Asteroid defense window calculation method and device based on multi-segment pseudospectral method

Abstract

The application provides a kind of asteroid defense window calculation method and device based on multi-section pseudospectral method, it is related to the technical field of asteroid interception, comprising: obtaining step, obtaining target data, and constructing dynamics model based on target data;Calculation step, based on the dynamics model, construct two-sided Kepler motion interception problem, and based on the two-sided Kepler motion interception problem, solve the current constraint condition;Determination step, based on the constraint condition, preset performance index and multi-section pseudospectral algorithm, determine the optimal impact trajectory between asteroid and impactor;Repeat the obtaining step, calculation step and determination step until the number of repeated execution reaches the preset number, obtain multiple optimal trajectories;Based on multiple optimal trajectories, determine the subpoint trajectory coverage area of variable orbit arc segment of impactor on the original operating orbit, solve the technical problem of low calculation efficiency of the existing asteroid defense window calculation method.

Description

Technical Field

[0001] This invention relates to the technical field of asteroid interception, and in particular to a method and apparatus for calculating asteroid defense windows based on the multi-segment pseudospectral method. Background Technology

[0002] Missions designed to impact asteroids require the design of launch and impact points, including timing, location, velocity, and angle, as well as the determination of the entire flight trajectory. In the early stages of mission design, to avoid excessively redundant orbital evolution calculations, a fast search method can be employed. Some design principles in this process are similar to those used in fast rendezvous mission planning.

[0003] In solving rapid rendezvous and docking problems, the essence is to solve the aircraft trajectory optimization problem. Kim and Spencer used a genetic algorithm to solve the optimal rendezvous problem. However, the genetic algorithm has poor local search capabilities, making it time-consuming and inefficient in the later stages of evolution. Fabien et al. considered an optimal control problem with multiple constraints, including state and control constraints, using the idea of ​​penalty functions to implement the constraints and employing the direct multiple-shot method for solution. Bock et al. combined the direct multiple-shot method with quadratic programming, coupling the parameterization of the state differential equation and the control parameterization, making the resulting new problem suitable for solving with a recursive quadratic programming algorithm. This algorithm has global convergence and superlinear local convergence speed. Moltoda and Stengel applied a class of simulated annealing algorithms to design optimal control systems. However, because simulated annealing algorithms have limited knowledge of the entire search space, they are not conducive to entering the most promising search region, resulting in low computational efficiency and strong dependence on parameters.

[0004] No effective solutions have yet been proposed to address the above problems. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide an asteroid defense window calculation method and apparatus based on the multi-segment pseudospectral method, so as to alleviate the technical problem of low computational efficiency of existing asteroid defense window calculation methods.

[0006] In a first aspect, embodiments of the present invention provide a method for calculating an asteroid defense window based on a multi-segment pseudospectral algorithm, comprising: an acquisition step, acquiring target data and constructing a dynamic model based on the target data, wherein the target data includes: the position vector and velocity vector of the asteroid at the current moment, and the original orbital elements of the impactor; the dynamic model includes: a dynamic adjustment segment dynamic model and a gliding segment dynamic model; a calculation step, constructing a bilateral Kepler motion interception problem based on the dynamic model, and solving the current constraints based on the bilateral Kepler motion interception problem; a determination step, determining the optimal impact trajectory between the asteroid and the impactor based on the current constraints, preset performance indicators, and the multi-segment pseudospectral algorithm; repeating the acquisition step, the calculation step, and the determination step until the number of repetitions reaches a preset number, obtaining multiple optimal trajectories; and determining the sub-satellite point trajectory coverage area of ​​the variable orbit arc segment of the impactor on its original orbit based on the multiple optimal trajectories.

[0007] Furthermore, acquiring target data includes: treating the asteroid as a point mass in a Cartesian geocentric inertial frame and determining the asteroid's current position and velocity vectors; performing dynamic integration based on Kepler's equations and the asteroid's current position and velocity vectors to determine the asteroid's trajectory; and determining the impactor's original orbital elements based on the asteroid's trajectory.

