Gliding guided projectile trajectory optimization method based on WOA-hpRPM algorithm

Abstract

The invention relates to a gliding guided projectile trajectory optimization method based on a WOA-hpRPM algorithm, and the method comprises the steps: taking the longitudinal plane motion of a gliding guided projectile as a research target, and building a longitudinal motion equation of the gliding guided projectile in a launching coordinate system; determining a ballistic objective function and constraint conditions, and establishing a ballistic optimization mathematical model; a WOA-hpRPM optimization algorithm is established, the algorithm adopts a double-ring optimization strategy, an outer ring adopts a WOA 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 WOA-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] The Whale Optimization Algorithm (WOA) is a meta-heuristic intelligent optimization algorithm inspired by the foraging behavior of whales. It was proposed by Seyedali Mirjalili and Andrew Lewis in 2016. Its mathematical model is based on the three main foraging behaviors of humpback whales: encircling prey, bubble net hunting, and searching for food. Compared with other heuristic algorithms, WOA has the characteristics of simple structure, strong search ability, and fast convergence speed. The traditional WOA algorithm has a good effect on 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. WOA 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 computational complexity, low memory usage, and the ability to effectively handle complex constraint problems. It has been widely used in solving trajectory optimization problems. When hpRPM is used alone, it may fall into the local optimal solution due to its local optimization characteristics. Therefore, how to obtain the optimal gliding trajectory while meeting 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 WOA-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 WOA-hpRPM optimization algorithm: This algorithm adopts a dual-loop optimization strategy, including inner loop optimization and outer loop optimization. The outer loop uses the WOA 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 under all constraints. Specifically:

[0009] Assume that the population consists of nPop particles. The WOA algorithm inputs the initialized particle position into the inner loop hpRPM algorithm. According to the fitness value J returned by the hpRPM algorithm, the initial optimal solution is saved, and a, A, C, l, and p are updated. If p < 0.5, the next step is entered; otherwise, according to the bubble net predation mechanism, the position is updated using formula (10); where a decreases linearly from 2 to 0 during the iteration process, A = 2 × a × ra and C = 2 × r represent coefficient vectors, and l and p are random numbers in [-1, 1].

[0010] X(t+1)=D′×e bl ×cos(2πl)+gbest (10)

[0011] D′=|gbest-X(t)| (11)

[0012] Where b is a constant that defines the shape of the spiral;

[0013] If |A| < 1, surround the prey and use formula (13) to update the position; otherwise, search for prey randomly and use formula (15) to update the position:

[0014] D = |C × gbest - X(t)| (12)

[0015] X(t+1)=gbest-A×D (13)

[0016] D1=|C×X rand (t)-X(t)| (14)

[0017] X(t+1)=X rand (t)-A×D1 (15)

[0018] Where t represents the current iteration number, A and C represent coefficient vectors, gbest represents the position vector of the currently obtained optimal solution, X(t) represents the current whale position vector, and X rand is a random position vector selected from the current population;

[0019] The updated position is input into hpRPM again. The objective function of hpRPM algorithm calculates the fitness value and returns the fitness value J to WOA algorithm to obtain the minimum fitness value of this iteration and compare it with the optimal fitness value obtained in the previous group iteration. If the maximum number of iterations is reached, the calculation is stopped. Otherwise, the position of the whale is updated and the next iteration is continued. The whale with the smallest fitness value in the last iteration is taken as the optimal individual. Finally, the global optimal position and the optimal fitness value J are output in WOA algorithm to obtain the optimal initial value of the inner loop.

[0020] 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.

[0021] 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.

[0022] The longitudinal motion equation of the gliding guided projectile is:

[0023]

[0024] 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 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.

[0025] 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.

[0026] The boundary constraints are:

[0027]

[0028] Where: t0 is the initial time, v0 and m0 are the initial velocity and initial mass respectively, x(t0) and y(t0) are the distance and elevation of the launch point respectively, and the launch angle θ(t0) is the parameter to be optimized;

[0029] Terminal constraints:

[0030]

[0031] 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;

[0032] Process constraints:

[0033] Ascent phase and inertia ascent phase:

[0034]

[0035] Boosting stage:

[0036]

[0037] 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;

[0038] Gliding section:

[0039]

[0040] Control constraints:

[0041] |α|≤α max (7)

[0042] Path constraints:

[0043]

[0044] in:

[0045] The objective function is:

[0046] min J=-x tf (9)

[0047] 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.

[0048] The dimension of the target search space is the number of optimization variables.

