Unmanned aerial vehicle path planning method based on global-local balanced whale optimization algorithm

Abstract

The application discloses a kind of based on global-local balanced whale optimization algorithm's unmanned plane path planning method: step 1, initialization;Step 2, obtain cyclic iteration parameter;Step 3, judge P<0.5, is then enter step 4, otherwise enter step 5;Step 4, judge |A|<1, is then search prey, otherwise capture prey, enter step 6;Step 5, judge rand>0.6, is then bubble net attack, otherwise bubble attack enhancement;Step 6, calculate each individual fitness value;If less than leader score, then update;Step 7, trigger mutation operation, fitness value less than the score of current leader is updated, enter step 8;Step 8, obtain new leader position;Step 9, fitness value less than the score of current leader is updated;Otherwise enter step 10;Step 10, output current leader score.The path scheme planned by the application has the lowest average total cost of flight, and shows higher convergence accuracy.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of unmanned aerial vehicle path planning, and relates to an unmanned aerial vehicle path planning method based on a global-local balanced whale optimization algorithm. BACKGROUND

[0002] With the rapid development of unmanned aerial vehicle technology, its application in the fields of military, agriculture, environmental monitoring, etc. is becoming increasingly widespread, especially in emergency rescue, logistics distribution, etc. However, it is a very challenging task to plan a safe route for an unmanned aerial vehicle in a complex environment. Such an environment not only contains geographical obstacles such as rugged mountain terrain, urban high-rise buildings, and rivers and waterfalls, but is also affected by dynamic factors such as weather changes and traffic conditions. Therefore, under these complex conditions, it has become an important problem to be solved to design an efficient and safe and feasible flight path for an unmanned aerial vehicle.

[0003] The mainstream solution to unmanned aerial vehicle path planning at present is usually to convert the environment model into a mathematical model, and to plan a safe, feasible and smooth flight trajectory from the starting point to the end point under the condition of meeting certain constraints. Intelligent algorithms for unmanned aerial vehicle autonomous path planning are divided into three categories: traditional optimization algorithms, intelligent optimization algorithms and machine learning algorithms. At present, traditional optimization algorithms have been widely applied in path planning, among which the A* algorithm as a classic heuristic search algorithm has been widely used due to its simplicity of implementation. However, when applied to large-scale and high-dimensional space, the search efficiency of the algorithm will decrease significantly, which limits its ability to solve the problem of flight path planning with multiple constraints. RRT algorithm is a typical path planning method based on space sampling, which does not need to discretize the flight environment, so it has a faster search speed, but this method is difficult to obtain the optimal flight path. The artificial potential field method is favored in path planning for its fast calculation speed and good real-time performance, but in large-scale and high-dimensional space environment, it may encounter local oscillation and local minimum problems, resulting in the generated path being unsuitable. This all shows that traditional optimization algorithms cannot simultaneously satisfy accuracy and time efficiency in solving multi-constraint path planning problems, and have certain limitations.

[0004] In recent years, many researchers have drawn inspiration from biological behavior or mathematical functions in nature to research and design intelligent optimization algorithms, applying them to UAV path planning. These algorithms, including SSA, GWO, BWO, SCA, and BOA, are able to rapidly determine the optimal path by applying diverse search strategies and performing multiple rounds of iteration. However, most intelligent optimization algorithms are probabilistic random search algorithms, which exhibit a high degree of randomness when solving specific engineering problems and exhibit poor coordination between global and local optimization. Therefore, preventing algorithms from falling into local optimal solutions and maximizing their global convergence speed remain key challenges faced by many intelligent algorithms.

[0005] WOA is an optimization algorithm proposed by Mirjalili S et al. in 2016, which is a meta-heuristic optimization algorithm that simulates the hunting behavior of humpback whales. It searches for the optimal solution by simulating three hunting strategies of humpback whales: surrounding prey, bubble net hunting, and searching for prey, with strong search ability, stable calculation, etc. Jiang R et al. proposed a whale army optimization algorithm, introduced the armed forces program, and adjusted the key parameters and basic principles of the original whale algorithm. Compared with traditional whale optimization algorithm and other high-performance swarm intelligence algorithms, this algorithm has faster convergence speed under lower computational complexity. Huang Y et al. proposed a whale optimization algorithm using piecewise learning and adaptive operator selection strategy for autonomous underwater vehicle path planning problem. The dynamic partition strategy and weighted mean scheme are used to construct virtual individuals, and virtual individuals are included in the whale optimization algorithm to construct an evolution pool to improve the optimization performance of the algorithm. The simulation results show that the robustness and search ability of the proposed algorithm are stronger than other comparative algorithms. Guo W et al. proposed an improved whale optimization algorithm based on wavelet mutation strategy and social learning, designed a new linear incremental probability to improve the global development ability, introduced an adaptive neighborhood learning strategy to promote information exchange between individuals, and integrated the Morlet wavelet mutation mechanism to avoid falling into local optimum. Wang C et al. proposed an adaptive adjustment mechanism based on whale optimization algorithm to dynamically modify the search during the iteration process, added controllable variables and applied the difference mutation evolution strategy to effectively coordinate the global and local optimum of the algorithm. Finally, the algorithm is applied to path planning problem, which shows faster convergence speed and higher convergence accuracy than the original whale algorithm and other six high-performance intelligent optimization algorithms, and has greater improvement in stability. Dai Y et al. proposed a new type of whale optimization algorithm (NWOA) for robot path planning problem in highly complex dynamic environment, used an adaptive scheme to speed up the algorithm convergence, set virtual obstacles to improve the algorithm's ability to escape from local optimum, and finally introduced a potential field factor to improve the robot obstacle avoidance performance. The simulation comparison shows the superiority of the proposed algorithm. Yin S et al. proposed an enhanced whale optimization algorithm to realize the path planning of unmanned aerial vehicle weather detection task in complex environment, introduced real-time boundary processing, quasi-opposite-based learning, and enhanced search mechanism into the standard whale optimization algorithm, which improved the convergence speed and global optimization ability of the algorithm. The simulation experiment shows that the path planning scheme given by the algorithm has higher quality than other improved algorithms.

