CN115848648A - Pseudo-spectrum orbit optimization method and device for impacting small planet by kinetic energy - Google Patents
Pseudo-spectrum orbit optimization method and device for impacting small planet by kinetic energy Download PDFInfo
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Abstract
The invention provides a pseudo-spectrum orbit optimization method and a pseudo-spectrum orbit optimization device for a kinetic energy impacting asteroid, which relate to the technical field of asteroid interception and comprise the following steps: constructing a multilateral Kepler motion rendezvous problem based on the motion parameters of the impactor, the motion parameters of the asteroid and the target parameters of the power adjusting section, and determining a terminal constraint condition of the power adjusting section by considering the impact condition between the impactor and the asteroid based on the constraint of the multilateral Kepler motion rendezvous problem; optimizing target parameters of the impactor based on terminal constraint conditions, preset performance indexes and a multi-segment pseudo-spectrum optimization algorithm to obtain optimized parameters; performing dynamic integration on the gliding section based on the optimized parameters to obtain the motion trail of the impactor; the method has the advantages that the motion trail graph of the impact process between the impactor and the asteroid is determined based on the motion trail of the impactor and the running trail of the asteroid, and the technical problem that the existing orbit determination method for impacting the asteroid by kinetic energy is low in efficiency and accuracy is solved.
Description
Technical Field
The invention relates to the technical field of asteroid interception, in particular to a pseudo-spectrum orbit optimization method and device for a kinetic energy impacting asteroid.
Background
For the kinetic energy impact asteroid task, which is essentially a multi-segment, multivariable and multi-constraint optimization problem, the current aircraft trajectory optimization problem has relevant research progress, for example, sentinella et al firstly adopt an indirect method to change the electric propulsion trajectory optimization problem into an edge value problem, then use a genetic algorithm to search for parameters which meet the edge value condition and minimize the error, and then use the obtained optimal parameters as initial values of an indirect method to gradually converge to an optimal solution. However, the indirect method has the disadvantages that the estimation of the covariates is needed, and the guessing of the initial values is high. Wang Hua, etc. solves the trajectory optimization problem under the condition of limited thrust by using a direct targeting method, provides a conversion process from an optimal control problem to a parameter optimization problem, and simultaneously converts state and control constraints, and the method is successfully applied to the solution of the rendezvous and docking problem. However, the direct method is limited in that most direct methods cannot give the co-modal information, and thus the optimality of the solution cannot be guaranteed. Dueri et al studied the planetary soft landing problem by first transforming the problem into a convex second order cone problem, which ensures global optimality of the solution, and then introduces an interior point method and gives a framework for real-time computation. Wong et al studied parallel tangent and penalty function combination algorithms that use penalty functions to deal with terminal constraints to accelerate convergence. Another common optimization algorithm is the particle swarm optimization. However, it is prone to premature convergence, especially in dealing with complex multimodal search problems. And the particle swarm algorithm has the problems of poor local optimization capability, local minimum trapping and the like.
No effective solution has been proposed to the above problems.
Disclosure of Invention
In view of this, the present invention aims to provide a pseudo-spectrum orbit optimization method and apparatus for a kinetic energy impacting a small planet, so as to alleviate the technical problem that the existing orbit determination method for a kinetic energy impacting a small planet is low in efficiency and precision.
In a first aspect, an embodiment of the present invention provides a pseudo-spectrum orbit optimization method for a kinetic energy impinging small planet, including: obtaining a motion parameter and a minor planet motion parameter of an impactor, and designing a target parameter of a power adjusting section of the impactor, wherein the target parameter comprises: optimizing state quantity, control quantity and additional parameters; constructing a multilateral Kepler motion rendezvous problem based on the motion parameters of the impactor, the motion parameters of the asteroid and the target parameters of the power adjusting section, and determining a terminal constraint condition of the power adjusting section based on the multilateral Kepler motion rendezvous problem and an impact condition between the impactor and the asteroid; optimizing the target parameters of the impactor based on the terminal constraint conditions, preset performance indexes and a multi-segment pseudo-spectrum optimization algorithm to obtain optimized parameters, wherein the target parameters comprise: altitude, speed, thrust and fuel quality parameters; performing dynamic integration on the gliding section based on the optimization parameters to obtain the motion track of the impactor; and determining a motion trail diagram of the impact process between the impactor and the asteroid on the basis of the motion trail of the impactor and the running trail of the asteroid.
Further, if the impactor motion parameters are an impactor initial position, an impactor initial speed and an impactor power configuration parameter, and the asteroid motion parameters are an asteroid initial position and an asteroid initial speed, constructing a multilateral kepler motion rendezvous problem based on the impactor motion parameters, the asteroid motion parameters and the target parameters of the power adjustment section, including: constructing a first kinematic model of the impactor based on the impactor motion parameters and the asteroid motion parameters; constructing a multilateral Kepler kinematic intersection problem by using a first kinematic model of the impactor and target parameters of the power adjusting section; and determining a first terminal constraint condition of a power adjusting section based on the multilateral Kepler motion intersection problem and the impact condition between the impactor and the minor planet.
Further, optimizing the target parameter of the impactor based on the terminal constraint condition, a preset performance index and a pseudo-spectrum optimization algorithm to obtain an optimized parameter, wherein the optimizing parameter comprises the following steps: 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 a first preset performance index; and performing Gaussian pseudo-spectrum discrete processing on the first preset performance index to determine a first optimization parameter.
Further, based on the optimization parameters, performing dynamic integration on the glide section to obtain the motion trajectory of the impactor, including: determining a first optimal impact approach point angle based on the first optimization parameter; calculating the optimal flight time of the impactor based on the first optimal impact approach point angle; and performing dynamic integration on the glide section based on the optimal flight time, the first terminal constraint condition and a two-body kinematics equation to obtain a first motion track of the impactor.
