GWO-hpRPM algorithm-based gliding guided cartridge trajectory optimization method

Abstract

The invention relates to a gliding guided projectile trajectory optimization method based on a GWO-hpRPM algorithm, and the method comprises the steps: taking the longitudinal plane motion of a gliding guided projectile as a research target in a launching coordinate system, and building a longitudinal motion equation of the gliding guided projectile; determining a ballistic objective function and constraint conditions, and establishing a ballistic optimization mathematical model; establishing a GWO-hpRPM optimization algorithm: the algorithm adopts a double-ring optimization strategy, an outer ring adopts a GWO algorithm to optimize a firing angle and ignition time, and an optimal initial value is provided for an inner ring; an inner ring adopts an hpRPM algorithm to solve an optimal control law u and a fitness value J, and finally a gliding trajectory with the farthest range is obtained under all constraint conditions; initial conditions are set, iterative calculation is carried out, and when the fitness of an objective function is converged, the optimal firing angle, ignition time and the optimal trajectory are obtained. A new solution is provided for the ballistic optimization problem of the gliding guided projectile, and a theoretical reference is also provided for other ballistic optimization problems of the same type.

Description

Technical Field

[0001] The invention relates to a trajectory optimization method, in particular to a trajectory optimization method for a gliding guided projectile based on a GWO-hpRPM algorithm. Background Art

[0002] The glide-guided projectile mainly improves the projectile range by optimizing the glide trajectory design. Therefore, the glide trajectory optimization is an important part of the overall design of the glide-guided projectile. The quality of the optimization result has an important impact on the overall performance index of the projectile. The trajectory optimization problem is essentially a nonlinear optimal control problem that seeks the optimal control law under multiple constraints to achieve the optimal performance index.

[0003] Gray Wolf Optimization (GWO) is an optimization method that simulates the social hierarchy and hunting behavior of gray wolf populations to find the optimal solution. In this algorithm, the levels of the gray wolf population are divided into four categories, namely α wolf, β wolf, δ wolf and ω wolf. α wolf is the most intelligent leader, who can keenly find the location of prey during hunting. β wolf can be considered as a military advisor and knows the location of prey better. δ wolf is responsible for assisting the first two levels of wolves, and ω wolf is responsible for tracking prey. Compared with other heuristic algorithms, GWO has the characteristics of high convergence accuracy, strong exploration and development capabilities, and easier implementation. The traditional GWO algorithm has good results for single-target trajectory optimization problems, but it may face some challenges when dealing with complex constrained optimization problems, especially when there are many constraints or the constraints are strict, GWO may not be able to obtain the optimal feasible solution. The hp adaptive Radau pseudo-spectral method (hpRPM) has the characteristics of high efficiency, small amount of calculation, small memory usage, and the ability to effectively handle complex constraint problems. It is widely used in solving trajectory optimization problems. When hpRPM is used alone, it may fall into a local optimal solution due to its local optimization characteristics. Therefore, how to obtain the optimal glide trajectory while satisfying complex multi-constraint conditions has become a technical problem that needs to be solved urgently in trajectory optimization. Summary of the invention

[0004] Purpose of the invention: The purpose of the invention is to propose a glide-guided projectile trajectory optimization method based on the GWO-hpRPM algorithm to obtain the glide trajectory with the longest range while satisfying all constraints.

[0005] Technical solution: The present invention comprises the following steps:

[0006] In the launch coordinate system, the longitudinal motion equation of the gliding guided projectile is established with the longitudinal motion of the gliding guided projectile as the research target.

[0007] Determine the trajectory objective function and constraints, and establish a trajectory optimization mathematical model;

[0008] Establish the GWO-hpRPM optimization algorithm: This algorithm adopts a dual-loop optimization strategy, including inner loop optimization and outer loop optimization. The outer loop uses the GWO algorithm to optimize the firing angle and ignition time to provide the optimal initial value for the inner loop; the inner loop uses the hpRPM algorithm to solve the optimal control law u and fitness value J, and finally obtains the glide trajectory with the longest range while satisfying all constraints.

[0009] Perform trajectory optimization solution and fitness evaluation: set initial conditions, perform iterative calculations, and obtain the optimal shooting angle, ignition time, and optimal trajectory when the fitness of the objective function converges.

