Defensive methods for irregularly shaped asteroids considering impact uncertainty

Abstract

The embodiment of the application relates to the technical field of deep space exploration and asteroid defense, and discloses an asteroid defense method considering irregular shape structures and hitting uncertainty, comprising the following steps: selecting a target asteroid, and obtaining orbit parameters and model data of the target asteroid; determining a state vector of a spacecraft when the spacecraft reaches the target asteroid according to orbit parameters of the earth and the target asteroid and initial parameters of the spacecraft; establishing a deflection amount function relationship by using a -Trumbore intersection function and a Monte Carlo simulation algorithm based on the state vector and the model data; optimizing the function relationship by using a genetic algorithm, determining an optimal first direction angle and an optimal second direction angle, and formulating a defense strategy of the target asteroid, so that the influence of irregular shape structures of the asteroid and the influence of hitting uncertainty of the spacecraft are comprehensively considered, and the defense capability for the asteroid is greatly improved.

Description

Technical Field

[0001] This application relates to the fields of deep space exploration and asteroid defense technology, and in particular to an asteroid defense method that takes into account irregular shapes and uncertainties in impact. Background Technology

[0002] The potential impact threat from asteroids is one of the greatest threats facing humanity. With increasingly frequent asteroid impacts on Earth, the development of strategies related to asteroid monitoring and defense has been listed as a key focus of deep space technology development internationally. Countries around the world have established various asteroid monitoring and early warning systems to address the potential impact threat, including: establishing comprehensive asteroid observation systems to promptly detect and track near-Earth asteroids through astronomical observations and space exploration, providing early warnings of possible collisions; and using observational data and numerical simulation methods to assess the orbits, sizes, velocities, and other parameters of near-Earth asteroids to determine their potential threat level to Earth.

[0003] In addition to asteroid monitoring and early warning strategies, the international community has been researching and exploring asteroid defense strategies. Currently researched defense strategies fall into two categories: deflection strategies and fragmentation strategies. Deflection strategies aim to apply mechanical force to the target asteroid, causing its orbit to deviate and thus avoiding risk. Fragmentation strategies utilize a series of high-speed kinetic energy penetrators to destroy the target asteroid, breaking it into fragments, and then guiding the fragments away from Earth or reducing their destructive potential. Fragmentation strategies are difficult to apply due to uncertainties and unpredictability; therefore, deflection strategies are a key research direction in asteroid defense. Deflection strategies mainly include pulse deflection strategies and sustained-action deflection strategies. Pulse deflection strategies mainly include kinetic energy impact methods and nuclear explosion methods, while sustained-action deflection strategies mainly include low-thrust propulsion methods, solar radiation pressure methods, gravitational traction methods, and mass-driven methods. Kinetic energy impact methods are currently the only option that comprehensively considers deflection effectiveness, safety, and feasibility.

[0004] However, the inventors of this application have discovered that the traditional kinetic energy impact method is limited by the carrying capacity of the launch vehicle and is not good at defending against asteroids with large mass and volume. The impact process faces the risk of asteroid fragmentation. At the same time, the actual impact process is limited and affected by various real physical conditions, which leads to the final deflection result of the asteroid deviating from the expected result. Summary of the Invention

[0005] The purpose of this application is to provide an asteroid defense method that considers irregular shapes and uncertainties in impact. When formulating asteroid defense strategies, the method comprehensively considers the influence of the asteroid's irregular shape and the spacecraft's impact uncertainty, utilizing... By employing intersection function and Monte Carlo simulation algorithms, and through qualitative and quantitative analysis, the optimal impact position of the spacecraft is determined to achieve the best deflection effect, significantly improving the defense capability against asteroids.

[0006] To address the aforementioned technical problems, embodiments of this application provide an asteroid defense method considering irregular shapes and impact uncertainties, comprising the following steps: selecting a target asteroid with a polyhedral model and acquiring the target asteroid's orbital parameters and model data; determining the spacecraft's state vector upon arrival at the target asteroid based on Earth's orbital parameters, the target asteroid's orbital parameters, and the spacecraft's initial parameters; and utilizing the state vector and the model data to... An intersection function and Monte Carlo simulation algorithm are used to establish a functional relationship between the deflection amount and a first and a second direction angle. The deflection amount is the amount of deflection of the target asteroid relative to its original orbit after being impacted by the spacecraft. The first and second direction angles are used to define the position where the spacecraft impacts the target asteroid. A genetic algorithm is used to optimize the functional relationship to determine the optimal first and second direction angles corresponding to the maximum value of the deflection amount. Based on the optimal first and second direction angles, a defense strategy for the target asteroid is formulated.

[0007] Embodiments of this application also provide an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the aforementioned asteroid defense method that takes into account irregular shapes and hit uncertainties.

[0008] Embodiments of this application also provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned asteroid defense method that takes into account irregular shapes and uncertainties in impact.