[0006] In addition, with the continuous progress of key technologies in the field of machine learning, some researchers have begun to explore the application of these technologies to path planning problems. Therefore, developing more efficient path planning algorithms has become a topic worthy of further study.

[0007] Although the above research has improved the convergence speed and accuracy of the whale optimization algorithm by introducing various different strategies, the algorithm still has shortcomings in terms of optimal value search accuracy and the ability to coordinate global and local development. New research is urgently needed to solve this problem. Summary of the Invention

[0008] The purpose of the present invention is to propose a global-local equalization whale optimization algorithm to solve the problems that the existing technology still has deficiencies in the accuracy of optimal value search and the ability to coordinate global and local development.

[0009] The algorithm mainly includes the following three improvement strategies: (1) Designing a bubble net attack enhancement strategy so that individuals have corresponding abilities to jump out of their current positions at different stages, thereby increasing the probability of the algorithm jumping out of the local optimum. (2) Introducing a failure parameter test mutation mechanism, that is, presetting trigger conditions. When the algorithm falls into the local optimum or progresses slowly, triggering the mutation operation can significantly improve the algorithm's global search ability and ability to jump out of the local optimum. (3) In order to enhance the algorithm's exploration ability, a stochastic gradient-assisted optimization method is proposed, which integrates the gradient into the standard whale optimization algorithm to improve the algorithm's optimization performance. At the same time, an energy reduction scheme is introduced to enhance its local exploration ability.

[0010] In order to achieve the above object, the present invention adopts the following technical solutions:

[0011] A UAV path planning method based on a global-local equilibrium whale optimization algorithm includes the following steps:

[0012] Step 1: Initialize the algorithm parameters and the position of individuals in the population; initialize the leader position, leader score, and convergence curve; traverse all individuals in the population, calculate the fitness value of each individual, and store it in the fitness array, and set the maximum number of no improvements;

[0013] Step 2: Obtain loop iteration parameters, including: (1) coefficient vector ;in ; is the number of iterations; T is the maximum number of iterations; (2) coefficient vector ; and is a random number in the range [0,1]; (3) To change the constant of the spiral shape, set it to 1; (4) yes Random numbers between; (5) P is a random number in the range [0,1]; (6) rand is a random number in the range [0,1];

[0014] Step 3, judge whether P <0.5, yes go to Step 4, otherwise go to Step 5;

[0015] Step 4, judge whether is yes, search for prey, update the position of the whale individual according to the following two formulas, and then go to Step 6;

[0016]

[0017]

[0018] wherein, t is the current time; surrounding step size, and is the coefficient vector; is the current leader position; is the current position of the whale individual; is the updated position of the whale individual;

[0019] is no, capture prey, update the position of the whale individual according to the following two formulas, and then go to Step 6;

[0020]

[0021]

[0022] wherein, t is the current time; surrounding step size, is the position of a whale individual randomly selected from the current population; is the current position of the whale individual; is the updated position of the whale individual;

[0023] Step 5, judge whether rand > 0.6, yes bubble net attack surrounds prey, update the position of the whale individual according to the following two formulas, and then go to Step 6;

[0024]

[0025]

[0026] is no, bubble attack enhancement, perform mutation operation according to the following formula, and then go to Step 6;

[0027]

[0028] wherein, is the current leader position; is a random number, is the position of the current whale individual; is the position of the updated whale individual;

[0029] Step 6, boundary check is performed on the updated whale individual position obtained in step 4 or step 5, and the position value of the whale individual within the boundary is retained, and the position value beyond the boundary is set to 0; the position of all current whale individuals is traversed, the fitness value of each whale individual is calculated and stored in the fitness array; for each whale individual, if its fitness value is less than the score of the current leader, the score and position of the leader are updated with the fitness value and the corresponding individual position respectively, and the non-improvement counter is reset; otherwise, it means that a better solution is not found, and the non-improvement counter is incremented by 1; step 7 is entered;

[0030] Step 7, whether the preset condition is met is judged, yes, the mutation operation is triggered, and boundary check is performed, and the position value of the individual within the boundary is retained, and the position value beyond the boundary is set to 0; the fitness value of each whale individual is calculated and compared with the score of the current leader, if the fitness value of the current individual is less than the score of the current leader, the score and position of the leader are updated with the objective function value and the position of the current individual respectively, and step 8 is entered; if the preset condition is not met, step 8 is directly entered;

[0031] Step 8, the step size is set, and the new leader position is obtained according to the step size and the current leader position X_new ; step 9 is entered;

[0032] Step 9, the fitness value of the new leader position is calculated, if it is less than the score of the current leader, the current leader position is updated with the new position , and step 10 is entered; otherwise, step 10 is directly entered;

[0033] Step 10, whether s < T is judged, yes, the s = s +1, and step 2 is returned; otherwise, the score of the current leader, that is, the optimal solution of the objective function, is output, and the objective function is a comprehensive cost function; wherein, the formula of the comprehensive cost function is as follows:

[0034]

[0035] wherein, to represent the voyage length cost, obstacle threat cost, flight height cost and path smoothing cost respectively, is the weight coefficient corresponding to different costs.

