Ballistic trajectory planning method based on inertia weight particle swarm algorithm

Abstract

The invention discloses a trajectory planning method based on an inertia weight particle swarm algorithm, and belongs to the technical field of aerospace vehicle launching trajectory planning. Firstly, a carrier mass center dynamics and kinematics equation is established; then, establishing a mathematical representation model of launching trajectory planning, constructing a fitness function of launching trajectory injection parameters, determining geometric significance of deviation between terminal injection parameters obtained by the function and expected injection parameters, and converting the deviation of the terminal injection parameters and the expected injection parameters into a multivariate function of trajectory planning model control input; a launching trajectory planning problem meeting an injection requirement is converted into a minimum value optimization problem of a multivariate function, and an inertia weight particle swarm optimization algorithm is adopted to carry out optimization solution. The method still has better convergence precision and convergence speed under the conditions of lower initial parameter precision and more input design parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of space vehicle launch trajectory planning, and in particular to a trajectory planning method based on inertia weighted particle swarm algorithm. Background Art

[0002] Space launch ballistics is a discipline that studies the establishment of space trajectory equations, trajectory design, launch plan planning, and trajectory calculation for space vehicles in complex, multi-field coupled environments. The ability to establish space trajectory equations, design launch trajectories, calculate trajectories, and perform performance analysis and evaluation is crucial for space launch testing and control, spacecraft measurement and control engineering, and space launch command.

[0003] A launch plan is a set of adjustable parameters that determine and control the active phase of a launch vehicle's flight, ensuring it provides the required orbital insertion parameters for the spacecraft under standard conditions. To ensure the payload's orbital insertion, while meeting the launch plan's constraints, the trajectory planning parameters must be rationally selected based on the specific launch vehicle type and structure, as well as the corresponding flight program variations.

[0004] Initially, adaptive guidance employed polynomial guidance, while iterative guidance inherits the principles of polynomial guidance and is a stepwise approximation method. Because it primarily relies on iteration to continuously solve for the optimal orbital insertion point and trajectory, it is called an iterative guidance method. Iterative guidance methods have been successfully applied to orbit insertion during the ascent phase of launch vehicles, offering robust calculation methods for various orbital conditions. However, with the advancement of future aerospace technology, the requirements for guidance accuracy in space missions will continue to increase. The strong nonlinearity and parameter uncertainty of current dynamic models hinder the development of high-precision guidance technology. Intelligent technology plays a crucial role in promoting the advancement of aerospace guidance technology.

[0005] Typically, we use Newton iteration, direct method, indirect method, etc. to conduct trajectory planning research. Among them, Newton iteration is a traditional iterative solution method. When applied to trajectory planning parameter design, it can effectively solve the nonlinear problem of the equation when designing parameters. However, it is difficult to ensure the convergence of the calculation for multi-objective optimization problems. In addition, convex optimization calculation methods have good convergence and high computational efficiency, but their various calculation methods have some limitations: for example, lossless convexification cannot solve under conditions where aerodynamic conditions cannot be ignored, sequential convexification relies on linearization accuracy and cannot guarantee the calculation accuracy, and LPSCP performs poorly when facing complex problems.

[0006] The particle swarm algorithm (PSO) offers advantages such as simple computational methods and low convergence requirements. Yang Xixiang, Jiang Zhenyu, and others used it to calculate trajectory planning, demonstrating its feasibility and superiority for such complex problems. However, its simple use of the maximum deviation to find the optimal solution reduces computational efficiency and ignores the inherent relationships between various parameters, making the penalty function in the calculation unfocused. This can significantly increase the computational effort when initial accuracy is low. Summary of the Invention

[0007] In response to the above-mentioned problems, the present invention aims to provide a trajectory planning method based on an inertia-weighted particle swarm algorithm. By analyzing the physical meaning of the parameters that need to be optimized in the trajectory planning of space vehicle launches, the spatial geometric relationship between the parameters is found, thereby establishing a fitness model suitable for the intelligent particle swarm algorithm. With the help of the particle swarm algorithm, the traditional trajectory planning parameter design is optimized, so that it can still have good convergence accuracy and convergence speed under the conditions of low initial parameter accuracy and a large number of input design parameters.

