A Pseudo-Spectral Orbit Optimization Method and Device for Kinetic Energy Impact on Asteroids

Abstract

The present invention provides a pseudo-spectral orbit optimization method and device for kinetic energy impact on asteroids, which relates to the technical field of asteroid interception, and includes: constructing a multi-sided Keplerian motion rendezvous problem based on the motion parameters of the impactor, the motion parameters of the asteroid, and the target parameters of the powered adjustment section, and determining the terminal constraint conditions of the powered adjustment section by considering the impact conditions between the impactor and the asteroid based on the constraints of the multi-sided Keplerian motion rendezvous problem; optimizing the target parameters of the impactor based on the terminal constraint conditions, preset performance indicators, and multi-segment pseudo-spectral optimization algorithm to obtain optimized parameters; performing dynamic integration on the glide section based on the optimized parameters to obtain the motion trajectory of the impactor; and determining the motion trajectory diagram of the impact process between the impactor and the asteroid based on the motion trajectory of the impactor and the running trajectory of the asteroid, thereby solving the technical problem of the low efficiency and accuracy of the existing orbit determination method for kinetic energy impact on asteroids.

Description

Technical Field

[0001] The present invention relates to the technical field of asteroid interception, and in particular, to a pseudo-spectral orbit optimization method and device for kinetic energy impact on asteroids. Background Technique

[0002] For the kinetic energy impact on asteroids mission, it is essentially a multi-stage, multi-variable, and multi-constraint optimization problem. Currently, there are relevant research progresses on the trajectory optimization problem of the aircraft. For example, Sentinella et al. first used the indirect method to transform the electric propulsion orbit optimization problem into a boundary value problem, then used the genetic algorithm to find the parameters that satisfy the boundary value conditions and minimize the error, and then used the obtained optimal parameters as the initial values of the indirect method to gradually converge to the optimal solution. However, the disadvantage of the indirect method is that it is necessary to estimate the co-state variables and has a high requirement for the guess of the initial values. Wang Hua et al. solved the trajectory optimization problem under thrust limitation by the direct shooting method, gave the transformation process from the optimal control problem to the parameter optimization problem, and also transformed the state and control constraints. This method has been successfully applied to the solution of the rendezvous and docking problem. However, the limitation of the direct method is that most direct methods cannot give the co-state information, so the optimality of the solution cannot be guaranteed. Dueri et al. studied the problem of planetary soft landing. First, the problem was transformed into a convex second-order cone problem, so as to ensure the global optimality of the solution, and then an interior point method was introduced and a real-time calculation framework was given. Wong et al. studied the combined algorithm of parallel tangent and penalty function, and used the penalty function to handle the terminal constraints to accelerate the convergence. In addition, the common optimization algorithms also include the particle swarm algorithm. However, it is prone to premature convergence, especially in dealing with complex multi-peak search problems. And the particle swarm algorithm has problems such as poor local optimization ability and falling into local minimum.

[0003] In view of the above problems, no effective solution has been proposed yet. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a pseudo-spectral orbit optimization method and device for kinetic energy impact on asteroids, so as to alleviate the technical problems of low efficiency and low accuracy of the existing orbit determination method for kinetic energy impact on asteroids.

[0005] In a first aspect, an embodiment of the present invention provides a pseudo-spectral orbit optimization method for kinetic energy impact on an asteroid, including: obtaining the motion parameters of the impactor and the motion parameters of the asteroid, and designing the target parameters of the power adjustment section of the impactor, where the target parameters include: optimized state variables, control variables, and additional parameters; based on the motion parameters of the impactor, the motion parameters of the asteroid, and the target parameters of the power adjustment section, constructing a multi-sided Keplerian motion rendezvous problem, and based on the multi-sided Keplerian motion rendezvous problem and the impact condition between the impactor and the asteroid, determining the terminal constraint conditions of the power adjustment section; based on the terminal constraint conditions, a preset performance index, and a multi-segment pseudo-spectral optimization algorithm, optimizing the target parameters of the impactor to obtain optimized parameters, where the target parameters include: altitude change parameters, velocity change parameters, thrust direction change parameters, and fuel mass change parameters; based on the optimized parameters, performing dynamic integration on the glide section to obtain the motion trajectory of the impactor; based on the motion trajectory of the impactor and the running trajectory of the asteroid, determining the motion trajectory diagram of the impact process between the impactor and the asteroid.

[0006] Further, if the motion parameters of the impactor are the initial position of the impactor, the initial velocity of the impactor, and the power configuration parameters of the impactor, and the motion parameters of the asteroid are the initial position of the asteroid and the initial velocity of the asteroid, then constructing a multi-sided Keplerian motion rendezvous problem based on the motion parameters of the impactor, the motion parameters of the asteroid, and the target parameters of the power adjustment section includes: constructing a first kinematic model of the impactor based on the motion parameters of the impactor and the motion parameters of the asteroid; constructing a multi-sided Keplerian motion rendezvous problem based on the first kinematic model of the impactor and the target parameters of the power adjustment section; and determining the first terminal constraint conditions of the power adjustment section based on the multi-sided Keplerian motion rendezvous problem and the impact condition between the impactor and the asteroid.

[0007] Further, optimizing the target parameters of the impactor to obtain optimized parameters based on the terminal constraint conditions, a preset performance index, and a pseudo-spectral optimization algorithm includes: determining the earliest impact time between the asteroid and the impactor, the latest impact time between the asteroid and the impactor, the maximum fuel consumption of the impactor, and the minimum fuel consumption of the impactor as the first preset performance index; performing Gaussian pseudo-spectral discretization processing on the first preset performance index to determine the first optimized parameters.

[0008] Further, based on the optimized parameters, perform dynamic integration on the glide segment to obtain the motion trajectory of the impactor, including: determining a first optimal impact eccentric anomaly based on the first optimized parameter; calculating an optimal flight time of the impactor based on the first optimal impact eccentric anomaly; performing dynamic integration on the glide segment based on the optimal flight time, the first terminal constraint condition, and the two-body kinematic equation to obtain a first motion trajectory of the impactor.

[0009] Further, if the impactor motion parameters further include the time required for the impactor to hit the asteroid, and the asteroid motion parameters are the initial position and initial velocity of the asteroid, then based on the impactor motion parameters, the asteroid motion parameters, and the target parameters of the power adjustment segment, construct a multi-sided Keplerian motion rendezvous problem, including: constructing a second kinematic model of the impactor based on the impactor motion parameters and the asteroid motion parameters; constructing a one-sided Kepler problem based on the first kinematic model of the impactor and the target parameters of the power adjustment segment; determining a second terminal constraint condition of the power adjustment segment based on the one-sided Kepler problem and the impact condition between the impactor and the asteroid.