Further, if the motion parameters of the impactor further include the time required by the impactor to impact an asteroid, and the motion parameters of the asteroid are an initial position of the asteroid and an initial speed of the asteroid, constructing a multilateral kepler motion intersection problem based on the motion parameters of the impactor, the motion parameters of the asteroid and target parameters of the power adjustment section, including: constructing a second kinematic model of the impactor based on the impactor motion parameters and the asteroid motion parameters; constructing a unilateral Kepler problem by using a first kinematic model of the impactor and target parameters of the power adjusting section; and determining a second terminal constraint condition of the power adjusting section based on the unilateral Kepler problem and the impact condition between the impactor and the asteroid.
Further, optimizing the target parameter of the impactor based on the terminal constraint condition, the preset performance index and the multi-segment pseudo-spectrum optimization algorithm to obtain an optimized parameter, wherein the optimizing parameter comprises: determining the minimum fuel consumption of the impactor as a second preset performance index; and performing Gaussian pseudo-spectrum discrete processing on the second preset performance index to determine a second optimization parameter.
Further, based on the optimization parameters, performing dynamic integration on the glide section to obtain the motion trajectory of the impactor, including: and performing dynamic integration on the glide section based on the time required by the impactor to impact the asteroid, the second optimization parameter, the second terminal constraint condition and a two-body kinematics equation to obtain a second motion trail of the impactor.
Further, determining a motion trail diagram of the impact process between the impactor and the asteroid based on the motion trail of the impactor and the running trail of the asteroid, wherein the motion trail diagram comprises the following steps: performing dynamic integration on the motion parameters of the minor planet to obtain the running track of the minor planet; and determining a motion trail diagram of the impact process between the impactor and the asteroid on the basis of the motion trail of the impactor and the running trail of the asteroid.
In a second aspect, an embodiment of the present invention further provides a pseudo-spectral orbit optimization apparatus for a kinetic energy impinging small planet, including: the system comprises an acquisition unit, a construction unit, an optimization unit, an integration unit and a determination unit, wherein the acquisition unit is used for acquiring the motion parameters of the impactor and the minor planet motion parameters and designing the target parameters of the power adjustment section of the impactor, and the target parameters comprise: optimizing the state quantity, the control quantity and the additional parameters; the construction unit is used for constructing a multilateral Kepler motion rendezvous problem based on the impactor motion parameters, the asteroid motion parameters and the target parameters of the power adjustment section, and determining a terminal constraint condition of the power adjustment section based on the multilateral Kepler motion rendezvous problem and the impact condition between the impactor and the asteroid; the optimization unit is configured to optimize a target parameter of the impactor based on the terminal constraint condition, a preset performance index and a multi-segment pseudo-spectrum optimization algorithm to obtain an optimized parameter, where the target parameter includes: altitude, speed, thrust and fuel quality parameters; the integration unit is used for performing dynamic integration on the glide section based on the optimization parameters to obtain the motion trail of the impactor; the determining unit is used for determining a motion trail graph of the impact process between the impactor and the asteroid based on the motion trail of the impactor and the running trail of the asteroid.
In a 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 that supports the processor to execute the method in the first aspect, and the processor is configured to execute the program stored in the memory.
In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium.
In the embodiment of the invention, through obtaining the motion parameters of the impactor and the minor planet motion parameters and designing the target parameters of the power adjusting section of the impactor, the target parameters comprise: optimizing the state quantity, the control quantity and the additional parameters; constructing a multilateral Kepler motion rendezvous problem based on the motion parameters of the impactor, the motion parameters of the asteroid and the target parameters of the power adjusting section, and determining a terminal constraint condition of the power adjusting section based on the multilateral Kepler motion rendezvous problem and an impact condition between the impactor and the asteroid; optimizing the target parameters of the impactor based on the terminal constraint conditions, preset performance indexes and a multi-segment pseudo-spectrum optimization algorithm to obtain optimized parameters, wherein the target parameters comprise: altitude, speed, thrust and fuel quality parameters; performing dynamic integration on the gliding section based on the optimization parameters to obtain the motion trail of the impactor; based on the motion trail of the impactor and the running trail of the asteroid, a motion trail graph of the impacting process between the impactor and the asteroid is determined, the purpose of accurately and efficiently determining the track of the little planet impacted by the kinetic energy of the impactor is achieved, the technical problem that an existing track determining method for impacting the asteroid by the kinetic energy is low in efficiency and precision is solved, and therefore the technical effect of improving the accuracy and efficiency of determining the track of the little planet impacted by the kinetic energy of the impactor is achieved.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
Fig. 1 is a flowchart of a pseudo-spectral orbit optimization method for a kinetic energy impacting a small planet according to an embodiment of the present invention;
FIG. 2 is a schematic view of the entire stroke of the impact when the motion parameters of the impactor do not include the time required for the impactor to impact the asteroid provided by the embodiment of the invention;
FIG. 3 is a graphical illustration of the change in track height, flight speed, engine thrust direction, fuel mass over time for a scenario with the earliest impact as a performance metric provided by an embodiment of the present invention;
FIG. 4 is a graphical illustration of the change in track height, flight speed, engine thrust direction, fuel mass over time for the case of the latest impact as a performance indicator provided by an embodiment of the present invention;
FIG. 5 is a schematic illustration of a full stroke trajectory of a striker provided in accordance with an embodiment of the present invention;
FIG. 6 is a schematic illustration of the overall impact process provided by an embodiment of the present invention;
FIG. 7 is a schematic illustration of another impact overall process provided by an embodiment of the present invention;
FIG. 8 is a schematic diagram of the entire impact process when the motion parameters of the impactor include the time required for the impactor to impact the asteroid provided by the embodiment of the invention;
FIG. 9 is a schematic illustration of the change in striker rail height, magnitude of flight velocity, fuel mass, and firing angle over time for the most fuel efficient case provided by an embodiment of the present invention;
FIG. 10 is a schematic diagram of a global optimized trajectory of a asteroid and an impactor provided by an embodiment of the invention;
FIG. 11 is a schematic diagram of a pseudo-spectral orbit optimization device for a small planet struck by kinetic energy according to an embodiment of the present invention;
figure 12 is a schematic diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
To make the objects, 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, and it is apparent that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The first embodiment is as follows:
in accordance with an embodiment of the present invention, there is provided an embodiment of a pseudo-spectral orbit optimization method for kinetic energy impinging small planets, it is noted that the steps illustrated in the flowchart of the figure may be performed in a computer system such as a set of computer executable instructions and that while a logical order is illustrated in the flowchart, in some cases the steps illustrated or described may be performed in an order different than here.