[0009] The embodiments of this application provide an asteroid defense method, electronic device, and computer-readable storage medium that consider irregular shapes and uncertainties in impact. These methods select asteroids with irregular shapes as defense targets and introduce a first direction angle and a second direction angle. The algorithm determines the ideal impact point and its corresponding impact plane, and analyzes the uncertainties of spacecraft impact on the impact plane based on Monte Carlo simulation. By establishing a functional relationship between deflection and two direction angles, the deflection capability of the spacecraft after impacting an asteroid at different impact angles is measured. Therefore, a defense strategy is formulated based on the first and second direction angles under optimal deflection capability. The formulated asteroid defense strategy conforms to the actual situation of asteroid and spacecraft impacts, achieving optimal deflection of the asteroid after impact, significantly improving the defense capability against asteroids, and reducing the threat of asteroids to Earth.

[0010] In some alternative embodiments, the step of utilizing the state vector and the model data... The intersection function and Monte Carlo simulation algorithm are used to establish the functional relationship between the deflection amount and the first and second direction angles. This includes: transforming the state vector into the body coordinate system of the target asteroid; introducing the first and second direction angles to locate the impact ray when the spacecraft collides with the target asteroid; and utilizing... An intersection algorithm is used to determine the ideal impact point and the impact plane; wherein the model data is expressed in the body coordinate system; the incident velocity vector of the spacecraft impacting the target asteroid is determined based on the impact ray and the state vector, and the momentum enhancement factor and its constraints are determined based on the incident velocity vector and the normal vector of the impact plane; an impact coordinate system is established based on the incident velocity vector and the ideal impact point, and a number of simulated impact points satisfying a two-dimensional Gaussian distribution are determined on the impact plane using a Monte Carlo simulation algorithm, and the intersection elements of each simulated impact point and the model data are determined in the impact coordinate system; the expected velocity increment of the ideal impact point is calculated based on the incident velocity vector, the momentum enhancement factor, and the normal vector of the intersection element corresponding to each simulated impact point; and a functional relationship between the deflection amount and the first and second direction angles is established based on the expected velocity increment and the deflection model corresponding to the target asteroid. Considering the uncertainty of the impact location, the ideal impact point of the spacecraft defined by the first and second direction angles is only a theoretical value. In reality, the spacecraft may hit any location nearby. Therefore, this application does not delve into the actual impact point of the spacecraft, but instead calculates the expected value of the velocity increment at the ideal impact point. The expected value of the velocity increment is used to represent the impact uncertainty. The deflection can be calculated through the expected value of the velocity increment, thereby obtaining the functional relationship between the deflection and the two direction angles.

[0011] In some optional embodiments, establishing the impact coordinate system based on the incident velocity vector and the ideal impact point includes: using the ideal impact point as the origin P, the direction pointing towards the north pole of the target asteroid as the N-axis, and the opposite direction of the incident velocity vector as the O-axis, and determining the W-axis based on the N-axis and the O-axis using the right-hand rule, thus establishing a P-NOW impact coordinate system. The NOW coordinate system is more suitable than the XYZ coordinate system for establishing the impact coordinate system.

[0012] In some alternative embodiments, the momentum enhancement factor and its constraints are determined based on the incident velocity vector and the normal vector of the impact plane using the following formula:

[0013]

[0014] in, Let be the incident velocity vector. β is the normal vector of the hit plane, and β is the momentum enhancement factor.

[0015] In some optional embodiments, the expected velocity increment of the ideal hit point is calculated using the following formula, based on the incident velocity vector, the momentum enhancement factor, and the normal vector of the intersecting surface element corresponding to each of the simulated hit points:

[0016]

[0017]

[0018] Wherein, γ is the mass ratio of the spacecraft to the target asteroid, and β is the momentum enhancement factor. Let be the incident velocity vector. Let P be the normal vector of the intersecting surface element corresponding to the g-th simulated hit point. g Let G be the Monte Carlo selection probability corresponding to the g-th simulated hit point, where G is the total number of simulated hit points. The velocity increment expected value for the ideal hit point.

[0019] In some optional embodiments, the deflection amount is established as a function of the first direction angle and the second direction angle based on the expected velocity increment and the deflection model corresponding to the target asteroid, using the following formula:

[0020]

[0021]

[0022]

[0023] Where T represents the deflection model corresponding to the target asteroid. P is the expected velocity increment of the ideal hit point. Impact F is the Monte Carlo selection probability corresponding to the ideal hit point. Target Let MC(·) represent the hit plane, MC(·) represent the Monte Carlo simulation algorithm, and MT(·) represent... Find the intersection function. Let θ be the first direction angle and θ be the second direction angle.

[0024] In some optional embodiments, the parameters of the genetic algorithm are set as follows: maximum number of generations is set to 1000, population size is set to 1000, crossover probability is set to 0.8, and tolerance is set to 1×10⁻⁶. -6 .

[0025] In some optional embodiments, selecting a target asteroid with a polyhedral model includes: selecting an asteroid with an absolute magnitude less than 24 and a polyhedral model from near-Earth objects as the target asteroid; the orbital parameters of the target asteroid include its semi-major axis a, orbital eccentricity e, orbital inclination i, right ascension of the intersection Ω, argument of perigee ω, mean perigee M, ephemeris, and time t of minimum orbital interception distance. moid When selecting target asteroids, choose those with a polyhedral shape and an absolute magnitude of less than 24. Such asteroids are relatively large, close to Earth, and pose a greater potential threat, thus making the defense strategy more valuable. Attached Figure Description

[0026] One or more embodiments are illustrated by way of example with reference to the accompanying drawings, and these illustrative descriptions do not constitute a limitation on the embodiments.