[0008] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0009] In one aspect, the present invention provides a trajectory planning method based on inertia weighted particle swarm optimization, comprising the following steps:

[0010] S1: Establish the center-of-mass dynamics and kinematics equations for space vehicles;

[0011] S2: Based on the center-of-mass dynamics and kinematics equations of a space vehicle, construct a mathematical representation of the vehicle trajectory planning problem with the launch trajectory planning design parameters of the space vehicle as input;

[0012] S3: Based on the inertia-weighted particle swarm algorithm, the mathematical representation problem of the vehicle trajectory planning established in step S2 is solved to determine the design parameters of the vehicle trajectory planning.

[0013] Furthermore, the kinematic equation of the space vehicle described in step S1 is

[0014]

[0015] Where m is the mass of the vehicle, d 2 r c.m. is the absolute acceleration vector of the vehicle's center of mass relative to the inertial coordinate system, t represents time, m·g is the earth's gravity, R is the aerodynamic force on the vehicle, P is the thrust of the rocket engine, and F c is the control force generated by the vehicle control actuator, F k ′ is the additional Coriolis force.

[0016] Furthermore, the mathematical representation of the vehicle trajectory planning in step S2 is expressed as

[0017]

[0018] Where x1, x2, ..., x n is the design parameter of the carrier trajectory planning, n represents the number of design parameters; design parameters The input value of the function, the calculated shutdown point parameter Output value for the function, is the standard value of the launch vehicle's orbital parameters, is the allowable error range.

[0019] Furthermore, the specific operation of step S3 includes the following steps:

[0020] S301: Determine an initialization model for the particle swarm algorithm based on the mathematical representation of the vehicle trajectory planning problem constructed in step S2;

[0021] S302: Calculate the fitness of the particle swarm;

[0022] S303: Iterate the particle swarm until the iteration conditions are met, and obtain the design parameters of the vehicle trajectory planning.

[0023] Furthermore, in step S301, let the number n of design parameters correspond to the search space of the particle swarm algorithm. There are m groups of initial values ​​of the design parameters, corresponding to the initial number of particles in the particle swarm algorithm. The specific value of each group of design parameters corresponds to the position vector of the particle in the particle swarm algorithm. Then the particle swarm algorithm is represented as m particles in the n-dimensional search space, where the position vector of the i-th particle is represented as X i =(X i1 , X i2 ,...,X in ), the velocity vector is represented by V i =(V i1 , V i2 ,...,V in ) indicates; P i =(P i1 , P i2 ,...,P in ) is the individual extreme value, P g =(P g1 , P g2 ,...,P gn ) is the group extreme value, i=1,2,…,m.

[0024] Furthermore, the method for calculating the fitness of the particle swarm in step S302 includes the following steps:

[0025] S3021: (y1, y2, ..., y n ) establishes an n-dimensional coordinate system for the coordinate axis and defines

[0026]

[0027] Where, Indicates As input conditions, the model calculates the output shutdown point parameters Distance standard orbital parameters spatial distance;

[0028] S3022: Vector Perform dimensionless normalization

[0029]

[0030] but

[0031]

[0032] Where,

[0033] The space vector Move to the origin of coordinates, and assume that the n-dimensional space region Ω is {-1≤y1≤1,1≤y2≤1,…,1≤y n ≤1}, then the input value Make In the spatial region Ω;

[0034] S3023: Assume that the weight relationship of each parameter output value is but

[0035]

[0036] Therefore, s=f(x1, x2, ..., x n )express A multivariate linear function of the particle fitness when used as a function input value;

[0037] When s=0, all output parameters meet the allowable error range, that is, the vehicle shutdown point parameters meet the orbit entry requirements.

[0038] Furthermore, the specific operation steps of step S303 are:

[0039] S3031: All particles are based on P i 、P g Update its own speed and position with the state of the previous moment. The speed update and position update formulas are:

[0040]

[0041] Among them, ω is the inertia weight; r1 and r2 are random numbers in the interval [0, 1]; c1 and c2 are acceleration factors; P in is the individual extreme value of the i-th particle; P gn is the group extreme value of the entire particle swarm; is the current position of the i-th particle; is the current velocity of the i-th particle;

[0042] S3032: Calculate the fitness value based on the updated particle position vector and velocity vector. When s=0, the iteration ends. The particle position vector here corresponds to the design parameter value. Otherwise, repeat steps S2 and S3 until s=0.

[0043] Furthermore, the inertia weight ω in step S301 decreases linearly with the number of iterations T, which can be expressed as

[0044]

[0045] Where w start is the initial inertia weight, w end is the inertia weight when the iteration reaches the maximum number, T max is the maximum number of iterations, and T is the number of iterations.

