normalization is 1.49597870691E+11 m, and the time unit after normalization The heliocentric gravitational parameter after normalization μ = 1, the detector thrust acceleration Γ max = 1.0×10 -4 m / s.

[0153] For the case where the target orbit is a circular orbit, if the elements of the first orbit and the target orbit are both as shown in Table 1, the Newton-Raphson method is used to solve Equation 15. After adjusting the first co-state value using the azimuth angles α and β of the detector thrust acceleration, the calculation is repeated 10 times, and the number of iterations is between 30 and 80 times, and the arrival point from the starting point of the first orbit to the corresponding point of the target orbit as shown Figure 6a can be obtained. As Figure 6a can be seen, when the detector is at the starting point of the first orbit, the direction of the thrust acceleration is almost opposite to the running direction, thereby reducing the orbital altitude; when the detector is at the arrival point of the target orbit, the direction of the thrust acceleration is almost opposite to the running direction, thereby enabling the detector to accurately reach the target orbit. Table 2 shows the co-state values corresponding to the position and velocity respectively in the case of a circular orbit, as well as the shortest time.

[0154] Table 2

[0155]

[0156]

[0157] For the case where the target orbit is an elliptical orbit, the eccentricity can be set to e = 0.2, and other conditions are the same as those for the target orbit being a circular orbit. After 60 iterations, the result as shown Figure 6bThe flight from the starting point of the first orbit to the arrival point of the target orbit pair is shown. From Figure 6b It can be seen that when the detector is at the starting point of the first orbit, the direction of the thrust acceleration is almost opposite to the running direction, so that the orbital altitude can be reduced; when the detector is at the arrival point of the target orbit, the direction of the thrust acceleration is almost opposite to the running direction, so that the detector can accurately reach the target orbit. Table 3 shows the co-state values corresponding to the position and velocity respectively in the elliptical orbit, as well as the shortest time.

[0158] Table 3

[0159] Independent variable Value <![CDATA λ > <![CDATA[[-9.284,17.306,-5.008] T > <![CDATA λ > <![CDATA[[-26.789,-59.292,-14.807] T > <![CDATA[t f > 14.157 TU

[0160] Based on the same inventive concept, an embodiment of the present invention further provides a detector. Since this detector is the detector in the method of the embodiment of the present invention, and the principle of this detector to solve problems is similar to that of the method, the implementation of this detector can refer to the implementation of the method, and the repeated parts will not be described again.

[0161] As Figure 7 shown, the detector includes a thruster 700 and a controller 701, wherein:

[0162] The controller 701 is configured to perform the following steps:

[0163] Obtain the first state information of the detector at the current moment at the first orbit position, and determine the second state information of the detector in the target orbit;

[0164] Determine the constraint conditions based on the second state information of the detector; and determine the transversality conditions according to the constraint conditions; wherein, when the detector reaches the target orbit, the terminal manifold of the constraint conditions is orthogonal to the terminal manifold of the transversality conditions;

[0165] Adjust the transversality conditions, wherein the coefficient matrix of the adjusted transversality conditions is invertible;

[0166] Determine the shortest time for the detector to reach the target orbit from the first orbit position according to the adjusted transversality conditions, the constraint conditions and the first state information of the detector;

[0167] Determine the flight trajectory of the detector from the first orbit position to the target orbit according to the first orbit position of the detector, the target orbit and the shortest time.

[0168] As an optional implementation manner, the controller 701 is specifically configured to perform:

[0169] Determine the shooting equations according to the adjusted transversality conditions and the constraint conditions;

[0170] Input the co-state value corresponding to each specified parameter included in the first state information of the detector into the shooting equations to obtain the shortest time for the detector to reach the target orbit from the first orbital position.

[0171] As an alternative implementation, the controller 701 is configured to determine the co-state value corresponding to each specified parameter included in the first state information of the detector in the following manner:

[0172] Randomly generate the first co-state value corresponding to the first specified parameter included in the first state information of the detector, and randomly generate the first transfer time for the detector to reach the target orbit from the first orbital position; wherein, the first specified parameter is the position information or velocity value of the detector on the first orbit at the current moment;

[0173] Based on the first co-state value and the first transfer time, determine the co-state value corresponding to each specified parameter when the Hamiltonian function takes the minimum value, wherein the independent variable parameters of the Hamiltonian function include the azimuth angle of the preset detector thrust acceleration.