[0049] The inner loop of hpRPM is to determine the state variable s, control variable u and constraint conditions, and the initial value of the parameter to be optimized according to the WOA input X = [θ0,t ig ] and the initial values ​​of other variables, solve the optimal control law u and fitness value J, output the values ​​of state variables and control variables changing over time, and finally return the fitness value J to the WOA algorithm.

[0050] The trajectory optimization solution and fitness evaluation include:

[0051] Set the initial value of iterative calculation;

[0052] The initial whale 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 WOA algorithm, and obtains and records the initial optimal individual and fitness value;

[0053] If p < 0.5, proceed to the next step; otherwise, according to the bubble net predation mechanism, the position is updated using formula (10);

[0054] If |A| < 1, surround the prey and use formula (13) to update the position; otherwise, search for prey randomly and use formula (15) to update the position;

[0055] The updated whale 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 WOA 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, the calculation is stopped, otherwise the whale position is updated and the next iteration is continued;

[0056] The whale 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.

[0057] The maximum number of iterations maxIt=8.

[0058] The upper and lower limits of the ignition time and the firing angle are respectively: UpB=[10,65°], LoB=[5,20°].

[0059] Beneficial effects: The present invention has the following advantages:

[0060] (1) The present invention fully integrates the powerful global search capability of the WOA 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 WOA 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 finally obtains the glide trajectory with the longest range under all constraints.

[0061] (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

[0062] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0063] The present invention will be further described below in conjunction with the accompanying drawings.

[0064] The glide-guided projectile trajectory optimization method based on the WOA-hpRPM algorithm of this embodiment combines the powerful global search capability of the WOA 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 WOA 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. Specifically, it includes the following steps:

[0065] 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:

[0066]

[0067] 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, XF is the center of pressure 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.

[0068] 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 = [θ0, 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,

[0069] (1) The boundary constraints are:

[0070]

[0071] Where: t0 is the initial time, v0 and m0 are the initial velocity and initial mass respectively, x(t0) and y(t0) are the distance and elevation of the launch point respectively, and the launch angle θ(t0) is the parameter to be optimized.

[0072] (2) Terminal constraints:

[0073]

[0074] 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.

[0075] (3) Process constraints:

[0076] Ascent phase and inertia ascent phase:

[0077]

[0078] Boosting stage:

[0079]

[0080] Where: t cl is the ignition end time, ignition time tig is the variable to be optimized, the engine working time t c =7s is a constant.

[0081] Gliding section:

[0082]

[0083] (4) Control constraints:

[0084] |α|≤α max (7)

[0085] Where: α max =10° is the maximum angle of attack.

[0086] (5) Path constraints:

[0087] 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.

[0088]

[0089] in:

[0090] The optimization target is the range of the gliding guided projectile, that is, the objective function is:

[0091] min J=-x tf (9)

[0092] 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.

[0093] S3. Establish WOA-hpRPM optimization algorithm: This algorithm adopts a dual-loop optimization strategy, including inner loop optimization and outer loop optimization. The outer loop uses the WOA 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:

[0094] Step 3-1: WOA outer loop: The dimension of the target search space is the number of optimization variables, which is 2. Assume that the population consists of nPop particles. The WOA algorithm initializes the particle 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 initial optimal solution, update a, A, C, l, p, if p < 0.5, go to step 3-2; otherwise, according to the bubble net predation mechanism, use formula (10) to update the position; where a decreases linearly from 2 to 0 with the iteration process, A = 2 × a × ra and C = 2 × r represent coefficient vectors, and l and p are random numbers in [-1, 1].

[0095] X(t+1)=D′×e bl ×cos(2πl)+gbest (10)

[0096] D′=|gbest-X(t)| (11)

[0097] Here, b is a constant that defines the shape of the spiral.

[0098] Step 3-2: If |A| < 1, surround the prey and use equation (13) to update the position; otherwise, randomly search for the prey and use equation (15) to update the position.

[0099] D = |C × gbest - X(t)| (12)

[0100] X(t+1)=gbest-A×D (13)

[0101] D1=|C×X rand (t)-X(t)| (14)

[0102] X(t+1)=X rand (t)-A×D1 (15)

[0103] Where t represents the current iteration number, A and C represent coefficient vectors, gbest represents the position vector of the currently obtained optimal solution, X(t) represents the current whale position vector, and X rand is a random position vector selected from the current population.

