Method and device for monitoring near-earth asteroid

Abstract

The invention provides a method and a device for monitoring a near-earth asteroid, belongs to the technical field of universe navigation, and can realize full-range monitoring of the near-earth asteroid in a relatively large range. The method comprises the following steps: determining a nominal orbit of a detection spacecraft according to an earth revolution orbit, solar center gravity and a genetic algorithm; acquiring a fuel consumption index function of the detection spacecraft; and based on the nominal orbit, the fuel consumption index function and a linear quadratic regulator, determining the control acceleration required by the detection spacecraft to run on the nominal orbit.

Description

Technical Field

[0001] The present invention relates to the technical field of space navigation, and particularly to a method and device for monitoring near-Earth asteroids. Background Art

[0002] Near-Earth Objects (NEOs) refer to asteroids or comets whose orbits intersect or are close to the Earth's orbit, and the distance between their perihelions and the sun is less than 1.3 astronomical units (AU, i.e., the average distance between the Earth and the sun). Since the orbits of near-Earth asteroids cross the Earth's orbital plane, an asteroid impact event may occur, resulting in huge economic losses.

[0003] Therefore, monitoring and defending against near-Earth asteroid impacts on the Earth is of great significance. However, the existing methods for monitoring near-Earth asteroids have limited observation ranges for near-Earth asteroids and cannot achieve full-range monitoring of near-Earth asteroids over a large area. Summary of the Invention

[0004] The present invention provides a method and device for monitoring near-Earth asteroids, which can achieve full-range monitoring of near-Earth asteroids over a large area.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] In a first aspect, the present invention provides a method for monitoring near-Earth asteroids, including: first, determining the nominal orbit of a detection spacecraft according to the Earth's orbital revolution, the solar central gravity, and a genetic algorithm. When the detection spacecraft operates on the nominal orbit, the detection spacecraft can monitor near-Earth asteroids coming from the direction of the sun, that is, the detection spacecraft and the Earth have the same running direction, the relative position relationship between the detection spacecraft and the Earth remains unchanged, and the field of view of the detection spacecraft points to the Earth. And obtaining the fuel consumption index function of the detection spacecraft. Then, based on the nominal orbit, the fuel consumption index function, and a linear quadratic regulator, determining the control acceleration required for the detection spacecraft to operate on the nominal orbit.

[0007] In a method for monitoring near-Earth asteroids provided by the present invention, the nominal orbit of a detection spacecraft is obtained by using the Earth's revolution orbit, the solar central gravity, and a genetic algorithm. On this basis, through the nominal orbit of the detection spacecraft, the fuel consumption index function of the detection spacecraft, and a linear quadratic regulator, the control acceleration required for the detection spacecraft to operate on the nominal orbit is calculated, so that the detection spacecraft operates on the nominal orbit as much as possible. Thereby, during the process of the detection spacecraft performing the task of monitoring near-Earth asteroids, the running direction of the detection spacecraft is always the same as that of the Earth, the detection spacecraft always maintains a fixed relative position relationship with the Earth, and the field of view of the spacecraft always points to the Earth. Furthermore, full-range monitoring of near-Earth asteroids within a large range can be achieved by the detection spacecraft.

[0008] In one implementation manner of the first aspect, determining the nominal orbit of the detection spacecraft includes:

[0009] The nominal orbit of the detection spacecraft is described by six orbital elements, and the six orbital elements of the nominal orbit include: the semi-major axis a of the nominal orbit nt , the eccentricity e of the nominal orbit nt , the inclination i of the nominal orbit nt , the argument of periapsis ω of the nominal orbit nt , the right ascension of the ascending node Ω of the nominal orbit nt and the mean anomaly M0 of the nominal orbit;

[0010] Set the optimization objective function of the nominal orbit, and the optimization objective function satisfies the following formula;

[0011]

[0012] where J represents the optimization objective; Δd k represents the maximum distance deviation, T represents the monitoring duration of the detection spacecraft for the near-Earth asteroid; d(t) represents the distance between the detection spacecraft and the Earth at time t, and d(t) = |r sc (t) - r eo (t)|, r sc (t) represents the distance between the detection spacecraft and the solar center at time t under the condition of only being affected by the solar central gravity, r eo (t) represents the distance between the Earth and the solar center at time t; d ref represents the distance between the nominal orbit and the solar center;

[0013] Set the feasible region of the orbital parameters of the nominal orbit of the detection spacecraft, and the feasible region of the orbital parameters satisfies: i nt = i eo , Ω nt = Ω eo , a nt∈[0.8a eo , 1.2a eo , e nt ∈[0.8e eo , 1.2e eo , ω nt ∈[0, π], M0∈[0, 2π]; where, i eo represents the orbital inclination of the Earth's revolution orbit, Ω eo represents the right ascension of the ascending node of the Earth's revolution orbit, a eo represents the semi-major axis of the Earth's revolution orbit, e eo represents the eccentricity of the Earth's revolution orbit; i eo , Ω eo , a eo and e eo are all the mean orbital elements of the Earth's revolution orbit;

[0014] Based on the optimization objective function, the feasible region of orbital parameters, and the genetic algorithm, the nominal orbit of the exploration spacecraft is optimized.

