阅读说明：本技术 一种求解无人机约束航路规划的混合烟花粒子群协同方法 (Mixed firework particle swarm cooperation method for solving unmanned aerial vehicle constrained route planning ) 是由 张祥银 夏爽 李秀智 于 2019-11-14 设计创作，主要内容包括：本发明涉及一种求解无人机约束航路规划的混合烟花粒子群协同算法,用于解决无人机航路规划问题。本方法采用两个种群并行独立搜索最优路径的方式,一个种群采用改进的烟花算法进行搜索,另一个种群采用粒子群优化算法。烟花通过爆炸在整个搜索空间中寻找最优解的大致区域并提供给粒子,为粒子之后的搜索指引方向。粒子则在接下来的迭代过程中向该区域进行细致的局部搜索。如此,两个种群结合进行搜索进而得到规划问题的最优解。在整个搜索过程中,通过设置安全等级来划分安全路径和不安全路径,然后在一次次的迭代过程中,逐步提高安全等级,进而将最优路径的搜索范围限制在安全的路径中,以保证规划出的路径的安全性。(The invention relates to a hybrid firework particle swarm cooperative algorithm for solving unmanned aerial vehicle constrained route planning, which is used for solving the problem of unmanned aerial vehicle route planning. The method adopts a mode that two groups search for the optimal path independently in parallel, wherein one group searches by adopting an improved firework algorithm, and the other group searches by adopting a particle swarm optimization algorithm. Fireworks find the approximate area of the optimal solution in the whole search space through explosion and provide the particle with the approximate area, and the direction is guided for the search after the particle. The particle then performs a detailed local search of the region in the following iteration. Thus, the two populations are combined to search to obtain the optimal solution of the planning problem. In the whole searching process, a safe path and an unsafe path are divided by setting a safety level, then the safety level is gradually improved in the iteration process of one time, and the searching range of the optimal path is limited in the safe path so as to ensure the safety of the planned path.)

1. A hybrid firework particle swarm cooperative method for solving unmanned aerial vehicle constrained route planning is characterized by comprising the following stages:

preparation and initialization phase

(1) Preparation of interestThe method comprises the steps of initializing a firework population and initializing a particle swarm, wherein the firework population is represented as a vector set X (t) { X ═ X₁(t),X₂(t),...,X_N(t) }, in which, X_i(t)＝{X_i1(t),X_i2(t),...,X_iD(t) } denotes the ith firework, i.e. corresponding to the ith complete path, i ═ 1,2 …, N, X_ij(t) represents the jth path point of the ith firework, j being 1, 2.. and D;

(2) calculating the path length f of the path P of the initialized firework population and the particle swarm_L(P), threat cost f_T(P) and a satisfaction grade mu (P), and searching the individual with the shortest path from the initialized firework population and the particle swarm as a global optimal solution x_gbest(t) initial value;

two groups independently search the optimal path stage in parallel, wherein the firework searching stage is as follows:

(3) through fireworks X_i(t) generating an explosion spark X_j(t)＝[X_j1(t),X_j2(t),...,X_jD(t)]，j＝1,2,...,S_iI.e. corresponding to a new complete path, X, of the drone_jk(t) denotes the kth path point for the jth explosion spark, k ═ 1, 2.., D;

(4) selecting the optimal N individuals in the fireworks and the explosion sparks by a grade comparison method to form a new fireworks group V (t) { V }₁(t),V₂(t),...,V_N(t), wherein the optimal individual is an optimal path obtained by a grade comparison method;

(5) to fireworks V_i(t) performing a mutation operation to generate a mutated spark V_i' (t), i.e. corresponding to a new complete path for the drone;

(6) firework V is selected through grade comparison method_i(t) and variant spark V_i' (t) the better individual, i ═ 1, …, N, constitutes a new firework population U (t) ═ U₁(t),U₂(t),...,U_N(t) }, where the optimal fireworks are U_best(t) worst fireworks are U_worst(t)；

Two groups independently search the optimal path stage in parallel, wherein the particle swarm search stage is as follows:

(7) updating the positions and the speeds of all the particles in the particle swarm to obtain the position of the next generation of particles

updating global optimal solution phase

(8) The worst fireworks U obtained in the fireworks searching stage_worst(t) and all the particles x (t +1) in the next generation obtained in the particle swarm search stage, and selecting the optimal individual U 'by a grade comparison method'_best(t) and is made of individual U'_best(t) replacing U in Firework population U (t)_worst(t) forming a next-generation firework population X (t +1), namely

X(t+1)＝{X₁(t+1),X₂(t+1),...,X_N(t+1)}；

(9) Selection of U by rank comparison method_best(t)、U′_best(t)、x_gbest(t) the optimal individual is updated to obtain the next generation global optimal solution x_gbest(t+1)；

(10) If the iteration times are reached, the operation is ended, and a global optimal solution x is output_gbest(t) solving the global optimum x_gbest(t) converting into an X-O-Y coordinate system, and outputting a planned optimal path of the unmanned aerial vehicle; otherwise, continuing to search the path.