[0046] On the other hand, the present invention also provides a trajectory planning system based on inertia weighted particle swarm algorithm, the trajectory planning system includes a basic model building module, a trajectory planning model building module and a particle swarm solving module;

[0047] The basic model building module is used to establish the center-of-mass dynamics and kinematics equations of a space vehicle;

[0048] The trajectory planning model building module is used to input design parameters and construct the mathematical representation problem of vehicle trajectory planning;

[0049] The particle swarm solver module solves the mathematical representation problem of the vehicle trajectory planning and determines the design parameters of the vehicle trajectory planning;

[0050] The basic model building module, the trajectory planning model building module and the particle swarm solving module are all implemented using the trajectory planning method described above.

[0051] The beneficial effects of the present invention are:

[0052] 1. The present invention discloses a trajectory planning method based on an inertia-weighted particle swarm algorithm. By establishing a fitness model for orbital insertion parameters, the deviation between the actual orbital insertion parameters obtained under the design parameters and the target orbital insertion parameters is given a geometric meaning. The established fitness model is applied to the inertia-weighted particle swarm algorithm, thereby improving the convergence speed while ensuring convergence accuracy. This method establishes an intelligent particle swarm algorithm suitable for orbit design parameter search with low initial parameter accuracy requirements, strong computational inheritability, and a simple calculation method. This algorithm solves the problems of complex iterative formulas when the input parameter accuracy requirements are high and the number of input parameters is too large, providing new ideas for future orbit parameter design methods.

[0053] 2. The present invention uses MTALAB to perform particle swarm intelligent solution, verifying the feasibility and superiority of this method. Under the condition of selecting multiple targets as the optimization scheme, the target trajectory parameters are solved. Compared with the traditional Newton method, it has the advantages of multiple selectable planning parameters, good algorithm inheritance, convenient and rapid solution, etc., and realizes the intelligent solution of a large number of planning parameters. Secondly, the present invention also uses a particle swarm algorithm with linearly decreasing inertia weight to solve the particle swarm model, ensuring the convergence accuracy and convergence speed of the calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 The figure is a flow chart for solving the mathematical representation problem of vehicle trajectory planning based on the inertia weighted particle swarm algorithm in the present invention.

[0055] Figure 2 is the vector in the n-dimensional coordinate system of the present invention The relative relationship with space Ω.

[0056] Figure 3 4 is a comparison curve of three inertia weights in Example 1 of the present invention.

[0057] Figure 4 Schematic diagram of the variation of the pitch control program angle in the present invention.

[0058] Figure 5 This is the optimal fitness change curve of the particle swarm in the simulation experiment of the present invention.

[0059] Figure 6 This is a schematic diagram of the orbit design for the active segment in the geocentric system in the simulation experiment of the present invention.

[0060] Figure 7 This is a curve showing the change of carrier speed over time in the simulation experiment of the present invention.

[0061] Figure 8 This is a curve showing the change of the carrier height over time in the simulation experiment of the present invention.

[0062] Figure 9 This is a curve showing the change of the vehicle's pitch angle over time in the simulation experiment of the present invention.

[0063] Figure 10 This is the convergence comparison result between the traditional Newton iterative algorithm and the method of the present invention when the same initial values ​​are used in the simulation experiment of the present invention.

[0064] Figure 11 This is the convergence performance curve of the traditional Newton iterative algorithm used in the simulation experiment of the present invention after first determining the approximate range of the final result according to the method of the present invention. DETAILED DESCRIPTION

[0065] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0066] Example 1:

[0067] The first embodiment provides a trajectory planning method based on inertia weighted particle swarm optimization algorithm, which specifically includes the following steps:

[0068] S1: Establish the center-of-mass dynamics and kinematics equations for space vehicles;

[0069] Specifically, the center of mass dynamics equation describes the relationship between the derivative of the velocity vector of the center of mass of the space vehicle (acceleration vector) and the comprehensive force on the center of mass. The center of the earth is selected as the position vector r c.m. After the starting point, the kinematic equation of the space vehicle can be established as:

[0070]

[0071] Where m is the mass of the vehicle, d 2 r c.m. is the absolute acceleration vector of the vehicle's center of mass relative to the inertial coordinate system, t represents time, m·g is the earth's gravity, R is the aerodynamic force on the vehicle, P is the thrust of the rocket engine, and F c is the control force generated by the vehicle control actuator, F k ′ is the additional Coriolis force.