[0015] In one implementation of the first aspect, based on the optimization objective function, the feasible region of orbital parameters, and the genetic algorithm, optimizing to obtain the nominal orbit of the exploration spacecraft includes:

[0016] Step 1: Randomly generate multiple candidate orbits within the feasible region of orbital parameters, and form a population with the multiple candidate orbits;

[0017] Step 2: Evaluate the fitness of each candidate orbit in the population through the optimization objective function;

[0018] Step 3: Select, crossover, and mutate the population according to the fitness of each candidate orbit in the population to obtain a new population;

[0019] Step 4: Repeat Step 2 to Step 3 until there is a candidate orbit in the population whose fitness reaches the fitness threshold, and then use the candidate orbit whose fitness reaches the fitness threshold as the nominal orbit of the exploration spacecraft.

[0020] In one implementation of the first aspect, the fuel consumption index function of the exploration spacecraft satisfies the following formula;

[0021]

[0022] where, J[u(·)] represents the fuel consumption index of the exploration spacecraft; t0 represents the starting time when the exploration spacecraft monitors the near-Earth asteroid, t f represents the ending time when the exploration spacecraft monitors the near-Earth asteroid; ΔX(t) represents the distance by which the exploration spacecraft deviates from the nominal orbit at time t, ΔX T(t) represents the transpose of ΔX(t); Q(t) represents the state weight matrix at time t; u(t) represents the control acceleration of the exploration spacecraft, u T (t) represents the transpose of u(t); R(t) represents the control input weight matrix at time t.

[0023] In one implementation of the first aspect, determining the control acceleration required for the exploration spacecraft to operate on the nominal orbit includes:

[0024] Based on the linear quadratic regulator, solving the fuel consumption index function of the exploration spacecraft to obtain the control acceleration required for the exploration spacecraft to operate on the nominal orbit; the acceleration satisfies the following formula;

[0025] u * (t) = -G(t)ΔX(t)

[0026] where, u * (t) represents the control acceleration required for the exploration spacecraft to operate on the nominal orbit at time t, G(t) represents the feedback gain matrix of the exploration spacecraft at time t, and ΔX(t) represents the distance of the exploration spacecraft from the nominal orbit at time t.

[0027] In one implementation of the first aspect, the feedback gain matrix G(t) of the exploration spacecraft at time t satisfies the following formula;

[0028] G(t) = R -1 (t)B T (y)K(t)

[0029] where, R -1 (t) represents the inverse matrix of the control input weight matrix at time t, B(t) represents the input matrix of the exploration spacecraft at time t, B T (t) represents the transpose of B(t), and K(t) satisfies the following formula;

[0030]

[0031] represents the derivative of K(t), A(t) represents the state matrix of the exploration spacecraft at time t, and Q(t) represents the state weight matrix at time t.

[0032] In the second aspect, the present invention provides a device for monitoring near-Earth asteroids, including a nominal orbit determination module, an index function acquisition module, and an acceleration determination module;

[0033] The nominal orbit determination module is used to determine the nominal orbit of the exploration spacecraft according to the Earth's revolution orbit, the solar central gravity, and the genetic algorithm; when the exploration spacecraft operates on the nominal orbit, the exploration spacecraft can monitor near-Earth asteroids coming from the direction of the sun, that is, the exploration spacecraft and the Earth have the same running direction, the relative position relationship between the exploration spacecraft and the Earth remains unchanged, and the field of view of the exploration spacecraft points to the Earth;

[0034] The index function acquisition module is used to acquire the fuel consumption index function of the exploration spacecraft;

[0035] The acceleration determination module is used to determine the control acceleration required for the exploration spacecraft to operate on the nominal orbit based on the nominal orbit, the fuel consumption index function, and the linear quadratic regulator.

[0036] In an implementation manner of the second aspect, the nominal orbit module is specifically used to describe the nominal orbit of the exploration spacecraft by using six orbital elements. The six orbital elements of the nominal orbit include: the semi-major axis a of the nominal orbit nt 、the eccentricity e of the nominal orbit nt 、the orbital inclination i of the nominal orbit nt 、the argument of perigee ω of the nominal orbit nt 、the right ascension of the ascending node Ω of the nominal orbit nt and the mean anomaly M0 of the nominal orbit;

[0037] Set the optimization objective function of the nominal orbit, and the optimization objective function satisfies the following formula;

[0038]

[0039] Among them, J represents the optimization objective; Δd k represents the maximum distance deviation, T represents the monitoring duration of the exploration spacecraft for near-Earth asteroids; d(t) represents the distance between the exploration spacecraft and the Earth at time t, and d(t) = |r sc (t)-r eo (t)|, r sc (t) represents the distance between the exploration spacecraft and the solar center at time t under the condition of only being affected by the solar central gravity, r eo (t) represents the distance between the Earth and the solar center at time t; d ref represents the distance between the nominal orbit and the solar center;

[0040] Set the feasible region of the orbital parameters of the nominal orbit of the exploration spacecraft, and the feasible region of the orbital parameters satisfies: i nt =i eo , Ω nt =Ω eo , a nt ∈[0.8a eo, 1.2a eo , e nt ∈ [0.8e eo , 1.2e eo , ω nt ∈ [0, π], M0 ∈ [0, 2π]; where, i eo represents the orbital inclination of the Earth's revolution orbit, Ω eo represents the right ascension of the ascending node of the Earth's revolution orbit, a eo represents the semi-major axis of the Earth's revolution orbit, a eo represents the eccentricity of the Earth's revolution orbit; i eo , Ω eo , a eo and e eo are all the mean orbital elements of the Earth's revolution orbit;

[0041] Based on the optimization objective function, the orbital parameter feasible region, and the genetic algorithm, the nominal orbit of the exploration spacecraft is optimized.