2. The hybrid firework particle swarm collaborative method for solving the unmanned aerial vehicle constrained route planning as claimed in claim 1, wherein: the preparation and initialization specifically comprises:

the preparation work is as follows: the starting point S, the target point T, the number H of the threat sources, the threat level of each threat source, the position in the flying environment and the threat radius of the unmanned aerial vehicle are known; the maximum number of iterations of the algorithm is NC_max；

The fireworks population is initialized as follows:

the method comprises the following steps: establishing a rotating coordinate system X ' -S-Y ' with ST as an X ' axis, converting the position coordinates of the starting point, the target point and the obstacle into the rotating coordinate system, and calculating the upper and lower boundaries S of a planned space_max、S_minThe path planned by the robot is P ═ { P ═ P₀,P₁,P₂,…,P_D,P_D+1In which P is₀、P_D+1Respectively representing a starting point S and a target point T, P_iRepresenting the ith waypoint;

step two: using D parallel linear clusters L₁,L₂,…,L_DDividing ST into D +1 segments in a perpendicular manner, wherein the distance between each segment is delta l | | | ST |/(D +1), the length of ST | | | | is the length of ST, and a path point P₁,P₂,…,P_DI.e. corresponding to a straight line L₁,L₂,…,L_DThe above step (1);

step three: and (3) initializing fireworks by setting the iteration number t as 1, wherein the number of the fireworks is N, the firework dimension is D, namely randomly generating N unmanned aerial vehicle paths, wherein each path has D path points, and the firework population is represented as a vector group X (t) as { X ═ X-₁(t),X₂(t),...,X_N(t) }, in which, X_i(t)＝{X_i1(t),X_i2(t),...,X_iD(t) } denotes the ith firework, i.e. corresponding to the ith complete path, i ═ 1,2 …, N, X_ij(t) represents the jth path point of the ith firework, j being 1, 2.. and D;

particle swarm initialization is as follows: setting the number of particles to N_pEach particle corresponds to a complete path, the dimension of each particle is D, namely, D path points exist in each path, the parameter search range and the speed limit are set, the initial position and the speed of each particle are randomly determined, namely, N is randomly generated_pAn unmanned aerial vehicle path and corresponding path point variable quantity, and storing the position of the particle in

3. According toThe hybrid firework particle swarm cooperative method for solving the unmanned aerial vehicle constrained route planning of claim 1, wherein: the path length f of the path P_L(P), threat cost f_T(P), satisfaction level μ (P), formula as follows:

in the above formula, | | P_i+1-P_iI represents a path point P_i+1And P_iThe euclidean distance between;

in the above formula t_jThreat level for jth threat source, P_0.1,_j,_kPath segment P for jth threat source_kP_k+1Probability of threat at point upper 1/10, P_0.3,_j,_kPath segment P for jth threat source_kP_k+1Probability of threat at point 3/10, and so on;

in the above equation, b is a rank calculation constant.

4. The hybrid firework particle swarm collaborative method for solving the unmanned aerial vehicle constrained route planning as claimed in claim 3, wherein:

the threat probability of the threat source is calculated as follows:

(1) probability of threat from mountain peak threat source P_P：

In the above formula, d is the distance from the unmanned aerial vehicle to the threat source, R_PA peak threat radius;

(2) threat probability P of radar threat source_R：

In the above formula, d is the distance from the unmanned aerial vehicle to the threat source, R_RmaxIs the radar threat radius;

(3) threat probability P of missile threat source_M：

In the above formula, d is the distance from the unmanned aerial vehicle to the threat source, R_MmaxThreat radius for the missile;

(4) probability of threat of antiaircraft gun threat source P_G：

In the above formula, d is the distance from the unmanned aerial vehicle to the threat source, R_GmaxIs the threat radius of the antiaircraft gun.

5. The hybrid firework particle swarm collaborative method for solving the unmanned aerial vehicle constrained route planning as claimed in claim 1, wherein: the fireworks generate explosion sparks, wherein the number of the explosion sparks and the calculation formula of the kth path point in the jth explosion spark are respectively as follows:

number of exploding sparks S_i，

Wherein N is₁The number of fireworks corresponding to the safe path is fireworks X_iSatisfaction grade of mu (X)_i) Path no less than α, N₂The number of fireworks corresponding to unsafe paths is fireworks X_iSatisfaction grade of mu (X)_i)<α path, β ∈ [0,1 ]]As a scaling parameter, M ∈ [10,100 ]]Is a constant for adjusting the number of explosion sparks generated, f_Lmax＝max(f_L(X_i) ) is the maximum path length value in the firework population with safe corresponding paths, i is 1,2, …, N₁，μ_min＝min(μ(X_i) For the minimum satisfactory level value in the fireworks population with unsafe corresponding paths, i is 1,2, …, N₂ε is the minimum number of machines and α is the safety rating, the formula is as follows:

in the above formula, ξ ∈ [0, 100] is the growth rate parameter, and t is the current iteration number

Kth path point X in jth explosion spark_jk：

X_jk＝X_ik+rand(-1,1)×A_i(19)

In the above formula, the first and second carbon atoms are,

X_ikthe kth path point representing the ith firework, k 1,2, D, rand () is a function that takes a random value within the interval,

A_ifor fireworks X_i(t) the corresponding explosion radius, the calculation formula is as follows:

N₁number of fireworks for safety of corresponding path, N₂The number of fireworks which correspond to the unsafe paths,is a constant for adjusting the size of the explosion radius,f_Lmin＝min(f_L(X_i) ) is the minimum path length value in the firework population with safe corresponding paths, i is 1,2, …, N₁，μ_max＝max(μ(X_i) For the maximum satisfactory level value in the fireworks population with unsafe corresponding paths, i is 1,2, …, N₂And ε is the minimum machine amount.

6. The hybrid firework particle swarm collaborative method for solving the unmanned aerial vehicle constrained route planning as claimed in claim 1, wherein: the grade comparison method specifically comprises the following steps:

in the iterative process, if two individuals R to be compared₁、R₂Corresponding to the path length f₁、f₂Degree of path satisfaction mu₁、μ₂The number of times the security level is α,

(1) mu.s of₁≥α、μ₂Not less than α, and f₁≤f₂Selecting R₁Is a better individual;

(2) when (1) is not satisfied, if μ₁＝μ₂And f is₁≤f₂Selecting R₁Is a better individual;

(3) when (1) and (2) are not satisfied, if μ₁>μ₂Selecting R₁Is a better individual.