[0174] As an alternative implementation, after the controller 701 randomly generates the first co-state value corresponding to the first specified parameter included in the first state information of the detector and randomly generates the first transfer time for the detector to reach the target orbit from the first orbital position, it is further configured to perform:

[0175] Adjust the first co-state value and the first transfer time respectively according to the azimuth angle of the detector thrust acceleration;

[0176] The controller 701 is specifically further configured to perform:

[0177] Based on the adjusted first co-state value and the adjusted first transfer time, determine the co-state value corresponding to each specified parameter when the Hamiltonian function takes the minimum value.

[0178] As an alternative implementation, the controller 701 is further configured to perform:

[0179] If inputting the co-state value corresponding to each specified parameter into the shooting equations cannot determine the shortest time, then re-execute the step of randomly generating the first co-state value corresponding to the first specified parameter included in the first state information of the detector and re-execute the step of randomly generating the first transfer time for the detector to reach the target orbit from the first orbital position;

[0180] Based on the re-determined first co-state value and the re-determined first transfer time, re-determine the new co-state value corresponding to each specified parameter of the detector when the Hamiltonian function takes the minimum value.

[0181] As an alternative implementation, when the target orbit is an elliptical orbit, the controller 701 is specifically further configured to determine the co-state value corresponding to each specified parameter included in the first state information of the detector in the following manner:

[0182] Determine a circular orbit associated with the target orbit, and determine the co-state value corresponding to each specified parameter included in the first state information of the detector in the case of the circular orbit;

[0183] Respectively use each co-state value in the case of the circular orbit as the co-state initial value corresponding to each specified parameter in the case of the elliptical orbit;

[0184] Based on the co-state initial value corresponding to each specified parameter in the case of the elliptical orbit, determine the co-state value corresponding to each specified parameter in the case of the elliptical orbit.

[0185] As an alternative implementation, the controller 701 is further configured to perform:

[0186] Control the detector to apply a set initial velocity and a set acceleration, and fly from the first orbit position to the target orbit according to the flight trajectory; the set initial velocity and the set acceleration are both determined according to the shortest time and the flight distance represented by the flight trajectory.

[0187] Based on the same inventive concept, an embodiment of the present invention further provides an electronic device. Since this electronic device is the electronic device in the method of the embodiment of the present invention, and the principle of this electronic device to solve problems is similar to that of the method, the implementation of this electronic device can refer to the implementation of the method, and the repeated parts will not be described again.

[0188] As Figure 8 shown, the electronic device includes a processor 800 and a memory 801. The memory 801 is used to store a program executable by the processor 800, and the processor 800 is used to read the program in the memory 801 and execute the following steps:

[0189] Obtain the first state information of the detector at the current moment at the first orbit position, and determine the second state information of the detector in the target orbit;

[0190] Determine the constraint conditions based on the second state information of the detector; and determine the transversality conditions according to the constraint conditions; wherein, when the detector reaches the target orbit, the terminal manifold of the constraint conditions is orthogonal to the terminal manifold of the transversality conditions;

[0191] Adjust the transversality conditions, wherein the coefficient matrix of the adjusted transversality conditions is invertible;

[0192] According to the adjusted transversality conditions, the constraint conditions, and the first state information of the detector, determine the shortest time for the detector to travel from the first orbital position to the target orbit;

[0193] According to the first orbital position of the detector, the target orbit, and the shortest time, determine the flight trajectory of the detector from the first orbital position to the target orbit.

[0194] As an optional implementation manner, the memory 801 is specifically configured to execute:

[0195] Determine the shooting equations according to the adjusted transversality conditions and the constraint conditions;

[0196] Input the co-state values corresponding to each specified parameter included in the first state information of the detector into the shooting equations to obtain the shortest time for the detector to travel from the first orbital position to the target orbit.

[0197] As an optional implementation manner, the memory 801 is configured to determine the co-state values corresponding to each specified parameter included in the first state information of the detector in the following manner:

[0198] Randomly generate the first co-state value corresponding to the first specified parameter included in the first state information of the detector, and randomly generate the first transfer time for the detector to travel from the first orbital position to the target orbit; wherein, the first specified parameter is the position information or velocity value of the detector on the first orbit at the current moment;

[0199] Based on the first co-state value and the first transfer time, determine the co-state values corresponding to each specified parameter when the Hamiltonian function takes the minimum value, wherein the independent variable parameters of the Hamiltonian function include the azimuth angle of the pre-set thrust acceleration of the detector.