[0008] Furthermore, based on the aforementioned dynamic model, a bilateral Keplerian motion interception problem is constructed, and based on the bilateral Keplerian motion interception problem, the current constraints are solved, including: determining the target parameters of the dynamic adjustment phase based on the dynamic model, wherein the target parameters include: optimized state variables, control variables, and additional parameters; constructing constraints based on the target parameters, and constructing the bilateral Keplerian motion interception problem based on the current constraints; determining the current constraints based on the impact conditions between the impactor and the asteroid in the bilateral Keplerian motion interception problem; wherein the state variables include: the position vector of the impactor in the dynamic adjustment phase, the velocity vector of the impactor in the dynamic adjustment phase, and the remaining fuel mass of the impactor in the dynamic adjustment phase; the control variable is the thrust direction vector of the impactor in the dynamic adjustment phase; the additional parameters include: the asteroid's orbital asymptote at the impact point between the impactor and the asteroid, the semi-circular diameter of the glide phase orbit, and the true asymptote of the impactor at the moment of entry into the dynamic adjustment phase.

[0009] Further, based on the current constraints, preset performance indicators, and a multi-segment pseudospectral algorithm, the optimal impact trajectory between the asteroid and the impactor is determined, including: solving the Lambert problem to determine the initial position and initial velocity of the impactor during the gliding phase based on the current constraints and the target data; determining the iterative calculation relationship of the current constraints based on the initial position and initial velocity of the impactor during the gliding phase; discretizing the preset performance indicators using the Lagrange pseudospectral algorithm to obtain discrete results, wherein the preset performance indicators are the minimum or maximum true anomaly angles at the moment the impactor enters the dynamic adjustment phase; calculating target parameters based on the iterative calculation relationship, the discrete results, the nonlinear dynamic equations, and the Lagrange interpolation polynomial, wherein the target parameters include: the optimal value of the state variables, the boundary conditions of the control variables, and the path constraints at the interpolation points; and determining the optimal impact trajectory between the asteroid and the impactor based on the target parameters.

[0010] Secondly, embodiments of the present invention also provide an asteroid defense window calculation device based on a multi-segment pseudospectral method, comprising: an acquisition unit, a calculation unit, a first determination unit, an execution unit, and a second determination unit, wherein the acquisition unit is used to perform an acquisition step, acquire target data, and construct a dynamic model based on the target data, wherein the target data includes: the position vector and velocity vector of the asteroid at the current moment, and the original orbital elements of the impactor, and the dynamic model includes: a dynamic adjustment segment dynamic model and a gliding segment dynamic model; the calculation unit is used to perform a calculation step, and construct a dynamic model based on the dynamic model. The problem involves a two-sided Kepler motion interception problem, and based on this problem, the current constraints are solved. The determining unit executes a determining step, based on the current constraints, preset performance indicators, and the Lardo pseudospectral algorithm, to determine the optimal impact trajectory between the asteroid and the impactor. The execution unit repeatedly executes the acquisition step, the calculation step, and the determining step until the number of repetitions reaches a preset number, resulting in multiple optimal trajectories. The second determining unit, based on these multiple optimal trajectories, determines the sub-satellite point trajectory coverage area of ​​the variable orbit arc segment of the impactor's original orbit.

[0011] Furthermore, the acquisition unit is configured to: treat the asteroid as a point mass in a Cartesian geocentric inertial frame and determine the position vector and velocity vector of the asteroid at the current moment; perform dynamic integration based on Kepler's equations and the position vector and velocity vector of the asteroid at the current moment to determine the trajectory of the asteroid; and determine the original orbital elements of the impactor based on the trajectory of the asteroid.

[0012] Further, the computing unit is used to: determine the target parameters of the dynamic adjustment phase based on the dynamic model, wherein the target parameters include: optimized state variables, control variables, and additional parameters; construct constraints based on the target parameters, and construct the bilateral Kepler motion interception problem based on the current constraints; determine the current constraints based on the impact conditions between the impactor and the asteroid in the bilateral Kepler motion interception problem; wherein the state variables include: the position vector of the impactor in the dynamic adjustment phase, the velocity vector of the impactor in the dynamic adjustment phase, and the remaining fuel mass of the impactor in the dynamic adjustment phase; the control variable is the thrust direction vector of the impactor in the dynamic adjustment phase; the additional parameters include: the apogee angle of the impact point between the impactor and the asteroid on the asteroid's orbit, the semi-circular diameter of the glide phase orbit, and the true apogee angle of the impactor when it enters the dynamic adjustment phase.