[0010] Further, based on the terminal constraint condition, a preset performance index, and a multi-segment pseudospectral optimization algorithm, optimize the target parameters of the impactor to obtain optimized parameters, including: determining the minimum fuel consumption of the impactor as a second preset performance index; performing Gaussian pseudospectral discretization processing on the second preset performance index to determine a second optimized parameter.

[0011] Further, based on the optimized parameters, perform dynamic integration on the glide segment to obtain the motion trajectory of the impactor, including: performing dynamic integration on the glide segment based on the time required for the impactor to hit the asteroid, the second optimized parameter, the second terminal constraint condition, and the two-body kinematic equation to obtain a second motion trajectory of the impactor.

[0012] Further, based on the motion trajectory of the impactor and the running trajectory of the asteroid, determine a motion trajectory diagram of the impact process between the impactor and the asteroid, including: performing dynamic integration on the asteroid motion parameters to obtain the running trajectory of the asteroid; determining a motion trajectory diagram of the impact process between the impactor and the asteroid based on the motion trajectory of the impactor and the running trajectory of the asteroid.

[0013] Second aspect, an embodiment of the present invention further provides a pseudo-spectral orbit optimization device for kinetic energy impact on an asteroid, including: an acquisition unit, a construction unit, an optimization unit, an integration unit, and a determination unit, where the acquisition unit is configured to acquire the impactor motion parameters and the asteroid motion parameters, and design the target parameters of the power adjustment section of the impactor, where the target parameters include: optimized state variables, control variables, and additional parameters; the construction unit is configured to construct a multi-sided Keplerian motion rendezvous problem based on the impactor motion parameters, the asteroid motion parameters, and the target parameters of the power adjustment section, and determine the terminal constraint conditions of the power adjustment section based on the multi-sided Keplerian motion rendezvous problem and the impact conditions between the impactor and the asteroid; the optimization unit is configured to optimize the target parameters of the impactor based on the terminal constraint conditions, a preset performance index, and a multi-segment pseudo-spectral optimization algorithm to obtain optimized parameters, where the target parameters include: altitude change parameters, velocity change parameters, thrust direction change parameters, and fuel mass change parameters; the integration unit is configured to perform dynamic integration on the glide section based on the optimized parameters to obtain the motion trajectory of the impactor; the determination unit is configured to determine the motion trajectory diagram of the impact process between the impactor and the asteroid based on the motion trajectory of the impactor and the running trajectory of the asteroid.

[0014] Third aspect, an embodiment of the present invention further provides an electronic device, including a memory and a processor, where the memory is used to store a program for supporting the processor to execute the method described in the first aspect above, and the processor is configured to execute the program stored in the memory.

[0015] Fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored.

[0016] In an embodiment of the present invention, by obtaining the impactor motion parameters and the asteroid motion parameters, and designing the target parameters of the power adjustment section of the impactor, where the target parameters include: optimized state variables, control variables, and additional parameters; based on the impactor motion parameters, the asteroid motion parameters, and the target parameters of the power adjustment section, a multi-sided Keplerian motion rendezvous problem is constructed, and based on the multi-sided Keplerian motion rendezvous problem and the impact condition between the impactor and the asteroid, the terminal constraint conditions of the power adjustment section are determined; based on the terminal constraint conditions, preset performance indicators, and a multi-segment pseudospectral optimization algorithm, the target parameters of the impactor are optimized to obtain optimized parameters, where the target parameters include: altitude change parameters, velocity change parameters, thrust direction change parameters, and fuel mass change parameters; based on the optimized parameters, dynamic integration is performed on the glide section to obtain the motion trajectory of the impactor; based on the motion trajectory of the impactor and the orbit of the asteroid, the motion trajectory diagram of the impact process between the impactor and the asteroid is determined, achieving the purpose of accurately and efficiently determining the orbit of the impactor's kinetic energy impact on the asteroid, and further solving the technical problem of the low efficiency and accuracy of the existing orbit determination method for the kinetic energy impact on the asteroid, thereby realizing the technical effect of improving the accuracy and efficiency of determining the orbit of the impactor's kinetic energy impact on the asteroid.

[0017] Other features and advantages of the present invention will be described in the following specification, and in part, will be obvious from the specification, or will be understood by implementing the present invention. The objectives and other advantages of the present invention are realized and obtained by the structures specifically pointed out in the specification, claims, and drawings.

[0018] To make the above objectives, features, and advantages of the present invention more obvious and understandable, the following specific preferred embodiments are given, and in conjunction with the accompanying drawings, detailed descriptions are as follows. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0020] Figure 1 It is a flowchart of a pseudospectral orbit optimization method for kinetic energy impact on an asteroid provided by an embodiment of the present invention;

[0021] Figure 2 It is a schematic diagram of the entire impact process when the impactor motion parameters provided by an embodiment of the present invention do not include the time required for the impactor to impact the asteroid;

[0022] Figure 3 Schematic diagram of the changes in orbital altitude, flight speed, engine thrust direction, and fuel mass over time under the condition of using the earliest impact as a performance index provided by an embodiment of the present invention;

[0023] Figure 4 Schematic diagram of the changes in orbital altitude, flight speed, engine thrust direction, and fuel mass over time under the condition of using the latest impact as a performance index provided by an embodiment of the present invention;

[0024] Figure 5 Schematic diagram of the entire trajectory of the impactor provided by an embodiment of the present invention;

[0025] Figure 6 Schematic diagram of the entire impact process provided by an embodiment of the present invention;

[0026] Figure 7 Another schematic diagram of the entire impact process provided by an embodiment of the present invention;

[0027] Figure 8 Schematic diagram of the entire impact process when the motion parameters of the impactor provided by an embodiment of the present invention include the time required for the impactor to hit the asteroid;

[0028] Figure 9 Schematic diagram of the changes in the orbital altitude, flight speed magnitude, fuel mass, and burning angle of the impactor over time under the condition of the most fuel-efficient provided by an embodiment of the present invention;

[0029] Figure 10 Schematic diagram of the entire optimized trajectory of the asteroid and the impactor provided by an embodiment of the present invention;

[0030] Figure 11 Schematic diagram of a pseudo-spectral orbit optimization device for kinetic energy impact on an asteroid provided by an embodiment of the present invention;

[0031] Figure 12 Schematic diagram of a dynamic electronic device provided by an embodiment of the present invention. Detailed implementation manners