7. The hybrid firework particle swarm collaborative method for solving the unmanned aerial vehicle constrained route planning as claimed in claim 1, wherein: the variant spark generation formula is as follows:

V_i′＝V_i+rand(-1,1)×(V_b-V_r) (21)

in the above formula, i is 1,2_bThe optimal fireworks in the fireworks group V (t), namely the optimal individuals selected by the grade comparison method, V_rFor the generated variant fireworks and removing V_iAnd (d) randomly selecting one firework from the unchanged fireworks in the outer V (t).

8. The hybrid firework particle swarm collaborative method for solving the unmanned aerial vehicle constrained route planning as claimed in claim 1, wherein: the particle velocity and position update formula is as follows:

v_i(t+1)＝ω·v_i(t)+c₁·rand(0,1)·(x_pbest,i(t)-x_i(t))+c₂·rand(0,1)·(x_gbest(t)-x_i(t)) (22)

x_i(t+1)＝x_i(t)+v_i(t+1) (23)

in formula (22), i ═ 1,2₁∈[0,2]、c₂∈[0,2]As an acceleration constant, ω ∈ [0,1 ]]For inertial weights, rand () is a function that takes random values within the interval.

9. The hybrid firework particle swarm collaborative method for solving the unmanned aerial vehicle constrained route planning as claimed in claim 1, wherein: the spark mapping rule in the firework searching stage is as follows:

X_jk＝S_min+|X_jk|％(S_max-S_min) (20)

in the above equation,% is a modulo operation.

10. The hybrid firework particle swarm collaborative method for solving the unmanned aerial vehicle constrained route planning as claimed in claim 1, wherein: the particle mapping rule in the particle search stage is as follows:

in the above formula, i is 1,2 …, N_p，j＝1,2,...,D。

Technical Field

The invention discloses a hybrid firework particle swarm cooperative algorithm for solving unmanned aerial vehicle constrained route planning, and belongs to the technical field of intelligent robot navigation and control and intelligent optimization.

Background

Path planning is an important research direction of robot navigation technology. The unmanned aerial vehicle route planning is to calculate the optimal or sub-optimal flight track of the unmanned aerial vehicle from a starting point to a target point in proper time under the comprehensive condition of considering the constraints of the voyage, the flight environment and the like, so that the unmanned aerial vehicle can avoid the threat of an enemy and the environmental obstacle and safely complete the preset task. With the rapid development and wide application of the unmanned aerial vehicle technology, under the condition that the modern air defense technology is improved day by day, the route planning is carried out by simply manually operating the unmanned aerial vehicle, the actual application requirements of modern complex tasks cannot be effectively met, and therefore a series of intelligent optimization algorithms taking the optimization problem as the core are obtained, and become important methods for solving the route planning of the unmanned aerial vehicle under the constraint condition.

The firework algorithm is firstly proposed in 2010 by professor of great northern pit mining at the intelligent society of international groups, the inspiration of the firework algorithm is derived from the explosion process of fireworks in actual life, the firework algorithm belongs to an intelligent optimization method of non-biological groups, the firework algorithm has excellent optimizing performance, is favored by researchers, and is widely applied to solving problems in the fields of clustering, network planning, image recognition, function optimization and the like. The basic idea of the firework algorithm is as follows: the population is composed of a plurality of individuals (sparks), and the adaptability of the individuals to the environment is better and better through the mutual cooperation of the individuals, so that the optimal solution is approached. In the whole solution space, sparks generated by fireworks explosion can appear in a neighborhood centered on the sparks, and the process is a search for a local area. In the firework algorithm, in order to balance the local search capability and the global exploration capability, better fireworks can generate more sparks in a smaller explosion range, poorer fireworks can generate a small amount of sparks in a larger explosion range, so that the better fireworks are responsible for better local search in a better area, the poorer fireworks are responsible for global search in a larger explosion range, and the collaborative search of the two is the group intelligence represented by the algorithm.

The particle swarm optimization algorithm is a swarm intelligence optimization technology and was proposed by doctor Eberhart and doctor Kennedy in 1995. The algorithm is derived from research on foraging behaviors of bird groups, and is an intelligent random optimization algorithm provided by simulating migration and cooperative behaviors in the foraging process of the bird groups. The basic idea is as follows: starting from a random position, each particle continuously adjusts the searching direction and speed according to the self historical optimal position and the optimal particle position, and then finds the optimal solution of the problem. The particle swarm optimization algorithm draws attention from the academic world with the advantages of easy realization, high precision, fast convergence and the like, and is widely applied to various fields such as engineering optimization, image processing and the like. However, the particle swarm optimization algorithm is apt to fall into a local optimal solution and stop moving when processing a complex problem, i.e. a phenomenon of premature convergence.

Disclosure of Invention

The invention provides a hybrid firework particle swarm cooperative Algorithm (FWPS Cooperation Algorihm, FWPSALC) for solving the constrained route planning of an unmanned aerial vehicle. The method aims to provide an effective unmanned aerial vehicle route planning method, an optimal flight path which is far away from threats and has the shortest path can be planned for the unmanned aerial vehicle quickly and well, and the unmanned aerial vehicle can be guaranteed to fly to a target place in the shortest time and the safest mode. The method solves the path planning problem of a single object, and does not relate to the collaborative path planning problem among multiple objects.

In the hybrid algorithm, a mode of independently searching the optimal path in parallel by two populations is adopted. One population is searched by adopting an improved firework algorithm, and the other population is searched by adopting a particle swarm optimization algorithm. When two populations are searched for each time, information is shared. The fireworks provide the particles with an approximate area of the optimal solution found throughout the search space by the explosion, directing the search behind the particles. And the particle performs a detailed local search of the region in the following iteration. Thus, the two populations are combined to search to obtain the optimal solution of the planning problem. In the whole searching process, a safe path and an unsafe path are divided by setting a safety level, then the safety level is gradually improved in the iteration process of one time, and the searching range of the optimal path is limited in the safe path so as to ensure the safety of the planned path.