[0200] As an optional implementation manner, after the memory 801 randomly generates the first co-state value corresponding to the first specified parameter included in the first state information of the detector and randomly generates the first transfer time for the detector to travel from the first orbital position to the target orbit, it is further configured to execute:

[0201] Adjust the first co-state value and the first transfer time respectively according to the azimuth angle of the detector thrust acceleration;

[0202] The memory 801 is specifically further configured to execute:

[0203] Based on the adjusted first co-state value and the adjusted first transfer time, determine the co-state value corresponding to each specified parameter of the detector when the Hamiltonian function takes the minimum value.

[0204] As an optional implementation manner, the memory 801 is further configured to execute:

[0205] If the shortest time cannot be determined by inputting the co-state value corresponding to each specified parameter into the shooting equations, re-execute the step of randomly generating the first co-state value corresponding to the first specified parameter included in the first state information of the detector, and re-execute the step of randomly generating the first transfer time of the detector from the first orbital position to the target orbit;

[0206] Based on the re-determined first co-state value and the re-determined first transfer time, re-determine the new co-state value corresponding to each specified parameter of the detector when the Hamiltonian function takes the minimum value.

[0207] As an optional implementation manner, when the target orbit is an elliptical orbit, the memory 801 is specifically further configured to determine the co-state value corresponding to each specified parameter included in the first state information of the detector in the following manner:

[0208] Determine a circular orbit associated with the target orbit, and determine the co-state value corresponding to each specified parameter included in the first state information of the detector in the case of the circular orbit;

[0209] Respectively use each co-state value in the case of the circular orbit as the co-state initial value corresponding to each specified parameter in the case of the elliptical orbit;

[0210] Based on the co-state initial value corresponding to each specified parameter in the case of the elliptical orbit, determine the co-state value corresponding to each specified parameter in the case of the elliptical orbit.

[0211] As an optional implementation manner, the memory 801 is further configured to execute:

[0212] Control the detector to apply a set initial velocity and a set acceleration, and fly from the first orbital position to the target orbit according to the flight trajectory; the set initial velocity and the set acceleration are both determined according to the shortest time and the flight distance represented by the flight trajectory.

[0213] Based on the same inventive concept, an embodiment of the present invention further provides a small-thrust trajectory optimization device. Since this device is the device in the method of the embodiment of the present invention, and the principle of solving problems by this device is similar to that of the method, the implementation of this device can refer to the implementation of the method, and the repeated parts will not be elaborated.

[0214] As Figure 9 shown, the device includes:

[0215] An acquisition module 901, configured to acquire first state information of the detector at the first orbital position at the current moment, and determine second state information of the detector in the target orbit;

[0216] A determination module 902, configured to determine a constraint condition based on the second state information of the detector; and determine a transversality condition according to the constraint condition; wherein, the terminal manifold of the constraint condition is orthogonal to the terminal manifold of the transversality condition when the detector reaches the target orbit;

[0217] An adjustment module 903, configured to adjust the transversality condition, wherein the coefficient matrix of the adjusted transversality condition is invertible;

[0218] A time calculation module 904, configured to determine the shortest time for the detector to fly from the first orbital position to the target orbit according to the adjusted transversality condition, the constraint condition, and the first state information of the detector;

[0219] A flight trajectory determination module 905, configured to determine the flight trajectory of the detector from the first orbital position to the target orbit according to the first orbital position of the detector, the target orbit, and the shortest time.

[0220] As an optional implementation manner, the time calculation module 904 is specifically configured to:

[0221] Determine a shooting equation set according to the adjusted transversality condition and the constraint condition;

[0222] Input the co-state value corresponding to each specified parameter included in the first state information of the detector into the shooting equation set to obtain the shortest time for the detector to fly from the first orbital position to the target orbit.