Fig. 1 is a flowchart of a pseudo-spectral orbit optimization method of a kinetic energy impinging a small planet, as shown in fig. 1, comprising the steps of:
step S102, obtaining a motion parameter and a minor planet motion parameter of the impactor, and designing a target parameter of a power adjusting section of the impactor, wherein the target parameter comprises: optimizing state quantity, control quantity and additional parameters;
step S104, constructing a multilateral Kepler motion intersection problem based on the motion parameters of the impactor, the motion parameters of the asteroid and the target parameters of the power adjusting section, and determining a terminal constraint condition of the power adjusting section based on the multilateral Kepler motion intersection problem and an impact condition between the impactor and the asteroid;
step S106, optimizing target parameters of the impactor based on the terminal constraint conditions, preset performance indexes and a multi-segment pseudo-spectrum optimization algorithm to obtain optimized parameters, wherein the target parameters comprise: altitude, speed, thrust and fuel quality parameters;
step S108, performing dynamics integration on the glide section based on the optimization parameters to obtain the motion trail of the impactor;
and step S110, determining a motion trail diagram of the impact process between the impactor and the asteroid based on the motion trail of the impactor and the running trail of the asteroid.
In the embodiment of the invention, the motion parameters of the impactor and the minor planet motion parameters are obtained, and the target parameters of the power adjusting section of the impactor are designed, wherein the target parameters comprise: optimizing the state quantity, the control quantity and the additional parameters; constructing a Kepler problem based on the motion parameters of the impactor, the motion parameters of the asteroid and the target parameters of the power adjusting section, and determining a terminal constraint condition of the power adjusting section based on the multilateral Kepler motion rendezvous problem and an impact condition between the impactor and the asteroid; optimizing the target parameters of the impactor based on the terminal constraint conditions, preset performance indexes and a multi-segment pseudo-spectrum optimization algorithm to obtain optimized parameters, wherein the target parameters comprise: altitude, speed, thrust and fuel quality parameters; performing dynamic integration on the gliding section based on the optimization parameters to obtain the motion track of the impactor; the method comprises the steps of determining a motion trail graph of the striking process between the striker and the asteroid based on the motion trail of the striker and the running trail of the asteroid, achieving the purpose of accurately and efficiently determining the track of the asteroid struck by the kinetic energy of the striker, and further solving the technical problem that the existing track determination method for striking the asteroid by the kinetic energy is low in efficiency and precision, so that the technical effect of improving the track accuracy and efficiency of determining the striking asteroid struck by the kinetic energy of the striker is achieved.
In the embodiment of the invention, two specific processes of the pseudo-spectral orbit optimization method for impacting the small planet by kinetic energy are designed according to different acquired motion parameters of the impactor, and the two processes are explained in detail below.
If the motion parameters of the impactor are the initial position of the impactor, the initial speed 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 speed of the asteroid, the step S104 includes the following steps:
step S11, constructing a first kinematic model of the impactor based on the impactor motion parameters and the minor planet motion parameters;
s12, constructing a multilateral Kepler motion intersection problem by using a first kinematic model of the impactor and target parameters of the power adjusting section;
and S13, determining a first terminal constraint condition of a power adjusting section based on the multilateral Kepler motion intersection problem and the impact condition between the impactor and the minor planet.
Step S106 includes the steps of:
step S21, 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 a first preset performance index;
and S22, performing Gaussian pseudo-spectrum discrete processing on the first preset performance index to determine a first optimization parameter.
Step S108 includes the steps of:
step S31, determining a first optimal impact approximate point angle based on the first optimization parameter;
step S32, calculating the optimal flight time of the impactor based on the first optimal impact approximate point angle;
and S33, performing dynamic integration on the gliding section based on the optimal flight time, the first terminal constraint condition and a two-body kinematics equation to obtain a first motion track of the impactor.
In the embodiment of the invention, if the motion parameters of the impactor are the initial position of the impactor, the initial speed 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 speed of the asteroid, two constant-value thrusts are designed in the embodiment of the invention.
Firstly, multi-section modeling is carried out on a power adjusting section and a gliding section of the impactor:
dynamic model of dynamic adjustment section of impactor:
in the cartesian Earth-centered inertial systems (ECI), the striker is considered to be a particle, the dynamics of which can be expressed as:
wherein r is m ＝[x(t)y(t)z(t)] T Is a position vector, v m ＝[v x (t)v y (t)v z (t)] T Is the velocity vector, μ is the earth's gravitational constant, T is the vacuum thrust, m is the mass of the impactor, g 0 Is the gravitational acceleration at sea level, I sp Is the engine specific impulse, u = [ u ] x (t)u y (t)u z (t)] T Is the direction of the thrust.