The specific technical scheme is as follows:

the mixed firework particle swarm cooperative algorithm provided by the invention gives consideration to the global search capability and the local search capability, has the characteristics of high convergence speed, strong robustness, strong optimization capability and the like, and can effectively solve the problem of unmanned aerial vehicle constrained route planning, and the specific application steps of the method are as follows:

preparation work: the starting point S of the unmanned aerial vehicle, the target point T, the number H of the threat sources, the threat level of each threat source, and the position and the threat radius in the flight environment are all known. The maximum number of iterations of the algorithm is NC_max。

The method comprises the following steps: establishing a rotating coordinate system X ' -S-Y ' with ST as an X ' axis, converting the position coordinates of the starting point, the target point and the obstacle into the rotating coordinate system, and calculating the upper and lower boundaries S of a planned space_max、S_minThe path planned by the robot is P ═ { P ═ P₀,P₁,P₂,…,P_D,P_D+1In which P is₀、P_D+1Respectively representing a starting point S and a target point T, P_iRepresenting the ith waypoint;

step two: using D parallel linear clusters L₁,L₂,…,L_DDividing ST into D +1 segments in a perpendicular manner, wherein the distance between each segment is delta l | | | ST |/(D +1), the length of ST | | | | is the length of ST, and a path point P₁,P₂,…,P_DI.e. corresponding to a straight line L₁,L₂,…,L_DThe above step (1);

step three: and (3) initializing fireworks by setting the iteration number t as 1, wherein the number of the fireworks is N, the firework dimension is D, namely randomly generating N unmanned aerial vehicle paths, wherein each path has D path points, and the firework population is represented as a vector group X (t) as { X ═ X-₁(t),X₂(t),...,X_N(t) }, in which, X_i(t)＝{X_i1(t),X_i2(t),...,X_iD(t) } denotes the ith firework, i.e. corresponding to the ith complete path, i ═ 1,2 …, N, X_ij(t) represents the jth path point of the ith firework, j being 1, 2.. and D;

step four: calculating the path length f of the path P corresponding to the fireworks in the fireworks group_L(P), threat cost f_T(P), satisfaction level μ (P), formula as follows:

in the above formula, | | P_i+1-P_iI represents a path point P_i+1And P_iThe euclidean distance between;

in the above formula t_jThreat level for jth threat source, P_0.1,_j,_kPath segment P for jth threat source_kP_k+1Probability of threat at point upper 1/10, P_0.3,_j,_kPath segment P for jth threat source_kP_k+1Probability of threat at point 3/10, and so on.

In the above equation, b is a rank calculation constant, and the value of the rank calculation constant is the median of the threat costs of the paths corresponding to all fireworks in step four.

Step five: initializing the particle group to set the number of particles to N_pEach particle corresponds to a complete path, the dimension of each particle is D, namely, D path points exist in each path, the parameter search range and the speed limit are set, the initial position and the speed of each particle are randomly determined, namely, N is randomly generated_pAn unmanned aerial vehicle path and corresponding path point variable quantity, and storing the position of the particle in

Performing the following steps;

step six: calculating the path length f of the path P corresponding to each particle in the particle group by the formulas (1), (2) and (3)_L(P), threat cost f_T(P), satisfaction grade μ (P);

step seven: saving the individual with the shortest corresponding path in all the fireworks and the particles in the fourth step and the sixth step in the global optimal solution x_gbest(t), namely the currently searched optimal path of the unmanned aerial vehicle, and the global optimal solution x_gbestThe initial value of (t) is calculated by the initialized firework population and the initialized particle swarm;

step eight, updating the security level α according to the following formula:

in the above formula, ξ belongs to [0, 100] as a growth rate parameter, and t is the current iteration number;

step nine: calculating fireworks X_i(t) number of explosion sparks S_iAnd a detonation radius A_iAnd generating an explosion spark X_j(t)＝[X_j1(t),X_j2(t),...,X_jD(t)]，j＝1,2,...,S_iI.e. corresponding to a new complete path, X, of the drone_jk(t) denotes the kth path point for the jth explosion spark, k ═ 1, 2.., D;

step ten: mapping the explosion sparks exceeding the boundary to a new position, and calculating the path length f of the path P corresponding to each spark in the explosion sparks by the formulas (1), (2) and (3)_L(P), threat cost f_T(P), a satisfaction level μ (P), said out-of-bounds meaning that waypoints on the spark exceed the upper and lower bounds of the planned space;

step eleven: selecting the optimal N individuals in the fireworks and the explosion sparks by a grade comparison method to form a new fireworks group V (t) { V }₁(t),V₂(t),...,V_N(t), wherein the optimal individual is an optimal path obtained by a grade comparison method;

step twelve: to fireworks V_i(t) performing a mutation operation to generate a mutated spark V_i' (t), i.e. corresponding to a new complete path for the drone;

step thirteen: mapping the variant sparks exceeding the boundary to new positions, and calculating the path length f of the path P corresponding to each spark in the variant sparks according to the formulas (1), (2) and (3)_L(P), threat cost f_T(P), satisfaction grade μ (P);

fourteen steps: firework V is selected through grade comparison method_i(t) and variant spark V_i' (t) inExcellent individuals, i ═ 1, …, N, constitute a new firework population U (t ═ U)₁(t),U₂(t),...,U_N(t) }, where the optimal fireworks are U_best(t) worst fireworks are U_worst(t)；

Step fifteen: updating the positions and the speeds of all the particles in the particle swarm to obtain the position of the next generation of particles