[0036] Compared with the prior art, the present application has the following technical effects:

[0037] The present application realizes the path planning of the unmanned aerial vehicle under the complex mountainous terrain through the global-local balanced whale optimization algorithm. In order to prevent the population from entering the aggregation state, the present application designs a bubble net attack enhancement strategy, and increases the mutation operation to improve the early convergence phenomenon in different stages of the algorithm. Secondly, the failure parameter inspection mutation mechanism is introduced, the preset termination rule is used to avoid excessive calculation of the algorithm, and the mutation operation is triggered to speed up the convergence speed of the algorithm. Finally, the random gradient auxiliary optimization method is designed, after determining the negative gradient direction in each iteration, the appropriate step length is selected to enhance the exploration ability of the algorithm to the optimal solution. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 is the cylindrical obstacle threat cost;

[0039] Figure 2 is the Altitude cost explanation (altitude cost);

[0040] Figure 3 is the Turning and climbing angle calculation (turning and climbing angle calculation);

[0041] Figure 4 is the path planning terrain environment model, wherein (a) is the terrain environment model 1, and (b) is the terrain environment model 2;

[0042] Figure 5 is the average convergence curve of the CEC2017 test function; wherein (1)~(30) are Function1~Function30.

[0043] Figure 6 is the path planning under the simple obstacle scene of terrain 1, wherein (a) is the overhead view, (b) is the side view, (c) is the 3D obstacle avoidance diagram, and (d) is the algorithm convergence diagram.

[0044] Figure 7 is the path planning under the complex obstacle scene of terrain 1, wherein (a) is the overhead view, (b) is the side view, (c) is the 3D obstacle avoidance diagram, and (d) is the algorithm convergence diagram.

[0045] Figure 8 is the path planning under the simple obstacle scene of terrain 2, wherein (a) is the overhead view, (b) is the side view, (c) is the 3D obstacle avoidance diagram, and (d) is the algorithm convergence diagram.

[0046] Figure 9This is the path planning in the scene with complex obstacles in terrain 2, where (a) is the top view, (b) is the side view, (c) is the 3D obstacle avoidance map, and (d) is the algorithm convergence map.

[0047] The present invention is further explained below with reference to the accompanying drawings and specific embodiments. DETAILED DESCRIPTION

[0048] 1. Problem Description of UAV Path Planning

[0049] In the present invention, the UAV path planning problem is solved by considering multiple constraints, assigning different weights to different constraints, and formulating a comprehensive cost function, and finding the minimum value to represent the optimal trajectory.

[0050] 1. Conditional constraints

[0051] When a drone is performing a mission, the priority is the flight distance. A shorter flight distance can greatly reduce fuel consumption and improve endurance. The drone is usually controlled by a ground control station to fly along the n flight points planned by the search map to form a flight path. , each journey point is a path node searched in a known map, and its coordinates are set to The flight length cost function can be obtained by accumulating the Euclidean distance between each two nodes. :

[0052] (1)

[0053] In addition to the flight length, the threat caused by obstacles during the flight must also be considered. The planned path must ensure that the drone can bypass obstacles during the flight to achieve safe operation. is the set of all threats. Assume that the threat caused by the obstacle is a cylinder, and its projection center coordinate is , the radius is , the diameter of the drone is Q , the safety buffer length is , the path formed between each two flight points during the flight of the drone The distance from the center coordinate is , specifically Figure 1 As shown, considering the above conditions, the threat cost function :

[0054] (2)

[0055] In some cases, such as aerial photography and experimental tasks, drones need to operate in a specific airspace. Flying too high will affect the resolution of aerial photography, while flying too low will cause unnecessary danger to people or animals and plants on the ground and affect the shooting field of view. Therefore, the flight altitude is usually limited to between two given extreme values, such as Figure 2 This helps to rationally allocate and use airspace resources and avoid conflicts and interference. During flight, the actual altitude is the terrain altitude plus the set altitude. The altitude cost calculation rules for setting the route point are as follows:

[0056] (3)

[0057] This rule restricts the drone to fly at the average level of the two extreme values, and stipulates that the flight cost will increase accordingly as the distance from the average level increases, thus forming the altitude cost function :

[0058] (4)

[0059] In drone path planning, smoothing cost is an important consideration. It is the cost introduced to ensure that the drone's flight path is as smooth as possible, avoiding sharp turns or altitude changes that increase the difficulty of controlling the aircraft and accelerate fuel consumption. Figure 3 As shown, the smoothing cost is set to include the body turning cost and the climbing cost, where is the climb angle at point j on path i, is the climb angle at the j-1th leg of path i; is the turning angle between two adjacent path segments on path i. for The unit vector in the direction of the coordinate axis, then the climbing angle It can be expressed as:

[0060] (5)

[0061] Steering angle Expressed as:

[0062] (6)

[0063] The smoothing cost can be expressed as:

[0064] (7)

[0065] in and They represent the cost coefficients of the steering angle and the climbing angle, respectively, and are both 1 in the path planning experiment.