[0032] 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. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0033] Embodiment 1:

[0034] According to an embodiment of the present invention, an embodiment of a pseudo-spectral orbit optimization method for kinetic energy impact on an asteroid is provided. It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. And although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0035] Figure 1 is a flowchart of a pseudo-spectral orbit optimization method for kinetic energy impact on an asteroid according to an embodiment of the present invention. As Figure 1 shown, the method includes the following steps:

[0036] Step S102, obtain the impactor motion parameters and the asteroid motion parameters, and design the target parameters of the power adjustment section of the impactor, where the target parameters include: optimized state variables, control variables, and additional parameters;

[0037] Step S104, based on the impactor motion parameters, the asteroid motion parameters, and the target parameters of the power adjustment section, construct a multi-sided Keplerian motion rendezvous problem, and based on the multi-sided Keplerian motion rendezvous problem and the impact condition between the impactor and the asteroid, determine the terminal constraint conditions of the power adjustment section;

[0038] Step S106, based on the terminal constraint conditions, preset performance indicators, and multi-segment pseudo-spectral optimization algorithm, optimize the target parameters of the impactor to obtain optimized parameters, where the target parameters include: altitude change parameters, velocity change parameters, thrust direction change parameters, and fuel mass change parameters;

[0039] Step S108, based on the optimized parameters, perform dynamic integration on the glide section to obtain the motion trajectory of the impactor;

[0040] Step S110, based on the motion trajectory of the impactor and the running trajectory of the asteroid, determine the motion trajectory diagram of the impact process between the impactor and the asteroid.

[0041] In an embodiment of the present invention, by obtaining the impactor motion parameters and the asteroid motion parameters, and designing the target parameters of the power adjustment section of the impactor, wherein the target parameters include: an optimized state quantity, a control quantity, and an additional parameter; based on the impactor motion parameters, the asteroid motion parameters, and the target parameters of the power adjustment section, a Kepler problem is constructed, and based on the multi-sided Kepler motion rendezvous problem and the impact condition between the impactor and the asteroid, the terminal constraint condition of the power adjustment section is determined; based on the terminal constraint condition, a preset performance index, and a multi-segment pseudospectral optimization algorithm, the target parameters of the impactor are optimized to obtain optimized parameters, wherein the target parameters include: a height change parameter, a speed change parameter, a thrust direction change parameter, and a fuel mass change parameter; based on the optimized parameters, the dynamics of the glide section is integrated to obtain the motion trajectory of the impactor; based on the motion trajectory of the impactor and the running trajectory of the asteroid, the motion trajectory diagram of the impact process between the impactor and the asteroid is determined, achieving the purpose of accurately and efficiently determining the orbit of the impactor's kinetic energy impact on the asteroid, and further solving the technical problem of the low efficiency and accuracy of the existing method for determining the orbit of the kinetic energy impact on the asteroid, thereby realizing the technical effect of improving the accuracy and efficiency of determining the orbit of the impactor's kinetic energy impact on the asteroid.

[0042] In an embodiment of the present invention, according to different obtained impactor motion parameters, the specific processes of designing two pseudospectral orbit optimization methods for the kinetic energy impact on the asteroid will be described in detail below.

[0043] If the impactor motion parameters are the impactor initial position, the impactor initial velocity, and the impactor power configuration parameters, and the asteroid motion parameters are the asteroid initial position and the asteroid initial velocity, then step S104 includes the following steps:

[0044] Step S11, based on the impactor motion parameters and the asteroid motion parameters, construct the first kinematic model of the impactor;

[0045] Step S12, construct a multi-sided Kepler motion rendezvous problem based on the first kinematic model of the impactor and the target parameters of the power adjustment section;

[0046] Step S13, based on the multi-sided Kepler motion rendezvous problem and the impact condition between the impactor and the asteroid, determine the first terminal constraint condition of the power adjustment section.

[0047] Step S106 includes the following steps:

[0048] Step S21: Determine the earliest impact time between the asteroid and the impactor, the latest impact time between the asteroid and the impactor, the maximum fuel consumption of the impactor, and the minimum fuel consumption of the impactor as the first preset performance indicators;

[0049] Step S22: Perform Gaussian pseudospectral discretization on the first preset performance indicators to determine the first optimization parameters.

[0050] Step S108 includes the following steps:

[0051] Step S31: Determine the first optimal impact argument of perigee based on the first optimization parameters;

[0052] Step S32: Calculate the optimal flight time of the impactor based on the first optimal impact argument of perigee;

[0053] Step S33: Perform dynamic integration on the glide segment based on the optimal flight time, the first terminal constraint conditions, and the two-body kinematic equations to obtain the first motion trajectory of the impactor.

[0054] In the embodiments of the present invention, if the impactor motion parameters are the impactor initial position, the impactor initial velocity, and the impactor power configuration parameters, and the asteroid motion parameters are the asteroid initial position and the asteroid initial velocity, two types of constant thrusts, large and small, are also designed in the embodiments of the present invention.

[0055] First, perform multi-segment modeling on the impactor power adjustment segment and the glide segment:

[0056] Dynamics model of the impactor power adjustment segment:

[0057] In the Earth centered inertial coordinates (ECI), the impactor is regarded as a particle, and its dynamics can be expressed as:

[0058]

[0059]

[0060]

[0061] where r m = [x(t) y(t) z(t)] T is the position vector, v m = [v x (t) v y (t) v z (t)] Tis the velocity vector, μ is the Earth's gravitational constant, T is the vacuum thrust, m is the mass of the impactor, g0 is the gravitational acceleration at sea level, and I sp is the specific impulse of the engine, u = [u x (t) u y (t) u z (t) ] T is the thrust direction.

[0062] Optimize the dynamic adjustment section. The optimized state variable x is the position vector r of the impactor m , the velocity vector v m and the remaining fuel mass m. The control variable is the thrust direction vector u. At the same time, introduce parameters, which are the eccentric anomaly E at the moment of hitting the asteroid and the semi-latus rectum p of the asteroid orbit as optimization variables. Let t0 be the initial time and t f be the terminal time when the impactor ends the dynamic adjustment.