[0013] Further, the determining unit is configured to: solve for the initial position and initial velocity of the impactor during the gliding phase using the Lambert problem based on the current constraints and the target data; determine the iterative calculation relationship of the current constraints based on the initial position and initial velocity of the impactor during the gliding phase; discretize the preset performance index using the Lado pseudospectral algorithm to obtain discrete results, wherein the preset performance index is the minimum or maximum true anomaly angle of the impactor when it enters the dynamic adjustment phase; calculate the target parameters based on the iterative calculation relationship, the discrete results, the nonlinear dynamic equations, and the Lagrange interpolation polynomial, wherein the target parameters include: the optimal value of the state variable, the boundary conditions of the control variable, and the path constraint conditions at the interpolation points; and determine the optimal impact trajectory between the asteroid and the impactor based on the target parameters.

[0014] Thirdly, embodiments of the present invention also provide an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the method described in the first aspect above, and the processor is configured to execute the program stored in the memory.

[0015] Fourthly, embodiments of the present invention also provide a computer-readable storage medium on which a computer program is stored.

[0016] In this embodiment of the invention, the following steps are implemented: An acquisition step involves acquiring target data and constructing a dynamic model based on the target data. The target data includes the asteroid's current position and velocity vectors, and the original orbital elements of the impactor. The dynamic model includes a dynamic adjustment phase dynamic model and a gliding phase dynamic model. A calculation step involves constructing a bilateral Kepler motion interception problem based on the dynamic model and solving for the current constraints. A determination step involves determining the optimal impact trajectory between the asteroid and the impactor based on the current constraints, preset performance indicators, and a Gaussian pseudospectral algorithm. The acquisition, calculation, and determination steps are repeated until a preset number of repetitions are reached, resulting in multiple optimal trajectories. Based on these multiple optimal trajectories, the sub-satellite point trajectory coverage area of ​​the variable orbit arc segment on the impactor's original orbit is determined. This achieves the goal of quickly and accurately solving for the asteroid defense window, thereby solving the technical problem of low computational efficiency in existing asteroid defense window calculation methods and improving the computational efficiency and accuracy of asteroid defense window calculation methods.

[0017] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention are realized and obtained in accordance with the structures particularly pointed out in the description, claims and drawings.

[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0019] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0020] Figure 1 A flowchart illustrating the asteroid defense window calculation method based on the multi-segment pseudospectral method provided in this embodiment of the invention;

[0021] Figure 2 A schematic diagram of the original trajectory of the impactor and the possible trajectory of the asteroid provided for an embodiment of the present invention;

[0022] Figure 3 A schematic diagram illustrating the impact process between the impactor and the asteroid, provided in an embodiment of the present invention;

[0023] Figure 4 A schematic diagram of the optimal impact trajectory provided in an embodiment of the present invention;

[0024] Figure 5 A schematic diagram of an asteroid defense window calculation device based on the multi-segment pseudospectral method provided in an embodiment of the present invention;

[0025] Figure 6 This is a schematic diagram of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] Example 1:

[0028] According to an embodiment of the present invention, an embodiment of an asteroid defense window calculation method based on a multi-segment pseudospectral method is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0029] Figure 1 This is a flowchart of an asteroid defense window calculation method based on the multi-segment pseudospectral method according to an embodiment of the present invention, such as... Figure 1 As shown, the method includes the following steps:

[0030] Step S102, the acquisition step, acquires target data, and constructs a dynamic model based on the target data, wherein the target data includes: the position vector and velocity vector of the asteroid at the current moment, and the original orbital elements of the impactor; the dynamic model includes: a dynamic adjustment phase dynamic model and a gliding phase dynamic model.

[0031] Step S104, calculation step: Based on the dynamic model, construct a bilateral Kepler motion interception problem, and based on the bilateral Kepler motion interception problem, solve for the current constraint conditions;

[0032] Step S106, Determine the optimal impact trajectory between the asteroid and the impactor based on the current constraints, preset performance indicators and multi-segment pseudo-spectral algorithm;

[0033] Step S108: Repeat the acquisition step, the calculation step, and the determination step until the number of repetitions reaches a preset number, and obtain multiple optimal trajectories;

[0034] Step S110: Based on the multiple optimal trajectories, determine the sub-satellite point trajectory coverage area of ​​the variable trajectory arc segment of the impactor on the original operating trajectory.