[0066] 2. Comprehensive cost function

[0067] In order to make the unmanned plane safely and efficiently reach the target, the planned path needs to guide the unmanned plane to realize collision-free flight considering the total distance length cost, threat cost, height cost and smooth cost, and the comprehensive cost function can be expressed as:

[0068] (8)

[0069] Wherein to respectively represent the cost of distance length, obstacle threat, flight height and path smoothness, and is the weight coefficient corresponding to different costs.

[0070] 3, Environment model

[0071] The scene selected for path planning is two scenes with different terrain structures in Christmas Island, Australia, as shown in Figure 4 (a) and (b), which are real digital elevation model maps (DEM) collected from LiDAR sensors, and each reference scene is divided into simple and complex scenes according to the number of obstacles, wherein the simple scene is set to 3 cylindrical obstacles, and the complex scene is set to 6 or 9 to test the path planning performance of the algorithm in different environments.

[0072] II. Design of global-local balanced whale optimization algorithm

[0073] Among the numerous swarm intelligence algorithms, the whale optimization algorithm has the characteristics of few parameters and simple structure, but it still has shortcomings in solving the complex optimization problem of unmanned plane path planning, therefore, the whale optimization algorithm is selected for analysis and research. After analyzing the standard whale optimization algorithm, this section improves the global-local balanced whale optimization algorithm by fusing multiple strategies, so that it can find the optimal path more efficiently in the complex terrain environment of unmanned plane path planning task.

[0074] 1. Standard whale optimization algorithm

[0075] The whale optimization algorithm simulates the unique hunting behavior of humpback whales, and according to the characteristics of whale predation, the hunting behavior of whales is divided into three stages: shrinkage surrounding predation, bubble net attack and random search, which are described in detail as follows:

[0076] (1) Shrinkage surrounding predation stage

[0077] In nature, whales can find the location of prey and surround them for predation, and in the algorithm, the optimal individual of the current population is assumed to be prey, and other whale individuals in the population surround the optimal whale position to update their own position, which is updated by formulas (9) and (10):

[0078] (9)

[0079] (10)

[0080] where, t is the current time; D is the surrounding step; A and C is the coefficient vector; is the current population's best position vector, i.e., the leader position; is the current whale's position; is the updated whale's position; where, and are random numbers in the range of [0, 1];

[0081] (11)

[0082] (12)

[0083] where, and are random numbers in the range of [0, 1]; the value of decreases linearly from 2 to 0, represented as:

[0084] (13)

[0085] is the maximum number of iterations.

[0086] (2) Bubble-net attack phase

[0087] When hunting, humpback whales move towards the prey in a spiral trajectory. In the whale optimization algorithm, the whale's position is updated by formulas (14) and (15):

[0088] (14)

[0089] (15)

[0090] where, is a constant that changes the shape of the spiral, usually set to 1; l is a random number between

[0091] The development stage of the whale optimization algorithm includes two stages: shrink wrap and bubble-net attack. When ​When the whale is in the shrinking encircling lasso, it moves along a spiral trajectory around the prey, so the whale has a 50% chance of choosing to encircle the prey and a 50% chance of choosing to attack the bubble net, which is obtained by formula (16):

[0092] (16)

[0093] wherein, is a random number between [0, 1].

[0094] (3) Random search and hunting phase

[0095] When , the whale searches and hunts randomly according to its position, and in the WOA, the whale updates its position by formula (17) and (18):

[0096] (17)

[0097] (18)

[0098] wherein, denotes the encircling step size, is the position of a whale individual randomly selected from the current population; is the current position of the whale individual; is the updated position of the whale individual.

[0099] 2、Global-local balanced whale optimization algorithm

[0100] After the WOA initializes the population, global exploration is performed by the random search strategy, but this method may lead to insufficient global search capability. With the progress of the algorithm, local search is achieved through the encircling hunting and spiral update phases, but due to the linear decrease of the convergence factor, it will lead to the imbalance between global and local search, so as to easily fall into a local optimal solution in the later stage of the algorithm. In view of the above shortcomings, the present application proposes a global-local balanced whale optimization algorithm. The bubble net attack enhancement strategy is designed to prevent the algorithm from falling into a local optimum, and the failure parameter test variation mechanism is introduced to improve the global search capability of the algorithm. In the later stage of the algorithm, the random gradient auxiliary optimization strategy is used to improve the optimization performance of the algorithm. The three improved strategies will be explained one by one as follows.

[0101] (1) Bubble net attack enhancement strategy

[0102] The standard whale optimization algorithm uses the same spiral attack and shrinkage to surround the prey to update the position of all individuals in the development stage, but this does not take into account that the ability of individuals to jump out of the current position is different in different stages. Only using the above two same position update modes, when the algorithm falls into local optimum, it will be difficult to escape due to the lack of change in position update. Therefore, in order to prevent the population from entering the aggregation state and causing the WOA to fall into the local optimum, a mutation method of enhancing bubble net attack is proposed. When the random number is less than or equal to 0.6, the new mutation operation is used to update the position of the optimal whale individual without changing the original update mode, and the mutation formula is shown in equation (19).