[0072] in,

[0073]

[0074] Where g is the acceleration of the earth's gravity; g r ′ is the component of the earth's gravitational acceleration in the direction of the earth's center; is the component of the Earth's gravitational acceleration in the direction of the Earth's rotation angular velocity; r 0 is the unit vector of the radius from the center of the earth; is the unit vector of the Earth's rotational angular velocity.

[0075] R = [-D, L, N] T (3)

[0076]

[0077] Where D is the aerodynamic drag; L is the aerodynamic lift; N is the aerodynamic lateral force; S ref is the aerodynamic reference area of ​​the vehicle; C D 、C L 、C N are the aerodynamic drag coefficient, lift coefficient and lateral force coefficient respectively; q is the dynamic pressure; ρ is the density of the Earth's atmosphere at the current altitude of the vehicle; and V is the speed of the vehicle relative to the Earth's atmosphere.

[0078]

[0079] Where, P s.t. is the static thrust of the engine generated by the pressure difference at the engine nozzle outlet; F′ rel Additional relative force caused by the mass-changing process; is the mass consumption per second of the vehicle's engine, u e is the average fuel injection velocity at the engine nozzle outlet.

[0080]

[0081] Where, ω I is the angular velocity of the vehicle relative to the inertial space; ρ e It is the vector from the center of mass of the vehicle to the center point of the cross section of the engine nozzle outlet.

[0082] S2: Based on the center-of-mass dynamics and kinematics equations of a space vehicle, construct a mathematical representation of the vehicle trajectory planning problem with the launch trajectory planning design parameters of the space vehicle as input;

[0083] Specifically, let the design parameters of the carrier trajectory planning be x1, x2, ..., x n , n represents the number of design parameters; the kinematic equations of the space vehicle established in step S1 can be used to directly calculate the parameters of the vehicle shutdown point, but the calculated values ​​cannot directly represent the rationality of the design parameters. Therefore, the following model is established:

[0084] Assume that the standard value of the carrier's orbital entry parameter is The allowable error range is By design parameters Calculated shutdown point parameters The sufficient conditions for meeting the design goals are:

[0085]

[0086] Let the design parameters The input value of the function, the calculated shutdown point parameter is the function output value, then for a fixed carrier, there is a corresponding relationship between its input and output:

[0087]

[0088] Obviously, the more precisely the initial design parameters are set, the lower the requirements for the calculation method. Conversely, if the initial design parameters are set too far, the calculation method will have poor convergence or even no convergence. However, in many cases, relatively precise initial design parameters are not known, which can sometimes result in the initial design parameters failing to meet the convergence conditions of the current calculation method, causing the calculation to diverge. Therefore, the present invention aims to find a global convergence search calculation method with low initial design parameter precision requirements and relatively efficient calculations.

[0089] Step S3: Based on the inertia-weighted particle swarm algorithm, the mathematical representation problem of the vehicle trajectory planning established in step S2 is solved to determine the design parameters of the vehicle trajectory planning.

[0090] The particle swarm algorithm has a good global search advantage and has relatively low requirements for initial values. At the same time, different flight parameters are often used as design targets according to different vehicle flight design requirements. The more design parameters there are, the more complex the calculation formula required for iteration. The particle swarm algorithm has the characteristics of strong inheritability and simple calculation formula. Therefore, the present invention uses the particle swarm algorithm to establish a simple spatial model to simplify the iterative method, so that it can participate in the iterative solution of a large number of parameter designs and optimize the solution model to a certain extent. The solution model of the particle swarm iterative algorithm in the present invention is shown in the attached figure. Figure 1 shown.

[0091] S301: Determine an initialization model for the particle swarm algorithm based on the mathematical representation of the vehicle trajectory planning problem constructed in step S2;

[0092] The standard particle swarm (PSO) algorithm initializes a group of particles and calculates the fitness of each particle to continuously iterate and obtain the optimal solution of the function. In this model, the number of design parameters n corresponds to the search space of the particle swarm algorithm. There are m groups of initial values ​​of the design parameters, which correspond to the number of initial particles in the particle swarm algorithm. The specific value of each group of design parameters corresponds to the position vector of the particle in the particle swarm algorithm. It can be assumed that there are m particles in the n-dimensional search space, where the position vector of the i-th particle is represented by X i =(X i1 , X i2,...,X in ), the velocity vector is represented by V i =(V i1 , V i2 ,...,V in ) represents. In the evolution process of the PSO algorithm, the individual extreme value is recorded as P i =(P i1 , P i2 ,...,P in ), the group extreme value is recorded as P g =(P g1 , P g2 ,...,P gn ).