[0027] Figure 1 This is a flowchart of an asteroid defense method that takes into account irregular shapes and uncertainties of impact, provided in one embodiment of this application;

[0028] Figure 2 This is a schematic diagram of model data for a polyhedral model of asteroid Bennu provided in one embodiment of this application;

[0029] Figure 3 In one embodiment of this application, based on the state vector of the spacecraft when it arrives at the target asteroid and the model data of the polyhedral model of the target asteroid, the following method is used: A flowchart is used to establish the functional relationship between the deflection amount and the first and second direction angles by finding the intersection function and Monte Carlo simulation algorithm.

[0030] Figure 4 This is a schematic diagram of the spacecraft impact location and transfer path provided in one embodiment of this application;

[0031] Figure 5 This is a schematic diagram of the constraint conditions for the momentum enhancement factor provided in one embodiment of this application;

[0032] Figure 6 This is a schematic diagram of the P-NOW hit coordinate system provided in one embodiment of this application;

[0033] Figure 7 This is a schematic diagram of a Monte Carlo simulation calculation process provided in one embodiment of this application;

[0034] Figure 8 This is a schematic diagram illustrating the distribution of the expected velocity increment values ​​for different ideal hit points provided in one embodiment of this application;

[0035] Figure 9 This is a schematic diagram of the structure of an electronic device provided in another embodiment of this application. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the various embodiments of this application will be described in detail below with reference to the accompanying drawings. However, those skilled in the art will understand that many technical details have been provided in the various embodiments of this application to help readers better understand this application. However, the technical solutions claimed in this application can be implemented even without these technical details and various changes and modifications based on the following embodiments. The division of the various embodiments below is for the convenience of description and should not constitute any limitation on the specific implementation of this application. The various embodiments can be combined with and referenced by each other without contradiction.

[0037] Establishing a near-Earth asteroid defense system is of significant scientific and engineering value and is a crucial component of deep space technology development. With increasingly frequent extraterrestrial impacts on Earth, the development of asteroid monitoring and defense strategies has been listed as a key focus of international deep space technology development. my country's 2021 White Paper on Space Activities emphasizes the importance of establishing an asteroid defense system and plans to gradually conduct detection, defense, verification, and testing of near-Earth asteroids in the future.

[0038] The potential impact threat of asteroids has always been one of the greatest threats facing humanity. To address this significant threat, countries worldwide have established various monitoring and early warning systems. These include, but are not limited to: establishing comprehensive asteroid observation systems to promptly detect and track near-Earth asteroids through astronomical observations and other means, providing early warnings of potential collisions; and using observational data and numerical simulations to assess the orbits, sizes, velocities, and other parameters of near-Earth asteroids to determine their potential threat level to Earth. Currently, the international community primarily focuses on the research and development of deflection strategies for hazardous asteroids. Existing deflection strategies include pulsed deflection strategies and sustained-action deflection strategies.

[0039] Pulsed deflection strategies involve using a spacecraft to apply instantaneous force or momentum changes to a target asteroid, thereby altering its motion. The key to this strategy is delivering a powerful impact to the asteroid within a short period, causing a change in its orbit. Pulsed deflection strategies are typically suitable for asteroids with short warning times, achieving orbital changes within a limited timeframe. Generally, pulsed deflection strategies include kinetic impact and nuclear explosion methods. Both are characterized by their ability to impact and deflect the target asteroid in a short time. Based on this characteristic, for hazardous asteroids with short warning times, a suitable pulsed deflection strategy can be selected by comprehensively considering the target size. However, the probability of fragmentation and the potential hazards caused by the target asteroid must be considered, weighing factors such as technical feasibility, deflection effectiveness, and mission safety to select an effective deflection strategy.

[0040] Continuous-action deflection strategies refer to altering an asteroid's orbit by continuously applying forces or changes in momentum. This strategy involves deploying spacecraft near the target asteroid and gradually changing its trajectory through continuous thrust or gravitational interactions. Continuous-action deflection strategies are applicable to asteroids with long warning times because they can gradually adjust the asteroid's orbit over a longer period. Compared to pulsed deflection strategies, continuous-action deflection strategies have a longer duration of action, primarily altering the asteroid's orbit by applying continuous forces or other forces to it. Continuous-action deflection strategies generally include low-thrust propulsion, solar radiation pressure, gravitational traction, and mass-driven methods. Continuous-action strategies can significantly reduce the risk of asteroid fragmentation. However, due to the long-term nature of these strategies, their applicability is limited, making them unsuitable for asteroid defense missions with short warning times. Furthermore, limited by current technological advancements, continuous-action deflection strategies have poor practicality, are cumbersome, and place high demands on the reliability and accuracy of spacecraft operating over extended periods. Furthermore, the motion model under asteroid spin coupling needs to be considered, which further increases the complexity of control and operation.