[0042] In a third aspect, the present invention provides an electronic device, including a processor and a memory coupled to the processor; the memory is used to store computer instructions, and when the electronic device runs, the processor executes the computer instructions stored in the memory, so that the electronic device executes the method described in the first aspect or any one of its implementation manners as above.

[0043] In a fourth aspect, the present invention provides a computer-readable storage medium, including computer program instructions, and when the computer program instructions are executed by a computer, the computer is caused to execute the method described in the first aspect or any one of its implementation manners as above.

[0044] In a fifth aspect, the present invention provides a computer program product, including computer program instructions, and when the computer program instructions run on a computer, the computer is caused to execute the method described in the first aspect or any one of its implementation manners as above.

[0045] The technical effects corresponding to the second to fifth aspects and their possible implementation manners as above can refer to the description of the technical effects of the first aspect and its possible implementation manners as above, and will not be elaborated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is one of the schematic diagrams of a method for monitoring near-Earth asteroids provided by an embodiment of the present application;

[0047] Figure 2 is the second schematic diagram of a method for monitoring near-Earth asteroids provided by an embodiment of the present application;

[0048] Figure 3It is a schematic diagram of the nominal orbit provided by an embodiment of the present application;

[0049] Figure 4 It is a schematic structural diagram of a device for monitoring near-earth asteroids provided by an embodiment of the present application. Detailed implementation manners

[0050] In the embodiments of the present application, words such as "exemplary" or "for example" are used to represent examples, illustrations or explanations. Any embodiment or design solution described as "exemplary" or "for example" in the embodiments of the present application should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Rather, the use of words such as "exemplary" or "for example" is intended to present relevant concepts in a specific manner.

[0051] In the description of the present invention, unless otherwise specified, the meaning of "multiple" refers to two or more. For example, multiple candidate orbits refer to two or more candidate orbits.

[0052] The method and device provided by the embodiments of the present application relate to space navigation, and can monitor near-earth asteroids through a detection satellite. Specifically, during the process of monitoring a near-earth asteroid by a detection spacecraft (such as a satellite, a space shuttle, etc.), the detection spacecraft is controlled to run as close as possible to the nominal orbit by controlling the acceleration to achieve the monitoring of the near-earth asteroid. The above nominal orbit is designed based on the earth's revolution orbit, the sun-centered gravity, and the genetic algorithm.

[0053] It can be understood that the above nominal orbit is an idealized orbit calculated through a mathematical model and dynamic simulation in the mission planning stage. In the embodiments of the present application, the above nominal orbit only considers the sun-centered gravity and does not consider other perturbations in actual operation (such as atmospheric drag, the non-spherical gravity of the earth, solar radiation pressure, the gravity of a third body, etc.).

[0054] In order to solve the problem in the background technology that the existing methods for monitoring near-earth asteroids have a limited observation range for near-earth asteroids and cannot achieve full-range monitoring of near-earth asteroids in a large range, the embodiments of the present application provide a method and a device for monitoring near-earth asteroids. By using the earth's revolution orbit, the sun-centered gravity, and the genetic algorithm, the nominal orbit of the detection spacecraft is obtained; and through the nominal orbit of the detection spacecraft, the fuel consumption index function of the detection spacecraft, and the linear quadratic regulator, the control acceleration is calculated, and the detection spacecraft is controlled to run as close as possible to the nominal orbit by controlling the acceleration, thereby achieving full-range monitoring of near-earth asteroids by the detection spacecraft in a large range.

[0055] Exemplarily, a method for monitoring near-Earth asteroids provided by an embodiment of the present invention can be executed by an electronic device with processing capabilities. For example, the electronic device can be a computer, a server, etc. Taking the electronic device as a computer as an example, the hardware part of the computer can include: a processor, a memory, a network interface, a user interface, a communication bus, etc.

[0056] Among them, the processor is used to control the electronic device to execute relevant processing and calculation tasks. For example, determining the nominal orbit of the exploration spacecraft, obtaining the fuel consumption index function of the exploration spacecraft, and determining the control acceleration required for the exploration spacecraft to operate on the nominal orbit, etc. The processor can include a central processing unit (CPU) or other processors. The processor can be single-core or multi-core. For example, the processor can include multiple CPUs.

[0057] The memory is used to store computer instructions and related data. For example, storing the nominal orbit of the exploration spacecraft, the fuel consumption index function of the exploration spacecraft, and the control acceleration required for the exploration spacecraft to operate on the nominal orbit, etc. The memory can be a random access memory (RAM), a read only memory (ROM), an erasable programmable read-only memory (EPROM), a flash memory, or an optical memory, a magnetic disk storage medium, or any other magnetic storage device, or any other medium capable of storing program code or data that can be accessed by a computer. Optionally, the memory can be integrated in the processor, and the memory can also be independent of the processor.

[0058] The network interface is used for the computer to communicate with other devices or communication networks. The network interface can be a transceiver with sending and receiving functions. Optionally, the network interface can include a standard wired interface, a wireless interface (such as a WI-FI interface, a Bluetooth interface, a 5G interface).

[0059] The communication bus is used to realize the connection and communication between different components. For example, the above-mentioned processor, memory, network interface, and user interface can be interconnected through the communication bus.

[0060] The user interface can include a display screen, an input unit (such as a keyboard). Optionally, the user interface can also include a standard wired interface, a wireless interface.

[0061] Those skilled in the art can understand that the above computer can also include more or fewer components, or combine certain components, or have different component arrangements. The embodiments of the present application do not limit this.