[0223] As an alternative implementation, each co-state value corresponding to each specified parameter included in the first state information of the detector is determined in the following manner:

[0224] Randomly generate a first co-state value corresponding to a first specified parameter included in the first state information of the detector, and randomly generate a first transfer time of the detector from the first orbital position to the target orbit; wherein, the first specified parameter is the position information or velocity value of the detector at the current moment on the first orbit;

[0225] Based on the first co-state value and the first transfer time, determine each co-state value corresponding to each specified parameter when the Hamiltonian function takes the minimum value, wherein the independent variable parameters of the Hamiltonian function include the azimuth angle of the preset detector thrust acceleration.

[0226] As an alternative implementation, after randomly generating a first co-state value corresponding to a first specified parameter included in the first state information of the detector and randomly generating a first transfer time of the detector from the first orbital position to the target orbit, the time calculation module 904 is specifically further configured to:

[0227] Adjust the first co-state value and the first transfer time respectively according to the azimuth angle of the detector thrust acceleration;

[0228] The time calculation module 904 is specifically configured to:

[0229] Based on the adjusted first co-state value and the adjusted first transfer time, determine each co-state value corresponding to each specified parameter when the Hamiltonian function takes the minimum value.

[0230] As an alternative implementation, the device further includes:

[0231] If the shortest time cannot be determined by inputting each co-state value corresponding to each specified parameter into the shooting equations, re-execute the step of randomly generating a first co-state value corresponding to a first specified parameter included in the first state information of the detector and re-execute the step of randomly generating a first transfer time of the detector from the first orbital position to the target orbit;

[0232] Based on the re-determined first co-state value and the re-determined first transfer time, re-determine each new co-state value corresponding to each specified parameter when the Hamiltonian function takes the minimum value.

[0233] As an alternative embodiment, when the target orbit is an elliptical orbit, the co-state values corresponding to each specified parameter included in the first state information of the detector are determined by the following method:

[0234] Determine a circular orbit associated with the target orbit, and determine the co-state values corresponding to each specified parameter included in the first state information of the detector in the case of the circular orbit;

[0235] Respectively use each co-state value in the case of the circular orbit as the initial co-state value corresponding to each specified parameter in the case of the elliptical orbit;

[0236] Based on the initial co-state values corresponding to each specified parameter in the case of the elliptical orbit, determine the co-state values corresponding to each specified parameter in the case of the elliptical orbit.

[0237] As an alternative embodiment, the device further includes:

[0238] Control the detector to apply a set initial velocity and a set acceleration, and fly from the first orbital position to the target orbit according to the flight trajectory; the set initial velocity and the set acceleration are both determined according to the shortest time and the flight distance represented by the flight trajectory.

[0239] Based on the same inventive concept, an embodiment of the present disclosure provides a computer storage medium, which includes: computer program code. When the computer program code runs on a computer, it causes the computer to execute any one of the small-thrust trajectory optimization methods described above. Since the principle of solving problems by the above computer storage medium is similar to that of the small-thrust trajectory optimization method, the implementation of the above computer storage medium can refer to the implementation of the method, and the repeated parts will not be elaborated.

[0240] In a specific implementation process, the computer storage medium may include: various storage media that can store program code, such as a Universal Serial Bus Flash Drive (USB), a mobile hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disc.

[0241] Based on the same inventive concept, embodiments of the present disclosure also provide a computer program product, which includes computer program code that, when running on a computer, causes the computer to execute the small-thrust trajectory optimization method described in any of the foregoing discussions. Since the principle of the above computer program product for solving problems is similar to that of the small-thrust trajectory optimization method, the implementation of the above computer program product can refer to the implementation of the method, and the repeated parts will not be elaborated.

[0242] The computer program product can adopt any combination of one or more readable media. The readable medium can be a readable signal medium or a readable storage medium. The readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples (non-exhaustive list) of the readable storage medium include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0243] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage and optical storage, etc.) containing computer-usable program code.

[0244] The present invention is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, and the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0245] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means embodying the functionality specified in the flowchart Figure 1 a flowchart or multiple flowcharts and / or blocks Figure 1 or the functions specified in a block or multiple blocks.

[0246] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable apparatus provide steps for implementing the functionality specified in the flowchart Figure 1 a flowchart or multiple flowcharts and / or blocks Figure 1 or the functions specified in a block or multiple blocks.

[0247] It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit and scope of the invention. Thus, if these modifications and variations of the present invention come within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.