[0063] Initial constraints:

[0064]

[0065] Process constraints:

[0066]

[0067] Terminal constraints:

[0068]

[0069] The dynamic model of the impactor and the asteroid's Keplerian motion:

[0070]

[0071]

[0072] After the impactor ends the dynamic adjustment section, it starts Keplerian motion. The asteroid always maintains Keplerian motion, and the remaining flight times of both and the position and velocity of the impact point (PIP) are released. This type of problem is called the multi-sided Keplerian motion rendezvous problem. The multi-sided Keplerian motion rendezvous problem can be expressed as follows:

[0073] Asteroid: The initial time is t0, the total flight time is Δt, and the position at the impact time is r T (t0 + Δt);

[0074] Impactor: The initial time of the power section is t0, the end time of the power section is t f , the gliding duration is Δt trans , the position at the impact time is r m (t0 + Δt);

[0075] Combined with the impact conditions, the following constraints can be obtained:

[0076]

[0077] In Equation (6), t f , r f , v f are the terminal constraints of the power section of the impactor. Combining the relationships between the variables in the figure, the impact condition constraints, and solving the Lambert problem, the terminal constraints are derived:

[0078] Given that the asteroid moves in a circular orbit in Keplerian motion, the position and velocity r T (t0), v T (t0) at the launch moment, the six orbital elements of the asteroid can be obtained (including the modulus of the specific angular momentum h, the eccentricity e, the orbital inclination i, the argument of perigee ω, and the right ascension of the ascending node Ω).

[0079]

[0080]

[0081]

[0082]

[0083]

[0084] Now, define a vector n that is perpendicular to the plane determined by the orbital angular momentum vector and the north pole axis (K):

[0085]

[0086] Define u0 as the sum of the true anomaly and the argument of perigee. Then, according to the vector projection theorem, the right ascension of the ascending node Ω, the argument of perigee ω, and the parameter u0 can be calculated:

[0087]

[0088]

[0089]

[0090] Then the true anomaly θ0 can be calculated

[0091] θ0 = u0 - ω (17)

[0092] The eccentric anomaly E0 can be expressed as:

[0093]

[0094] The mean anomaly of the asteroid at the initial moment:

[0095] M(t0) = M0 = E0 - e sin E0 (19)

[0096] The eccentric anomaly of the asteroid at the impact moment is the optimized parameter E to be predicted. Given the true anomaly θ and the mean anomaly M of the asteroid at the time of impact, the following can be deduced:

[0097]

[0098] M = E - e sin E (21)

[0099] The total flight time of the asteroid is Δt. The position and velocity of the asteroid at the moment of impact are r PIP , v PIP .

[0100]

[0101]

[0102]

[0103]

[0104]

[0105] M ZXZ = M Z (Ω)M X (i)M Z (ω, θ) (24)

[0106]

[0107] Based on the above derivation, the initial position and velocity of the impactor in the gliding section are deduced in reverse. Since the flight trajectory is continuous, the initial position and velocity at this stage are also the terminal state r f , v f .

[0108] After that, the Lambert problem is solved. Let the transfer true anomaly Δθ and the gliding time Δt of the impactor in the last section trans , as well as the Lagrangian coefficients f, g,

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115]

[0116] So far, the iterative calculation relationship of the terminal constraint can be established:

[0117] t f -t0 = Δt - Δt trans (33)

[0118]

[0119] In addition, the power adjustment section has two segments with large and small thrusts, which are connected together through a series of connection conditions. These constraints ensure continuous changes in position and speed between segments and consider the mutation of mass:

[0120] r (p) (t f ) - r (p+1) (t0) = 0

[0121] v (p) (t f ) - v (p+1) (t0) = 0

[0122] m (p) (t f ) - m (p+1) (t0) = 0

[0123] r (2) (t f ) = r(t f )

[0124] v (2) (t f ) = v(t f )

[0125] m (2) (t f ) = m(t f ) (35)

[0126] Among them, the superscript (p) represents the number of each stage, and p takes 1, 2.

[0127] Next, take the earliest and latest impact times and the maximum and minimum fuel consumptions as the performance index J, and perform Gaussian pseudospectral discretization. The specific derivation process is as follows:

[0128] J = m(t f ), J = -m(t f), J = t f , J = -t f (36)

[0129] First, the general nonlinear system dynamics equation is as follows:

[0130]

[0131] where the state variable x(t) ∈ R n , the control variable u(t) ∈ R m , and the time t ∈ [t0, t 2 .

[0132] After that, the time domain is transferred to the time interval [-1, 1] because the support points of the Lagrange interpolation polynomial are selected as the orthogonality points located in the time interval [-1, 1], which is completed by the following mapping function.

[0133]

[0134] Taking τ as the independent variable, the state variable and the control variable are approximately represented by the Lagrange interpolation polynomial as follows:

[0135]

[0136]

[0137]

[0138]

[0139] It can be seen that L i (τ) and L i * (τ) have the following properties:

[0140]

[0141] Differentiating the approximate expressions of the state variable and the control variable gives:

[0142]

[0143] And can be obtained offline by the following formula:

[0144]

[0145] Thus, the dynamic differential equation constraint is converted into an algebraic constraint:

[0146]

[0147] The terminal state is approximated by Gaussian integration and should satisfy:

[0148]

[0149] The performance index is also approximated by Gaussian integration:

[0150]

[0151] where ω k is the Gaussian weight.

[0152] After the above processing, the optimal control problem is transformed into finding the boundary conditions of the optimal state variables X i (i = 0,..., N) and the control variables:

[0153]

[0154] and the path constraints at the interpolation points:

[0155] C(X K , U k , τ k ; t0, t f ) ≤ 0 (k = 1,..., N) (50)

[0156] Thus, the optimal control problem is transformed into a nonlinear programming problem.

[0157] According to the optimized eccentric anomaly E of the asteroid impact point, the overall optimal flight time Δt is calculated, and then the dynamics of the glide section of the impactor is integrated based on the two-body problem over the integration interval t to achieve the overall trajectory optimization.

[0158]

[0159]

[0160] r (3) (0) = r (2) (t f ) (53)

[0161] v (3) (0) = v (2) (t f ) (54)

[0162] t ∈ [0, Δt + t0 - t f (55)

[0163] As Figure 2 shown, Figure 2 the schematic diagram of the entire impact process when the motion parameters of the impactor do not include the time required for the impactor to hit the asteroid.

[0164] Through the present invention, the optimal state quantity and control quantity of the powered adjustment section that satisfy the constraint conditions can be quickly calculated, where the control quantity is the thrust direction vector [u x , u y , u z . Figure 3 It is the variation of the orbital altitude, flight speed, engine thrust direction, and fuel mass with time under the condition of taking the earliest impact as the performance index. Figure 4 It is the variation of the orbital altitude, flight speed, engine thrust direction, and fuel mass with time under the condition of taking the latest impact as the performance index. By comparing the two figures, it can also be seen that the flight speed in the case of the earliest impact is significantly greater than that in the case of the latest impact, and the remaining fuel masses in these two cases are roughly the same and are all consumed. Figure 5 For the glide section, the transfer orbit is obtained by integrating the two-body motion dynamics, and then combined with the powered adjustment section orbit optimized by the Gauss pseudospectral method to complete the generation of the entire section trajectory. It can be seen that after the short-time powered adjustment is completed, the impactor freely glides and impacts the asteroid for a longer time. Figure 6 It is a schematic diagram of the entire impact process of the impactor and the asteroid. Figure 7 It is the simulation result of the impact scenario after adding the asteroid orbit, and the impactor can accurately impact the asteroid.