[0010] The longitudinal motion equation of the gliding guided projectile is:

[0011]

[0012] Where: α is the angle of attack, δ is the rudder deflection angle, C D0 is the zero lift drag coefficient, C Dδ0 is the zero-lift drag coefficient of the rudder surface, C′ L is the lift coefficient derivative, C′ Lδ is the derivative of the lift coefficient of the rudder surface, k T , k B are the induced drag coefficient of the rudder surface and the induced drag coefficient of the missile body, X R To control the rudder pressure center position, X F is the center of pressure position of the wing assembly, X G is the center of gravity of the whole projectile, v is the velocity, θ is the ballistic inclination angle, x and y are the flight distance and flight altitude of the sliding-guided projectile respectively, is the dynamic pressure, S is the characteristic area, m is the mass of the projectile, g is the gravitational acceleration, F p is the average thrust of the rocket engine, m c It is the mass dissipation rate of rocket booster engine charge.

[0013] The trajectory optimization mathematical model is established as follows: the firing angle and the ignition time are used as optimization variables, and are recorded as X = [θ 0 ,t ig ], taking boundary constraints, terminal constraints, process constraints, control constraints and path constraints as constraints and range as objective function, an optimization mathematical model is established.

[0014] The boundary constraints are:

[0015]

[0016] Where: t 0 is the initial moment, v 0 、m 0 are the initial velocity and initial mass respectively, x(t 0 ),y (t 0 ) are the distance and elevation of the launch point, respectively, and the launch angle θ(t 0 ) is the parameter to be optimized;

[0017] Terminal constraints:

[0018]

[0019] Where: t f is the terminal moment, v tfmin =210m / s is the expected minimum falling speed, θ tfmax =-90°,θ tfmin =-60° are the expected maximum and minimum falling angles respectively; y T =0 is the target elevation coordinate;

[0020] Process constraints:

[0021] Ascent phase and inertia ascent phase:

[0022]

[0023] Boosting stage:

[0024]

[0025] Where: t cl is the ignition end time, ignition time t ig is the variable to be optimized, the engine working time t c is a constant;

[0026] Gliding section:

[0027]

[0028] Control constraints:

[0029] |α|≤α max (7)

[0030] Path constraints:

[0031]

[0032] in:

[0033] The objective function is:

[0034] min J=-x tf (9)

[0035] The mathematical description of the trajectory optimization problem is: at time [t 0 ,t f], under the constraints of equations (2) to (8), the optimal control variables α and the angle of fire θ (t 0 ), ignition time t ig , so that the objective function (9) is minimized.

[0036] The outer loop of GWO is: The dimension of the target search space is the number of optimization variables. Assuming that the population consists of nPop particles, the GWO algorithm initializes the gray wolf position X = [θ 0 ,t ig ] is input into the inner loop hpRPM algorithm, where θ 0 =[θ 01 ,θ 02 ,…,θ 0nPop ] T , t ig =[t ig1 ,t ig2 ,…t ignPop ] T , according to the fitness value J returned by the hpRPM algorithm, save the top three gray wolves α, β and δ with the best fitness values, obtain and record the initial optimal individual and fitness value; update the position X of the gray wolf according to formula (13), and input the updated position into hpRPM again. The hpRPM algorithm calculates the fitness value according to the objective function in formula (9), returns the fitness value J to the GWO algorithm, obtains the minimum fitness value of this iteration, and compares it with the optimal fitness value obtained in the previous group iteration. If the maximum number of iterations is reached, stop the calculation, otherwise update the position of the gray wolf according to formula (13), continue the next iteration, and the gray wolf with the smallest fitness value in the last iteration is taken as the optimal individual; finally, output the global optimal position and optimal fitness value J in the GWO algorithm, and obtain the optimal initial value of the inner loop;

[0037]

[0038] C i =2·rand,i=1,2,3 (11)

[0039] Among them, X α , X β , X δ Indicates the current position of the gray wolves α, β, δ. 1 , C 2 , C 3 represents the random vector coefficient, X represents the current position of the gray wolf, and D α , D β , D δ represents the distance between individual wolf ω and the prey;

[0040] After determining the positions of gray wolves α, β, and δ, the wolves attack and capture the surrounding prey. The corresponding mathematical model is as follows:

[0041]

[0042] Where X 1 , X 2 , X 3 They represent the positions that the individual ω wolf needs to adjust under the influence of α wolf, β wolf and δ wolf, and take the average value, as shown in formula (13).