Claims

1. A low-thrust trajectory optimization method, characterized in that: The method comprises: Acquire first state information of the first orbital position of the detector at a current moment, and determine second state information of the detector in the target orbit; Determining a constraint condition based on the second state information of the probe; and determining a cross-section condition based on the constraint condition; wherein the terminal manifold of the constraint condition is orthogonal to the terminal manifold of the cross-section condition when the probe reaches the target orbit; Adjusting the transversal condition, wherein a coefficient matrix of the adjusted transversal condition is invertible; Determining the shortest time for the probe to move from the first orbital position to the target orbit according to the adjusted cross-sectional condition, the constraint condition and the first state information of the probe; A flight trajectory of the probe from the first orbital position to the target orbit is determined based on the first orbital position of the probe, the target orbit and the shortest time.

2. The method according to claim 1, characterized in that Determining the shortest time for the probe to move from the first orbital position to the target orbit according to the adjusted cross-sectional condition, the constraint condition and the first state information of the probe includes: Determine the target shooting equation group according to the adjusted cross-sectional condition and the constraint condition; The co-state value corresponding to each designated parameter included in the first state information of the probe is input into the target shooting equation group to obtain the shortest time for the probe to move from the first orbital position to the target orbit.

3. The method according to claim 2, characterized in that Determine the corresponding co-state value of each specified parameter included in the first state information of the detector in the following manner: Randomly generate a first co-state value corresponding to a first specified parameter included in the first state information of the probe, and randomly generate a first transfer time of the probe from the first orbital position to the target orbit; wherein the first specified parameter is the position information or speed value of the probe on the first orbit at the current moment; Based on the first co-state value and the first transfer time, the co-state value corresponding to each specified parameter of the probe when the Hamiltonian function takes a minimum value is determined, wherein the independent variable parameters of the Hamiltonian function include the azimuth angle of the preset thrust acceleration of the probe.

4. The method according to claim 3, characterized in that After randomly generating a first co-state value corresponding to a first specified parameter included in the first state information of the probe, and randomly generating a first transfer time of the probe from the first orbital position to the target orbit, the method further includes: adjusting the first co-state value and the first transfer time respectively according to the azimuth angle of the probe thrust acceleration; The determining, based on the first co-state value and the first transfer time, the co-state value corresponding to each designated parameter of the detector when the Hamiltonian function takes a minimum value comprises: Based on the adjusted first co-state value and the adjusted first transfer time, the co-state value corresponding to each designated parameter of the detector when the Hamiltonian function takes a minimum value is determined.

5. The method according to claim 3 or 4, characterized in that The method further comprises: If the co-state value corresponding to each designated parameter is input into the target shooting equation group and the shortest time cannot be determined, the steps of randomly generating the first co-state value corresponding to the first designated parameter included in the first state information of the detector and randomly generating the first transfer time of the detector from the first orbital position to the target orbit are re-executed; Based on the re-determined first co-state value and the re-determined first transfer time, a new co-state value corresponding to each designated parameter of the detector when the Hamiltonian function takes a minimum value is re-determined.

6. The method according to claim 2, characterized in that When the target orbit is an elliptical orbit, the co-state value corresponding to each designated parameter included in the first state information of the detector is determined in the following manner: Determine a circular orbit associated with the target orbit, and determine a corresponding co-state value of each specified parameter included in the first state information of the detector in the case of the circular orbit; Using each co-state value in the circular orbit case as the co-state initial value corresponding to each specified parameter in the elliptical orbit case; Based on the co-state initial value respectively corresponding to each designated parameter in the elliptical orbit case, the co-state value respectively corresponding to each designated parameter in the elliptical orbit case is determined.

7. The method according to any one of claims 1 to 4 and 6, characterized in that After determining the flight trajectory of the probe from the first orbital position to the target orbit, the method further includes: The probe is controlled to apply a set initial speed and a set acceleration to fly from the first orbital position to the target orbit according to the flight trajectory; the set initial speed and the set acceleration are both determined based on the shortest time and the flight distance represented by the flight trajectory.

8. A detector, characterized in that: The method comprises a thruster and a controller, wherein the controller is configured to execute the steps of the method according to any one of claims 1 to 7.

9. An electronic device, characterized in that: It comprises a processor and a memory, wherein the memory is used to store a program executable by the processor, and the processor is used to read the program in the memory and execute the steps of the method according to any one of claims 1 to 7.

10. A computer 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 according to any one of claims 1 to 7 are implemented.

Images