Optimizing the power adjusting section, wherein the optimized state quantity x is the position vector r of the impactor m Velocity vectorv m And the residual fuel mass m, wherein the control quantity is a thrust direction vector u, and parameters are introduced, namely a minor planet hitting time approximate point angle E and a minor planet orbit radius p are respectively used as optimization quantities. Let t 0 Is an initial time, t f The end time at which the power adjustment of the striker is ended.
Initial constraint:
and (3) process constraint:
and (4) terminal constraint:
dynamic models of impactor and asteroid kepler motions:
the multilateral kepler motion intersection problem is called as the multilateral kepler motion intersection problem, and can be expressed as follows:
minor planets: at an initial time t 0 Total time of flight Δ t, impact time position r T (t 0 +Δt)；
A striker: the initial moment of the power section is t 0 End of power sectionAt time tf, duration of glide Δ t trans The impact time position is r m (t 0 +Δt)；
The following constraints can be obtained in combination with the impact conditions:
in the formula (6), t f ，r f ，v f For terminal constraint of a power section of the impactor, combining relationships among variables in a graph and impact condition constraint, solving a Lambert problem, and deducing the terminal constraint:
knowing the position and speed r of the asteroid circular orbit in kepler motion at the moment of launch T (t 0 ),v T (t 0 ) Six orbits of the small planet (including a modulus h of specific angular momentum, an eccentricity e, an orbit inclination angle i, an amplitude angle omega of a near place and a right ascension omega of a rising intersection point) can be obtained,
h＝r×v (10)
now, a vector n is defined, which is perpendicular to the plane defined by the orbital angular momentum vector and the north pole axis (K):
n＝K×h (15)
definition u 0 Is the sum of the true perigee angle and the perigee argument. Then, according to the theorem of vector projection, it can be countedCalculating the ascension angle omega of the intersection point, the argument omega of the perigee and the parameter u 0 ：
The true anomaly angle θ can then be calculated 0
θ 0 ＝u 0 -ω (17)
Angle of approach E 0 Can be expressed as:
mean-approximate-point angle of initial moment of asteroid:
M(t 0 )＝M 0 ＝E 0 -e sin E 0 (19)
the off-near point angle of the asteroid at the impact moment is an optimization parameter E to be predicted, and by setting the true near point angle theta and the mean near point angle M of the asteroid during impact, the following can be deduced:
M＝E-e sin E (21)
the whole flight time of the asteroid is delta t, and the position and the speed of the struck asteroid are r PIP ,v PIP 。
M ZXZ ＝M Z (Ω)M X (i)M Z (ω,θ) (24)
The initial position and the speed of the impactor in the glide section are reversely deduced according to the deduction, and the initial position and the speed are the terminal state r of the power adjusting section in the stage due to the continuous flight path f ,v f 。
Then solving the Lambert problem, and setting the transfer true near point angle delta theta and glide time delta t of the impactor at the last section trans And the lagrangian coefficients f, g,
so far, an iterative computation relationship of terminal constraints can be established:
t f -t 0 ＝Δt-Δt trans (33)
in addition, the power adjusting section has two sections with large and small thrust forces which are connected together through a series of connecting conditions. These constraints guarantee continuous variation of position and speed from segment to segment and take account of abrupt changes in quality:
r (p) (t f )-r (p+1) (t 0 )＝0
v (p) (t f )-v (p+1) (t 0 )＝0
m (p) (t f )-m (p+1) (t 0 )＝0
r (2) (t f )＝r(t f )
v (2) (t f )＝v(t f )
m (2) (t f )＝m(t f ) (35)
wherein, the superscript (p) represents the number of each stage, and p is 1,2.
Then, taking the earliest and latest impact time and the largest and smallest consumed fuel as a performance index J, and carrying out Gaussian pseudo-spectrum dispersion, wherein the specific derivation process is as follows:
J＝m(t f )，J＝-m(t f )，J＝t f ，J＝-t f (36)
first, the generalized nonlinear system dynamics equation is as follows:
wherein the state variable x (t) ∈ R n Control variable u (t) e R m Time t ∈ [ t ] 0 ，t 2 ]。
The time domain is then transferred to the time interval [ -1,1] because the support points of the lagrange interpolation polynomial are chosen to be the orthogonal points located in the time interval [ -1,1], which is done by the following mapping function.
Taking τ as an independent variable, the state variable and the control variable are approximately expressed by a Lagrange interpolation polynomial as follows:
can know L i (τ) and L i * (τ) has the following properties:
differentiating the approximate expressions of the state variables and the control variables to obtain:
while
Can be obtained offline by:
the kinetic differential equation constraint is thus converted into an algebraic constraint:
the end state is approximated by a gaussian integral and should satisfy:
the performance index is also approximated by a gaussian integral:
wherein ω is k Is a gaussian weight.
Through the above processing, the optimal control problem is changed to find the optimal state variable X i (i =0, …, N) and boundary conditions of control variables:
and path constraints on the interpolation points:
thereby converting the optimal control problem into a nonlinear programming problem.
And (3) solving the optimal flight time delta t of the whole course according to the optimized minor planet impact point approximate point angle E, and performing dynamic integration on the glider section of the impactor on an integration interval t according to the two-body problem to realize the whole course track optimization.
r (3) (0)＝r (2) (t f ) (53)
v (3) (0)＝v (2) (t f ) (54)
t∈[0，Δt+t 0 -t f ] (55)
As shown in fig. 2, the motion parameters of the impactor shown in fig. 2 do not include the time required for the impactor to impact the asteroid, and the impact is complete.