And velocity

Sixthly, the steps are as follows: mapping the particles beyond the boundary to a new position, and calculating the path length f of the path P corresponding to each particle by the formulas (1), (2) and (3)_L(P), threat cost f_T(P), a satisfaction grade mu (P), wherein the path points on the particles beyond the boundary exceed the upper and lower boundaries of the planning space, or the variation of the path points on the particles exceeds the set speed range;

seventeen steps: the updated ith particle is stored in x_pbest(t) comparing grades of ith particles, selecting the better particles to store in x_pbestIn (t +1), i is 1,2_p；

Eighteen steps: all the particles x (t +1) in the next generation and the worst fireworks U in step 14 are selected by a grade comparison method_worst(t) most preferred individual U'_best(t) and the step 14 of removing U from the firework group U (t)_worst(t) the fireworks except for (t) form the next-generation firework group X (t +1) ═ X₁(t+1),X₂(t+1),...,X_N(t+1)}；

Nineteen steps: selection of U by rank comparison method_best(t)、U′_best(t)、x_gbest(t) the optimal individual is updated to obtain the next generation global optimal solution x_gbest(t+1)；

Twenty steps: let t be t +1, judge whether t satisfies>NC_max. If not, returning to the step eight for iteration; if yes, the operation is considered to be finished, and outputGlobal optimal solution x_gbest(t)。

Twenty one: solving the global optimum x_gbestAnd (t) converting into an X-O-Y coordinate system, and outputting the planned optimal path of the unmanned aerial vehicle.

Supplementary explanation:

the coordinate conversion formula in the first step is as follows:

in the above formula (x)_s,y_s) The initial position of the robot is (X, Y), (X ', Y ') are respectively the coordinate position of any one same point in a coordinate system X-O-Y and X ' -S-Y ', and theta is the included angle between the X ' axis and the X axis.

The upper and lower boundaries of the planning space in the first step are points in the threat region of the threat source, which are farthest from the ST axis, and then extend outwards for a certain safety distance, and the calculation formula is as follows:

in the above formula y_threatjIs the Y' axis coordinate of the jth threat source after coordinate transformation, j is 1,2_jFor the threat radius of the jth threat source, max { } is a function of taking the maximum value, min { } is a function of taking the minimum value, and Δ d belongs to [5, 50 ∈ [ ]]Is a safe distance.

When calculating the path threat level, the threat probabilities of different threat sources are calculated as follows:

(1) probability of threat from mountain peak threat source P_P：

In the above formula, d is the distance from the unmanned aerial vehicle to the threat source, R_PIs the peak threat radius.

(2) Threat probability P of radar threat source_R：

In the above formula, d is the distance from the unmanned aerial vehicle to the threat source, R_RmaxIs the radar threat radius.

(3) Threat probability P of missile threat source_M：

In the above formula, d is the distance from the unmanned aerial vehicle to the threat source, R_MmaxThe threat radius for the missile.

(4) Probability of threat of antiaircraft gun threat source P_G：

In the above formula, d is the distance from the unmanned aerial vehicle to the threat source, R_GmaxIs the threat radius of the antiaircraft gun.

In the fifth step, the particle swarm positions are expressed as vector setsWherein x is_i(t)＝[x_i1(t),x_i2(t),...,x_iD(t)]Indicating the position of the ith particle, i.e. the position corresponding to the ith complete path, i-1, 2 …, N_p，x_ij(t) represents the position of the jth path point of the ith particle, j is 1,2

Wherein v is_i(t)＝[v_i1(t),v_i2(t),...,v_iD(t)]Representing the speed of the ith particle, i.e. the amount of change, v, of the ith path_ij(t) represents the variation of the jth path point of the ith particle, j is 1,2_min,S_max]The maximum and minimum particle velocity values are calculated as follows:

v_max＝0.01×(S_max-S_min) (11)

v_min＝-0.01×(S_max-S_min) (12)

in step nine, the number of explosion sparks S_iThe calculation formula is as follows:

in the formulae (13) and (14), N₁The number of fireworks corresponding to the safe path is fireworks X_iSatisfaction grade of mu (X)_i) Path no less than α, N₂The number of fireworks corresponding to unsafe paths is fireworks X_iSatisfaction grade of mu (X)_i)<α path, β ∈ [0,1 ]]As a scaling parameter, M ∈ [10,100 ]]Is a constant for adjusting the number of explosion sparks generated, f_Lmax＝max(f_L(X_i) ) is the maximum path length value in the firework population with safe corresponding paths, i is 1,2, …, N₁，μ_min＝min(μ(X_i) For the minimum satisfactory level value in the fireworks population with unsafe corresponding paths, i is 1,2, …, N₂ε is the minimum number of machines and is 2^-52For avoiding zero operation.

When fireworks X_iSatisfaction grade of mu (X)_i) When the path is not less than α, the number of explosion sparks is calculated by formula (13) when the corresponding path is safe, and when the fireworks X are displayed_iSatisfaction grade of mu (X)_i)<α, when the corresponding path is not safe, the number of explosion sparks is calculated by the formula (14) to prevent fireworks X_iToo many or too few explosion sparks are generated, and the number S of explosion sparks calculated by the formula (13) or (14)_iThe following formula is used for limitation:

in the above equation, round () is a function rounded according to the rounding principle; a-0.6 and b-0.05 are two constants.

In the ninth step, the explosion radius A of the explosion spark_iThe calculation formula is as follows:

in the formulae (16) and (17), N₁Number of fireworks for safety of corresponding path, N₂The number of fireworks which correspond to the unsafe paths,is a constant for adjusting the size of the explosion radius, f_Lmin＝min(f_L(X_i) ) is the minimum path length value in the firework population with safe corresponding paths, i is 1,2, …, N₁，μ_max＝max(μ(X_i) For the maximum satisfactory level value in the fireworks population with unsafe corresponding paths, i is 1,2, …, N₂ε is the minimum number of machines and is 2^-52For avoiding zero operation.