[0035] In this embodiment of the invention, the following steps are implemented: An acquisition step involves acquiring target data and constructing a dynamic model based on the target data. The target data includes the asteroid's current position and velocity vectors, and the original orbital elements of the impactor. The dynamic model includes a dynamic adjustment segment dynamic model and a gliding segment dynamic model. A calculation step involves constructing a bilateral Kepler motion interception problem based on the dynamic model and solving for the current constraints. A determination step involves determining the optimal impact trajectory between the asteroid and the impactor based on the current constraints, preset performance indicators, and a multi-segment pseudospectral algorithm. The acquisition, calculation, and determination steps are repeated until a preset number of repetitions are reached, resulting in multiple optimal trajectories. Based on these multiple optimal trajectories, the sub-satellite point trajectory coverage area of ​​the variable orbit arc segment on the impactor's original orbit is determined. This achieves the goal of quickly and accurately solving for the asteroid defense window, thereby solving the technical problem of low computational efficiency in existing asteroid defense window calculation methods and improving the computational efficiency and accuracy of asteroid defense window calculation methods.

[0036] In this embodiment of the invention, step S102 includes the following steps:

[0037] In the Cartesian geocentric inertial frame, the asteroid is treated as a point mass, and its current position vector and velocity vector are determined.

[0038] Based on Kepler's equations and the asteroid's current position and velocity vectors, dynamic integration is performed to determine the asteroid's trajectory.

[0039] Based on the asteroid's trajectory, the original orbital elements of the impactor were determined.

[0040] In this embodiment of the invention, in the Cartesian geocentric inertial coordinate system (ECI), the asteroid is considered as a point mass, and according to the Kepler equations and the obtained asteroid state vector [r]... T0 ,v T0The target is discovered at time t0. Dynamic integration is performed to obtain the target's trajectory, and the state vector is converted into orbital elements through the function h.

[0041]

[0042]

[0043] In section 2, the impactor's mission is divided into two phases: the power adjustment phase and the gliding phase.

[0044] Dynamic model of the impactor's dynamic adjustment section:

[0045]

[0046]

[0047]

[0048] Where, r m =[x(t)y(t)z(t)] T It is a position vector, v m =[v x (t) v y (t) v z (t)] T It is a velocity vector, μ is the Earth's gravitational constant, T is the vacuum thrust, m is the impactor mass, g0 is the gravitational acceleration at sea level, and I sp It is the engine's specific impulse, u = [u x (t) u y (t) u z (t)] T It is the direction of thrust.

[0049] like Figure 2 As shown, Figure 2 The solid line represents the impactor's original trajectory, while the multiple dashed lines represent the possible trajectories of the incoming asteroid.

[0050] In this embodiment of the invention, step S104 includes the following steps:

[0051] Based on the kinematic model, the target parameters for the dynamic adjustment segment are determined, wherein the target parameters include: optimized state variables, control variables, and additional parameters;

[0052] Based on the target parameters, constraints are constructed, and based on the current constraints, the bilateral Kepler motion interception problem is constructed.

[0053] Based on the aforementioned bilateral Keplerian motion interception problem, the impact conditions between the impactor and the asteroid are determined, and the current constraint conditions are established.

[0054] The state quantities include: the position vector of the impactor in the power adjustment section, the velocity vector of the impactor in the power adjustment section, and the remaining fuel mass of the impactor in the power adjustment section;

[0055] The control quantity is the thrust direction vector of the impactor in the power adjustment section;

[0056] The additional parameters include: the angle of asteroid's orbit at the point of impact between the impactor and the asteroid, the semi-circular diameter of the glide phase orbit, and the true angle of asteroid's orbit at the moment the impactor enters the dynamic adjustment phase.

[0057] In this embodiment of the invention, the dynamic adjustment section is optimized, and the optimized state variable x is the impactor position vector r. m Velocity vector v m The remaining fuel mass *m* is used as the control variable, and the thrust direction vector *u* is used as the control variable. Simultaneously, parameters to be optimized are introduced: the apogee angle *E* of the impact point (PIP) on the asteroid orbit, the semi-circular diameter *p* of the glide segment orbit, and the true apogee angle *θ0* on the initial orbit when the impactor begins its dynamic maneuver. The impactor's maneuver time is *t0*, and the final time of the impactor's dynamic maneuver is *t*. f .

[0058] The current constraints are as follows.

[0059] Initial constraints:

[0060]

[0061] The function f converts the orbital elements coe0 and the true anterior angle θ0 into the impactor state vector.