[0043] The inner loop of hpRPM is: Determine the state variables s , control variables u and constraints, according to the initial value of the parameter to be optimized input by GWO X = [θ 0 ,t ig ] and the initial values ​​of other variables, solve the optimal control law u and fitness value J, output the changing values ​​of state variables and control variables over time, and finally return the fitness value J to the GWO algorithm.

[0044] The trajectory optimization solution and fitness evaluation include:

[0045] Set the initial value of iterative calculation;

[0046] The initial particle swarm is passed to the initial value required by hpRPM. The hpRPM algorithm calculates the fitness value of the objective function according to formula (9), returns the fitness value J to the GWO algorithm, and obtains and records the initial optimal individual and fitness value;

[0047] Update the position of the gray wolf according to formula (13);

[0048] The updated position of the gray wolf is passed to the initial value required by hpRPM again. The hpRPM algorithm calculates the fitness value of the objective function according to formula (9), returns the fitness value J to the GWO algorithm, obtains the minimum fitness value of this iteration, and compares it with the optimal fitness value obtained in the previous group iteration. If the maximum number of iterative calculations is reached, the calculation is stopped, otherwise the particle speed and position are updated according to formula (13) and the next iteration is continued;

[0049] The gray wolf with the smallest fitness value in the last iteration is taken as the optimal individual, and the corresponding trajectory is the optimal trajectory. The optimal individual gbest is the optimal shooting angle and ignition time corresponding to the optimal trajectory.

[0050] The maximum number of iterations maxIt=10.

[0051] The upper and lower limits of the ignition time and the firing angle are respectively: UpB=[10,65°], LoB=[5,20°].

[0052] Beneficial effects: The present invention has the following advantages:

[0053] (1) The present invention fully integrates the powerful global search capability of the GWO algorithm and the excellent local optimization capability of the hpRPM algorithm, and adopts a dual-loop optimization strategy, including inner loop optimization and outer loop optimization. The outer loop uses the GWO algorithm to optimize the firing angle and ignition time, providing the optimal initial value for the inner loop; the inner loop uses the hpRPM algorithm to solve the optimal control law u and fitness value J, and finally obtains the glide trajectory with the longest range under all constraints.

[0054] (2) The present invention can make full use of existing design experience to obtain the optimal trajectory that satisfies multiple constraints such as boundary constraints, process constraints, terminal constraints, control constraints, and path constraints of the gliding guided projectile. It provides a new solution to the trajectory optimization problem of the gliding guided projectile, and also provides a theoretical reference for other similar trajectory optimization problems. It has strong theoretical research significance and engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0056] The present invention will be further described below in conjunction with the accompanying drawings.

[0057] The glide-guided projectile trajectory optimization method based on the GWO-hpRPM algorithm of this embodiment combines the powerful global search capability of the GWO algorithm and the excellent local optimization capability of the hpRPM algorithm, and adopts a dual-loop optimization strategy, including inner loop optimization and outer loop optimization. The outer loop uses the GWO algorithm to optimize the firing angle and ignition time, providing the optimal initial value for the inner loop; the inner loop uses the hpRPM algorithm to solve the optimal control law and fitness value, and finally obtains the glide trajectory with the longest range under all constraints. Specifically, it includes the following steps:

[0058] S1. In the launch coordinate system, taking the longitudinal plane motion of the gliding guided projectile as the research target, the longitudinal motion equation of the gliding guided projectile is established:

[0059]

[0060] Where: α is the angle of attack, δ is the rudder deflection angle, C D0 is the zero lift drag coefficient, C Dδ0 is the zero-lift drag coefficient of the rudder surface, C′ L is the lift coefficient derivative, C′ Lδ is the derivative of the lift coefficient of the rudder surface, k T , k B are the induced drag coefficient of the rudder surface and the induced drag coefficient of the missile body, X R To control the rudder pressure center position, X Fis the center of pressure position of the wing assembly, X G is the center of gravity of the whole projectile, v is the velocity, θ is the ballistic inclination angle, x and y are the flight distance and flight altitude of the sliding-guided projectile respectively, is the dynamic pressure, S is the characteristic area, m is the mass of the projectile, g is the gravitational acceleration, F p is the average thrust of the rocket engine, m c It is the mass dissipation rate of rocket booster engine charge.