When fireworks X_iSatisfaction grade of mu (X)_i) When the path is not less than α, the explosion radius is calculated by formula (16) when the corresponding path is safe, and when the fireworks X are displayed_iSatisfaction grade of mu (X)_i)<α, when the corresponding path is not safe, the explosion radius is calculated by formula (17) to prevent fireworks X_iIf the explosion radius is too small, the calculated explosion radius A is compared with the explosion radius A calculated by the formula (16) or (17)_iThe following formula is used for limitation:

in the above formula, A_min∈[0,40]The minimum explosion radius of the fireworks.

The fireworks generate an explosion spark, wherein the calculation formula of the kth path point in the explosion spark is as follows:

X_jk＝X_ik+rand(-1,1)×A_i(19)

in the above equation, rand () is a function that takes a random value within an interval.

The spark mapping rule is as follows:

X_jk＝S_min+|X_jk|％(S_max-S_min) (20)

in the above equation,% is a modulo operation.

The grade comparison method specifically comprises the following steps:

in the iterative process, if two individuals R to be compared₁、R₂Corresponding to the path length f₁、f₂Degree of path satisfaction mu₁、μ₂And the safety level α, the quality of the individual is judged by adopting a level comparison method, and the specific method is as follows:

(1) mu.s of₁≥α、μ₂Not less than α, and f₁≤f₂Selecting R₁Is a better individual;

(2) when (1) is not satisfied, if μ₁＝μ₂And f is₁≤f₂Selecting R₁Is a better individual;

(3) when (1) and (2) are not satisfied, if μ₁>μ₂Selecting R₁Is a better individual;

in step twelve, the variant spark generation formula is as follows:

V_i′＝V_i+rand(-1,1)×(V_b-V_r) (21)

in the above formula, i is 1,2_bThe optimal fireworks in the fireworks group V (t), wherein the optimal fireworks are the optimal path, V_rFor the generated variant fireworks and removing V_iA random one of the non-mutated fireworks in the outer v (t);

in step fifteen, the particle velocity and position update formula is as follows:

v_i(t+1)＝ω·v_i(t)+c₁·rand(0,1)·(x_pbest,i(t)-x_i(t))+c₂·rand(0,1)·(x_gbest(t)-x_i(t)) (22)

x_i(t+1)＝x_i(t)+v_i(t+1)(23)

in formula (22), i is 1,2_p，c₁∈[0,2]、c₂∈[0,2]As an acceleration constant, ω ∈ [0,1 ]]For inertial weights, rand () is a function that takes random values within the interval.

In step sixteen, the particle mapping rule is as follows:

in the above formula, i is 1,2 …, N_p，j＝1,2,...,D。

Has the advantages that:

the invention provides a hybrid firework particle swarm cooperative algorithm for solving unmanned aerial vehicle constrained route planning. The method adopts a mode of searching an optimal solution in parallel by two groups, one group adopts an improved firework algorithm, the other group adopts a particle swarm algorithm, and finally the optimal route of the unmanned aerial vehicle is found in an information sharing mode. The particle swarm algorithm has good local search capability, overcomes the defect of local development capability of the firework algorithm, and is easy to fall into a local optimal solution. The improved firework algorithm obtains individuals with higher diversity through a new variation mode, improves the diversity of firework groups, enables the algorithm to have better global search capability, further effectively avoids trapping in a local optimal solution, and makes up for the defects of a particle swarm algorithm. The algorithm has better global search capability and local search capability through the cooperative cooperation of the two groups, and meanwhile, the constraint conditions are better processed by adopting a grade comparison method, so that a better unmanned aerial vehicle flight path is planned. The hybrid firework particle swarm cooperative algorithm has good optimization performance, high convergence precision and strong robustness, and can plan a shorter safe path, thereby being an effective unmanned aerial vehicle route planning method.

Drawings

Fig. 1 is a schematic diagram of coordinate transformation.

FIG. 2 is a flow chart of a mixed firework particle swarm cooperative algorithm.

FIG. 3 is a path planning diagram of a particle swarm collaborative algorithm of mixed fireworks.

FIG. 4 is a statistical data table obtained from the path planning result of the particle swarm collaborative algorithm for mixed fireworks.

Fig. 5 is a graph of average path length evolution.

Detailed Description

The present invention will be further described with reference to specific implementation processes, which are illustrated in the environment of fig. 3 as an example:

preparation work: let the flying speed v of the unmanned aerial vehicle be 1 m/s. The parameters take the following values: maximum number of iterations NC _max500, 20 safety distance delta d, 15 growth rate parameter ξ, 30 constant M of explosion spark particles, 0.8 parameter β, minimum explosion radius A of fireworks _min20; constant of acceleration c₁＝0.8、c₂0.8; the inertial weight ω is 0.9. Let the coordinate of the starting point be S ═ 50,50]The coordinate of the target point is T ═ 950,550]The firework and particle dimension D is 25.

The method comprises the following steps: establishing a rotating coordinate system X ' -S-Y ' taking ST as an axis X ', and converting the position coordinates of the starting point, the target point and the obstacle into the rotating coordinate system, wherein the coordinate conversion formula is as follows:

in the above formula (x)_s,y_s) The initial position of the robot is (X, Y), (X ', Y ') are respectively the coordinate position of any one same point in a coordinate system X-O-Y and X ' -S-Y ', and theta is the included angle between the X ' axis and the X axis.

Calculating the upper and lower boundaries S of the planning space_max、S_minThe formula is as follows:

in the above formula y_threatjFor coordinate transformationAnd changing the Y' axis coordinate of the jth threat source, wherein j is 1,2_jAnd for the threat radius of the jth threat source, max { } is a function of taking the maximum value, and min { } is a function of taking the minimum value.