The invention can quickly calculate the optimal state quantity and the control quantity of the power adjusting section meeting the constraint condition, wherein the control quantity is a thrust direction vector u x ，u y ，u z ]. FIG. 3 shows the track height and flying speed in the case of the earliest impact as a performance indexEngine thrust direction, fuel mass change over time. Fig. 4 is a graph of the change in the rail height, the flight speed, the engine thrust direction, and the fuel mass with time in the case of the latest impact as a performance index. Comparing the two figures also shows that the airspeed at the earliest impact event is significantly greater than the airspeed at the latest impact event, and the remaining fuel mass is approximately the same in both cases, with total depletion. In fig. 5, the transition orbit of the gliding section is calculated through two-body motion dynamics integration, and then the whole-section orbit generation is completed by combining the power adjusting section orbit optimized by the Gaussian pseudospectrum, so that the impactor can freely glide and impact the small planet after the short-time power adjustment is completed. Fig. 6 is a schematic diagram of the whole process of the striking of the striker with the small planet. Fig. 7 is the simulation result of the impact scene after the orbit of the asteroid is added, and the impactor can accurately impact the asteroid.
In the embodiment of the invention, the impactor impacts the asteroid through three stages of high-thrust flight, low-thrust flight and free glide. And segmenting the task according to the power configuration and the initial state, respectively modeling in the power adjusting section and the gliding section, and selecting reasonable state quantity, control quantity and parameters for optimization. And (4) according to the multilateral Kepler motion intersection problem and the impact condition, deriving the terminal constraint of the power section. All constraints and performance indexes are set, and the derivative of the state variable to time is approximated by differentiating the global interpolation polynomial under the condition of pseudo-spectrum dispersion, so that the differential equation constraint is converted into a group of algebraic constraints. The optimal control problem is converted into a parameter optimization problem with a series of algebraic constraints, namely a nonlinear programming problem (NLP), the feasible solution of the NLP problem is the optimal state quantity and the optimal control quantity of the terminal position and speed constraints, and the rapid planning of the optimal track with the dynamic adjustment section is realized.
And taking the terminal state of the power adjusting section as the initial state of the gliding section, and performing integral solution on the orbit of the gliding section according to a Keplerian equation to realize the whole planning of the whole task.
If the motion parameters of the impactor further include the time required by the impactor to impact the asteroid, and the motion parameters of the asteroid are the initial position and the initial speed of the asteroid, the step S104 includes the following steps:
step S41, constructing a second kinematic model of the impactor based on the impactor motion parameters and the asteroid motion parameters;
s42, constructing a unilateral Kepler problem by using a first kinematic model of the impactor and target parameters of the power adjusting section;
and S43, determining a second terminal constraint condition of the power adjusting section based on the unilateral Kepler problem and the impact condition between the impactor and the asteroid.
Step S106 includes the steps of:
step S51, optimizing the target parameters of the impactor based on the terminal constraint conditions, the preset performance indexes and the multi-segment pseudo-spectrum optimization algorithm to obtain optimized parameters, wherein the method comprises the following steps:
step S52, determining the minimum fuel consumption of the impactor as a second preset performance index;
and S53, performing Gaussian pseudo-spectrum discrete processing on the second preset performance index to determine a second optimization parameter.
Step S108 includes the steps of:
and S61, performing dynamic integration on the glide section based on the time required by the impactor to impact the asteroid, the second optimization parameter, the second terminal constraint condition and a two-body kinematics equation to obtain a second motion track of the impactor.
In the embodiment of the invention, if the motion parameters of the impactor further comprise the time required by the impactor to impact the asteroid, the motion parameters of the asteroid are the initial position and the initial speed of the asteroid.
Firstly, modeling the power adjusting section and the gliding section of the impactor in a segmented mode:
dynamic model of dynamic adjustment section of impactor:
in the cartesian Earth-centered inertial systems (ECI), the striker is considered to be a particle, the dynamics of which can be expressed as:
wherein r is m ＝[x(t)y(t)z(t)] T Is a position vector, v m ＝[v x (t)v y (t)v z (t)] T Is the velocity vector, μ is the earth's gravitational constant, T is the vacuum thrust, m is the spacecraft mass, g 0 Is the gravitational acceleration at sea level, I sp Is the engine specific impulse, u = [ u ] x (t)u y (t)u z (t)] T Is the direction of the thrust.
Optimizing the power adjusting section:
state quantity x = [ r = m v m m]Control quantity of
And optimizing the parameter p.
Wherein the striker position vector r m Velocity vector v m And the residual fuel mass m is a state quantity, the thrust direction vector u is a control quantity, and the glider glide section half-path p of the impactor is an optimization parameter. Let t 0 At initial moments, t, of striker and target firing, respectively f The end time at which the striker finishes its power adjustment.
Initial constraint:
and (3) process constraint:
and (4) terminal constraint:
dynamic models of impactor and asteroid kepler motions:
the impactor starts Kepler movement after finishing the power adjustment section, and the asteroid always keeps Kepler movement, as shown in figure 3. Initial time t 0 Total time of flight Δ t, initial state r of the impactor and the small planet T (t 0 )、r m (t 0 ) Fixed and the remaining flight times of both are released from the Point of Impact (PIP) position r (t + Δ t), velocity v (t + Δ t), which is called the multilateral kepler motion crossing problem, which can be expressed as follows:
minor planets: at an initial time t 0 Total time of flight is Δ t, and terminal position is r T (t 0 +Δt)；
A striker: the initial moment of the power section is t 0 The end time is t f Duration of glide is Δ t trans ；
The following constraints can be obtained in combination with the impact conditions:
if the total time for realizing the hitting task is fixed, the terminal position of the target, namely the position of the impact point PIP, can be determined to be fixed due to the fact that the initial state and the dynamics law of the small planet are known. The above-described multilateral kepler motion intersection problem will degrade into a unilateral kepler problem, which translates into a multi-constrained optimization problem that strikes a fixed point.