[0062] Optionally, asFigure 1 As shown in Figure 1 , a method for monitoring near-Earth asteroids provided by an embodiment of the present application includes S101 - S103:

[0063] S101. Determine the nominal orbit of the exploration spacecraft according to the Earth's revolution orbit, the solar central gravity, and the genetic algorithm;

[0064] In the embodiment of the present application, when the exploration spacecraft operates on the nominal orbit, the exploration spacecraft can monitor near-Earth asteroids coming from the direction of the sun, that is, the exploration spacecraft and the Earth have the same running direction, and the relative position relationship between the exploration spacecraft and the Earth remains unchanged (that is, the exploration spacecraft is always at a fixed distance in front of / behind the Earth), and the field of view of the exploration spacecraft points to the Earth;

[0065] In one implementation, in combination with Figure 1 , as Figure 2 shown in Figure 2 , the above S101 includes S1011 - S1014;

[0066] S1011. Describe the nominal orbit of the exploration spacecraft using six orbital elements;

[0067] The six orbital elements of the above nominal orbit include: semi-major axis a nt , eccentricity e nt , orbital inclination i nt , argument of perigee ω nt , right ascension of the ascending node Ω nt and mean anomaly M0. Then, the six orbital elements of the above nominal orbit can be expressed as X = [a nt , e nt , i nt , Ω nt , ω nt , M0];

[0068] It should be understood that the six orbital elements are six basic parameters for describing the orbit of an astronomical object or a spacecraft around a central celestial body (such as the Earth), which are derived from Kepler's laws; the six orbital elements completely define the shape, spatial orientation, and instantaneous position of the nominal orbit;

[0069] S1012. Set the optimization objective function of the nominal orbit;

[0070] The above optimization objective function satisfies the following formula;

[0071]

[0072] Among them, J represents the optimization objective; Δd kdenotes the maximum distance deviation, T denotes the monitoring duration of the exploration spacecraft for the near-Earth asteroid; d(t) denotes the distance between the exploration spacecraft and the Earth at time t, and d(t) = |r sc (t) - r eo (t)|, r sc (t) denotes the distance between the exploration spacecraft and the center of the sun at time t under the condition of only being affected by the central gravitational force of the sun, r eo (t) denotes the distance between the Earth and the center of the sun at time t; d ref denotes the distance between the nominal orbit and the center of the sun, that is, the nominal design distance;

[0073] It should be understood that in the process of determining the nominal orbit of the exploration spacecraft in the embodiments of the present application, only the perturbation of the central gravitational force of the sun on the exploration spacecraft (that is, the influence of the central gravitational force of the sun on the exploration spacecraft deviating from the nominal orbit) is considered; on this basis, the state equation of the exploration spacecraft constructed satisfies the following formula;

[0074]

[0075] Among them, r represents the position vector of the exploration spacecraft in the heliocentric inertial coordinate system, r points from the center of the sun to the exploration spacecraft, and here r has the same physical meaning as r sc (t) in the above optimization objective function; is the derivative of r; v represents the velocity vector of the exploration spacecraft in the heliocentric inertial coordinate system, is the derivative of v, represents the acceleration of the exploration spacecraft in the heliocentric inertial coordinate system; μ s represents the gravitational constant of the sun;

[0076] Since the heliocentric inertial coordinate system belongs to the commonly used coordinate system in the technical field, the embodiments of the present application will not elaborate on it here;

[0077] S1013. Set the feasible region of the orbital parameters of the nominal orbit of the exploration spacecraft;

[0078] The feasible region of the orbital parameters satisfies: i nt = i eo , Ω nt = Ω eo , a nt ∈[0.8a eo , 1.2a eo , e nt ∈[0.8e eo , 1.2e eo , ω nt ∈[0, π], M0 ∈[0, 2π];

[0079] Among them, ieo represents the orbital inclination of the Earth's orbit, Ω eo Indicates the right ascension of the ascending node of the Earth's orbit, a eo represents the semi-major axis of the Earth's orbit, e eo represents the eccentricity of the Earth's orbit; i eo ,Ω eo 、a eo and e eo are the average orbital elements of the Earth's orbit;

[0080] S1014. Based on the optimization objective function, the feasible region of orbital parameters and the genetic algorithm, optimize and obtain the nominal orbit of the exploration spacecraft;

[0081] In one application scenario, the above S1013 includes the following contents:

[0082] Step 1: randomly generate multiple candidate orbits within the feasible region of orbital parameters, and form a population of the multiple candidate orbits;

[0083] Specifically, multiple candidate orbits are generated from the feasible domain of orbital parameters. Each candidate orbit in the multiple candidate orbits is regarded as an individual. Multiple candidate orbits (i.e., multiple individuals) are aggregated to obtain an initial population. The encoding of each individual is a six-dimensional vector, and the six-dimensional vector of the k-th individual can be expressed as X k =[a k ,e k ,i k ,Ω k ,ω k ,M k ];

[0084] Optionally, Latin Hypercube Sampling (LHS) may be used to generate multiple candidate tracks, or other methods may be used. The present embodiment does not further limit the method for generating multiple candidate tracks.