Step two: using 25 parallel linear tufts L₁,L₂,…,L₂₅Dividing ST into 26 segments vertically, wherein the distance delta l of each segment is 39.6;

step three: initializing fireworks by the iteration number t being 1, wherein the number of the fireworks is 8, the dimension of the fireworks is 25, and the fireworks are represented as a vector set X (t) being X₁(t),X₂(t),…,X₈(t) }, in which, X_i(t)＝[X_i1(t),X_i2(t),…,X_i25(t)]Denotes the ith firework, i is 1,2 …,8, X_ij(t) represents the jth path point of the ith firework, j being 1, 2.. 25;

step four: calculating the path length, the threat cost and the satisfaction grade of the path corresponding to the fireworks in the fireworks group, wherein the formula is as follows:

path length f of path P_L(P) the calculation formula is as follows:

in the above formula, | | P_i+1-P_iAnd | | represents the euclidean distance between the path points Pi +1 and Pi.

Threat cost f of path P_T(P) the calculation formula is as follows:

in the above formula t_jThreat level for jth threat source, P_0.1,j,kPath segment P for jth threat source_kP_k+1On the upper part

Probability of threat at a point.

The threat probabilities of different threat sources are calculated as follows:

(1) probability of threat from mountain peak threat source P_P：

In the above formula, d is the distance from the unmanned aerial vehicle to the threat source, R_PIs the peak threat radius.

(2) Threat probability P of radar threat source_R：

In the above formula, d is the distance from the unmanned aerial vehicle to the threat source, R_RmaxIs the radar threat radius.

(3) Threat probability P of missile threat source_M：

In the above formula, d is the distance from the unmanned aerial vehicle to the threat source, R_MmaxThe threat radius for the missile.

(4) Probability of threat of antiaircraft gun threat source P_G：

In the above formula, d is the distance from the unmanned aerial vehicle to the threat source, R_GmaxIs the threat radius of the antiaircraft gun.

The satisfaction level μ (P) of the path P is calculated as follows:

in the above equation, b is a rank calculation constant, and the value of the rank calculation constant is the median of the threat costs of the paths corresponding to all fireworks in step four.

Step five: initializing a particle group, setting the number of particles to be 15, each particle corresponding to a complete path, the dimension of each particle to be 25, and the position of the particle group to be a vector group x (t) ([ x ])₁(t),x₂(t),...,x₁₅(t)]Wherein x is_i(t)＝[x_i1(t),x_i2(t),...,x_i25(t)]Position of the ith particle, i is 1,2 …,15, x_ij(t) denotes the position of the jth path point of the ith particle, j 1, 2.., 25, and the velocity is expressed as a vector set v (t) [ v ] v ═ v₁(t),v₂(t),...,v₁₅(t)]Wherein v is_i(t)＝[v_i1(t),v_i2(t),...,v_i25(t)]Indicates the velocity, v, of the ith particle_ij(t) represents the variation of the jth path point of the ith particle, j is 1,2_min,S_max]Speed limit v_min、v_maxThe calculation formula is as follows:

v_max＝0.01×(S_max-S_min) (35)

v_min＝-0.01×(S_max-S_min) (36)

randomly determining the initial position and velocity of each particle and storing the position of the particle in

Performing the following steps;

step six: calculating the path length, threat cost and satisfaction grade of the path corresponding to each particle in the particle swarm according to formulas (28) to (34);

step seven: saving the individual with the shortest corresponding path in all the fireworks and the particles in the fourth step and the sixth step in the global optimal solution x_gbestIn (t), the optimal path of the unmanned aerial vehicle is searched at present;

step eight, updating the security level α, wherein the updating formula is as follows:

step nine: calculating fireworks X_i(t) number of explosion sparks S_iThe calculation formula is as follows:

in the formulae (38) and (39), N₁Number of fireworks for safety of corresponding path, N₂Number of fireworks unsafe for corresponding path, f_Lmax＝max(f_L(X_i) ) is the maximum path length value in the firework population with safe corresponding paths, i is 1,2, …, N₁，μ_min＝min(μ(X_i) For the minimum satisfactory level value in the fireworks population with unsafe corresponding paths, i is 1,2, …, N₂ε is the minimum number of machines and is 2^-52For avoiding zero operation. When fireworks X_iSatisfaction grade of mu (X)_i) When the path is not less than α, the number of explosion sparks is calculated by the formula (38) when the corresponding path is safe, and when the fireworks X_iSatisfaction grade of mu (X)_i)<α, i.e. when the corresponding path is not safe, the number of explosion sparks is calculated by formula (39) to prevent fireworks X_iToo many or too few explosion sparks are generated, and the number S of explosion sparks calculated by the formula (38) or (39) is calculated_iThe restriction is performed by equation (40).

Calculating fireworks X_i(t) corresponding explosion radius A_iThe calculation formula is as follows:

in the equations (41) and (42),

is a constant for adjusting the size of the explosion radius, N₁Number of fireworks for safety of corresponding path, N₂Number of fireworks unsafe for corresponding path, f_Lmin＝min(f_L(X_i) ) is the minimum path length value in the firework population with safe corresponding paths, i is 1,2, …, N₁，μ_max＝max(μ(X_i) For the maximum satisfactory level value in the fireworks population with unsafe corresponding paths, i is 1,2, …, N₂ε is the minimum number of machines and is 2^-52For avoiding zero operation. When fireworks X_iSatisfaction grade of mu (X)_i) When the path is not less than α, the explosion radius is calculated by formula (41) when the corresponding path is safe, and when the fireworks X are displayed_iSatisfaction grade of mu (X)_i)<α, when the corresponding path is not safe, the explosion radius is calculated by formula (42) to prevent fireworks X_iIf the explosion radius is too small, the calculated explosion radius A is compared with the explosion radius A calculated by the formula (41) or (42)_iThe restriction is performed by equation (43).