In the formula (6), t f ,t f ,v f For terminal constraint of the power section of the impactor, combining the relationship among variables and impact condition constraint in fig. 3, solving the lambert problem, and deducing the terminal constraint:
knowing the position and speed r of the asteroid in the circular orbit at the moment of launch T (t 0 ),v T (t 0 ) Six orbits of the small planet can be obtained (including a modulus h of specific angular momentum, an eccentricity e, an orbit inclination angle i, an amplitude angle omega of a place close to the orbit, and a right ascension omega of a rising intersection point),
h＝r×v (64)
now, a vector n is defined, which is perpendicular to the plane defined by the orbital angular momentum vector and the north pole axis (K):
n＝K×h (69)
definition u 0 Is the sum of the true perigee angle and the perigee argument. Then, according to the vector projection theorem, the ascension Ω of the intersection point, the argument ω of the perigee, and the parameter u can be calculated 0 ：
The true anomaly angle θ can then be calculated 0
θ 0 ＝u 0 -ω (71)
Angle of approach E 0 Can be expressed as:
mean-approximate-point angle of initial moment of asteroid:
M(t 0 )＝M 0 ＝E 0 -e sin E 0 (73)
since the mission total flight Δ t, e =0 is known, the mean anomaly M of the impact position PIP can be determined.
The position and the speed of the asteroid at the time of impact are r T (t 0 +Δt),v T (t 0 +Δt)。
M ZXZ ＝M Z (Ω)M X (i)M Z (ω,θ) (76)
The initial position and the speed of the impactor in the gliding section are reversely deduced according to the derivation, and the initial state in the stage is also the terminal state r of the power adjusting section due to the continuous flight path f ,v f 。
Then solving the Lambert problem, and setting the transfer true near point angle delta theta and glide time delta t of the impactor at the last section rans Optimizing parameters of half-path p and Lagrange coefficients f, g,
so far, an iterative computation relationship of terminal constraints can be established:
t f -t 0 ＝Δt-Δt trans (85)
taking the most fuel-saving as a performance index J, and carrying out pseudo-spectrum dispersion, wherein the specific derivation process is as follows:
J＝-m(t f ) (87)
first, the nonlinear system dynamics equation is generalized:
wherein the state variable x (t) ∈ R n Control variable u (t) e R m Time t e [ t ∈ ] 0 ,t 2 ]。
The time domain is then transferred to the time interval [ -1,1] because the support points of the lagrange interpolation polynomial are chosen to be the orthogonal points located in the time interval [ -1,1], which is done by the following mapping function.
Taking tau as an independent variable, and approximating the state variable and the control variable by a Lagrange interpolation polynomial:
can know L i (tau) and L i * (τ) has the following properties:
differentiating the approximate expressions of the state variable and the control variable to obtain:
and then
Can be obtained offline by:
the kinetic differential equation constraint is thus converted into an algebraic constraint:
the end state is approximated by a gaussian integral and should satisfy:
the performance index is also approximated by a gaussian integral:
wherein ω is k Is a gaussian weight.
Through the above processing, the optimal control problem shifts to finding the boundary conditions of the optimal state variables Xi (i =0, …, N) and the control variables.
And path constraints on interpolation points
C(X K ,U k ,τ k ；t 0 ,t f )≤0(k＝1,…,N) (101)
Thereby converting the optimal control problem into a nonlinear programming problem.
And performing dynamic integration on the glider section of the impactor in an integration interval t according to a given target flight time delta t and a two-body problem, so as to realize the whole-process trajectory optimization.
r (2) (0)＝r (1) (t f ) (104)
v (2) (0)＝v (1) (t f ) (105)
t∈[0,Δt+t 0 -t f ](106)
Fig. 8 is a schematic diagram of the whole impact process when the motion parameters of the impactor provided by the embodiment of the invention comprise the time required by the impactor to impact the asteroid.
By the method, the flight time can be quickly calculated, and the trajectory of the impinger impinging on the small planet is optimized under the condition that the initial state is fixed. The included angle between the current thrust vector and the velocity vector is defined as a combustion angle, and fig. 9 shows the changes of the rail height of the impactor, the flying speed, the fuel quality and the combustion angle along with the time under the condition of fuel saving. Fig. 10 shows the optimized whole-course track of the asteroid and the impactor, the impactor runs on the initial orbit, the impact task is carried out at a specific position and speed, the power adjustment is firstly carried out, the track of the power section is optimized under the requirement of the most fuel-saving, and then the gliding section is entered to hit the target.
In the embodiment of the invention, the impactor impacts the asteroid through two stages of power adjustment and free gliding. And segmenting the task according to the power configuration and the initial state, respectively modeling in the power adjusting section and the gliding section, and selecting reasonable state quantity, control quantity and parameters for optimization. And (4) deriving terminal constraint of the power section according to the multilateral Kepler motion intersection problem and the impact condition. Setting all constraints and performance indexes, and approximating the time derivative of the state variable by differentiating a global interpolation polynomial under the condition of pseudo-spectrum dispersion so as to convert the constraint of a differential equation into a group of algebraic constraints. The optimal control problem is converted into a parameter optimization problem with a series of algebraic constraints, namely a nonlinear programming problem (NLP), the feasible solution of the NLP problem is the optimal state quantity, the optimal control and the optimal parameters of the terminal position and speed constraints, and the rapid planning of the optimal track with the dynamic adjustment section is realized.