[0061] S2. Determine the trajectory objective function and constraint conditions, and establish a trajectory optimization mathematical model: take the firing angle and ignition time as optimization variables, denoted as X = [θ 0 ,t ig ], the upper and lower boundaries of the optimized variable ignition time and firing angle are: UpB = [10, 65°], LoB = [5, 20°]. With boundary constraints, terminal constraints, process constraints, control constraints and path constraints as constraints, and firing range as the objective function, an optimization mathematical model is established. Among them,

[0062] (1) The boundary constraints are:

[0063]

[0064] Where: t 0 is the initial moment, v 0 、m 0 are the initial velocity and initial mass respectively, x(t 0 ), y (t 0 ) are the distance and elevation of the launch point, respectively, and the launch angle θ(t 0 ) are the parameters to be optimized.

[0065] (2) Terminal constraints:

[0066]

[0067] Where: t f is the terminal moment, v tfmin =210m / s is the expected minimum falling speed, θ tfmax =-90°,θ tfmin =-60° are the expected maximum and minimum falling angles respectively; y T =0 is the target elevation coordinate.

[0068] (3) Process constraints:

[0069] Ascent phase and inertia ascent phase:

[0070]

[0071] Boosting stage:

[0072]

[0073] Where: t cl is the ignition end time, ignition time t ig is the variable to be optimized, the engine working time t c =7s is a constant.

[0074] Gliding section:

[0075]

[0076] (4) Control constraints:

[0077] |α|≤α max (7)

[0078] Where: α max =10° is the maximum angle of attack.

[0079] (5) Path constraints:

[0080] In order to ensure that the gliding guided projectile has sufficient control ability during flight, the minimum value of dynamic pressure q is set min =10000Pa. At the same time, considering the limitation of the missile structure strength, the maximum normal overload is set to n ymax =2g.

[0081]

[0082] in:

[0083] The optimization target is the range of the gliding guided projectile, that is, the objective function is:

[0084] min J=-x tf (9)

[0085] The mathematical description of the trajectory optimization problem is: at time [t 0 ,t f ], under the constraints of equations (2) to (8), the optimal control variables α and the angle of fire θ (t 0 ), ignition time t ig , so that the objective function (9) is minimized.

[0086] S3. Establish GWO-hpRPM optimization algorithm: This algorithm adopts a dual-loop optimization strategy, including inner loop optimization and outer loop optimization. The outer loop uses the GWO algorithm to optimize the firing angle and ignition time, providing the optimal initial value for the inner loop; the inner loop uses the hpRPM algorithm to solve the optimal control law u and fitness value J, and finally obtains the longest range glide trajectory under all constraints. Specifically:

[0087] GWO outer loop: The dimension of the target search space is the number of optimization variables, which is 2; assuming that the population consists of nPop particles, the GWO algorithm initializes the gray wolf position X = [θ 0 ,t ig ] is input into the inner loop hpRPM algorithm, where θ 0 =[θ 01 ,θ 02 ,…,θ 0nPop ] T , t ig =[t ig1 ,t ig2 ,…t ignPop ] T , according to the fitness value J returned by the hpRPM algorithm, save the top three gray wolves α, β and δ with the best fitness values, obtain and record the initial optimal individual and fitness value. Then, update the position X of the gray wolf according to formula (13), and input the updated position into hpRPM again. The hpRPM algorithm calculates the fitness value according to the objective function in formula (9), returns the fitness value J to the GWO algorithm, obtains the minimum fitness value of this iteration, and compares it with the optimal fitness value obtained in the previous group iteration. If the maximum number of iterations is reached, stop the calculation, otherwise update the position of the gray wolf according to formula (13), and continue the next iteration. The gray wolf with the smallest fitness value in the last iteration is the optimal individual. Finally, output the global optimal position and optimal fitness value J in the GWO algorithm, and obtain the optimal initial value of the inner loop;

[0088]

[0089] C i =2·rand,i=1,2,3 (11)

[0090] Among them, X α , X β , X δ Indicates the current position of the gray wolves α, β, δ. 1 , C 2 , C 3 represents the random vector coefficient, X represents the current position of the gray wolf, and D α , D β , D δ Represents the distance between the wolf individual ω and the prey.