[0165] In the embodiment of the present invention, the impactor realizes the impact on the asteroid through three stages: large-thrust flight, small-thrust flight, and free gliding. The task is segmented according to the power configuration and initial state, and modeling is carried out respectively in the powered adjustment section and the glide section. Reasonable state quantities, control quantities, and parameters are selected for optimization. According to the multi-sided Kepler motion rendezvous problem and the impact conditions, the terminal constraints of the powered section are deduced. All constraints and performance indexes are set. Under the pseudospectral discretization condition, the derivative of the state variable with respect to time is approximated by differentiating the global interpolation polynomial, so as to convert the differential equation constraint into a set of algebraic constraints. The optimal control problem is transformed into a parameter optimization problem with a series of algebraic constraints, that is, a nonlinear programming problem (NLP). The feasible solution of the obtained NLP problem is the optimal state quantity and optimal control quantity that ensure the terminal position and velocity constraints, realizing the rapid planning of the optimal trajectory with a powered adjustment section.

[0166] Taking the terminal state of the powered adjustment section as the initial state of the glide section, the orbit of the glide section is integrated and solved according to the Kepler equation to complete the overall planning of the entire task.

[0167] If the motion parameters of the impactor further include the time required for the impactor to impact the asteroid, and the motion parameters of the asteroid are the initial position of the asteroid and the initial velocity of the asteroid, then step S104 includes the following steps:

[0168] Step S41: Based on the impactor motion parameters and the asteroid motion parameters, construct the second kinematic model of the impactor;

[0169] Step S42: Based on the first kinematic model of the impactor and the target parameters of the power adjustment section, construct a one-sided Kepler problem;

[0170] Step S43: Based on the one-sided Kepler problem and the impact conditions between the impactor and the asteroid, determine the second terminal constraint conditions of the power adjustment section.

[0171] Step S106 includes the following steps:

[0172] Step S51: Based on the terminal constraint conditions, preset performance indicators, and multi-segment pseudospectral optimization algorithm, optimize the target parameters of the impactor to obtain optimized parameters, including:

[0173] Step S52: Determine the minimum fuel consumption of the impactor as the second preset performance indicator;

[0174] Step S53: Perform Gaussian pseudospectral discretization on the second preset performance indicator to determine the second optimized parameter.

[0175] Step S108 includes the following steps:

[0176] Step S61: Based on the time required for the impactor to hit the asteroid, the second optimized parameter, the second terminal constraint conditions, and the two-body kinematic equation, perform dynamic integration on the glide section to obtain the second motion trajectory of the impactor.

[0177] In the embodiments of the present invention, if the impactor motion parameters further include the time required for the impactor to hit the asteroid, the asteroid motion parameters are the initial position of the asteroid and the initial velocity of the asteroid.

[0178] First, perform segmented modeling on the power adjustment section and the glide section of the impactor:

[0179] Dynamics model of the power adjustment section of the impactor:

[0180] In the Earth centered inertial coordinates (ECI), the impactor is regarded as a particle, and its dynamics can be expressed as:

[0181]

[0182]

[0183]

[0184] where r m = [x(t) y(t) z(t)] T is the position vector, v m = [v x (t) v y (t) v z (t)] T is the velocity vector, μ is the gravitational constant of the Earth, T is the vacuum thrust, m is the mass of the spacecraft, g0 is the gravitational acceleration at sea level, I sp is the specific impulse of the engine, u = [u x (t) u y (t) u z (t)] T is the thrust direction.

[0185] Optimize the dynamic adjustment section:

[0186] The state variable x = [r m v m m], and the control variable is the optimization parameter p.

[0187] Among them, the impactor position vector r m , velocity vector v m and the remaining fuel mass m are state variables, the thrust direction vector u is the control variable, and the semi-latus rectum p of the impactor glide section is the optimization parameter. Let t0 be the initial times of the launch of the impactor and the target respectively, and t f be the terminal time when the impactor ends the dynamic adjustment.

[0188] Initial constraints:

[0189]

[0190] Process constraints:

[0191]

[0192] Terminal constraints:

[0193]

[0194] The Keplerian motion dynamics model of the impactor and the asteroid:

[0195]

[0196]

[0197] After the impactor ends the dynamic adjustment section, it starts Keplerian motion, and the asteroid always maintains Keplerian motion, as Figure 3 . The initial time t0, the total flight time Δt, and the initial states r of the impactor and the asteroidT (t0), r m (t0) is fixed, while the remaining flight times of both and the position r(t + Δt) and velocity v(t + Δt) of the impact point (PIP) are released. This type of problem is called the multi-sided Keplerian motion rendezvous problem, and the multi-sided Keplerian motion rendezvous problem can be expressed as follows:

[0198] Asteroid: The initial time is t0, the total flight time is Δt, and the terminal position is r T (t0 + Δt);

[0199] Impactor: The initial time of the powered phase is t0, and the end time is t f with a gliding duration of Δt trans ;

[0200] Combining the impact conditions gives the following constraints:

[0201]

[0202] If the total time to achieve the hitting mission is fixed, since the initial state and dynamic law of the asteroid are known, the terminal position of the target, i.e., the position of the impact point PIP, can be determined to be fixed. Then the multi-sided Keplerian motion rendezvous problem introduced above will degenerate into a one-sided Kepler problem, and the problem is transformed into a multi-constraint optimization problem of hitting a fixed point.