[0062] Process constraints:

[0063]

[0064] Terminal constraints:

[0065]

[0066] After the impactor completes its power adjustment phase, it enters the second glide phase, beginning Keplerian motion. The asteroid continues this Keplerian motion, and the second phase begins at time t. f When the remaining flight time, the location and velocity of the point of impact (PIP) are all left unsaid, this type of problem is called a two-sided Keplerian motion interception problem, which can be represented as follows:

[0067] Asteroid: Initial time is t0, total flight time is Δt, final position is r. T (t0+Δt);

[0068] Impactor: The initial time of the power segment is t0, and the end time of the power segment is t. f The second stage gliding duration is Δt. trans The final position of the entire process is r. M (t f +Δt trans );

[0069] Based on the impact conditions, the following current constraints can be obtained:

[0070]

[0071] In this embodiment of the invention, step S106 includes the following steps:

[0072] Based on the current constraints and the target data, the initial position and initial velocity of the impactor during the glide phase are solved using the Lambert problem.

[0073] Based on the initial position and initial velocity of the impactor during the gliding phase, the iterative calculation relationship of the current constraint conditions is determined;

[0074] The preset performance indicators are discretized using the Lado pseudospectral algorithm to obtain discrete results. The preset performance indicators include the minimum true anterior angle and the maximum true anterior angle of the impactor when it enters the dynamic adjustment phase.

[0075] Based on the iterative calculation relationship, the discrete results, the nonlinear dynamic equation, and the Lagrange interpolation polynomial, the target parameters are calculated, wherein the target parameters include: the optimal value of the state variable, the boundary conditions of the control variable, and the path constraint conditions at the interpolation point;

[0076] Based on the target parameters, the optimal impact trajectory between the asteroid and the impactor is determined.

[0077] In an embodiment of the present invention, t f ,r f ,v f For the terminal constraint conditions of the impactor's power section, combined with Figure 3 The relationships between variables and collision constraints are determined, and the Lambert problem is solved. Further, the iterative relationship of the terminal constraints is derived. The specific process is as follows:

[0078] Given that the impactor is undergoing Keplerian motion in a circular orbit, and the true anomaly angle at the moment of orbit change is θ0, combined with the input initial orbital elements ceo0 (specific angular momentum modulus h, eccentricity e, orbital inclination i, perigee argument ω, and right ascension of the ascending node Ω), the state vector of the impactor at the moment of orbit change can be calculated [r]. M0 ,v M0 ].

[0079] coe0=[h,e,i,ω,Ω] (10)

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] With [r M0 ,v M0 [Initial state, flying under control u] f Time to r f The position is then glided along a transfer trajectory with a semi-major diameter of p to the PIP position r. PIP According to [r] T0 ,v T0 r is calculated from the approach angle E of the PIP on the target orbit. PIP .

[0086] coe T =[h T ,e T i T ,ω T ,Ω T ]

[0087] coe T =h(r T0 ,v T0 ,μ) (15)

[0088]

[0089] M PIP =Ee T sinE (17)

[0090]

[0091]

[0092]

[0093]

[0094] M ZXZ =M Z (Ω)M X (i)M Z (ω,θPIP (19)

[0095]

[0096] Based on the above derivation, the initial position and velocity of the impactor during the gliding phase are obtained by solving the Lambert problem. Since the flight trajectory is continuous, the initial state of this gliding phase is the terminal state r of the power adjustment phase. f ,v f Let the true approach angle Δθ of the impactor in the final segment and the position r at the end of the segment be... PIP and gliding time Δt trans and the Lagrange coefficient The following relationship can be established

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104] At this point, the iterative calculation relationship of the terminal constraints can be established.

[0105] t f -t0=Δt-Δt trans (28)

[0106]

[0107] The true anterior angle θ0 at the moment when the preset performance index enters the dynamic adjustment phase is discretized using the pseudospectral algorithm, and the discretized result is as follows:

[0108] J = θ0, J = -θ0 (30)

[0109] First, the generalized nonlinear system dynamics equations

[0110]

[0111] Where the state variable x(t)∈R n The control quantity u(t)∈R m Time t∈[t0,t 2 ].

[0112] The time domain is then shifted to the time interval [-1,1] because the support points of the Lagrange interpolation polynomial are chosen as orthogonal points in the time interval [-1,1], which is accomplished by the following mapping function.

[0113]

[0114] Taking τ as the independent variable, the state variable and the control variable are approximately represented by Lagrange interpolation polynomials.

[0115]

[0116]

[0117]

[0118]

[0119] It can be known that L i (τ) and L i * (τ) has the following properties

[0120]

[0121] Differentiating the approximate expressions for the state variables and control variables yields...

[0122]

[0123] and It can be obtained offline using the following formula.