[0104] Step 3-3: Update the position X and input the updated position into hpRPM again. The hpRPM algorithm calculates the fitness value according to the objective function in step 2, returns the fitness value J to the WOA 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 continue to update the position of the whale and continue to the next iteration. The whale with the smallest fitness value in the last iteration is the optimal individual. Finally, the global optimal position and the optimal fitness value J are output in the WOA algorithm to obtain the optimal initial value of the inner loop;

[0105] hpRPM inner loop: Determine the state variable s, control variable u and constraints, and the initial value of the parameter to be optimized X=[θ0,t ig ] and the initial values ​​of other variables, solve the optimal control law u and fitness value J, output the values ​​of state variables and control variables changing over time, and finally return the fitness value J to the WOA algorithm.

[0106] 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:

[0107] S41, setting the initial value of iterative calculation;

[0108] S42, passing the initial whale position 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 WOA algorithm, obtains and records the initial optimal individual and fitness value;

[0109] S43, if p < 0.5, then enter S44; otherwise, according to the bubble net predation mechanism, use formula (10) to update the position;

[0110] S44, if |A| < 1, surround the prey and update the position using formula (13); otherwise, randomly search for the prey and update the position using formula (15);

[0111] S45. The updated whale 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 WOA 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 whale position is updated and the next iteration is continued; the maximum number of iterations maxIt=8.

[0112] S46. The whale 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.

[0113] like Figure 1 As 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 WOA-hpRPM algorithm is used for solving to quickly obtain the optimal trajectory that meets the requirements.

[0114] In the launching coordinate system, the longitudinal motion equation of the gliding guided projectile is established.

[0115]

[0116] 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 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.

[0117] (1) Establishment of trajectory optimization mathematical model

[0118] The existing trajectory is used as the reference scheme, and the ignition time and firing angle are used as the optimization variables, which are recorded as X = [θ0, t ig ], the upper and lower boundaries are: UpB = [10, 65°], LoB = [5, 20°]

[0119] Constraints include boundary constraints, process constraints, terminal constraints, control constraints, and path constraints, as follows: (1) Boundary constraints

[0120]

[0121] Where: t0 is the initial time, v0 and m0 are the initial velocity and initial mass respectively, x(t0) and y(t0) are the distance and elevation of the launch point respectively, and the launch angle θ(t0) is the parameter to be optimized.

[0122] (2) Terminal constraints

[0123]

[0124] 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.

[0125] (3) Process constraints

[0126] Ascent phase and inertia ascent phase:

[0127]

[0128] Boosting stage:

[0129]

[0130] 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.

[0131] Gliding section:

[0132]

[0133] (4) Control constraints

[0134] |α|≤α max (7)

[0135] Where: α max =10° is the maximum angle of attack.

[0136] (5) Path constraints

[0137] 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.

[0138]

[0139] in:

[0140] The optimization target is the range of the gliding guided projectile, that is, the objective function is:

[0141] min J=-x tf (9)

[0142] 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;

[0143] (2) Establishing the WOA-hpRPM algorithm model

[0144] The algorithm adopts a dual-loop optimization strategy, including inner loop optimization and outer loop optimization. The outer loop uses the WOA 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.

[0145] WOA 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 WOA algorithm initializes the particle 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 initial optimal solution, and update a, A, C, l, and p. If p < 0.5, determine whether |A| is less than 1. If |A| < 1, surround the prey and use formula (13) to update the position; if |A| ≥ 1, randomly search for prey and use formula (15) to update the position; otherwise, according to the bubble net predation mechanism, use formula (10) to update the position; where a decreases linearly from 2 to 0 with the iteration process, A = 2 × a × ra and C = 2 × r represent coefficient vectors, and l and p are random numbers in [-1, 1].

[0146] X(t+1)=D′×e bl ×cos(2πl)+gbest (10)

[0147] D′=|gbest-X(t)| (11)

[0148] Here, b is a constant that defines the shape of the spiral.

[0149] D = |C × gbest - X(t)| (12)

[0150] X(t+1)=gbest-A×D (13)

[0151] D1=|C×X rand (t)-X(t)| (14)

[0152] X(t+1)=X rand (t)-A×D1 (15)

[0153] Where t represents the current iteration number, A and C represent coefficient vectors, gbest represents the position vector of the currently obtained optimal solution, X(t) represents the current whale position vector, and X rand is a random position vector selected from the current population.

[0154] The updated position X is input into hpRPM again. The hpRPM algorithm calculates the fitness value according to the objective function of formula (9), and returns the fitness value J to the WOA algorithm to obtain the minimum fitness value of this iteration and compare it with the optimal fitness value obtained in the previous group iteration. If the maximum number of iterations is reached, the calculation is stopped. Otherwise, the position of the whale is updated and the next iteration is continued. The whale with the smallest fitness value in the last iteration is taken as the optimal individual. Finally, the global optimal position and the optimal fitness value J are output in the WOA algorithm to obtain the optimal initial value of the inner loop.