[0091] After determining the positions of gray wolves α, β, and δ, the wolves attack and capture the surrounding prey. The corresponding mathematical model is as follows:

[0092]

[0093]

[0094] Where X 1 , X 2 , X 3 They respectively represent the position that the individual ω wolf needs to adjust under the influence of α wolf, β wolf and δ wolf. The average value is taken here, as shown in formula (13).

[0095] hpRPM inner loop: determining state variables s , control variables u and constraints, according to the initial value of the parameter to be optimized input by GWO X = [θ 0 ,t ig ] and the initial values ​​of other variables, solve the optimal control law u and fitness value J, output the changing values ​​of state variables and control variables over time, and finally return the fitness value J to the GWO algorithm.

[0096] S4. Perform trajectory optimization and fitness evaluation: set initial conditions, perform iterative calculations, and obtain the best firing angle, ignition time, and optimal trajectory when the fitness of the objective function converges. Specifically include:

[0097] S41, setting the initial value of iterative calculation;

[0098] S42, passing the initial particle swarm to the initial value required by hpRPM, the hpRPM algorithm calculates the fitness value of the objective function according to formula (9), returns the fitness value J to the GWO algorithm, obtains and records the initial optimal individual and fitness value;

[0099] S43, updating the position of the gray wolf according to formula (13);

[0100] S44, the updated position of the gray wolf is passed to the initial value required by hpRPM again, the hpRPM algorithm calculates the fitness value of the objective function according to formula (9), returns the fitness value J to the GWO algorithm, obtains the minimum fitness value of this iteration, and compares it with the optimal fitness value obtained in the previous group iteration. If the maximum number of iterative calculations is reached, the calculation is stopped, otherwise the particle speed and position are updated according to formula (13) and the next iteration is continued; the maximum number of iterations maxIt=10.

[0101] S45. The gray wolf with the smallest fitness value in the last iteration is taken as the optimal individual, and the corresponding trajectory is the optimal trajectory. The optimal individual gbest is the optimal shooting angle and ignition time corresponding to the optimal trajectory.

[0102] like Figure 1As shown in the figure, it is assumed that the glide-guided projectile adopts a boost-glide trajectory scheme, flies in the atmosphere throughout the entire flight, and satisfies certain constraints during the flight: boundary constraints, process constraints, terminal constraints, control constraints, and path constraints. Without loss of generality, only the longitudinal motion of the glide-guided projectile is considered here, the existing trajectory is used as a reference scheme, the angle of attack is used as the control variable, and the GWO-hpRPM algorithm is used for solving to quickly obtain the optimal trajectory that meets the requirements.

[0103] In the launching coordinate system, the longitudinal motion equation of the gliding guided projectile is established.

[0104]

[0105] Where: α is the angle of attack, δ is the rudder deflection angle, C D0 is the zero lift drag coefficient, C Dδ0 is the zero-lift drag coefficient of the rudder surface, C′ L is the lift coefficient derivative, C′ Lδ is the derivative of the lift coefficient of the rudder surface, k T , k B are the induced drag coefficient of the rudder surface and the induced drag coefficient of the missile body, X R To control the rudder pressure center position, X F is the center of pressure position of the wing assembly, X G is the center of gravity of the whole projectile, v is the velocity, θ is the ballistic inclination angle, x and y are the flight distance and flight altitude of the sliding-guided projectile respectively, is the dynamic pressure, S is the characteristic area, m is the mass of the projectile, g is the gravitational acceleration, F p is the average thrust of the rocket engine, m c It is the mass dissipation rate of rocket booster engine charge.

[0106] (1) Establishment of trajectory optimization mathematical model

[0107] Take the existing trajectory as the reference scheme, and the ignition time and firing angle as the optimization variable, denoted as X = [θ 0 ,t ig ], the upper and lower boundaries are: UpB = [10, 65°], LoB = [5, 20°]

[0108] Constraints include boundary constraints, process constraints, terminal constraints, control constraints, and path constraints, as follows: (1) Boundary constraints

[0109]

[0110] Where: t 0 is the initial moment, v 0 、m 0 are the initial velocity and initial mass respectively, x(t 0 ), y (t0 ) are the distance and elevation of the launch point, respectively, and the launch angle θ(t 0 ) are the parameters to be optimized.