Generating an explosion spark X_j(t)＝[X_j1(t),X_j2(t),...,X_jD(t)]，j＝1,2,...,S_i，X_jk(t) denotes the kth path point for the jth explosion spark, k ═ 1, 2.

X_jk＝X_ik+rand(-1,1)×A_i(44)

Step ten: mapping the explosion sparks beyond the boundary to a new position, wherein the mapping formula is as follows:

X_jk＝S_min+|X_jk|％(S_max-S_min) (45)

calculating the path length, threat cost and satisfaction grade of the path corresponding to each spark in the explosion sparks according to formulas (28) to (34);

step eleven: selecting the optimal 8 individuals from the fireworks and the explosion sparks by a grade comparison method to form a new fireworks group V (t) { V }₁(t),V₂(t),...,V₈(t) judging whether the individual is good or bad by adopting a grade comparison method, such asThe following:

if two individuals to be compared R₁、R₂Corresponding to the path length f₁、f₂Degree of path satisfaction mu₁、μ₂The number of times the security level is α,

(1) mu.s of₁≥α、μ₂Not less than α, and f₁≤f₂Selecting R₁Is a better individual;

(2) when (1) is not satisfied, if μ₁＝μ₂And f is₁≤f₂Selecting R₁Is a better individual;

(3) when (1) and (2) are not satisfied, if μ₁>μ₂Selecting R₁Is a better individual;

step twelve: to fireworks V_i(t) performing a mutation operation to generate a mutated spark V_i' (t), the variation formula is as follows:

V_i′＝V_i+rand(-1,1)×(V_b-V_r) (46)

in the above formula, i is 1,2_bIs the optimal firework in the firework group V (t), V_rFor the generated variant fireworks and removing V_iAnd (d) randomly selecting one firework from the unchanged fireworks in the outer V (t).

Step thirteen: mapping the variant sparks exceeding the boundary to a new position by a formula (45), and calculating the path length, the threat cost and the satisfaction grade of the path corresponding to each spark in the variant sparks by formulas (28) to (34);

fourteen steps: firework V is selected through grade comparison method_i(t) and variant spark V_i' (t) the superior individuals, constitute a new firework population U (t) ═ U₁(t),U₂(t),…,U₈(t) }, where the optimal fireworks are U_best(t) worst fireworks are U_worst(t)；

Step fifteen: updating the positions and the speeds of all the particles in the particle swarm to obtain the position of the next generation of particles

And velocity

The update formula is as follows:

v_i(t+1)＝0.9·v_i(t)+0.8·rand(0,1)·(x_pbest,i(t)-x_i(t))+0.8·rand(0,1)·(x_gbest(t)-x_i(t)) (22)

x_i(t+1)＝x_i(t)+v_i(t+1) (23)

in the formula (22), i ═ 1, 2.., 15, rand () is a function that takes random values within an interval.

Sixthly, the steps are as follows: mapping the particles beyond the boundary to a new position, wherein the mapping formula is as follows:

in the above formula, i is 1,2 …,15, j is 1, 2.

Calculating the path length, threat cost and satisfaction grade of the path corresponding to each particle by formulas (28) to (34);

seventeen steps: the updated ith particle is stored in x_pbest(t) comparing grades of ith particles, selecting the better particles to store in x_pbestIn (t +1), i is 1,2_p；

Eighteen steps: all particles x (t +1) and U in the next generation were selected by rank comparison method_worst(t) most preferred individual U'_best(t) and the difference of U in the firework group U (t)_worst(t) the fireworks except for (t) form the next-generation firework group X (t +1) ═ X₁(t+1),X₂(t+1),…,X_N(t+1)}；

Nineteen steps: selection of U by rank comparison method_best(t)、U′_best(t)、x_gbest(t) the optimal individual is updated to obtain the next generation global optimal solution x_gbest(t+1)；

Twenty steps: let t be t +1, judge whether t satisfies>NC_max. If not, returning to the step eight for iteration; if yes, the operation is considered to be finished, and a global optimal solution x is output_gbest(t)。

Twenty one: solving the global optimum x_gbestAnd (t) converting into an X-O-Y coordinate system, and outputting the planned optimal path of the unmanned aerial vehicle.

Fig. 3 shows the unmanned aerial vehicle route planning result obtained through the calculation steps, fig. 4 shows the numerical result of 50 times of independent route planning by the mixed firework particle swarm cooperative algorithm, and fig. 5 is an average path length evolution curve of 50 times of independent route planning by the mixed firework particle swarm cooperative algorithm. As can be seen from FIG. 3, the unmanned aerial vehicle route drawn by the mixed firework particle swarm collaborative calculation method is safe and smooth, and is a good unmanned aerial vehicle flight path. In fig. 4, the second column is the length of the shortest path planned in the 50-time planning, the third column is the average value of all path lengths in the 50-time planning, the fourth column is the median of all path lengths in the 50-time planning, the fifth column is the standard deviation of the path lengths in the 50-time planning, the sixth column is the length of the longest path planned in the 50-time planning, the seventh column is the success rate of the 50-time planning, namely, the average time of one-time algorithm planning in the 50-time planning is listed as the success rate of the planning, namely, the unmanned aerial vehicle can safely move from the starting point to the target point. From the data in fig. 4, it can be derived: the hybrid firework particle swarm cooperative algorithm is adopted to plan the unmanned aerial vehicle route, a better unmanned aerial vehicle flight path can be planned in the allowed planning time, the algorithm has the strongest robustness, and the success rate is high. Therefore, the mixed firework particle swarm cooperative algorithm provided by the invention is an effective unmanned aerial vehicle route planning method, can stably plan a better unmanned aerial vehicle flight path, and ensures that the unmanned aerial vehicle can safely run to a target point.