[0085] Step 2: Evaluate the fitness of each candidate track in the population by optimizing the objective function;

[0086] Exemplarily, the fitness of each candidate track can be calculated by a fitness function; the fitness function satisfies the following formula:

[0087]

[0088] Among them: F k is the fitness of the kth individual, α is the distance deviation penalty coefficient, Δd k The maximum distance deviation of each individual (i.e., each candidate orbit) during the monitoring time T of the exploration spacecraft for the near-Earth asteroid;

[0089] The above Δd k Satisfy the following formula;

[0090]

[0091] The above d(t)=|r sc (t)-r 地 (t)| is the real-time satellite-to-ground distance, d ref is the nominal design distance; it can be understood that the above From the above optimization objective function;

[0092] Step 3: According to the fitness of each candidate track in the population, the population is selected, crossed, and mutated to obtain a new population;

[0093] It should be understood that the above-mentioned selection, crossover, and mutation are all operators of the genetic algorithm;

[0094] In one application scenario, the selection process is as follows: a number of excellent individuals are selected based on their fitness (i.e., candidate tracks) to prepare for crossover and mutation. Specifically, the selection can be performed using a roulette wheel method, where the probability of each individual being selected satisfies the following formula:

[0095]

[0096] Where: p k is the probability of the kth individual being selected, N is the number of individuals in the population, f k =K*F k , K is the coefficient;

[0097] The above crossover operation process is: select two or more individuals for crossover to generate new offspring, and the new individuals carry the characteristics of the parent genes; specifically, a discrete crossover method is adopted, and the pth individual σ p and the qth individual σ q The crossover operation method at position j (i.e., the jth vector in the above six-dimensional vector) satisfies the following formula:

[0098]

[0099] Among them, β is a random number in the interval [0,1], σ pj is the pth individual σ p The jth vector in σ qj is the qth individual σ q The jth vector in ;

[0100] The operation process of the above mutation is as follows: mutate the offspring individuals, introduce random changes to increase the diversity of the population and prevent premature convergence; specifically, generate new chromosomes through basic bit mutation, and the i-th chromosome σ of the k-th individual ki The mutation operation method is as follows:

[0101]

[0102] f(g) = r2(1 - g / G max ) 2

[0103] In the formula: σ max and σ min are the upper and lower boundaries of the chromosome σ ki respectively, g is the current iteration number, G max is the maximum reproduction number, r2 is a random number, and r is a random number between [0, 1];

[0104] Step 4: Repeat Step 2 to Step 3 until there is a candidate orbit in the population whose fitness reaches the fitness threshold (that is, the stop condition for population update is that there is a candidate orbit in the population whose fitness reaches the fitness threshold), and then use the candidate orbit whose fitness reaches the fitness threshold as the nominal orbit of the exploration spacecraft. The finally obtained nominal orbit is as Figure 3 shown;

[0105] Optionally, in the above Step 4, the stop condition for population update can also be that the iteration number of the population reaches the maximum reproduction number. The embodiments of the present application do not limit the stop condition for population update;

[0106] S102. Obtain the fuel consumption index function of the exploration spacecraft;

[0107] Optionally, the fuel consumption index function of the exploration spacecraft satisfies the following formula;

[0108]

[0109] Among them, J[u(·)] represents the fuel consumption index of the exploration spacecraft; t0 represents the starting time when the exploration spacecraft monitors the near-Earth asteroid, and t f represents the ending time when the exploration spacecraft monitors the near-Earth asteroid; ΔX(t) represents the distance of the exploration spacecraft from the nominal orbit at time t, and ΔX T (t) represents the transpose of ΔX(t); Q(t) represents the state weight matrix at time t; u(t) represents the control acceleration of the exploration spacecraft, and u T (t) represents the transpose of u(t); R(t) represents the control input weight matrix at time t;

[0110] The derivation process of the above formula (1) will be described in detail below;

[0111] Step 1: Set the nonlinear control system of the exploration spacecraft;

[0112] The nonlinear control system of the exploration spacecraft satisfies the following formula;

[0113]

[0114] where x is the state variable of the exploration spacecraft, and x ∈ R n , u ∈ R r is the control quantity, f ∈ R n is a nonlinear vector function; it can be understood that x, y, and z respectively represent the position components of the exploration spacecraft on the x-axis, y-axis, and z-axis in the heliocentric inertial coordinate system, respectively represent the velocity components of the exploration spacecraft on the x-axis, y-axis, and z-axis in the heliocentric inertial coordinate system. The above x can be directly obtained by the orbit recurrence calculation of the exploration spacecraft; t0 is the starting time for the exploration spacecraft to monitor near-Earth asteroids, and t f is the ending time for the exploration spacecraft to monitor near-Earth asteroids;

[0115] Step 2: Design the control law of the exploration spacecraft;

[0116] Design the control law u. The control law u can control the state variable x(t) of the exploration spacecraft to be near the ideal state x 0 (t) (i.e., the nominal orbit); the so-called ideal state x 0 (t) is the solution corresponding to the ideal control u 0 (t), that is:

[0117]

[0118] where, is the state quantity of the exploration spacecraft at time t0 in the ideal state;

[0119] Step 3: Design the fuel consumption index function of the exploration spacecraft;

[0120] Set the performance index of the exploration spacecraft to satisfy:

[0121]

[0122] where Q(t) is the state weight matrix, and Q(t) is an n-order symmetric positive definite matrix. Q(t) is used to penalize the state deviation; S(t) is an n×r positive definite matrix; R(t) is the control input weight matrix, and R(t) is an r-order symmetric positive definite matrix. R(t) is used to penalize the magnitude of the control input; F is usually an n×n-order symmetric non-negative definite constant matrix;

[0123] Specifically, the above-mentioned x T (t f )Fx(t f ) represents an additional term added to meet the requirement that x(t f is close to x f ) at time t in the actual engineering control design; the above-mentioned x 0 (t f )Q(t)x(t) represents the cost of the system state deviating from the desired state; the above-mentioned u T (t)R(t)u(t) represents the energy consumption of the control input; T (t)R(t)u(t) represents the energy consumption of the control input;