[0111] (2) Terminal constraints

[0112]

[0113] Where: t f is the terminal moment, v tfmin =210m / s is the expected minimum falling speed, θ tfmax =-90,θ tfmin =-60 are the expected maximum and minimum falling angles respectively; y T =0 is the target elevation coordinate.

[0114] (3) Process constraints

[0115] Ascent phase and inertia ascent phase:

[0116]

[0117] Boosting stage:

[0118]

[0119] Where: t cl is the ignition end time, ignition time t ig is the variable to be optimized, the engine working time t c =7s is a constant.

[0120] Gliding section:

[0121]

[0122] (4) Control constraints

[0123] |α|≤α max (7)

[0124] Where: α max =10° is the maximum angle of attack.

[0125] (5) Path constraints

[0126] In order to ensure that the gliding guided projectile has sufficient control ability during flight, the minimum value of dynamic pressure q is set min =10000Pa. At the same time, considering the limitation of the missile structure strength, the maximum normal overload is set to n ymax =2g.

[0127]

[0128] in:

[0129] The optimization target is the range of the gliding guided projectile, that is, the objective function is:

[0130] min J=-x tf (9)

[0131] The mathematical description of the trajectory optimization problem is: at time [t 0 ,t f ], under the constraints of equations (2) to (8), the optimal control variables α and the angle of fire θ (t 0 ), ignition time t ig , so that the objective function (9) is minimized;

[0132] (2) Establishing the GWO-hpRPM algorithm model

[0133] The algorithm adopts a dual-loop optimization strategy, including inner loop optimization and outer loop optimization. The outer loop uses the GWO algorithm to optimize the firing angle and ignition time, providing the optimal initial value for the inner loop; the inner loop uses the hpRPM algorithm to solve the optimal control law. u and fitness value J, and finally the glide trajectory with the longest range is obtained while satisfying all constraints.

[0134] GWO outer loop: The dimension of the target search space is the number of optimization variables, which is 2; suppose the group consists of nPop gray wolves, and the GWO algorithm initializes the gray wolf position X = [θ 0 ,t ig ] is input into the inner loop hpRPM algorithm, where θ 0 =[θ 01 ,θ 02 ,…,θ 0nPop ] T , t ig =[t ig1 ,t ig2 ,…t ignPop ] T , according to the fitness value J returned by the hpRPM algorithm, save the top three gray wolves α, β and δ with the best fitness values, obtain and record the initial optimal individual and fitness value. Then, update the position X of the gray wolf according to formula (13), and input the updated position into hpRPM again. The hpRPM algorithm calculates the fitness value according to the objective function of formula (9), returns the fitness value J to the GWO algorithm, obtains the minimum fitness value of this iteration, and compares it with the optimal fitness value obtained in the previous group iteration. If the maximum number of iterations is reached, stop the calculation, otherwise update the position of the gray wolf according to formula (13), and continue the next iteration. The gray wolf with the smallest fitness value in the last iteration is the optimal individual. Finally, output the global optimal position and optimal fitness value J in the GWO algorithm to obtain the optimal initial value of the inner loop;

[0135]

[0136] C i =2·rand,i=1,2,3 (11)

[0137] Among them, X α , X β , X δ Indicates the current position of the gray wolves α, β, δ. 1 , C 2 , C 3 represents the random vector coefficient, X represents the current position of the gray wolf, and D α , D β , D δ Represents the distance between the wolf individual ω and the prey.

[0138] After determining the positions of gray wolves α, β, and δ, the wolves attack and capture the surrounding prey. The corresponding mathematical model is as follows:

[0139]

[0140] Where X 1 , X 2 , X 3 They respectively represent the position that the individual ω wolf needs to adjust under the influence of α wolf, β wolf and δ wolf. The average value is taken here, as shown in formula (13).

[0141] hpRPM inner loop: determining state variables s , control variables u and constraints, according to the initial value of the parameter to be optimized input by GWO X = [θ 0 ,t ig ] and the initial values ​​of other variables, solve the optimal control law u and fitness value J, output the changing values ​​of state variables and control variables over time, and finally return the fitness value J to the GWO algorithm.

[0142] (4) Perform trajectory iterative optimization solution and fitness evaluation.

[0143] (a) First, set the initial value of the iterative calculation. If the particle population is 10, then we can get 10 initial gray wolf positions. The initial population is formed, and the maximum number of particle iterations is 8.