[0203] In Equation (6), t f , r f , v f are the terminal constraints of the powered phase of the impactor. Combining Figure 3 the relationships between the variables in, the impact condition constraints, and solving the Lambert problem, the terminal constraints are derived:

[0204] It is known that the asteroid performs Keplerian motion in a circular orbit, and the position and velocity r T (t0), v T (t0) at the launch time are known. The six orbital elements of the asteroid (including the magnitude of the specific angular momentum h, eccentricity e, orbital inclination i, argument of perigee ω, right ascension of the ascending node Ω) can be obtained,

[0205]

[0206]

[0207]

[0208]

[0209]

[0210] Now, define a vector n that is perpendicular to the plane determined by the orbital angular momentum vector and the north pole axis (K):

[0211]

[0212] Define u0 as the sum of the true anomaly and the argument of perigee. Then, according to the vector projection theorem, the right ascension of the ascending node Ω, the argument of perigee ω, and the parameter u0 can be calculated:

[0213]

[0214]

[0215]

[0216] Then the true anomaly θ0 can be calculated

[0217] θ0 = u0 - ω (71)

[0218] The eccentric anomaly E0 can be expressed as:

[0219]

[0220] The mean anomaly of the asteroid at the initial time:

[0221] M(t0) = M0 = E0 - e sinE0 (73)

[0222] Since the total flight time Δt of the mission is known and e = 0, the mean anomaly M of the impact position PIP can be obtained.

[0223]

[0224] The position and velocity of the asteroid at the time of impact are r T (t0 + Δt), v T (t0 + Δt).

[0225]

[0226]

[0227]

[0228]

[0229] M ZXZ = M Z (Ω)M X (i)M Z (ω, θ) (76)

[0230]

[0231] Based on the above derivation, the initial position and velocity of the impactor in the gliding section are deduced backwards. Since the flight trajectory is continuous, the initial state at this stage is also the terminal state r of the power adjustment section f , v f .

[0232] After that, the Lambert problem is solved. Let the transfer true anomaly Δθ and gliding time Δt of the impactor in the last section trans , the optimized parameter semi-latus rectum p, and the Lagrange coefficients f, g

[0233]

[0234]

[0235]

[0236]

[0237]

[0238]

[0239]

[0240] So far, the iterative calculation relationship of the terminal constraint can be established:

[0241] t f - t0 = Δt - Δt trans (85)

[0242]

[0243] Taking the minimum fuel consumption as the performance index J and performing pseudo-spectral discretization, the specific derivation process is as follows:

[0244] J = -m(t f ) (87)

[0245] First, the general nonlinear system dynamics equation:

[0246]

[0247] Among them, the state variable x(t) ∈ R n , the control variable u(t) ∈ R m , and the time t ∈ [t0, t 2 .

[0248] After that, the time domain is shifted to the time interval [-1, 1], because the support points of the Lagrange interpolation polynomial are selected as the orthogonal points located in the time interval [-1, 1], which is accomplished by the following mapping function.

[0249]

[0250] Taking τ as the independent variable, the state variables and control variables are approximately represented by the Lagrange interpolation polynomial:

[0251]

[0252]

[0253]

[0254]

[0255] It can be seen that L i (τ) and L i * (τ) have the following properties:

[0256]

[0257] Differentiating the approximate expressions of the state variables and control variables gives:

[0258]

[0259] And can be obtained offline by the following formula:

[0260]

[0261] Thus, the dynamic differential equation constraint is converted into an algebraic constraint:

[0262]

[0263] The terminal state is approximated by Gaussian integration and should satisfy:

[0264]

[0265] The performance index is also approximated by Gaussian integration:

[0266]

[0267] where ω k is the Gaussian weight.

[0268] After the above processing, the optimal control problem is transformed into finding the optimal state variable X i(i = 0, ..., N) and the boundary conditions of the control variables.

[0269]

[0270] And the path constraints at the interpolation points

[0271] C(X K , U k , τ k ; t0, t f ) ≤ 0 (k = 1, …, N) (101)

[0272] Thus, the optimal control problem is transformed into a nonlinear programming problem.

[0273] According to the given target flight time Δt, perform dynamic integration on the glide section of the impactor based on the two-body problem over the integration interval t to achieve the trajectory optimization of the whole process.

[0274]

[0275]

[0276] r (2) (0) = r (1) (t f ) (104)

[0277] v (2) (0) = v (1) (t f ) (105)

[0278] t ∈ [0, Δt + t0 - t f (106)

[0279] Figure 8 This is a schematic diagram of the whole impact process when the impactor motion parameters provided by the embodiment of the present invention include the time required for the impactor to hit the asteroid.

[0280] Through the present invention, it is possible to quickly calculate the trajectory optimization of the impactor hitting the asteroid under the condition of a fixed initial state and a given flight time. Define the angle between the current thrust vector and the velocity vector as the burning angle. Figure 9 In the case of the most fuel-efficient situation, it shows the variation of the impactor's orbital altitude, flight speed magnitude, fuel mass, and burning angle with time. Figure 10 It shows the optimized trajectory of the whole process of the asteroid and the impactor. The impactor operates on the initial orbit, performs the impact mission at a specific position and velocity. First, it makes a dynamic adjustment, and under the requirement of the most fuel-efficient situation, it optimizes the trajectory of the powered section, and then enters the glide section to hit the target.

[0281] In the embodiment of the present invention, the impactor realizes the impact on the asteroid through two stages: power adjustment and free gliding. The task is segmented according to the power configuration and the initial state, and modeling is carried out in the power adjustment stage and the gliding stage respectively. Reasonable state variables, control variables and parameters are selected for optimization. According to the multi-sided Keplerian motion rendezvous problem and the impact conditions, the terminal constraints of the power stage are deduced. All constraints and performance indicators are set. Under the condition of pseudo-spectral discretization, the derivative of the state variable with respect to time is approximated by differentiating the global interpolation polynomial, so as to convert the differential equation constraint into a set of algebraic constraints. The optimal control problem is transformed into a parameter optimization problem with a series of algebraic constraints, that is, a non-linear programming problem (NLP). The feasible solution of the obtained NLP problem is the optimal state variables, optimal control and optimal parameters that ensure the terminal position and velocity constraints, and realizes the rapid planning of the optimal trajectory of the powered adjustment stage.

[0282] Whether the asteroid can be successfully impacted mainly depends on the final position and velocity of the powered adjustment stage. Therefore, the reasonable and rapid optimization of the powered adjustment stage becomes a key technology.

[0283] Embodiment 2:

[0284] The embodiment of the present invention also provides a pseudo-spectral orbit optimization device for kinetic energy impact on an asteroid. The pseudo-spectral orbit optimization device for kinetic energy impact on an asteroid is used to execute the pseudo-spectral orbit optimization method for kinetic energy impact on an asteroid provided in the above content of the embodiment of the present invention. The following is a specific introduction to the pseudo-spectral orbit optimization device for kinetic energy impact on an asteroid provided by the embodiment of the present invention.