Whether the asteroid can be hit successfully or not depends mainly on the final position and speed of the power adjusting section. Therefore, the reasonable and fast optimization of the power adjusting section becomes a key technology.
The second embodiment:
the embodiment of the invention also provides a pseudo-spectrum orbit optimization device for striking the small planet by the kinetic energy, which is used for executing the pseudo-spectrum orbit optimization method for striking the small planet by the kinetic energy provided by the embodiment of the invention.
As shown in fig. 11, fig. 11 is a schematic diagram of the pseudo-spectrum orbit optimization device for striking a small planet with kinetic energy, and the pseudo-spectrum orbit optimization device for striking a small planet with kinetic energy includes: an acquisition unit 10, a construction unit 20, an optimization unit 30, an integration unit 40 and a determination unit 50.
The acquisition unit is used for acquiring the motion parameters of the impactor and the minor planet motion parameters and designing the target parameters of the power adjustment section of the impactor, wherein the target parameters comprise: optimizing the state quantity, the control quantity and the additional parameters;
the construction unit is used for constructing a multilateral Kepler motion rendezvous problem based on the impactor motion parameters, the asteroid motion parameters and the target parameters of the power adjustment section, and determining a terminal constraint condition of the power adjustment section based on the multilateral Kepler motion rendezvous problem and the impact condition between the impactor and the asteroid;
the optimization unit is configured to optimize a target parameter of the impactor based on the terminal constraint condition, a preset performance index and a multi-segment pseudo-spectrum optimization algorithm to obtain an optimized parameter, where the target parameter includes: altitude variation parameters, speed variation parameters, thrust direction variation parameters and fuel mass variation parameters;
the integration unit is used for performing dynamic integration on the gliding section based on the optimization parameters to obtain the motion trail of the impactor;
the determination unit is used for determining a motion trail graph of the impact process between the impactor and the asteroid based on the motion trail of the impactor and the running trail of the asteroid.
In the embodiment of the invention, the motion parameters of the impactor and the minor planet motion parameters are obtained, and the target parameters of the power adjusting section of the impactor are designed, wherein the target parameters comprise: optimizing the state quantity, the control quantity and the additional parameters; constructing a multilateral Kepler motion rendezvous problem based on the motion parameters of the impactor, the motion parameters of the asteroid and the target parameters of the power adjusting section, and determining a terminal constraint condition of the power adjusting section based on the multilateral Kepler motion rendezvous problem and an impact condition between the impactor and the asteroid; optimizing the target parameters of the impactor based on the terminal constraint conditions, preset performance indexes and a multi-segment pseudo-spectrum optimization algorithm to obtain optimized parameters, wherein the target parameters comprise: altitude, speed, thrust and fuel quality parameters; performing dynamic integration on the gliding section based on the optimization parameters to obtain the motion track of the impactor; the method comprises the steps of determining a motion trail graph of the striking process between the striker and the asteroid based on the motion trail of the striker and the running trail of the asteroid, achieving the purpose of accurately and efficiently determining the track of the asteroid struck by the kinetic energy of the striker, and further solving the technical problem that the existing track determination method for striking the asteroid by the kinetic energy is low in efficiency and precision, so that the technical effect of improving the track accuracy and efficiency of determining the striking asteroid struck by the kinetic energy of the striker is achieved.
Example three:
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 the first embodiment, and the processor is configured to execute the program stored in the memory.
Referring to fig. 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, wherein the processor 60, the communication interface 63 and the memory 61 are connected through the bus 62; the processor 60 is arranged to execute executable modules, such as computer programs, stored in the memory 61.
The Memory 61 may include a high-speed Random Access Memory (RAM) and may also include a non-volatile Memory (non-volatile Memory), such as at least one disk Memory. The communication connection between the network element of the system 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, a wide area network, a local network, a metropolitan area network, and the like can be used.
The bus 62 may be an ISA bus, PCI bus, EISA bus, or the like. The bus may be divided into an address bus, a data bus, a control bus, etc. For ease of illustration, only one double-headed arrow is shown in FIG. 12, but that does not indicate only one bus or one type of bus.
The memory 61 is used for storing a program, the processor 60 executes the program after receiving an execution instruction, and the method executed by the apparatus defined by the flow process disclosed in any of the foregoing embodiments of the present invention may be applied to the processor 60, or implemented by the processor 60.
The processor 60 may be an integrated circuit chip having signal processing capabilities. In implementation, the steps of the above method may be performed by instructions in the form of hardware integrated logic circuits or software in the processor 60. The Processor 60 may be a general-purpose Processor, including a Central Processing Unit (CPU), a Network Processor (NP), and the like; the device 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, discrete hardware components. The various methods, steps and logic blocks disclosed in the embodiments of the present invention may be implemented or performed. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like. The steps of the method disclosed in connection with the embodiments of the present invention may be directly implemented by a hardware decoding processor, or implemented by a combination of hardware and software modules in the decoding processor. The software modules may be located in ram, flash, rom, prom, or eprom, registers, etc. as is well known in the art. The storage medium is located in a memory 61, and the processor 60 reads the information in the memory 61 and, in combination with its hardware, performs the steps of the above method.
Example four:
the embodiment of the present invention further provides a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the computer program performs the steps of the method in the first embodiment.
In addition, in the description of the embodiments of the present invention, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the several embodiments provided in the present application, it should be understood that the disclosed system, apparatus and method may be implemented in other ways. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units is only one logical division, and there may be other divisions when actually implemented, and for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection of devices or units through some communication interfaces, and may be in an electrical, mechanical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one position, or may be distributed on multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit.
Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: those skilled in the art can still make modifications or changes to the embodiments described in the foregoing embodiments, or make equivalent substitutions for some features, within the scope of the disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (11)
1. A pseudo-spectral orbit optimization method for a kinetic energy impacting small planet is characterized by comprising the following steps:
obtaining a motion parameter and a minor planet motion parameter of the impactor, and designing a target parameter of a power adjusting section of the impactor, wherein the target parameter comprises: optimizing the state quantity, the control quantity and the additional parameters;
constructing a multilateral Kepler motion rendezvous problem based on the motion parameters of the impactor, the motion parameters of the asteroid and the target parameters of the power adjusting section, and determining a terminal constraint condition of the power adjusting section by considering the impact condition between the impactor and the asteroid based on the multilateral Kepler motion rendezvous problem;
optimizing the target parameters of the impactor based on the terminal constraint conditions, preset performance indexes and a multi-segment pseudo-spectrum optimization algorithm to obtain optimized parameters, wherein the target parameters comprise: altitude, speed, thrust and fuel quality parameters;
performing dynamic integration on the gliding section based on the optimization parameters to obtain the motion track of the impactor;
and determining a motion trail diagram of the impact process between the impactor and the asteroid on the basis of the motion trail of the impactor and the running trail of the asteroid.
2. The method of claim 1, wherein if the impactor motion parameters are impactor initial position, impactor initial speed and impactor power configuration parameters and the asteroid motion parameters are asteroid initial position and asteroid initial speed, constructing a multilateral Keplerian motion rendezvous problem based on the impactor motion parameters, the asteroid motion parameters and the target parameters of the power adjustment segment comprises:
constructing a first kinematic model of the impactor based on the impactor motion parameters and the asteroid motion parameters;
constructing a multilateral Kepler motion intersection problem by using a first kinematic model of the impactor and target parameters of the power adjusting section;
and determining a first terminal constraint condition of a power adjusting section based on the multilateral Kepler motion intersection problem and the impact condition between the impactor and the minor planet.
3. The method of claim 2, wherein optimizing the target parameter of the impactor based on the terminal constraint condition, a preset performance index and a multi-segment pseudo-spectrum optimization algorithm to obtain an optimized parameter comprises:
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 a first preset performance index;
and performing pseudo-spectrum discrete processing on the first preset performance index to determine a first optimization parameter.
4. The method of claim 3, wherein dynamically integrating the glide segment based on the optimization parameter to obtain the trajectory of the impactor comprises:
determining a first optimal impact approach point angle based on the first optimization parameter;
calculating the optimal flight time of the impactor based on the first optimal impact approach point angle;
and performing dynamic integration on the glide section based on the optimal flight time, the first terminal constraint condition and a two-body kinematics equation to obtain a first motion track of the impactor.
5. The method of claim 2, wherein if the impactor motion parameters further include the time required for the impactor to impact the asteroid, and the asteroid motion parameters are an asteroid initial position and an asteroid initial velocity, constructing the kepler problem based on the impactor motion parameters, the asteroid motion parameters, and the target parameters of the power adjustment segment comprises:
constructing a second kinematic model of the impactor based on the impactor motion parameters and the asteroid motion parameters;
constructing a unilateral Kepler problem by using a first kinematic model of the impactor and target parameters of the power adjusting section;
and determining a second terminal constraint condition of the power adjusting section based on the unilateral Kepler problem and the impact condition between the impactor and the asteroid.
6. The method of claim 5, wherein optimizing the target parameter of the impactor based on the terminal constraint condition, a preset performance index and a multi-segment pseudo-spectrum optimization algorithm to obtain an optimized parameter comprises:
determining the minimum fuel consumption of the impactor as a second preset performance index;
and performing pseudo-spectrum discrete processing on the second preset performance index to determine a second optimization parameter.
7. The method of claim 6, wherein dynamically integrating the glide slope based on the optimization parameters to obtain the trajectory of the impactor comprises:
and performing dynamic integration on the glide section based on the time required by the impactor to impact the asteroid, the second optimization parameter, the second terminal constraint condition and a two-body kinematics equation to obtain a second motion trail of the impactor.
8. The method of claim 1, wherein 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 comprises:
performing dynamic integration on the motion parameters of the asteroid to obtain the running track of the asteroid;
and determining a motion trail diagram of the impact process between the impactor and the asteroid on the basis of the motion trail of the impactor and the running trail of the asteroid.
9. A pseudo-spectral orbit optimization device for a small planet impacted by kinetic energy, comprising: an acquisition unit, a construction unit, an optimization unit, an integration unit and a determination unit, wherein,
the acquisition unit is used for acquiring the motion parameters of the impactor and the minor planet motion parameters and designing the target parameters of the power adjustment section of the impactor, wherein the target parameters comprise: optimizing the state quantity, the control quantity and the additional parameters;
the construction unit is used for constructing a multilateral Kepler motion rendezvous problem based on the impactor motion parameters, the asteroid motion parameters and the target parameters of the power adjustment section, and determining a terminal constraint condition of the power adjustment section based on the multilateral Kepler motion rendezvous problem and the impact condition between the impactor and the asteroid;
the optimization unit is configured to optimize a target parameter of the impactor based on the terminal constraint condition, a preset performance index and a pseudo-spectrum optimization algorithm to obtain an optimized parameter, where the target parameter includes: altitude, speed, thrust and fuel quality parameters;
the integration unit is used for performing dynamic integration on the glide section based on the optimization parameters to obtain the motion trail of the impactor;
the determining unit is used for determining a motion trail graph of the impact process between the impactor and the asteroid based on the motion trail of the impactor and the running trail of the asteroid.
10. An electronic device comprising a memory for storing a program that enables a processor to perform the method of any of claims 1 to 8 and a processor configured to execute the program stored in the memory.
11. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method according to any one of the claims 1 to 8.
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