[0124]

[0125] Thus, the constraints of the dynamic differential equations are transformed into algebraic constraints.

[0126]

[0127] The final state, approximated by integration, should satisfy the following conditions:

[0128]

[0129] Performance metrics are also approximated using integration.

[0130]

[0131] Where ω k These are Gaussian weights.

[0132] After the above processing, the optimal control problem is transformed into finding the optimal value X of the state variable. i(i = 0, ..., N) and boundary conditions of control quantities

[0133]

[0134] and path constraints at interpolation points

[0135] C(X k U k ,τ k ;t0,t f )≤0 (k=1,..,N) (44)

[0136] This transforms the optimal control problem into a nonlinear programming problem, and then, based on the optimal values ​​of the state variables, the boundary conditions of the control variables, and the path constraints at the interpolation points, the optimal impact trajectory between the asteroid and the impactor is determined.

[0137] Finally, repeat steps S102-S106 above, as follows: Figure 4 The optimal impact trajectory corresponding to all possible trajectories of the asteroid is obtained. Then, based on multiple optimal trajectories, the sub-planetary point trajectory coverage area of ​​the variable orbit arc segment of the impactor on the original orbit is determined.

[0138] In this embodiment of the invention, a multi-segment pseudospectral optimization algorithm is used to discretize the state and control variables of the optimal control problem on a series of LG collocation points. These collocation points are then used to construct a Lagrange interpolation polynomial to approximate the state and control variables. By differentiating the global interpolation polynomial, the time derivative of the state variables is approximated, thereby transforming the differential equation constraints into a set of algebraic constraints. This enables the determination of a collision window that satisfies multiple constraints and allows for impacting multiple incoming asteroids in a short time.

[0139] Example 2:

[0140] This invention also provides an asteroid defense window calculation device based on the multi-segment pseudospectral method. This device is used to execute the asteroid defense window calculation method based on the multi-segment pseudospectral method provided in the above-described embodiments of this invention. The following is a detailed description of the device provided in this invention.

[0141] like Figure 5 As shown, Figure 5 The above-mentioned asteroid defense window calculation device based on the multi-segment pseudo-spectral method includes: an acquisition unit 10, a calculation unit 20, a first determination unit 30, an execution unit 40, and a second determination unit 50.

[0142] The acquisition unit is used to perform the acquisition steps, acquire target data, and construct a dynamic model based on the target data. The target data includes: the position vector and velocity vector of the asteroid at the current moment, and the original orbital elements of the impactor. The dynamic model includes: a dynamic adjustment phase dynamic model and a gliding phase dynamic model.

[0143] The computing unit is used to perform computing steps, construct a bilateral Kepler motion interception problem based on the dynamic model, and solve the current constraint conditions based on the bilateral Kepler motion interception problem.

[0144] The determining unit is used to perform the determining steps, and determine the optimal impact trajectory between the asteroid and the impactor based on the current constraints, preset performance indicators and multi-segment pseudo-spectral algorithm.

[0145] The execution unit is used to repeatedly execute the acquisition step, the calculation step, and the determination step until the number of repetitions reaches a preset number, thereby obtaining multiple optimal trajectories.

[0146] The second determining unit is used to determine the sub-satellite point trajectory coverage area of ​​the variable trajectory arc segment of the impactor on the original operating trajectory based on the multiple optimal trajectories.

[0147] In this embodiment of the invention, the following steps are implemented: An acquisition step involves acquiring target data and constructing a dynamic model based on the target data. The target data includes the asteroid's current position and velocity vectors, and the original orbital elements of the impactor. The dynamic model includes a dynamic adjustment segment dynamic model and a gliding segment dynamic model. A calculation step involves constructing a bilateral Kepler motion interception problem based on the dynamic model and solving for the current constraints. A determination step involves determining the optimal impact trajectory between the asteroid and the impactor based on the current constraints, preset performance indicators, and a multi-segment pseudospectral algorithm. The acquisition, calculation, and determination steps are repeated until a preset number of repetitions are reached, resulting in multiple optimal trajectories. Based on these multiple optimal trajectories, the sub-satellite point trajectory coverage area of ​​the variable orbit arc segment on the impactor's original orbit is determined. This achieves the goal of quickly and accurately solving for the asteroid defense window, thereby solving the technical problem of low computational efficiency in existing asteroid defense window calculation methods and improving the computational efficiency and accuracy of asteroid defense window calculation methods.