[0093] S302: Calculate the fitness of the particle swarm;

[0094] Specifically, (y1, y2, ..., y n ) is used as the coordinate axis to establish an n-dimensional coordinate system, and the relationship can be obtained:

[0095]

[0096] The physical meaning is: As input conditions, the model calculates the output shutdown point parameters Distance standard orbital parameters spatial distance.

[0097] At the same time, in order to solve the problem of inconsistent effects on particle fitness caused by the change of variable units and magnitude, the vector Perform the following dimensionless normalization:

[0098]

[0099] From the above, we can get the relationship

[0100]

[0101] Where,

[0102] The space vector Move to the origin of coordinates, and assume that the n-dimensional space region Ω is {-1≤y1≤1,-1≤y2≤1,…,-1≤y n ≤1}, then the problem is transformed into: Find the input value Make In the space region Ω, as shown in the following Figure 2 shown.

[0103] When y iWhen (i=1,2,…,n) satisfies the error condition, dy i =0, then z i =0, at this time, Assume that the weight relationship of each parameter output value is Given a function input value pair output The degree of influence can be calculated based on the weight of the impact. To improve the operation efficiency, otherwise, let the weight of each parameter output value be 1 / n.

[0104]

[0105] At this point, we get the functional relationship:

[0106] s=f(x1,x2,...,x n ) (14)

[0107] Where s is A multivariate linear function of the particle fitness when used as a function input value.

[0108] When s=0, all output parameters meet the allowable error range, that is, the vehicle shutdown point parameters meet the orbit entry requirements.

[0109] S303: Iterate the particle swarm until the iteration conditions are met, and obtain the design parameters of the vehicle trajectory planning.

[0110] During the iteration process, all particles will be i 、P g The speed and position are updated based on the state of the previous moment. The speed and position update formulas are as follows:

[0111]

[0112] Where i = 1, 2, ..., m; ω is the inertia weight; r1 and r2 are random numbers in the interval [0, 1]; c1 and c2 are acceleration factors; P in is the individual extreme value of the i-th particle; P gn is the group extreme value of the entire particle swarm; X in k is the current position of the i-th particle; is the current velocity of the ith particle.

[0113] When designing a vehicle's flight trajectory, the next step of constraint and precise solution is generally performed based on a rough solution of a value range. Therefore, when the particle swarm algorithm is used to solve the design parameters, what is actually solved is the local optimal solution within the known range of the objective function. According to the research on the particle swarm algorithm, smaller weights often help to search for local optimal solutions. In this invention, a particle swarm algorithm with linearly decreasing inertia weight is used to solve the particle swarm model, so that it can improve the convergence accuracy of the particle swarm algorithm without affecting the convergence accuracy. The three inertia weight methods are as follows:

[0114]

[0115] Where w start is the initial inertia weight, w end is the inertia weight when the iteration reaches the maximum number, T max is the maximum number of iterations, T is the number of iterations. When setting and selecting the inertia weight parameters, it is necessary to select an appropriate method according to different situations. The third inertia weight method is used in the present invention.

[0116] The comparison of the three inertia weights is shown in the attached figure. Figure 3 As shown. Figure 3 As can be seen from the figure, the decline rate of w3 is moderate. In the early stage of iteration, the inertia weight is large, which helps the particle swarm to conduct global search and avoid falling into the local optimum. In the later stage of iteration, the inertia weight of the w3 curve is small, which helps the particle swarm converge to the optimal solution or the approximate optimal solution more quickly. Therefore, the w3 inertia weight method selected in the present invention can not only ensure that the particle swarm searches widely in the exploration space, but also help improve the global search ability and convergence speed of the algorithm.

[0117] The fitness value is calculated based on the updated particle position vector and velocity vector. When s = 0, the iteration ends, and the particle position vector here corresponds to the design parameter value; otherwise, steps S2 and S3 are repeated until s = 0.