[0144] (b) The initial gray wolf position is passed to the initial value required by hpRPM. The hpRPM algorithm calculates the fitness value of the objective function according to formula (9), returns the fitness value J to the GWO algorithm, and obtains and records the initial optimal individual and fitness value;

[0145] (c) Update the position of the gray wolf according to formula (13);

[0146] (d) The updated gray wolf position is passed to the initial value required by hpRPM again. The hpRPM algorithm calculates the fitness value of the objective function according to formula (9), returns the fitness value J to the GWO algorithm, obtains the minimum fitness value of this iteration, and compares it with the optimal fitness value obtained in the previous group iteration. If the maximum number of particle iteration calculations is reached, the calculation is stopped. Otherwise, the gray wolf position is updated according to formula (13) and the next iteration is continued.

[0147] (e) The individual with the smallest fitness value in the last iteration is taken as the optimal individual, and the corresponding trajectory is the optimal trajectory. The optimal individual gbest is the optimal shooting angle and ignition time corresponding to the optimal trajectory.

Claims

1. A glide-guided projectile trajectory optimization method based on the GWO-hpRPM algorithm, characterized in that: The following steps are involved: In the launch coordinate system, the longitudinal motion equation of the gliding guided projectile is established with the longitudinal motion of the gliding guided projectile as the research target. Determine the trajectory objective function and constraints, and establish a trajectory optimization mathematical model; Establish the GWO-hpRPM optimization algorithm: This algorithm adopts a dual-loop optimization strategy, including inner loop optimization and outer loop optimization. The outer loop uses the GWO algorithm to optimize the firing angle and ignition time to provide the optimal initial value for the inner loop; the inner loop uses the hpRPM algorithm to solve the optimal control law u and fitness value J, and finally obtains the glide trajectory with the longest range while satisfying all constraints. Perform trajectory optimization solution and fitness evaluation: set initial conditions, perform iterative calculations, and obtain the optimal shooting angle, ignition time, and optimal trajectory when the fitness of the objective function converges.

2. The glide-guided projectile trajectory optimization method based on the GWO-hpRPM algorithm according to claim 1, characterized in that: The longitudinal motion equation of the gliding guided projectile is: Where: α is the angle of attack, δ is the rudder deflection angle, C D0 is the zero lift drag coefficient, C Dδ0 is the zero-lift drag coefficient of the rudder surface, C L ′ is the lift coefficient derivative, C′ Lδ is the derivative of the lift coefficient of the rudder surface, k T , k B are the induced drag coefficient of the rudder surface and the induced drag coefficient of the missile body, X R To control the rudder pressure center position, X F is the center of pressure position of the wing assembly, X G is the center of gravity of the whole projectile, v is the velocity, θ is the ballistic inclination angle, x and y are the flight distance and flight altitude of the sliding-guided projectile respectively, is the dynamic pressure, S is the characteristic area, m is the mass of the projectile, g is the gravitational acceleration, F p is the average thrust of the rocket engine, m c It is the mass dissipation rate of rocket booster engine charge.

3. The glide-guided projectile trajectory optimization method based on the GWO-hpRPM algorithm according to claim 1 or 2, characterized in that: The trajectory optimization mathematical model is established as follows: the firing angle and the ignition time are used as optimization variables, denoted as X = [θ0, t ig ], taking boundary constraints, terminal constraints, process constraints, control constraints and path constraints as constraints and range as objective function, an optimization mathematical model is established.

4. The glide-guided projectile trajectory optimization method based on the GWO-hpRPM algorithm according to claim 3 is characterized in that: The boundary constraints are: Among them: t0 is the initial time, v0 and m0 are the initial velocity and initial mass respectively, x(t0), y (t0) are the distance and elevation of the launch point, respectively, and the launch angle θ(t0) is the parameter to be optimized; Terminal constraints: Where: t f is the terminal moment, v tfmin =210m / s is the expected minimum falling speed, θ tfmax =-90°,θ tfmin =-60° are the expected maximum and minimum falling angles respectively; y T =0 is the target elevation coordinate; Process constraints: Ascent phase and inertia ascent phase: Boosting stage: Where: t cl is the ignition end time, ignition time t ig is the variable to be optimized, the engine working time t c is a constant; Gliding section: Control constraints: |α|≤α max (7) Path constraints: in:

5. The glide-guided projectile trajectory optimization method based on the GWO-hpRPM algorithm according to claim 4, characterized in that: The objective function is: minJ=-x tf (9) The mathematical description of the trajectory optimization problem is: at time [t0,t f ], under the constraints of equations (2) to (8), the optimal control variables α, firing angle θ(t0), ignition time t ig , so that the objective function (9) is minimized.