[0148] Example 3:

[0149] This invention also provides an electronic device, including a memory and a processor. The memory is used to store a program that supports the processor in executing the method described in Embodiment 1 above, and the processor is configured to execute the program stored in the memory.

[0150] See Figure 6 This invention also provides an electronic device 100, including: a processor 60, a memory 61, a bus 62 and a communication interface 63, wherein the processor 60, the communication interface 63 and the memory 61 are connected through the bus 62; the processor 60 is used to execute executable modules, such as computer programs, stored in the memory 61.

[0151] The memory 61 may include high-speed random access memory (RAM) or non-volatile memory, such as at least one disk storage device. Communication between this system network element and at least one other network element is achieved through at least one communication interface 63 (which can be wired or wireless), such as the Internet, wide area network, local area network, metropolitan area network, etc.

[0152] Bus 62 can be an ISA bus, PCI bus, or EISA bus, etc. The bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 6 The symbol is represented by a single double-headed arrow, but this does not mean that there is only one bus or one type of bus.

[0153] The memory 61 is used to store programs. After receiving an execution instruction, the processor 60 executes the program. The method executed by the device for defining the flow process disclosed in any of the foregoing embodiments of the present invention can be applied to the processor 60 or implemented by the processor 60.

[0154] Processor 60 may be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method can be completed by the integrated logic circuitry in the hardware of processor 60 or by instructions in software form. Processor 60 can be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), etc.; it can also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this invention. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this invention can be directly embodied in the execution of a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. The storage medium is located in memory 61. Processor 60 reads the information in memory 61 and, in conjunction with its hardware, completes the steps of the above method.

[0155] Example 4:

[0156] This invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the steps of the method described in Embodiment 1 above.

[0157] Furthermore, in the description of the embodiments of the present invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention based on the specific circumstances.

[0158] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0159] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Additionally, the shown or discussed mutual couplings, direct couplings, or communication connections may be through some communication interfaces; indirect couplings or communication connections between devices or units may be electrical, mechanical, or other forms.

[0160] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0161] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0162] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for calculating asteroid defense windows based on the multi-segment pseudospectral method, characterized in that, include: The acquisition steps involve acquiring target data and constructing a dynamic model based on the target data. The target data includes: the current position vector and velocity vector of the asteroid, and the original orbital elements of the impactor. The dynamic model includes: a dynamic adjustment phase dynamic model and a gliding phase dynamic model. The calculation steps, based on the dynamic model, construct a bilateral Keplerian motion interception problem, and based on the bilateral Keplerian motion interception problem, solve for the current constraints, including: determining the target parameters of the dynamic adjustment phase based on the dynamic model, wherein the target parameters include: optimized state variables, control variables, and additional parameters; constructing constraints based on the target parameters, and constructing the bilateral Keplerian motion interception problem based on the current constraints; determining the current constraints based on the impact conditions between the impactor and the asteroid in the bilateral Keplerian motion interception problem; wherein the state variables include: the position vector of the impactor in the dynamic adjustment phase, the velocity vector of the impactor in the dynamic adjustment phase, and the remaining fuel mass of the impactor in the dynamic adjustment phase; the control variable is the thrust direction vector of the impactor in the dynamic adjustment phase; the additional parameters include: the asteroid's orbital asymptote at the impact point between the impactor and the asteroid, the semi-circular diameter of the glide phase orbit, and the true asymptote of the impactor at the moment of entry into the dynamic adjustment phase; The determination steps, based on the current constraints, preset performance indicators, and a multi-segment pseudospectral algorithm, determine the optimal impact trajectory between the asteroid and the impactor. These steps include: solving the Lambert problem to determine the initial position and initial velocity of the impactor during the gliding phase based on the current constraints and the target data; determining the iterative calculation relationship of the current constraints based on the initial position and initial velocity of the impactor during the gliding phase; discretizing the preset performance indicators using the pseudospectral algorithm to obtain discrete results, where the preset performance indicators are the minimum and maximum true anomaly angles of the impactor when it enters the dynamic adjustment phase; calculating target parameters based on the iterative calculation relationship, the discrete results, the nonlinear dynamic equations, and the Lagrange interpolation polynomial, where the target parameters include: the optimal values ​​of the state variables, the boundary conditions of the control variables, and the path constraints at the interpolation points; and determining the optimal impact trajectory between the asteroid and the impactor based on the target parameters. Repeat the acquisition step, the calculation step, and the determination step until the number of repetitions reaches a preset number, to obtain multiple optimal trajectories; Based on the multiple optimal trajectories, the sub-satellite point trajectory coverage area of ​​the variable trajectory arc segment on the original operating trajectory of the impactor is determined.