[0285] As Figure 11 shown, Figure 11 is a schematic diagram of the pseudo-spectral orbit optimization device for kinetic energy impact on an asteroid. The pseudo-spectral orbit optimization device for kinetic energy impact on an asteroid includes: an acquisition unit 10, a construction unit 20, an optimization unit 30, an integration unit 40 and a determination unit 50.

[0286] The acquisition unit is used to acquire the motion parameters of the impactor and the motion parameters of the asteroid, and design the target parameters of the powered adjustment stage of the impactor, where the target parameters include: optimized state variables, control variables and additional parameters;

[0287] The construction unit is used to construct a multi-sided Keplerian motion rendezvous problem based on the motion parameters of the impactor, the motion parameters of the asteroid and the target parameters of the powered adjustment stage, and determine the terminal constraint conditions of the powered adjustment stage based on the multi-sided Keplerian motion rendezvous problem and the impact conditions between the impactor and the asteroid;

[0288] The optimization unit is configured to optimize the target parameters of the impactor based on the terminal constraint conditions, preset performance metrics, and multi-segment pseudospectral optimization algorithm to obtain optimized parameters, where the target parameters include: altitude change parameter, velocity change parameter, thrust direction change parameter, and fuel mass change parameter;

[0289] The integration unit is configured to perform dynamic integration on the glide segment based on the optimized parameters to obtain the motion trajectory of the impactor;

[0290] The determination unit is configured to determine the motion trajectory diagram of the impact process between the impactor and the asteroid based on the motion trajectory of the impactor and the running trajectory of the asteroid.

[0291] In an embodiment of the present invention, by obtaining the motion parameters of the impactor and the motion parameters of the asteroid, and designing the target parameters of the power adjustment segment of the impactor, where the target parameters include: optimized state variables, control variables, and additional parameters; based on the motion parameters of the impactor, the motion parameters of the asteroid, and the target parameters of the power adjustment segment, a multi-sided Keplerian motion rendezvous problem is constructed, and based on the multi-sided Keplerian motion rendezvous problem and the impact conditions between the impactor and the asteroid, the terminal constraint conditions of the power adjustment segment are determined; based on the terminal constraint conditions, preset performance metrics, and multi-segment pseudospectral optimization algorithm, the target parameters of the impactor are optimized to obtain optimized parameters, where the target parameters include: altitude change parameter, velocity change parameter, thrust direction change parameter, and fuel mass change parameter; based on the optimized parameters, dynamic integration is performed on the glide segment to obtain the motion trajectory of the impactor; based on the motion trajectory of the impactor and the running trajectory of the asteroid, the motion trajectory diagram of the impact process between the impactor and the asteroid is determined, achieving the purpose of accurately and efficiently determining the orbit of the impactor's kinetic energy impacting the asteroid, and further solving the technical problem of the low efficiency and accuracy of the existing method for determining the orbit of the kinetic energy impact on the asteroid, thereby realizing the technical effect of improving the accuracy and efficiency of determining the orbit of the impactor's kinetic energy impacting the asteroid.

[0292] Embodiment Three:

[0293] An embodiment of the present invention further provides an electronic device, including a memory and a processor, where the memory is used to store a program that supports the processor to execute the method described in Embodiment One above, and the processor is configured to execute the program stored in the memory.

[0294] See Figure 12, an embodiment of the present invention further provides an electronic device 100, including: a processor 60, a memory 61, a bus 62, and a communication interface 63, where the processor 60, the communication interface 63, and the memory 61 are connected through the bus 62; the processor 60 is configured to execute an executable module stored in the memory 61, such as a computer program.

[0295] Among them, the memory 61 may include a high-speed random access memory (RAM), and may also include a non-volatile memory, such as at least one disk memory. The communication connection between the system network element and at least one other network element is realized through at least one communication interface 63 (which may be wired or wireless), and the Internet, wide area network, local area network, metropolitan area network, etc. can be used.

[0296] The bus 62 may be an ISA bus, a PCI bus, an EISA bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc. For the sake of convenience of representation, Figure 12 only a bidirectional arrow is used in the figure, but it does not mean that there is only one bus or one type of bus.

[0297] Among them, the memory 61 is used to store a program, and after receiving an execution instruction, the processor 60 executes the program. The method executed by the device defined by the flow process disclosed in any one of the foregoing embodiments of the present invention can be applied to the processor 60 or implemented by the processor 60.

[0298] The processor 60 may be an integrated circuit chip with the ability to process signals. In the implementation process, each step of the above method can be completed by the integrated logic circuit of the hardware in the processor 60 or the instructions in the form of software. The above-mentioned processor 60 may be a general-purpose processor, including a central processing unit (CPU for short), a network processor (NP for short), etc.; it may also be a digital signal processor (DSP for short), an application specific integrated circuit (ASIC for short), a field-programmable gate array (FPGA for short) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. It can implement or execute the various methods, steps and logic block diagrams disclosed in the embodiments of the present invention. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. The steps of the method disclosed in combination with the embodiments of the present invention can be directly embodied as being executed and completed by the hardware decoding processor, or executed and completed by a combination of the hardware and software modules in the decoding processor. The software module may be located in a mature storage medium in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. This storage medium is located in the memory 61, and the processor 60 reads the information in the memory 61 and combines its hardware to complete the steps of the above method.

[0299] Embodiment 4:

[0300] The embodiment of the present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is run by a processor, it executes the steps of the method described in Embodiment 1 above.

[0301] In addition, in the description of the embodiments of the present invention, unless otherwise clearly specified and limited, the terms "installation", "connection" and "connection" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be a direct connection or an indirect connection through an intermediate medium, and it may be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0302] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. In addition, the terms "first", "second", "third" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance.

[0303] In several embodiments provided by the present application, it should be understood that the disclosed systems, devices, and methods can be implemented in other ways. The device embodiments described above are only illustrative. For example, the division of the units is only a logical function division, and there may be other division methods in actual implementation. For another example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed coupling or direct coupling or communication connection between each other can be through some communication interfaces. The indirect coupling or communication connection of the devices or units can be in electrical, mechanical, or other forms.

[0304] The units described as separate components may or may not be physically separated. The components displayed as units may or may not be physical units, that is, they can be located in one place or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0305] In addition, in each embodiment of the present invention, the functional units can be integrated in a processing unit, or each unit can exist physically alone, or two or more units can be integrated in one unit.