[0118] Example 2:

[0119] Example 2 Based on Example 1, the launch azimuth angle A0 and the slope constant of the vacuum flight segment are used. Taking the third-stage shutdown time t7 as an example of the design parameter, the mathematical representation problem of the carrier trajectory planning in step S2 is further explained.

[0120] According to the characteristics of the active phase flight of the carrier, the active phase flight program design is usually divided into two parts: the atmospheric flight phase and the vacuum flight phase. The first stage is designed in the dense atmospheric flight phase, and the second stage and above are basically designed in the thin atmosphere or vacuum flight phase. The change rules are as shown in the attached figure. Figure 4 Pitch control program angle There are many design methods, and this embodiment only adopts one of them for research. The control model is designed as:

[0121]

[0122] Where, Pitch control program angle The derivative with respect to time t; t1 needs to be determined in combination with the ground thrust-to-weight ratio of the carrier, α 1，max is the maximum value of the absolute value of the angle of attack, a is a design constant parameter, 0~t1 is the first-level vertical flight segment, t1~t2 is the first-level turning flight segment, t2~t3 is the first and second-level constant procedure flight segment, t3~t4 is the second-level constant slope turning flight segment, is the constant slope value of the second-level constant slope turning flight segment; t4~t5 is the second and third-level constant value procedure flight segment, t5~t6 is the third-level constant slope turning flight segment, It is the constant slope value of the third-level constant slope turning flight segment; t6~t7 is the third-level constant value procedure flight segment.

[0123] When planning and designing a launch vehicle's launch plan, the apogee altitude, perigee altitude, orbital inclination, and true anomaly angle of the orbital entry point are usually given. When designing a launch vehicle's launch trajectory, these requirements are usually converted into four terminal equality constraints (shutdown point constraints), expressed as follows:

[0124]

[0125] Where h k is the height of the vehicle when it enters orbit and shuts down; R e is the radius of the Earth at the ground projection point of the entry point; μ is the Earth's gravitational constant; a1 is the semi-major axis of the orbit; e1 is the orbit eccentricity; i0 is the orbit inclination. k 、V k ,θ k 、i k They are respectively the distance from the Earth's center, velocity, velocity inclination and orbital inclination when the vehicle enters orbit and is shut down.

[0126] Accordingly, the mathematical representation of the vehicle trajectory planning problem is that the design input parameters satisfy the following relationship:

[0127]

[0128] Where, θ(t k )、r(t k )、V(t k )、i(t k ) are t kThe velocity and inclination angle of the carrier at the time of shutdown (entry into orbit), the distance from the center of the Earth, the velocity and the orbital inclination angle; θ * k 、r * k 、V * k 、i * k are the velocity inclination, distance from the Earth’s center, speed, and orbital inclination required for the vehicle to enter orbit; Δθ, Δr, ΔV, and Δi are the maximum velocity inclination deviation, maximum distance from the Earth’s center deviation, maximum velocity deviation, and maximum orbital inclination deviation required for the vehicle to enter orbit, respectively.

[0129] Therefore, the launch azimuth angle A0 and the slope constant of the vacuum flight segment are The mathematical representation problem of the trajectory planning of the carrier with the third stage shutdown time t7 as the design parameter is transformed into the problem of finding is the optimal solution (zero value solution) of the multivariate function of the variables, so that the deviations in the constraints are within the allowable range, that is,

[0130]

[0131] Where, are the input values ​​of the design parameters, is the output value of the function, corresponding to θ(t k )、r(t k )、V(t k )、i(t k ), F * (X) is the standard value of the parameters required when the carrier enters orbit, corresponding to θ in formula (20) * r 、r * k 、V * k 、i * k ΔF is the maximum deviation value of the parameters required when the carrier enters orbit, corresponding to Δθ, Δr, ΔV, and Δi in formula (20). By optimizing and solving formula (21) through the inertia weighted particle swarm algorithm in step S3 of embodiment 1, the optimal launch azimuth angle A0 and the slope constant of the vacuum flight segment can be obtained. and the third level shutdown time t7.

[0132] Simulation experiment:

[0133] This simulation experiment selects the launch azimuth angle A0 and the slope constant of the vacuum flight segment The third-stage shutdown time t7 is a design parameter and serves as the input of the vehicle's trajectory parameter fitness function. The orbital semi-major axis a1, orbital eccentricity e1, and orbital inclination i0 are selected as target orbital insertion parameters. The allowable errors of the flight vehicle's orbital insertion parameters are set to: {|a1|≤1km, |e1|≤0.01, |i0|≤0.1°}. Based on the known flight parameters and orbital insertion conditions of a certain type of vehicle, a particle swarm intelligent solution of the design parameters is performed.