[0103] (19)

[0104] wherein, is the current leader position; is a random number, is the current position of the whale individual; is the updated position of the whale individual.

[0105] (2) Failure parameter test mutation mechanism

[0106] In the optimization algorithm, the termination rule (Termination Criteria) determines when to stop the iterative running of the algorithm. Therefore, selecting the appropriate termination rule can avoid excessive calculation and ensure that the algorithm finds a satisfactory solution within a reasonable time. For the above analysis, to improve the performance of the algorithm, a failure parameter test mutation mechanism is proposed, which triggers the mutation operation by setting the following algorithm running termination conditions:

[0107] No better fitness value is found for consecutive iterations. In this embodiment, when the algorithm runs for 5 consecutive iterations without finding a better fitness value, the mutation operation is triggered.

[0108] The specific formula of the mutation operation is as follows:

[0109] According to the current iteration number and the maximum iteration number T Calculate the mutation step size:

[0110] (20)

[0111] Calculate the mutation vector and apply it to the position of the whale:

[0112] (21)

[0113] wherein, is the mutation vector; ; Generate a random number matrix with 1 row and dim columns.

[0114] Apply the mutation vector to the current whale's position and perform a bounds check.

[0115] (twenty two)

[0116] The purpose of introducing the above mutation operation is to increase population diversity and avoid falling into local optimal solutions, thereby improving the global search ability and convergence speed of the algorithm.

[0117] (3) Stochastic gradient-assisted optimization method

[0118] The standard whale optimization algorithm may experience incomplete local exploration during operation. By integrating the gradient into the swarm intelligence algorithm, a hybrid algorithm is formed to combine the advantages of both and improve the algorithm's optimization performance. The independent variable changes along the gradient vector direction to maximize the change in the function value. In the algorithm, the objective function is the optimization goal. Based on the above analysis, a stochastic gradient-assisted optimization method is proposed. After determining the negative gradient direction in each iteration, an appropriate step size is selected. , so that the objective function value can be minimized to enhance the algorithm's ability to explore the optimal solution. The specific operations are as follows:

[0119] (twenty three)

[0120] in, represents the gradient at the current leader position; is the updated step size; the gradient at the current leader position is shown in formula (24):

[0121] (twenty four)

[0122] in, f is the objective function (specifically in the UAV path planning method, the objective function is the comprehensive cost function); is a set of unit orthogonal vectors, Dim represents the dimension of the optimization problem being solved; is the current position of the whale in the i-th dimension; Dim represents the dimension of the optimization problem to be solved. is a set of unit orthogonal vectors. To enhance the ability of swarm intelligence algorithms to solve optimization problems and enable hybrid algorithms to solve problems independently of the mathematical properties of the problem, the gradient is approximated using the forward difference formula as the definition of the derivative. The calculation formula is shown in (25):

[0123] (25)

[0124] in, is the current i-dimensional leader position; is a small positive number, set to 10 -6 The step size along the negative gradient direction in equation (23) is obtained by a line search method, as shown in equation (26):

[0125] (26)

[0126] where, is a scale factor, is set to 1.8. is the current step size; is the updated step size; new variables X1 and X2 representing the updated position of the individual are calculated by equations (27) and (28), and the fitness values of X1 and X2 are calculated to obtain f1 and f2, respectively.

[0127] (27)

[0128] (28)

[0129] Based on the above, a global-local balanced whale optimization algorithm (GLBWOA) is designed. First, the original population initialization and random search strategy are adopted, and then in the bubble net hunting stage, a bubble attack enhancement strategy is designed, and in the case of unchanged original spiral line updating mode, a mutation method is introduced to improve the ability to jump out of the local optimum. Then, a failure parameter checking mutation mechanism is introduced, and the condition for triggering the termination of the algorithm is set to avoid excessive calculation, and the global search ability is improved and the algorithm convergence speed is accelerated by increasing the mutation operation. Finally, a random gradient auxiliary optimization is adopted to make the algorithm search the global optimal value as much as possible, and balance the global and local exploration ability of the algorithm. The global-local balanced whale optimization algorithm designed below is used for unmanned aerial vehicle path planning.

[0130] III. Unmanned aerial vehicle path planning method based on global-local balanced whale optimization algorithm

[0131] The unmanned aerial vehicle path planning method based on the global-local balanced whale optimization algorithm provided by the application comprises the following steps:

[0132] Step 1, initialize algorithm parameters, positions of individuals in the population; initialize leader position, leader score, convergence curve; traverse all individuals in the population, calculate the fitness value of each individual, and store it in the fitness array, and set the maximum number of unimproved times. Specifically as follows:

[0133] Call the initialization function, according to the given upper limit ub , lower limit lbnumber of individuals in the population N and dimension dim, initializing the positions of individuals in the population;

[0134] set the initial value of leader position Leader_pos as a zero vector with dim dimension; set the initial value of leader score Leader_score as infinity (for minimization problem); create a zero vector GLBWOA_Convergence_curve (i.e. convergence curve) with length iter;

[0135] traverse all individuals, for each individual, calculate its fitness value using fobj function and store it in the i-th element of the fitness array. Positions(i, :) represents the position of the i-th individual. Set the maximum number of no improvement times to 5, and initialize the no improvement times counter to 0.