[0306] Finally, it should be noted that the above-described embodiments are only specific embodiments of the present invention, used to illustrate the technical solutions of the present invention, rather than limiting them. The protection scope of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that any person skilled in the art within the technical scope disclosed by the present invention can still modify the technical solutions recorded in the foregoing embodiments or can easily think of changes, or perform equivalent replacements for some of the technical features; and these modifications, changes, or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention and should all be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A pseudo-spectral orbit optimization method for kinetic energy impact on asteroids, characterized in that Including: Obtain the impactor motion parameters and the asteroid motion parameters, and design the target parameters for the power adjustment section of the impactor. Among them, the target parameters include: optimized state variables, control variables, and additional parameters; If the impactor motion parameters are the initial position of the impactor, the initial velocity of the impactor, and the power configuration parameters of the impactor, and the asteroid motion parameters are the initial position of the asteroid and the initial velocity of the asteroid, then based on the impactor motion parameters and the asteroid motion parameters, construct the first kinematic model of the impactor; based on the first kinematic model of the impactor and the target parameters of the power adjustment section, construct the multi-sided Keplerian motion rendezvous problem; based on the multi-sided Keplerian motion rendezvous problem and the impact conditions between the impactor and the asteroid, determine the first terminal constraint conditions for the power adjustment section; If the impactor motion parameters further include the time required for the impactor to hit the asteroid, and the asteroid motion parameters are the initial position of the asteroid and the initial velocity of the asteroid, then based on the impactor motion parameters and the asteroid motion parameters, construct the second kinematic model of the impactor; based on the first kinematic model of the impactor and the target parameters of the power adjustment section, construct the one-sided Kepler problem; based on the one-sided Kepler problem and the impact conditions between the impactor and the asteroid, determine the second terminal constraint conditions for the power adjustment section; Based on the first terminal constraint conditions or the second terminal constraint conditions, the preset performance index, and the multi-segment pseudospectral optimization algorithm, optimize the target parameters of the impactor to obtain the optimized parameters. Among them, the target parameters include: altitude change parameters, velocity change parameters, thrust direction change parameters, and fuel mass change parameters; Based on the optimized parameters, perform dynamic integration on the glide section to obtain the motion trajectory of the impactor; Based on the motion trajectory of the impactor and the motion trajectory of the asteroid, determine the motion trajectory diagram of the impact process between the impactor and the asteroid.

2. The method according to claim 1, characterized in that, Based on the first terminal constraint conditions, the preset performance index, and the multi-segment pseudospectral optimization algorithm, optimize the target parameters of the impactor to obtain the optimized parameters, including: Determine the earliest impact time between the asteroid and the impactor, the latest impact time between the asteroid and the impactor, the maximum fuel consumption of the impactor, and the minimum fuel consumption of the impactor as the first preset performance index; Perform pseudospectral discretization on the first preset performance index to determine the first optimized parameter.

3. The method according to claim 2, wherein Based on the optimized parameters, perform dynamic integration on the glide section to obtain the motion trajectory of the impactor, including: Based on the first optimized parameter, determine the first optimal impact eccentric anomaly; Based on the first optimal impact eccentric anomaly, calculate the optimal flight time of the impactor; Based on the optimal flight time, the first terminal constraint conditions, and the two-body kinematic equation, perform dynamic integration on the glide section to obtain the first motion trajectory of the impactor.

4. The method according to claim 1, wherein Based on the second terminal constraint condition, the preset performance index, and the multi-segment pseudospectral optimization algorithm, optimize the target parameters of the impactor to obtain optimized parameters, including: Determine the minimum fuel consumption of the impactor as the second preset performance index; Perform pseudospectral discretization on the second preset performance index to determine the second optimized parameter.

5. The method according to claim 4, wherein Based on the optimized parameters, perform dynamic integration on the glide segment to obtain the motion trajectory of the impactor, including: Based on the time required for the impactor to hit the asteroid, the second optimized parameter, the second terminal constraint condition, and the two-body kinematic equation, perform dynamic integration on the glide segment to obtain the second motion trajectory of the impactor.

6. The method according to claim 1, wherein Based on the motion trajectory of the impactor and the running trajectory of the asteroid, determine the motion trajectory diagram of the impact process between the impactor and the asteroid, including: Perform dynamic integration on the motion parameters of the asteroid to obtain the running trajectory of the asteroid; Based on the motion trajectory of the impactor and the running trajectory of the asteroid, determine the motion trajectory diagram of the impact process between the impactor and the asteroid.

7. A pseudo-spectral orbit optimization device for kinetic energy impact on asteroids, characterized in that, Including: An acquisition unit, a construction unit, an optimization unit, an integration unit, and a determination unit, where The acquisition unit is used to acquire the motion parameters of the impactor and the motion parameters of the asteroid, and design the target parameters of the power adjustment section of the impactor, where the target parameters include: optimized state variables, control variables, and additional parameters; The construction unit is used to, if the motion parameters of the impactor are the initial position of the impactor, the initial velocity of the impactor, and the power configuration parameters of the impactor, and the motion parameters of the asteroid are the initial position of the asteroid and the initial velocity of the asteroid, then construct the first kinematic model of the impactor based on the motion parameters of the impactor and the motion parameters of the asteroid; construct the multi-sided Kepler motion rendezvous problem based on the first kinematic model of the impactor and the target parameters of the power adjustment section; determine the first terminal constraint condition of the power adjustment section based on the multi-sided Kepler motion rendezvous problem and the impact condition between the impactor and the asteroid; if the motion parameters of the impactor further include the time required for the impactor to hit the asteroid, and the motion parameters of the asteroid are the initial position of the asteroid and the initial velocity of the asteroid, then construct the second kinematic model of the impactor based on the motion parameters of the impactor and the motion parameters of the asteroid; construct the one-sided Kepler problem based on the first kinematic model of the impactor and the target parameters of the power adjustment section; determine the second terminal constraint condition of the power adjustment section based on the one-sided Kepler problem and the impact condition between the impactor and the asteroid; The optimization unit is used to optimize the target parameters of the impactor based on the first terminal constraint condition or the second terminal constraint condition, the preset performance index, and the pseudospectral optimization algorithm to obtain optimized parameters, where the target parameters include: altitude change parameters, velocity change parameters, thrust direction change parameters, and fuel mass change parameters; The integration unit is configured to perform dynamic integration on the gliding section based on the optimization parameter to obtain the motion trajectory of the impactor. The determination unit is configured to determine a motion trajectory diagram of the impact process between the impactor and the asteroid based on the motion trajectory of the impactor and the motion trajectory of the asteroid.

8. An electronic device, characterized in that, It includes a memory and a processor. The memory is used to store a program that supports the processor to execute the method according to any one of claims 1 to 6, and the processor is configured to execute the program stored in the memory.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is run by the processor, it executes the steps of the method according to any one of claims 1 to 6 above.

Images