2. The method according to claim 1, characterized in that, Obtain the target data, including: In the Cartesian geocentric inertial frame, the asteroid is treated as a point mass, and its current position vector and velocity vector are determined. Based on Kepler's equations and the asteroid's current position and velocity vectors, dynamic integration is performed to determine the asteroid's trajectory. Based on the asteroid's trajectory, the original orbital elements of the impactor were determined.

3. A computational device for asteroid defense window based on the multi-segment pseudospectral method for executing the method according to any one of claims 1 to 2, characterized in that, include: The unit comprises an acquisition unit, a calculation unit, a first determining unit, an execution unit, and a second determining unit, wherein... The acquisition unit is used to perform the acquisition steps, acquire target data, and construct a dynamic model based on the target data. The target data includes: the position vector and velocity vector of the asteroid at the current moment, and the original orbital elements of the impactor. The dynamic model includes: a dynamic adjustment phase dynamic model and a gliding phase dynamic model. The computing unit is used to perform computing steps, construct a bilateral Kepler motion interception problem based on the dynamic model, and solve the current constraint conditions based on the bilateral Kepler motion interception problem. The determining unit is used to perform the determining step, which determines the optimal impact trajectory between the asteroid and the impactor based on the current constraints, preset performance indicators and the Lardo pseudospectral algorithm. The execution unit is used to repeatedly execute the acquisition step, the calculation step, and the determination step until the number of repetitions reaches a preset number, thereby obtaining multiple optimal trajectories. The second determining unit is used to determine the sub-satellite point trajectory coverage area of ​​the variable trajectory arc segment of the impactor on the original operating trajectory based on the multiple optimal trajectories.

4. The apparatus according to claim 3, characterized in that, The acquisition unit is used for: In the Cartesian geocentric inertial frame, the asteroid is treated as a point mass, and its current position vector and velocity vector are determined. Based on Kepler's equations and the asteroid's current position and velocity vectors, dynamic integration is performed to determine the asteroid's trajectory. Based on the asteroid's trajectory, the original orbital elements of the impactor were determined.

5. The apparatus according to claim 3, characterized in that, The computing unit is used for: Based on the aforementioned dynamic model, the target parameters for the dynamic adjustment segment are determined, wherein the target parameters include: optimized state variables, control variables, and additional parameters; Based on the target parameters, constraints are constructed, and based on the current constraints, the bilateral Kepler motion interception problem is constructed. Based on the aforementioned bilateral Keplerian motion interception problem, the impact conditions between the impactor and the asteroid are determined, and the current constraint conditions are established. The state quantities include: the position vector of the impactor in the power adjustment section, the velocity vector of the impactor in the power adjustment section, and the remaining fuel mass of the impactor in the power adjustment section; The control quantity is the thrust direction vector of the impactor in the power adjustment section; The additional parameters include: the angle of asteroid's orbit at the point of impact between the impactor and the asteroid, the semi-circular diameter of the glide phase orbit, and the true angle of asteroid's orbit at the moment the impactor enters the dynamic adjustment phase.

6. The apparatus according to claim 5, characterized in that, The determining unit is used for: Based on the current constraints and the target data, the initial position and initial velocity of the impactor during the glide phase are solved using the Lambert problem. Based on the initial position and initial velocity of the impactor during the gliding phase, the iterative calculation relationship of the current constraint conditions is determined; The preset performance index is discretized using the Lado pseudospectral algorithm to obtain a discrete result, wherein the preset performance index is the minimum or maximum true perimeter angle of the impactor when it enters the dynamic adjustment phase. Based on the iterative calculation relationship, the discrete results, the nonlinear dynamic equation, and the Lagrange interpolation polynomial, the target parameters are calculated, wherein the target parameters include: the optimal value of the state variable, the boundary conditions of the control variable, and the path constraint conditions at the interpolation point; Based on the target parameters, the optimal impact trajectory between the asteroid and the impactor is determined.

7. An electronic device, characterized in that, The device includes a memory and a processor, the memory being used to store a program that enables the processor to execute the method of any one of claims 1 to 2, and the processor being configured to execute the program stored in the memory.

8. A computer-readable storage medium storing a computer program thereon, characterized in that, When a computer program is run by a processor, it performs the steps of the method described in any one of claims 1 to 2.

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