[0134] 30 particles were selected for iterative optimization of the particle swarm, and the third inertia weight was used for optimization iteration. The results are shown in the attached figure. Figure 5 The best fitness changes are shown in Table 1 below.

[0135] Table 1 Iterative results of particle optimal fitness

[0136]

[0137] The orbital parameter errors are shown in Table 2 below (if the accuracy needs to be improved, it can be achieved by adjusting the allowable error range).

[0138] Table 2 Actual orbital parameter errors

[0139]

[0140] The active phase flight trajectory of the carrier rocket is as follows Figure 6 The change of carrier speed with time is shown in the attached figure. Figure 7 As shown in the attached figure, the change of the vehicle height with time is shown in the attached figure. Figure 8 As shown in the attached figure, the pitch angle of the vehicle changes with time. Figure 9 As shown in the above attached Figure 6-9 It can be seen from the figure that the trajectory planning method of the present invention has a fast convergence speed while ensuring the convergence accuracy, which shows that the trajectory parameter solution model of the algorithm can well achieve the goal of iterative optimization of design parameters.

[0141] Substitute the initial value of the particle swarm algorithm in this simulation experiment into the traditional Newton iterative algorithm. The comparison results of the convergence curves between the traditional Newton iterative algorithm and the algorithm of the present invention are shown in the attached figure. Figure 10 As shown. Figure 10It can be seen from the figure that due to the strong coupling and complexity of the ballistic equation, it is easy to fall into the local coupling of certain parameters when using the traditional Newton iterative solution method, resulting in the divergence of the overall iteration. However, the method of the present invention can achieve convergence. In order to solve this problem, the present invention first determines the approximate range of the optimization parameters when using the Newton iterative solution equation, and then solves it in combination with the Newton solution equation. According to the optimization result obtained by the particle swarm algorithm, a suitable initial value is given and it is iterated again. The final convergence curve result is shown in the attached figure. Figure 11 As shown in the attached Figure 11 It can be seen from the figure that the Newton iteration method has better convergence only when it gives a solution close to the final optimization result. Its convergence has strict requirements on the initial value setting, while the method in the present invention has lower requirements on the initial value and better convergence.

[0142] Example 3:

[0143] Embodiment 3 provides a space vehicle launch trajectory planning system based on an inertia-weighted particle swarm algorithm, wherein the trajectory planning system includes a basic model building module, a trajectory planning model building module, and a particle swarm solving module;

[0144] The basic model building module is used to establish the center-of-mass dynamics and kinematics equations of a space vehicle;

[0145] The trajectory planning model building module is used to input design parameters and construct the mathematical representation problem of vehicle trajectory planning;

[0146] The particle swarm solver module solves the mathematical representation problem of the vehicle trajectory planning and determines the design parameters of the vehicle trajectory planning;

[0147] The basic model building module, the trajectory planning model building module and the particle swarm solving module are all implemented using the trajectory planning method described in the first embodiment.

[0148] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A trajectory planning method based on inertia weighted particle swarm optimization algorithm, characterized in that: The following steps are included: S1: Establish the center-of-mass dynamics and kinematics equations for space vehicles; S2: Based on the center-of-mass dynamics and kinematics equations of a space vehicle, construct a mathematical representation of the vehicle trajectory planning problem with the launch trajectory planning design parameters of the space vehicle as input; S3: Based on the inertia-weighted particle swarm algorithm, the mathematical representation problem of the vehicle trajectory planning established in step S2 is solved to determine the design parameters of the vehicle trajectory planning.

2. The trajectory planning method based on inertia-weighted particle swarm optimization algorithm according to claim 1, characterized in that: The kinematic equation of the space vehicle described in step S1 is Where m is the mass of the vehicle, d 2 r c.m. is the absolute acceleration vector of the vehicle's center of mass relative to the inertial coordinate system, t represents time, m·g is the earth's gravity, R is the aerodynamic force on the vehicle, P is the thrust of the rocket engine, and F c is the control force generated by the vehicle control actuator, F k ′ is the additional Coriolis force.