[0124] In the embodiment of the present application, the distance ΔX by which the exploration spacecraft deviates from the nominal orbit is used to replace the state vector x(t) of the spacecraft; that is, there is ΔX(t) = x(t) - z(t), where z(t) represents the state vector of the exploration spacecraft when the exploration spacecraft is located on the nominal orbit at time t, and z(t) can be directly obtained by converting the six orbital elements of the nominal orbit; since converting the state vector through the six orbital elements belongs to a common technical means in the technical field, the embodiment of the present application does not further elaborate on the above process;

[0125] Further, due to infinite time (t f →∞), the terminal term x T (t f )Fx(t f ) and the mixed term x T (t)S(t)u(t) in the performance index satisfaction formula of the above-mentioned exploration spacecraft are eliminated, and the above formula (1) can be derived;

[0126] In the embodiment of the present application, the fuel consumption index function of the above-mentioned exploration spacecraft can be the above formula or other formulas, and the embodiment of the present application does not limit the specific form of the fuel consumption index function of the exploration spacecraft;

[0127] S103. Based on the nominal orbit, the fuel consumption index function, and the linear quadratic regulator, determine the control acceleration required for the exploration spacecraft to operate on the nominal orbit;

[0128] In an application scenario, the fuel consumption index function of the exploration spacecraft is solved based on the linear quadratic regulator to obtain the control acceleration required for the exploration spacecraft to operate on the nominal orbit; the acceleration satisfies the following formula;

[0129] u * (t) = -G(t)ΔX(t)

[0130] where u *(t) represents the control acceleration required for the exploration spacecraft to operate on the nominal orbit at time t, G(t) represents the feedback gain matrix of the exploration spacecraft at time t, and ΔX(t) represents the distance by which the exploration spacecraft deviates from the nominal orbit at time t;

[0131] The feedback gain matrix G(t) of the exploration spacecraft at the above-mentioned time t satisfies the following formula;

[0132] G(t) = R -1 (t)B T (t)K(t)

[0133] Among them, R -1 (t) represents the inverse matrix of the control input weight matrix at time t, B(t) represents the input matrix of the exploration spacecraft at time t, B T (t) represents the transpose of B(t), and K(t) satisfies the following formula;

[0134]

[0135] represents the derivative of K(t), A(t) represents the state matrix of the exploration spacecraft at time t, and Q(t) represents the state weight matrix at time t;

[0136] The derivation process of the formula satisfied by the above K(t) is described in detail below;

[0137] Applying the maximum principle can solve the optimal control form of the above formula (1), and the Hamiltonian function of the above formula (1) is as follows;

[0138]

[0139] The conjugate equation satisfied by ψ(t) (i.e., the co-state variable) in the above formula is as follows;

[0140]

[0141] The transversality condition satisfied by ψ(t) (i.e., the co-state variable) in the above formula is as follows;

[0142] ψ(t f ) = -FΔX(t f )

[0143] Let ψ(t) = -K(t)ΔX(t), and the solution is:

[0144] u * (t) = R -1 (t)B T (t)ψ = -R -1 (t)B T (t)K(t)ΔX *\(\lambda(t)= -G(t)\Delta X\) * \(\lambda\)

[0145] where \(K(t)\) is an \(n\times n\) time - varying matrix, which is only related to \(A(t)\), \(B(t)\), \(Q(t)\), \(R(t)\), \(F\) and \(t\) f and is independent of the initial conditions of the probe spacecraft;

[0146] Then the formula satisfied by the above \(K(t)\) is given by the Riccati matrix differential equation with the terminal condition \(K(t\) f ) = F;

[0147] In one implementation, the state matrix \(A(t)\) of the probe spacecraft at time \(t\) is as follows;

[0148]

[0149] where \(r(t)\) represents the position component of the probe spacecraft in the heliocentric inertial coordinate system at time \(t\);

[0150] The input matrix \(B(t)\) of the probe spacecraft at time \(t\) is as follows;

[0151]

[0152] The control acceleration of the probe spacecraft at time \(t\) is: \(u(t)=[u\) x (t),u\) y (t),u\) z (t)] T ; \(u\) x (t) is the control acceleration of the probe spacecraft on the \(x\) - axis in the heliocentric inertial coordinate system at time \(t\), \(u\) y (t) is the control acceleration of the probe spacecraft on the \(y\) - axis in the heliocentric inertial coordinate system at time \(t\), \(u\) z (t) is the control acceleration of the probe spacecraft on the \(z\) - axis in the heliocentric inertial coordinate system at time \(t\);

[0153] The state weight matrix \(Q(t)\) at time \(t\) satisfies: \(Q(t)=10\) 4 \(\times diag(1,1,1,1,1,1)\), and the control input weight matrix \(R(t)\) at time \(t\) satisfies: \(R(t)=diag(1,1,1)\).

[0154] It should be understood that the selection of the parameter matrices \(Q(t)\) and \(R(t)\) in the LQR controller also affects the elimination of errors. \(Q(t)\) represents the weights of the position error and velocity error in the orbit - keeping control; when \(R(t)\) is selected to be small, it may cause a large control energy, and a large \(R\) may lead to a long control time and low control accuracy.