[0041] It is important to note that selecting a suitable deflection strategy requires comprehensive consideration of multiple factors, including the characteristics of the asteroid, the warning time, its size, and the feasibility of the strategy. Detailed engineering and numerical simulation studies should also be conducted to evaluate its effectiveness and potential impact.

[0042] Currently, the concepts and theories of kinetic impact, nuclear explosion, and gravitational traction are quite mature. The kinetic impact method was validated on September 27, 2022, during NASA's (National Aeronautics and Space Administration) DART (Double Asteroid Redirection Test) program, achieving a change in orbit for approximately 33 minutes on the asteroid Demophores. The gravitational traction method, compared to other methods, does not require contact with the asteroid's surface and is relatively independent of the asteroid's physical properties; however, its implementation requires consideration of complex scenarios such as the asteroid's irregular shape and spin characteristics, making it highly complex. The nuclear explosion method is the only means of deflecting the orbit of hazardous asteroids with short warning times and large structures. Other concepts are currently under development due to objective technological limitations.

[0043] The biggest advantage of kinetic impact and nuclear explosion methods compared to other methods is that they can utilize the impact or explosion to save mission execution time, making them technically feasible and eliminating the need for the reliability and stability guarantees required for long-term system operation, as with continuous deflection strategies. However, both methods involve significant uncertainties, and the energy released during the impact or explosion may exceed the asteroid's critical specific energy, increasing the risk of asteroid fragmentation and thus posing a greater threat. In contrast, the energy release of kinetic impact is far less than that of nuclear explosion. Although the deflection effect is worse than that of nuclear explosion, the uncertainty and uncontrollability of the impact are less, and the probability of asteroid fragmentation is also lower. Therefore, kinetic impact is currently the only option that comprehensively considers deflection effect, safety, and feasibility.

[0044] However, while kinetic impact methods have significant advantages over other strategies, they are limited by the payload capacity of launch vehicles, making them less effective against asteroids of larger mass and size. The impact process also carries the risk of asteroid fragmentation. Furthermore, actual impacts are subject to various real-world physical conditions, such as the uncertainty of spacecraft impact accuracy, leading to deviations in the final asteroid deflection from expectations. Additionally, developing asteroid defense strategies requires considering the complex dynamics of the space environment. Most asteroids have irregular shapes and structures, necessitating careful consideration of the specific scenarios in actual deflection missions to design effective and reasonable defense strategies.

[0045] To address the technical problem mentioned above, where spacecraft are subject to various real-world physical conditions during actual impacts, leading to deviations in the final deflection of asteroids from expectations, one embodiment of this application proposes an asteroid defense method considering irregular shapes and impact uncertainties, applied to a server. The implementation details of this embodiment's asteroid defense method considering irregular shapes and impact uncertainties are described below. These details are provided for ease of understanding and are not essential for implementing this solution. The specific flow of this embodiment's asteroid defense method considering irregular shapes and impact uncertainties can be as follows: Figure 1 As shown, it includes:

[0046] Step 101: Select the target asteroid with a polyhedral model and obtain the target asteroid's orbital parameters and model data.

[0047] In the specific implementation, because this application needs to consider the two major effects of the irregular shape and structure of the asteroid and the uncertainty of impact during spacecraft collision, this application only selects asteroids with polyhedral models as candidates. When selecting target asteroids, analysis of near-Earth objects can be performed on the NEODyS website (NearEarth Objects Dynamic Site) under the ESA (European Space Agency) to select suitable target asteroids.

[0048] In some cases, considering that larger hazardous asteroids pose a greater potential threat to Earth, when selecting target asteroids with polyhedral models, it is necessary to choose asteroids with an absolute magnitude of less than 24 (H < 24) and polyhedral models from among near-Earth objects. Such asteroids are larger in size, closer to Earth, and pose a greater potential threat to Earth, thus making the formulated defense strategy more valuable.

[0049] In some cases, after selecting a target asteroid, its orbital parameters and polyhedral model data can be downloaded from NASA's website. The target asteroid's orbital parameters include its semi-major axis (a), orbital eccentricity (e), orbital inclination (i), right ascension of the nodes (Ω), argument of perigee (ω), mean perigee (M), ephemeris, and time of minimum intercept distance (t). moid .

[0050] In some cases, the server selected Bennu as the target asteroid, with a mass denoted as m. p Its polyhedral model data can be as follows Figure 2 As shown, its orbital parameters are shown in Table 1 below.

[0051] Table 1: Orbital parameters of asteroid Bennu

[0052]

[0053] In Table 1, AU stands for Astronomical Unit, which is the average distance between the Earth and the Sun. MJD2000 refers to the number of days from 12:00:00 noon (UT) on January 1, 2000 (Greenwich Mean Time) to a specific date and time.

[0054] Step 102: Determine the state vector of the spacecraft when it reaches the target asteroid based on the Earth's orbital parameters, the target asteroid's orbital parameters, and the spacecraft's initial parameters.

[0055] Specifically, the deflection effect is determined by the impact location and impact force. The impact force is related to the mass and velocity of the spacecraft when it impacts the target asteroid, and is defined in this application as the state vector of the spacecraft when it arrives at the target asteroid. The server can determine the state vector of the spacecraft when it arrives at the target asteroid based on the Earth's orbital parameters, the target asteroid's orbital parameters, and the spacecraft's initial parameters.