6. The glide-guided projectile trajectory optimization method based on the GWO-hpRPM algorithm according to claim 5, characterized in that: The outer loop of GWO is: The dimension of the target search space is the number of optimization variables. Assuming that the population consists of nPop particles, the GWO algorithm initializes the gray wolf position X = [θ0,t ig ] is input into the inner loop hpRPM algorithm, where θ0 = [θ 01 ,θ 02 ,… ,θ 0nPop ] T , t ig =[t ig1 ,t ig2 ,…t ignPop ] T , according to the fitness value J returned by the hpRPM algorithm, save the top three gray wolves α, β and δ with the best fitness values, obtain and record the initial optimal individual and fitness value; update the position X of the gray wolf according to formula (13), and input the updated position into hpRPM again. The hpRPM algorithm calculates the fitness value according to the objective function in formula (9), returns the fitness value J to the GWO algorithm, obtains the minimum fitness value of this iteration, and compares it with the optimal fitness value obtained in the previous group iteration. If the maximum number of iterations is reached, stop the calculation, otherwise update the position of the gray wolf according to formula (13), continue the next iteration, and the gray wolf with the smallest fitness value in the last iteration is taken as the optimal individual; finally, output the global optimal position and optimal fitness value J in the GWO algorithm, and obtain the optimal initial value of the inner loop; C i =2·rand,i=1,2,3 (11) Among them, X α , X β , X δ represents the current position of the gray wolf α, β, δ. C1, C2, C3 represent random vector coefficients, X represents the current position of the gray wolf, D α , D β , D δ represents the distance between individual wolf ω and the prey; After determining the positions of gray wolves α, β, and δ, the wolves attack and capture the surrounding prey. The corresponding mathematical model is as follows: Among them, X1, X2, and X3 represent the positions that the individual ω wolf needs to adjust under the influence of α wolf, β wolf, and δ wolf, respectively, and take the average value, as shown in formula (13).

7. The glide-guided projectile trajectory optimization method based on the GWO-hpRPM algorithm according to claim 6, characterized in that: The inner loop of hpRPM is as follows: determine the state variable s, control variable u and constraint conditions, and calculate the initial value of the parameter to be optimized according to the GWO input X=[θ0,t ig ] and the initial values ​​of other variables, solve the optimal control law u and fitness value J, output the changing values ​​of state variables and control variables over time, and finally return the fitness value J to the GWO algorithm.

8. The glide-guided projectile trajectory optimization method based on the GWO-hpRPM algorithm according to claim 7, characterized in that: The trajectory optimization solution and fitness evaluation include: Set the initial value of iterative calculation; The initial particle swarm is passed to the initial value required by hpRPM. The hpRPM algorithm calculates the fitness value of the objective function according to formula (9), returns the fitness value J to the GWO algorithm, and obtains and records the initial optimal individual and fitness value; Update the position of the gray wolf according to formula (13); The updated position of the gray wolf is passed to the initial value required by hpRPM again. The hpRPM algorithm calculates the fitness value of the objective function according to formula (9), returns the fitness value J to the GWO algorithm, obtains the minimum fitness value of this iteration, and compares it with the optimal fitness value obtained in the previous group iteration. If the maximum number of iterative calculations is reached, the calculation is stopped, otherwise the particle speed and position are updated according to formula (13) and the next iteration is continued; The gray wolf with the smallest fitness value in the last iteration is taken as the optimal individual, and the corresponding trajectory is the optimal trajectory. The optimal individual gbest is the optimal shooting angle and ignition time corresponding to the optimal trajectory.

9. The glide-guided projectile trajectory optimization method based on the GWO-hpRPM algorithm according to claim 8, characterized in that: The maximum number of iterations maxIt=10.

10. The glide-guided projectile trajectory optimization method based on the GWO-hpRPM algorithm according to claim 3, characterized in that: The upper and lower limits of the ignition time and the firing angle are respectively: UpB=[10,65°], LoB=[5,20°].

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