[0136] Step 2, obtain the loop iteration parameters, including:

[0137] (1) coefficient vector ; wherein ; is the number of iterations; T is the maximum number of iterations;

[0138] (2) coefficient vector ; and are random numbers in the range of [0, 1];

[0139] (3) is a constant that changes the spiral shape, set to 1;

[0140] (4) is a random number between ;

[0141] (5) P is a random number in [0, 1];

[0142] (6) rand is a random number in the range of [0, 1].

[0143] Step 3, judge whether P <0.5, if yes, go to step 4, otherwise go to step 5;

[0144] Step 4, judge whether , if yes, search for prey, update the position of the whale individual according to the following two formulas, and then go to step 6;

[0145]

[0146]

[0147] where, t is the current time; denotes the surrounding step size, and is the coefficient vector; is the current leader position; is the current position of the whale individual; is the updated position of the whale individual;

[0148] Otherwise, the prey is captured, and the position of the whale individual is updated according to the following two equations; then go to step 6.

[0149]

[0150]

[0151] where, t is the current time; denotes the surrounding step size, is the position of a whale individual randomly selected from the current population; is the current position of the whale individual; is the updated position of the whale individual;

[0152] Step 5, judge whether rand > 0.6, is then the bubble net attacks the surrounding prey, and the position of the whale individual is updated according to the following two equations, and then go to step 6;

[0153]

[0154]

[0155] Otherwise, the bubble attack is enhanced, and the mutation operation is carried out according to the following equation, and then go to step 6;

[0156]

[0157] where, is the current leader position; is a random number, is the current position of the whale individual; is the updated position of the whale individual.

[0158] Step 6, boundary check is performed on the updated whale individual position obtained in step 4 or step 5, and the position values of individuals within the boundary (i.e. within the upper and lower limits set in step 1) are retained, and the position values beyond the boundary are set to 0. The positions of all current whale individuals are traversed, the fitness value of each individual is calculated and stored in the fitness array. For each individual, if its fitness value is less than the score of the current leader, the score and position of the leader are updated with the fitness value and the corresponding individual position respectively, and the number of non-improvement times counter is reset (i.e. set to 0); otherwise, it means that a better solution is not found, and the number of non-improvement times is incremented by 1; go to step 7.

[0159] Step 7, determine whether the preset condition (the number of non-improvement times obtained by continuous multiple iterations is not less than the maximum number of non-improvement times) is met, yes, trigger the mutation operation, and perform boundary check to retain the position values of individuals within the boundary, and set the position values beyond the boundary to 0; calculate the fitness value of each whale individual and compare it with the score of the current leader, if the fitness value of the current individual is less than the score of the current leader, update the score and position of the leader with the objective function value and the position of the current individual respectively, and go to step 8; if the preset condition is not met, go to step 8 directly.

[0160] Specifically, the mutation operation is triggered according to the preset condition, including:

[0161] After continuous multiple iterations, the number of non-improvement times is not less than the maximum number of non-improvement times, i.e. a better fitness value is not found, in this embodiment, when the algorithm runs for 5 continuous iterations without finding a better fitness value, the mutation operation is triggered.

[0162] Specifically, the mutation operation includes:

[0163] According to the current iteration number and the maximum iteration number T , the mutation step is calculated, and the formula is as follows:

[0164] ;

[0165] The mutation vector is calculated, and the formula is as follows:

[0166]

[0167] Wherein, is the mutation vector; ; is a random number matrix of 1 row and dim columns.

[0168] The mutation vector is applied to update the position of the whale individual, and the formula is as follows:

[0169] .

[0170] Step 8, set the step size, and get the new leader position according to the step size and the current leader position X_new ; enter step 9. Step 8 includes the following sub-steps:

[0171] Step 81, randomly generate a step size in the range of [0, 0.01], and calculate the gradient at the position of the current leader according to the following formula:

[0172]

[0173] Wherein, represents the gradient at the position of the current leader; f is the objective function (specifically, the objective function in the unmanned aerial vehicle path planning method is the comprehensive cost function); is a set of unit orthogonal vectors, Dim represents the dimension of the optimization problem to be solved; is the current i-th dimensional whale individual position;

[0174]

[0175] Wherein, is the current i-th dimensional leader position; is a small positive number, set to 10 -6 .

[0176] Step 82, calculate the new variables X1 and X2 for representing the updated position of the individual by the following two formulas, and calculate the fitness values f1 and f2 of X1 and X2 respectively;

[0177]

[0178]

[0179] According to the fitness values f1 and f2, the updated step size is obtained, and the formula is as follows:

[0180]

[0181] Wherein, is a scale factor, in this embodiment, is set to 1.8; is the current step size; is the updated step size;

[0182] Step 83, according to the updated step size and the current leader position, the new leader position is calculated by the following formula X_ new ; enter step 9.

[0183] ;

[0184] Step 9, calculate the fitness value of the new position, if it is less than the current leader score, adopt the new position Step 10, update the current leader position, go to Step 10; otherwise, go to Step 10 directly;

[0185] Step 10, judge whether s < T is, then let s = s + 1, return to Step 2; otherwise, output the current leader score, which is the optimal solution of the objective function, that is, the comprehensive cost function.