[0056] In practical implementation, the state vector information of the spacecraft at the moment it leaves Earth's near-Earth orbit in the heliocentric inertial coordinate system—namely, its position and velocity vectors—is very similar to the Earth's state vector information in that coordinate system, and therefore can be considered identical. When the spacecraft departs from Earth at time t0 (leaving Earth's near-Earth orbit) and arrives at t... d When Earth reaches the target asteroid at time t0, this transfer phase can be calculated by examining the ephemeris of Earth and the target asteroid at those two moments to obtain the corresponding position and velocity vectors. The position and velocity vectors of Earth at time t0 are denoted as... and t d The position vector and velocity vector of the target asteroid at any given time are denoted as follows: and

[0057] Based on this, the velocity pulse sizes dv1 and dv2 required during the Lambert transfer process can be calculated using the following formulas:

[0058]

[0059] (dv1, dv2) = (V S，0 -V E，0 V N，d -V S，d )

[0060] In the formula, Lambert(·) represents the Lambert orbital transfer process. Let be the velocity vector of the spacecraft at time t0. For spacecraft in t d The velocity vector corresponding to each instant.

[0061] At this time, the spacecraft is at t d The effective remaining mass at the moment of arrival at the target asteroid can be calculated using the Tsiolkovsky formula. Assuming the additional velocity provided by the launch vehicle's payload unit when the spacecraft leaves Earth orbit is 2.5 km / s, the mass of the spacecraft at this moment can be calculated as follows:

[0062]

[0063] In the formula, m0 is the mass of the spacecraft at launch, and I sp Let g be the specific impulse of the spacecraft, g0 be the magnitude of the gravitational force in the space environment in which the spacecraft is located, and m1 be the magnitude of the gravitational force of the spacecraft at time t. d Effective remaining mass at any given time.

[0064] Since the purpose of this application is to deflect an asteroid by impact, the final stage of the transfer only needs to consider the positional constraints between the spacecraft and the target asteroid, that is, only the requirement of the initial velocity pulse dv1 of the transfer stage needs to be considered.

[0065] Therefore, the server can determine the state vector of the spacecraft when it arrives at the target asteroid based on the Earth's orbital parameters, the target asteroid's orbital parameters, and the spacecraft's initial parameters, including the spacecraft's initial mass and initial velocity pulse dv1.

[0066] Step 103, based on the state vector and the model data, using... Using the intersection function and Monte Carlo simulation algorithm, establish the functional relationship between the deflection amount and the first and second direction angles.

[0067] In practical implementation, after obtaining the state vector of the spacecraft upon arrival at the target asteroid, the server can utilize the state vector and the model data of the target asteroid's polyhedral model to... Using the intersection function and Monte Carlo simulation algorithm, a functional relationship between the deflection amount and the first and second direction angles is established. Here, the deflection amount is the amount of deflection of the target asteroid relative to its original orbit after being impacted by the spacecraft, and the first and second direction angles are used to define the position where the spacecraft impacts the target asteroid.

[0068] In some cases, the server utilizes the state vector of the spacecraft upon arrival at the target asteroid and model data from the polyhedral model of the target asteroid. By using the intersection function and Monte Carlo simulation algorithm, the functional relationship between the deflection and the first and second direction angles can be established. This can be achieved through methods such as... Figure 3The steps shown are implemented as follows:

[0069] Step 1031: Transform the state vector into the target asteroid's body coordinate system, introduce a first direction angle and a second direction angle to locate the impact ray when the spacecraft collides with the target asteroid, and utilize... The intersection algorithm determines the ideal hit point and the hit plane.

[0070] In practical implementation, considering that the radius of the target asteroid is negligible relative to the entire transfer path of the spacecraft, it can be assumed that the transfer path S between the spacecraft and the target asteroid at different impact locations is... Transfer The general principle is the same; the impact point of the spacecraft can be considered as any location on one side of its flight path. The specific effect is as follows: Figure 4 As shown. To facilitate calculations, the server can transform the spacecraft's state vector when it reaches the target asteroid to the target asteroid's body coordinate system O. A -X A V A Z A In the model, the polyhedral model of the target asteroid is represented in the body coordinate system. Its analytical representation can be achieved by introducing two azimuth angles in the body coordinate system, namely the first orientation angle. Second direction angle θ, The impact ray O at the time of spacecraft impacting the target asteroid can be located based on the first and second orientation angles. A P, server utilizes Find the intersection function to determine the ideal impact point and impact plane of the spacecraft hitting the target asteroid according to the impact ray.

[0071] Step 1032: Determine the incident velocity vector of the spacecraft when it collides with the target asteroid based on the incident ray and the state vector, and determine the momentum enhancement factor and its constraint conditions based on the incident velocity vector and the normal vector of the impact plane.