[0155] In summary, in a method for monitoring near-Earth asteroids provided by an embodiment of the present application, the nominal orbit of a detection spacecraft is obtained by using the Earth's revolution orbit, the solar central gravity, and a genetic algorithm. On this basis, the control acceleration required for the detection spacecraft to operate on the nominal orbit is calculated through the nominal orbit of the detection spacecraft, the fuel consumption index function of the detection spacecraft, and a linear quadratic regulator, so that the detection spacecraft operates on the nominal orbit as much as possible. As a result, during the process of the detection spacecraft performing the task of monitoring near-Earth asteroids, the running direction of the detection spacecraft is always the same as that of the Earth, the detection spacecraft always maintains a fixed relative position relationship with the Earth, and the field of view of the spacecraft always points to the Earth. Since the orbital altitude of the nominal orbit provided by the embodiment of the present application can be set according to the actual situation, the method provided by the embodiment of the present application can be used to monitor near-Earth asteroids within a large range. Further, since the detection spacecraft always maintains a fixed relative position relationship with the Earth, the method provided by the embodiment of the present application can achieve full-range monitoring of near-Earth asteroids, and thus achieve full-range monitoring of near-Earth asteroids by the detection spacecraft within a large range.

[0156] Correspondingly, an embodiment of the present application provides a device for monitoring near-Earth asteroids, as Figure 4 shown, including a nominal orbit determination module 501, an index function acquisition module 502, and an acceleration determination module 503.

[0157] Among them, the nominal orbit determination module 501 is configured to determine the nominal orbit of the detection spacecraft according to the Earth's revolution orbit, the solar central gravity, and a genetic algorithm. When the detection spacecraft operates on the nominal orbit, the detection spacecraft can monitor near-Earth asteroids coming from the direction of the sun, that is, the running direction of the detection spacecraft is the same as that of the Earth, the relative position relationship between the detection spacecraft and the Earth remains unchanged, and the field of view of the detection spacecraft points to the Earth. For example, the nominal orbit determination module 501 is configured to implement S101 of the above method for monitoring near-Earth asteroids.

[0158] The index function acquisition module 502 is configured to acquire the fuel consumption index function of the detection spacecraft. For example, the index function acquisition module 502 is configured to implement S102 of the above method for monitoring near-Earth asteroids.

[0159] The acceleration determination module 503 is configured to determine the control acceleration required for the detection spacecraft to operate on the nominal orbit based on the nominal orbit, the fuel consumption index function, and a linear quadratic regulator. For example, the acceleration determination module 503 is configured to implement S103 of the above method for monitoring near-Earth asteroids.

[0160] Optionally, the nominal orbit determination module 501 is specifically configured to: describe the nominal orbit of the exploration spacecraft using six orbital elements. Set an optimization objective function for the nominal orbit. Set the feasible region of the orbital parameters of the nominal orbit of the exploration spacecraft. Based on the optimization objective function, the feasible region of the orbital parameters, and the genetic algorithm, optimize to obtain the nominal orbit of the exploration spacecraft. For example, the nominal orbit determination module 5021 is specifically configured to implement S1011 - S1014 of the above method for monitoring near - Earth asteroids.

[0161] Each module of the above - mentioned device for monitoring near - Earth asteroids can also be used to execute other steps in the above - mentioned method embodiments. All relevant contents involved in the above - mentioned method embodiments can be cited in the function descriptions of the corresponding functional modules and will not be elaborated here.

[0162] The embodiment of the present application also provides an electronic device, including: a processor and a memory coupled to the processor; the memory is used to store computer instructions. When the electronic device runs, the processor executes the computer instructions stored in the memory so that the electronic device executes the method in the above - mentioned embodiments. Among them, the processor can implement the above - mentioned nominal orbit determination module 501, the index function acquisition module 502, and the acceleration determination module 503; the above - mentioned memory can also be used to store the nominal orbit of the exploration spacecraft, the fuel consumption index function of the exploration spacecraft, and the control acceleration required for the exploration spacecraft to operate on the nominal orbit, etc.

[0163] The embodiment of the present application also provides a computer - readable storage medium, which includes a computer program. When the computer program runs on a computer, it is used to execute the method in the above - mentioned embodiments.

[0164] The embodiment of the present application also provides a computer program product, which includes computer program instructions. When the computer program instructions run on a computer, it is used to execute the method in the above - mentioned embodiments.

[0165] Each embodiment in this specification is described in a progressive manner. The same or similar parts among the embodiments can be referred to each other. Each embodiment focuses on the differences from other embodiments.

[0166] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for monitoring near-Earth asteroids, characterized in that, Including: Determine the nominal orbit of the exploration spacecraft according to the Earth's revolution orbit, the solar central gravity, and the genetic algorithm; When the exploration spacecraft operates on the nominal orbit, the exploration spacecraft can monitor near-Earth asteroids coming from the direction of the sun, that is, the exploration spacecraft has the same running direction as the Earth, the relative position relationship between the exploration spacecraft and the Earth remains unchanged, and the field of view of the exploration spacecraft points to the Earth; Obtain the fuel consumption index function of the exploration spacecraft; Based on the nominal orbit, the fuel consumption index function, and the linear quadratic regulator, determine the control acceleration required for the exploration spacecraft to operate on the nominal orbit.