[0155] hpRPM inner loop: Determine the state variable s, control variable u and constraints, and the initial value of the parameter to be optimized X=[θ0,t ig ] and the initial values ​​of other variables, solve the optimal control law u and fitness value J, output the values ​​of state variables and control variables changing over time, and finally return the fitness value J to the WOA algorithm.

[0156] (4) Perform trajectory iterative optimization solution and fitness evaluation.

[0157] (a) First, set the initial value of the iterative calculation. If the particle population is 10, then 10 initial whale positions can be obtained. The initial population is formed, and the maximum number of particle iterations is 8.

[0158] (b) The initial whale 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 WOA algorithm, and obtains and records the initial optimal individual and fitness value;

[0159] (c) Update the whale’s location;

[0160] (d) The updated whale 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 WOA 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 whale position is updated and the next iteration is continued;

[0161] (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 method for optimizing the trajectory of a gliding guided projectile based on the WOA-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 WOA-hpRPM optimization algorithm: This algorithm adopts a dual-loop optimization strategy, with the inner loop using the hpRPM algorithm and the outer loop using the WOA algorithm. Specifically: Assume that the population consists of nPop particles. The WOA algorithm inputs the initialized particle position into the inner loop hpRPM algorithm. According to the fitness value J returned by the hpRPM algorithm, the initial optimal solution is saved, and a, A, C, l, and p are updated. If p < 0.5, the next step is entered; otherwise, according to the bubble net predation mechanism, the position is updated using formula (10); where a decreases linearly from 2 to 0 during the iteration process, A = 2 × a × ra and C = 2 × r represent coefficient vectors, and l and p are random numbers in [-1, 1]. X(t+1)=D′×e bl ×cos(2πl)+gbest (10) D′= | gbest-X(t) | (11) Where b is a constant that defines the shape of the spiral; If A < 1, surround the prey and use formula (13) to update the position; otherwise, search for prey randomly and use formula (15) to update the position: D = |C × gbest - X(t)| (12) X(t+1)=gbest-A×D (13) D1=|C×X rand (t)-X(t)| (14) X(t+1)=X rand (t)-A×D1 (15) Where t represents the current iteration number, A and C represent coefficient vectors, gbest represents the position vector of the currently obtained optimal solution, X(t) represents the current whale position vector, and X rand is a random position vector selected from the current population; The updated position is input into hpRPM again. The objective function of hpRPM algorithm calculates the fitness value and returns the fitness value J to WOA algorithm to obtain the minimum fitness value of this iteration and compare it with the optimal fitness value obtained in the previous group iteration. If the maximum number of iterations is reached, the calculation is stopped. Otherwise, the position of the whale is updated and the next iteration is continued. The whale with the smallest fitness value in the last iteration is taken as the optimal individual. Finally, the global optimal position and the optimal fitness value J are output in WOA algorithm to obtain the optimal initial value of the inner loop. 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 WOA-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 L ' δ 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 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 WOA-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, and are recorded as X = [θ0, t ig ] with boundary constraints, terminal constraints, process constraints, control constraints and path constraints as constraints Constraint conditions are taken, and range is taken as the objective function to establish an optimization mathematical model.

4. The glide-guided projectile trajectory optimization method based on the WOA-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 WOA-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 WOA-hpRPM algorithm according to claim 1, characterized in that: The dimension of the target search space is the number of optimization variables.

7. The glide-guided projectile trajectory optimization method based on the WOA-hpRPM algorithm according to claim 1, characterized in that: 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 WOA X = [θ0,t ig ] and the initial values ​​of other variables, solve the optimal control law u and fitness value J, output the values ​​of state variables and control variables changing over time, and finally return the fitness value J to the WOA algorithm.

8. The glide-guided projectile trajectory optimization method based on the WOA-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 whale 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 WOA algorithm, and obtains and records the initial optimal individual and fitness value; If p < 0.5, proceed to the next step; otherwise, according to the bubble net predation mechanism, the position is updated using formula (10); If A < 1, surround the prey and use formula (13) to update the position; otherwise, search for prey randomly and use formula (15) to update the position; The updated whale 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 WOA 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, the calculation is stopped, otherwise the whale position is updated and the next iteration is continued; The whale 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 WOA-hpRPM algorithm according to claim 8, characterized in that: The maximum number of iterations maxIt=8.

10. The glide-guided projectile trajectory optimization method based on the WOA-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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