[0072] In practical implementation, the incident velocity vector at the moment of impact with the target asteroid can be calculated based on the impact ray and the state vector of the spacecraft when it reaches the target asteroid. The incident velocity vector is denoted as... During the final stage of the spacecraft's orbital transfer, the impact position on the target asteroid is random, but the impact direction follows the transfer law. That is, the spacecraft can only hit the target asteroid from one side of its flight direction. Therefore, this application sets a constraint condition for the momentum enhancement factor. The server can determine the momentum enhancement factor and its constraint condition based on the incident velocity vector and the normal vector of the impact plane.

[0073] In some cases, the server determines the momentum enhancement factor and its constraints based on the incident velocity vector and the normal vector of the impact plane using the following formula:

[0074]

[0075] In the formula, Let be the incident velocity vector. Let be the normal vector of the plane of impact, and β be the momentum enhancement factor. That is, the constraint condition for the momentum enhancement factor is set, and the actual manifestation of the constraint condition for the momentum enhancement factor can be as follows: Figure 5 As shown.

[0076] Step 1033: Establish a hit coordinate system based on the incident velocity vector and the ideal hit point. Use the Monte Carlo simulation algorithm to determine several simulated hit points that satisfy a two-dimensional Gaussian distribution on the hit plane, and determine the intersection elements of each simulated hit point and the model data in the hit coordinate system.

[0077] In the specific implementation, after the server determines the incident velocity vector when the spacecraft collides with the target asteroid, it can establish a collision coordinate system based on the incident velocity vector and the ideal impact point. The server uses the ideal impact point as the origin P, the direction pointing towards the north pole of the target asteroid as the N-axis, and the opposite direction of the incident velocity vector as the O-axis. The W-axis is then determined based on the N-axis and O-axis using the right-hand rule, resulting in the following coordinate system: Figure 6 The P-NOW hit coordinate system is shown. The NOW coordinate system is more suitable for establishing the hit coordinate system than the XYZ coordinate system.

[0078] After establishing the P-NOW hit coordinate system, the analysis and processing of the hit position uncertainty problem can be performed. The server assumes that the actual hit situation follows a two-dimensional Gaussian distribution under the hit plane. Therefore, the Monte Carlo simulation algorithm can be used to determine several simulated hit points that satisfy the two-dimensional Gaussian distribution on the hit plane (i.e., the NW plane of the P-NOW hit coordinate system), thus obtaining several sets of simulated hit point data that satisfy the two-dimensional Gaussian distribution. The server establishes an incident line perpendicular to the hit plane for each set of data, and then uses... The algorithm determines the intersection element F of each incident line and the model data. Pen And the hit location. Since the incident line will penetrate the model, the calculated number of intersecting surface elements Num(F) is used. Pen )≥2, but in reality, the spacecraft will only hit a single surface element in a single hit, and the priority is the surface element F with the largest hit value in the Outer direction of the hit location. Target That is, F Target =max{Outer i |F i ∈F Pen This allows for the analysis of hit problems across all simulated surface elements. Monte Carlo simulations can be performed as follows: Figure 7 As shown.

[0079] Step 1034: Calculate the expected value of the velocity increment at the ideal hit point based on the incident velocity vector, momentum enhancement factor, and the normal vector of the intersecting surface element corresponding to each simulated hit point.

[0080] In the specific implementation, the server calculates the expected velocity increment of the ideal hit point using the following formula, based on the incident velocity vector, momentum enhancement factor, and the normal vector of the intersecting surface element corresponding to each simulated hit point:

[0081]

[0082]

[0083] In the formula, γ is the mass ratio of the spacecraft to the target asteroid, and β is the momentum enhancement factor. Let be the incident velocity vector. Let P be the normal vector of the intersecting surface element corresponding to the g-th simulated hit point. g Let G be the Monte Carlo selection probability corresponding to the g-th simulated hit point, and G be the total number of simulated hit points. This represents the expected velocity increment at the ideal hit point. The distribution of the expected velocity increment at different ideal hit points is as follows: Figure 8 As shown.

[0084] Step 1035: Based on the expected value of the velocity increment and the deflection model corresponding to the target asteroid, establish the functional relationship between the deflection amount and the first and second direction angles.

[0085] Specifically, based on the expected value of the speed increment The deflection model T corresponding to the target asteroid can be used to calculate the deflection amount. The expected value of the velocity increment corresponds to an ideal hit point, which is actually determined by the first direction angle. The second direction angle θ is used for positioning. Based on this, the deflection amount can be established. Relative to the first direction angle The functional relationship between the second direction angle θ and the second direction angle.

[0086] In some cases, the deflection model T corresponding to the target asteroid can use the deflection model proposed by Colombo and Vasile. and G d They are represented as follows:

[0087]

[0088]

[0089] In the formula, the subscript d represents the time t during impact. d The parameter, the subscript moid in tmoid The parameters for the time are: a, b, p, e, i, Ω, w, and M, which are the orbital parameters of the target asteroid, where a is the semi-major axis, b is the semi-minor axis, p is the semi-path radius, e is the orbital eccentricity, i is the orbital inclination, Ω is the right ascension of the intersection point, ω is the argument of perigee, and M is the mean perigee angle. Used to determine whether the orbit is an elliptical orbit, Δt = t moid -t d ξ is the time of the deflection process, μ is the gravitational constant of the Sun, ξ is the true anomaly angle of the target asteroid's orbit, and h is the angular momentum. * =ξ+w, which is the angular distance of the ascending node at the corresponding time.