3. The trajectory planning method based on inertia weighted particle swarm optimization algorithm according to claim 2, characterized in that: The mathematical representation of the vehicle trajectory planning problem described in step S2 is expressed as Where x1, x2, ..., x n is the design parameter of the carrier trajectory planning, n represents the number of design parameters; design parameters The input value of the function, the calculated shutdown point parameter Output value for the function, is the standard value of the launch vehicle's orbital parameters, is the allowable error range.

4. The trajectory planning method based on inertia weighted particle swarm optimization algorithm according to claim 3, characterized in that: The specific operation of step S3 includes the following steps: S301: Determine an initialization model for the particle swarm algorithm based on the mathematical representation of the vehicle trajectory planning problem constructed in step S2; S302: Calculate the fitness of the particle swarm; S303: Iterate the particle swarm until the iteration conditions are met, and obtain the design parameters of the vehicle trajectory planning.

5. The trajectory planning method based on inertia weighted particle swarm optimization algorithm according to claim 4, characterized in that: In step S301, let the number of design parameters n correspond to the search space of the particle swarm algorithm. There are m groups of initial values ​​of the design parameters, which correspond to the initial number of particles in the particle swarm algorithm. The specific value of each group of design parameters corresponds to the position vector of the particle in the particle swarm algorithm. The particle swarm algorithm is represented as m particles in the n-dimensional search space, where the position vector of the i-th particle is represented as X i =(X i1 , X i2 ,...,X in ), the velocity vector is represented by V i =(V i1 , V i2 ,...,V in ) indicates; P i =(P i1 , P i2 ,...,P in ) is the individual extreme value, P g =(P g1 , P g2 ,...,P gn ) is the group extreme value, i=1,2,…,m.

6. The trajectory planning method based on inertia weighted particle swarm optimization algorithm according to claim 5, characterized in that: The method for calculating the fitness of the particle swarm in step S302 includes the following steps: S3021: (y1, y2, ..., y n ) establishes an n-dimensional coordinate system for the coordinate axis and defines Where, Indicates As input conditions, the model calculates the output shutdown point parameters Distance standard orbital parameters spatial distance; S3022: Vector Perform dimensionless normalization but Where, The space vector Move to the origin of coordinates, and assume that the n-dimensional space region Ω is {-1≤y1≤1,1≤y2≤1,…,-1≤y n ≤1}, then the input value Make In the spatial region Ω; S3023: Assume that the weight relationship of each parameter output value is but Therefore, s=f(x1, x2, ..., x n )express A multivariate linear function of the particle fitness when used as a function input value; When s=0, all output parameters meet the allowable error range, that is, the vehicle shutdown point parameters meet the orbit entry requirements.

7. The trajectory planning method based on inertia weighted particle swarm optimization algorithm according to claim 6, characterized in that: The specific operation steps of step S303 are: S3031: All particles are based on P i 、P g Update its own speed and position with the state of the previous moment. The speed update and position update formulas are: Among them, ω is the inertia weight; r1 and r2 are random numbers in the interval [0, 1]; c1 and c2 are acceleration factors; P in is the individual extreme value of the i-th particle; P gn is the group extreme value of the entire particle swarm; X in k is the current position of the i-th particle; is the current velocity of the i-th particle; S3032: Calculate the fitness value based on the updated particle position vector and velocity vector. When s=0, the iteration ends. The particle position vector here corresponds to the design parameter value. Otherwise, repeat steps S2 and S3 until s=0.

8. The trajectory planning method based on inertia weighted particle swarm optimization algorithm according to claim 7, characterized in that: The inertia weight ω in step S301 decreases linearly with the number of iterations T, which can be expressed as Where w start is the initial inertia weight, w end is the inertia weight when the iteration reaches the maximum number, T max is the maximum number of iterations, and T is the number of iterations.

9. A trajectory planning system based on inertia-weighted particle swarm optimization algorithm, characterized by: The trajectory planning system includes a basic model building module, a trajectory planning model building module and a particle swarm solving module; The basic model building module is used to establish the center-of-mass dynamics and kinematics equations of a space vehicle; The trajectory planning model building module is used to input design parameters and construct the mathematical representation problem of vehicle trajectory planning; The particle swarm solver module solves the mathematical representation problem of the vehicle trajectory planning and determines the design parameters of the vehicle trajectory planning; The basic model building module, the trajectory planning model building module and the particle swarm solving module are all implemented by the trajectory planning method described in any one of claims 1-8.

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