[0186] Wherein, the formula of the comprehensive cost function is as follows:

[0187]

[0188] Wherein, to respectively represent the cost of voyage length, threat of obstacle, navigation height and path smoothness, is the weight coefficient corresponding to different costs, which is set to , , , in the path planning experiment.

[0189] 1) Voyage length cost function :

[0190]

[0191] Wherein, is the coordinate of the voyage point; n is the number of voyage points;

[0192] 2) Threat cost function :

[0193]

[0194] Wherein, is the set of all threats, the threat caused by the obstacle is a cylinder, the projection center coordinate of which is , the radius is , Q is the diameter of the unmanned aerial vehicle, is the length of the safety buffer zone, the distance between the path formed by every two voyage points and the center coordinate in the flight process of the unmanned aerial vehicle is ;

[0195] 3) Altitude cost function : ​​

[0196]

[0197]

[0198] where, is the jth waypoint of path i, is the maximum flight height of the restriction, set to 200, is the minimum flight height of the restriction, set to 100 in the experiment.

[0199] 4) Smooth cost :

[0200]

[0201] where, and represent the cost coefficients of the turning angle and the climb angle, respectively; is the climb angle at waypoint j of path i, is the climb angle at waypoint j-1 of path i; is the turning angle of two adjacent path segments on path i; take is a unit vector in the direction of the coordinate axis, then is represented as:

[0202]

[0203] where, is the path vector formed by the path;

[0204]

[0205] where, is the waypoint coordinate projected on the plane formed by the x-axis and the y-axis, is projected on the plane formed by the x-axis and the y-axis, is and the path vector formed by the two points, is projected on the plane formed by the x-axis and the y-axis, is and the path vector formed by the two points.

[0206] Four, algorithm time complexity analysis and simulation experiment

[0207] Let the population size be N , and the search space dimension beD , the maximum number of iterations is T , the time complexity of the basic WOA algorithm is O(NDT) The GLBWOA proposed in this invention is based on WOA and introduces three different strategies for improvement. The time complexity of the bubble network attack enhancement strategy is O(NDT) The time complexity of the failure parameter test mutation mechanism and the stochastic gradient assisted optimization method is also O(NDT) Compared with the basic WOA algorithm, the time complexity of GLBWOA does not increase, and the algorithm execution efficiency does not decrease. The following will illustrate the superiority of the algorithm proposed in this invention through performance testing and path planning experiments.

[0208] Path planning is inherently a complex optimization problem. This section will use a test function to examine the optimization capabilities of the proposed algorithm. We will also find the optimal path on a real-world elevation map and compare it with other mainstream high-performance metaheuristic algorithms. Numerical experiments will demonstrate the superiority of GLBWOA. All experiments in this study were conducted on a Windows 11 platform equipped with a 13th Gen Intel Core™ i9-13900HX @ 2.20 GHz processor, using MATLAB 2024a for simulation.

[0209] (1) Optimization performance test

[0210] The optimization performance of GLBWOA was tested using IEEE CEC2017 functions. In addition to comparing it with the basic WOA algorithm, three high-performance intelligent optimization algorithms, BWO, SCA, and BOA, were also added for comparison. The dimension was set to 30. To ensure a fair comparison, the maximum evaluation time was set to 10,000 times the dimension, the population size was set to 30, and the maximum number of iterations was set to 500. Each algorithm was independently run 100 times, and the best, worst, mean, median, and standard deviation were recorded to evaluate the optimization performance. To more intuitively demonstrate the difference between the proposed algorithm and other algorithms, a Wilcoxon rank sum test was used at a significance level of 5%. A rank sum test value less than 5% indicates a significant difference between the two samples; otherwise, no significant difference exists. The test results are shown in Table 1. As can be seen from Table 1, among the 30 CEC2017 test functions, GLBWOA exhibits superior numerical performance across all metrics, with the exception of some individual functions where its stability is slightly inferior to that of the other algorithms.

[0211] Table 1 Test results of each algorithm in CEC2017 (significant values ​​are in bold)

[0212]

[0213] The ultimate goal of improving the algorithm is to find the optimal solution in the shortest time, such as Figure 5 The average convergence curve of function test is shown. It can be observed that, compared with the remaining 4 high-performance intelligent optimization algorithms, GLBWOA has stronger global search ability and ability to jump out of local optimum, and can achieve rapid convergence to find the optimal value in 30 optimization functions, which shows that it can quickly find a better path in a shorter time in path planning problems.

[0214] In summary, in the CEC2017 function test set, GLBWOA can find the optimal value in 30 functions, and has faster convergence speed than BWO, SCA, BOA and standard WOA, except that functions F1, F2, F3, F4, F5, F18, F19, F26 and F30 need to be iterated for 100 generations to find the optimal value. The rest of the functions can reach the convergence speed within 100 iterations, and GLBWOA performs well in various indicators, reflecting its universality. Therefore, the algorithm GLBWOA designed by the application has good optimization performance, which will be tested in the actual height map to test its ability to find the optimal track in the real complex environment.