[0090] In some cases, the server establishes a functional relationship between the deflection amount and the first and second orientation angles based on the expected velocity increment and the deflection model corresponding to the target asteroid, using the following formula:

[0091]

[0092]

[0093]

[0094] In the formula, T represents the deflection model corresponding to the target asteroid. P is the expected velocity increment at the ideal hit point. Impact F represents the Monte Carlo selection probability corresponding to the ideal hit point. Target MC(•) represents the hit plane (intersecting element), MT(·) represents the Monte Carlo simulation algorithm, and MC(•) represents the intersecting element. Find the intersection function. Let θ be the first direction angle and θ be the second direction angle.

[0095] Based on this, the impact analysis of the uncertainty of the impact position is completed. The ideal impact point of the spacecraft defined by the first and second direction angles is only a theoretical value. In reality, the spacecraft may hit any position in its vicinity. Therefore, this application does not delve into the actual impact point of the spacecraft, but instead calculates the expected value of the velocity increment at the ideal impact point. The expected value of the velocity increment is used to represent the impact uncertainty. The deflection can be calculated through the expected value of the velocity increment, thereby obtaining the functional relationship between the deflection and the two direction angles.

[0096] Step 104: Optimize the functional relationship using a genetic algorithm to determine the optimal first direction angle and optimal second direction angle corresponding to the maximum value of the deflection, and formulate a defense strategy for the target asteroid based on the optimal first direction angle and optimal second direction angle.

[0097] In the specific implementation, after the server establishes the functional relationship between the deflection amount and the first and second direction angles, it then uses the GA (Genetic Algorithm) to optimize the functional relationship, which is expressed as follows: Based on this, the optimal first and second direction angles corresponding to the maximum value of the deflection are determined, and a defense strategy for the target asteroid is formulated according to the optimal first and second direction angles.

[0098] In some examples, the genetic algorithm parameters are set as follows: maximum number of generations is set to 1000, population size is set to 1000, crossover probability is set to 0.8, and tolerance is set to 1×10⁻⁶. -6 .

[0099] In practice, the optimal hit position can be determined based on the optimal first and optimal second orientation angles. By combining the initial mass of the spacecraft, the launch time of the spacecraft, and the initial velocity pulse of the spacecraft during the transfer phase, the optimal defense strategy can be formulated for the target asteroid to achieve the optimal deflection distance. This defense strategy takes into account the uncertainty of the hit, so even if the spacecraft does not hit the optimal hit position determined based on the optimal first and optimal second orientation angles, the optimal deflection distance can still be achieved.

[0100] In this embodiment, an asteroid with an irregular shape is selected as the defense target. A first azimuth angle and a second azimuth angle are introduced. The algorithm determines the ideal impact point and its corresponding impact plane, and analyzes the uncertainties of spacecraft impact on the impact plane based on Monte Carlo simulation. By establishing a functional relationship between deflection and two direction angles, the deflection capability of the spacecraft after impacting an asteroid at different impact angles is measured. Therefore, a defense strategy is formulated based on the first and second direction angles under optimal deflection capability. The formulated asteroid defense strategy conforms to the actual situation of asteroid and spacecraft impacts, providing a practical reference for the actual implementation of dangerous asteroid deflection missions. After the spacecraft impact, the asteroid achieves optimal deflection, significantly improving the defense capability against asteroids and reducing the threat of asteroids to Earth.

[0101] The steps of the various methods described above are only for clarity. In practice, they can be combined into one step or some steps can be split into multiple steps. As long as they include the same logical relationship, they are all within the scope of protection of this patent. Adding insignificant modifications or introducing insignificant designs to the algorithm or process, but without changing the core design of the algorithm and process, are also within the scope of protection of this patent.

[0102] Another embodiment of this application relates to an electronic device, such as... Figure 9As shown, it includes: at least one processor 201; and a memory 202 communicatively connected to the at least one processor 201; wherein the memory 202 stores instructions executable by the at least one processor 201, the instructions being executed by the at least one processor 201 to enable the at least one processor 201 to perform the asteroid defense methods considering irregular shapes and hit uncertainties in the above embodiments.

[0103] The memory and processor are connected via a bus, which can include any number of interconnecting buses and bridges, connecting various circuits of one or more processors and memories. The bus can also connect various other circuits, such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.

[0104] The processor manages the bus and general processing, and also provides various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory is used to store data used by the processor during operation.

[0105] Another embodiment of this application relates to a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements the method embodiments described above.

[0106] That is, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (which may be a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0107] Those skilled in the art will understand that the above embodiments are specific embodiments for implementing this application, and in practical applications, various changes can be made to them in form and detail without departing from the spirit and scope of this application.