2. The method according to claim 1, wherein The determination of the nominal orbit of the exploration spacecraft includes: The nominal orbit of the detection spacecraft is described by six orbital elements, and the six orbital elements of the nominal orbit include: the semi-major axis a of the nominal orbit nt , the eccentricity e of the nominal orbit nt , the orbital inclination i of the nominal orbit nt , the argument of perigee ω of the nominal orbit nt , the right ascension of the ascending node Ω of the nominal orbit nt and the mean anomaly M0 of the nominal orbit; Set the optimization objective function of the nominal orbit, and the optimization objective function satisfies the following formula; where J represents the optimization objective; Δd k represents the maximum distance deviation, T represents the monitoring duration of the detection spacecraft for the near-Earth asteroid; d(t) represents the distance between the detection spacecraft and the Earth at time t, and d(t) = |r sc (t) - r eo (t)|, r sc (t) represents the distance between the detection spacecraft and the center of the sun at time t when only under the gravitational force of the center of the sun, r eo (t) represents the distance between the Earth and the center of the sun at time t; d ref represents the distance between the nominal orbit and the center of the sun; Set the feasible region of the orbital parameters of the nominal orbit of the exploration spacecraft, where the feasible region of the orbital parameters satisfies: i nt = i eo , Ω nt = Ω eo , a nt ∈ [0.8a eo , 1.2a eo , e nt ∈ [0.8e eo , 1.2e eo , ω nt ∈ [0, π], M0 ∈ [0, 2π]; where, i eo represents the orbital inclination of the Earth's revolution orbit, Ω eo represents the right ascension of the ascending node of the Earth's revolution orbit, a eo represents the semi-major axis of the Earth's revolution orbit, e eo represents the eccentricity of the Earth's revolution orbit; Based on the optimization objective function, the orbit parameter feasible region, and the genetic algorithm, optimize to obtain the nominal orbit of the exploration spacecraft.

3. The method according to claim 2, wherein The optimization to obtain the nominal orbit of the exploration spacecraft based on the optimization objective function, the orbit parameter feasible region, and the genetic algorithm includes: Step 1: Randomly generate multiple candidate orbits within the orbit parameter feasible region, and form a population with the multiple candidate orbits; Step 2: Evaluate the fitness of each candidate orbit in the population through the optimization objective function; Step 3: Select, crossover, and mutate the population according to the fitness of each candidate orbit in the population to obtain a new population; Step 4: Repeat Step 2 to Step 3 until there is a candidate orbit in the population whose fitness reaches the fitness threshold, and then use the candidate orbit whose fitness reaches the fitness threshold as the nominal orbit of the exploration spacecraft.

4. The method according to claim 1, wherein The fuel consumption index function of the exploration spacecraft satisfies the following formula; Among them, J[u(·)] represents the fuel consumption index of the exploration spacecraft; t0 represents the starting time when the exploration spacecraft monitors the near-Earth asteroid, and t f represents the ending time when the exploration spacecraft monitors the near-Earth asteroid; ΔX(t) represents the distance by which the exploration spacecraft deviates from the nominal orbit at time t, and ΔX T (t) represents the transpose of ΔX(t); Q(t) represents the state weight matrix at time t; u(t) represents the control acceleration of the exploration spacecraft, and u T (t) represents the transpose of u(t); R(t) represents the control input weight matrix at time t.

5. The method according to claim 1 or 4, characterized in that, The determination of the control acceleration required for the exploration spacecraft to operate on the nominal orbit includes: Solve the fuel consumption index function of the exploration spacecraft based on the linear quadratic regulator to obtain the control acceleration required for the exploration spacecraft to operate on the nominal orbit; the acceleration satisfies the following formula; u * (t) = -G(t)ΔX(t) where, u * (t) represents the control acceleration required for the exploration spacecraft to operate on the nominal orbit at time t, G(t) represents the feedback gain matrix of the exploration spacecraft at time t, and ΔX(t) represents the distance by which the exploration spacecraft deviates from the nominal orbit at time t.

6. The method according to claim 5, wherein The feedback gain matrix G(t) of the exploration spacecraft at time t satisfies the following formula; G(t) = R -1 (t)B T (t)K(t) wherein, R -1 (t) represents the inverse matrix of the control input weight matrix at time t, B(t) represents the input matrix of the detection spacecraft at time t, B T (t) represents the transpose of B(t), and K(t) satisfies the following formula; represents the derivative of K(t), A(t) represents the state matrix of the exploration spacecraft at time t, and Q(t) represents the state weight matrix at time t.

7. A device for monitoring near-Earth asteroids, characterized in that, Including a nominal orbit determination module, an index function acquisition module, and an acceleration determination module; The nominal orbit determination module is used to determine the nominal orbit of the exploration spacecraft according to the Earth's revolution orbit, the solar central gravity, and the genetic algorithm; When the exploration spacecraft operates on the nominal orbit, the exploration spacecraft can monitor near-Earth asteroids coming from the direction of the sun, that is, the exploration spacecraft has the same running direction as the Earth, the relative position relationship between the exploration spacecraft and the Earth remains unchanged, and the field of view of the exploration spacecraft points to the Earth; The index function acquisition module is used to obtain the fuel consumption index function of the exploration spacecraft; The acceleration determination module is configured to determine the control acceleration required for the exploration spacecraft to operate on the nominal orbit based on the nominal orbit, the fuel consumption index function, and the linear quadratic regulator.

8. An electronic device, characterized in that, It includes a processor and a memory coupled to the processor; the memory is used to store computer instructions, and when the electronic device runs, the processor executes the computer instructions stored in the memory so that the electronic device executes the method according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, It includes computer program instructions, and when the computer program instructions are executed by a computer, the computer is made to execute the method according to any one of claims 1 to 6.

10. A computer program product, characterized in that, It includes computer program instructions, and when the computer program instructions run on a computer, the computer is made to execute the method according to any one of claims 1 to 6.

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