Claims

1. An asteroid defense method considering irregular shape and impact uncertainty, characterized in that, include: Select a target asteroid with a polyhedral model and obtain the orbital parameters and model data of the target asteroid; Based on the Earth's orbital parameters, the target asteroid's orbital parameters, and the spacecraft's initial parameters, determine the spacecraft's state vector when it reaches the target asteroid; Based on the state vector and the model data, the Möller-Trumbore intersection function and Monte Carlo simulation algorithm are used to establish a functional relationship between the deflection amount and the first and second direction angles; wherein, the deflection amount is the deflection of the target asteroid relative to its original orbit after being impacted by the spacecraft, and the first and second direction angles are used to define the position where the spacecraft impacts the target asteroid; The genetic algorithm is used to optimize the functional relationship to determine the optimal first direction angle and the optimal second direction angle corresponding to the maximum value of the deflection, and a defense strategy for the target asteroid is formulated based on the optimal first direction angle and the optimal second direction angle.

2. The asteroid defense method considering irregular shape and impact uncertainty according to claim 1, characterized in that, The step of establishing a functional relationship between the deflection amount and the first and second direction angles based on the state vector and the model data, using the Möller-Trumbore intersection function and Monte Carlo simulation algorithm, includes: The state vector is transformed into the body coordinate system of the target asteroid, and a first direction angle and a second direction angle are introduced to locate the impact ray when the spacecraft impacts the target asteroid. The Möller-Trumbore intersection function is used to determine the ideal impact point and impact plane. The model data is expressed in the body coordinate system. The incident velocity vector of the spacecraft when it collides with the target asteroid is determined based on the incident velocity vector and the normal vector of the impact plane, and the momentum enhancement factor and its constraint conditions are determined based on the incident velocity vector and the normal vector of the impact plane. A hit coordinate system is established based on the incident velocity vector and the ideal hit point. A number of simulated hit points satisfying a two-dimensional Gaussian distribution are determined on the hit plane using the Monte Carlo simulation algorithm. The intersection elements of each simulated hit point and the model data are determined in the hit coordinate system. The expected value of the velocity increment at the ideal hit point is calculated based on the incident velocity vector, the momentum enhancement factor, and the normal vector of the intersecting surface element corresponding to each simulated hit point. Based on the expected velocity increment and the deflection model corresponding to the target asteroid, a functional relationship between the deflection amount and the first and second orientation angles is established.

3. The asteroid defense method considering irregular shape and impact uncertainty according to claim 2, characterized in that, The establishment of the hit coordinate system based on the incident velocity vector and the ideal hit point includes: The P-NOW hit coordinate system is established with the ideal hit point as the origin P, the direction pointing to the north pole of the target asteroid as the N axis, and the opposite direction of the incident velocity vector as the O axis. The W axis is determined based on the N axis and the O axis using the right-hand rule.

4. The asteroid defense method considering irregular shape and impact uncertainty according to claim 3, characterized in that, The momentum enhancement factor and its constraints are determined using the following formula, based on the incident velocity vector and the normal vector of the impact plane: ； in, Let be the incident velocity vector. Let be the normal vector of the hit plane. The momentum enhancement factor is denoted as .

5. The asteroid defense method considering irregular shape and impact uncertainty according to claim 3, characterized in that, The expected velocity increment of the ideal hit point is calculated using the following formula, based on the incident velocity vector, the momentum enhancement factor, and the normal vector of the intersecting surface element corresponding to each simulated hit point: ； ； in, The mass ratio of the spacecraft to the target asteroid. The momentum enhancement factor is... Let be the incident velocity vector. For the first The normal vector of the intersecting surface element corresponding to each simulated hit point. For the first The Monte Carlo selection probability corresponding to each simulated hit point The total number of simulated hit points. The velocity increment expected value for the ideal hit point.

6. The asteroid defense method considering irregular shape and impact uncertainty according to claim 5, characterized in that, The following formula establishes a functional relationship between the deflection amount and the first and second orientation angles, based on the expected velocity increment and the deflection model corresponding to the target asteroid: ； ； ； in, For deflection amount, The deflection model corresponding to the target asteroid. The Monte Carlo probability is selected for the ideal hit point. Indicates the hit plane, This refers to the Monte Carlo simulation algorithm. This represents the Möller–Trumbore intersection function. The first direction angle, This is the second direction angle.

7. The asteroid defense method considering irregular shape and impact uncertainty according to any one of claims 1 to 6, characterized in that, The parameters of the genetic algorithm are set as follows: maximum number of generations is set to 1000, population size is set to 1000, crossover probability is set to 0.8, and tolerance is set to... .

8. The asteroid defense method considering irregular shape and impact uncertainty according to any one of claims 1 to 6, characterized in that, The selected target asteroid with a polyhedral model includes: Among near-Earth objects, asteroids with an absolute magnitude of less than 24 and a polyhedral model were selected as target asteroids. The orbital parameters of the target asteroid include its semi-major axis. a Orbital eccentricity e Track inclination i Right ascension of the intersection Ω Perigeal argument ω , and the near point angle M Ephemeris and minimum orbital interception distance time .

9. An electronic device, characterized in that, include: At least one processor; as well as, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the asteroid defense method as described in any one of claims 1 to 8, taking into account irregular shapes and hit uncertainties.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements any one of the asteroid defense methods according to claims 1 to 8, taking into account irregular shapes and uncertainties in impact.

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