[0215] (2) Path planning experiment

[0216] The experiment was carried out in two environments with different terrain structures in Christmas Island, Australia, where the Figure 1 The range of the terrain is 1045x879xZ m, and the Figure 2 The range of the terrain is 450x450xZ m. According to the number and position of the threat cylinders, it is divided into simple and complex scenes, and the waypoint is set to n=10. In order to make a fair comparison, all algorithm parameters are unified, where the population size is set to 30 and the maximum iteration number is set to 200. Due to the randomness of meta-heuristic algorithms, in order to better illustrate the algorithm performance and ensure the reliability of the results, each algorithm is independently run 30 times, and the total cost is used as the main performance index of path planning, and the weight coefficient of each cost function is set to , , , The constraint condition parameters of the simulation experiment are shown in Table 2.

[0217] Table 2 Constraint condition parameter setting

[0218]

[0219] Terrain 1 simple scene obstacle parameters as shown in Table 3. Assuming the path starting point is (200, 100, 150), the end point is set to (800, 800, 150), and the optimal path between the two points is planned. As shown in Figure 6 The path planning effect in the terrain 1 simple scene is shown, from Figure 6 The top view of (a) and Figure 6 The side view of (b) can be seen that all algorithms can generate a feasible path that meets the requirements of the four constraint conditions of path length, obstacle threat, height limit, climbing angle and turning angle. In order to more intuitively observe the situation of the path avoiding obstacles, the terrain structure is hidden for observation, as shown in Figure 6 (c), it can be seen that the generated path can effectively avoid collision, and the path is relatively smooth, which meets the needs of real flight.

[0220] Table 3 Terrain 1 simple obstacle scene parameter setting

[0221]

[0222] According to the terrain mountain distribution, the terrain 1 complex environment obstacle setting is as shown in Table 4, and the start and end points are the same as above. As shown in Figure 7 The path planning effect in the terrain 1 complex scene is shown, with the increase of obstacles, the complexity of path solving rises, and the difficulty of algorithm solving optimal path increases. It can be seen that all algorithms generate a path that can guide the safe flight of the unmanned aerial vehicle without collision, but the paths generated by different algorithms are quite different. Among them, the path generated by BWO has more sharp turns, which is difficult for actual flight. The average total cost of the path planned by BOA is the highest, and the optimal path is not found. Compared with the above, the paths generated by SCA, WOA and GLBWOA are more suitable for actual flight of the unmanned aerial vehicle. Among the three, GLBWOA has the fastest convergence speed, and the optimal path can be found in about 10 iterations. The average total cost is the same as WOA, which is the lowest, which reflects the superiority of the algorithm proposed in the present application.

[0223] Table 4 Terrain 1 complex scene obstacle parameter setting

[0224]

[0225] The path planning experiment is continued in the terrain 2 to further detect the ability of the path planning algorithm proposed in the present application, wherein the path starting point is set to (10, 10, 200), the end point is set to (400, 400, 150), the simple scene obstacle setting is as shown in Table 5, and the solved path is as shown in Figure 8As shown, it can be observed from (a) and (b) that the path change generated by GLBWOA is smoother without sudden change, which is better than the other four algorithms. From (c), it can be seen that the algorithms BOA and BWO fall into local optimum at the beginning of the algorithm, which eventually leads to premature convergence and plans a path with a higher total cost. GLBWOA quickly escapes after falling into a local extreme value and continuously searches for a global optimal path, showing good optimization performance. As can be seen from (d), the algorithm proposed in the application can quickly escape when it falls into local optimum in the early stage of the algorithm, while other algorithms fall into local optimum for a long time in the iteration, indicating that the introduction of the bubble net attack enhancement strategy has stronger ability to escape from local optimum. By observing the average convergence curve of the iteration number of GLBWOA from 0 to 50 generations, it can be seen that after falling into local optimum for a short time, the algorithm triggers the mutation mechanism to quickly find the global optimal value, indicating the effectiveness of the introduction of the failure parameter test mechanism, which can greatly improve the global search ability of the algorithm.

[0226] Table 5 Terrain 2 simple obstacle scene parameter setting

[0227]

[0228] In the terrain 2 complex obstacle scene, the starting point and the end point are the same as above, the obstacle parameter setting is as shown in Table 6, and the result is as shown in Figure 9 As shown, it can be seen that the related algorithms all give their respective path planning results and the planned paths all avoid the mountains and threat sources in the environment. It can be observed that although GLBWOA sacrifices the path length cost to plan the path, it effectively reduces the height change and steering adjustment of the UAV flight, reduces the height cost and smooth cost, and effectively avoids obstacles, reduces the threat cost, thereby reducing the total cost, and the average total cost planned in the 5 algorithms is the lowest. From Figure 9 (d), it can be seen that the BWO and WOA algorithms gradually begin to converge at about 30 generations, but GLBWOA is still searching for a global optimal path, showing that the algorithm has strong local exploration ability and global exploration performance, indicating that the introduction of the gradient kinetic energy strategy in the algorithm can escape from the local minimum point, and the updating method is designed to effectively avoid missing the global optimal solution.

[0229] Table 6 Terrain 2 complex obstacle scene parameter setting

[0230]

[0231] The average flight total cost data of path planning in 4 benchmark scenarios is shown in Table 7, and it can be observed that GLBWOA and the remaining algorithms can generate paths to guide the UAV to achieve collision-free flight, and in addition to the same flight total cost as the standard WOA algorithm in the terrain 1 simple obstacle scenario, the flight total cost of the remaining 3 benchmark scenarios is reduced by 19%, 10.6% and 24.9% respectively compared with the standard WOA, and the convergence speed, convergence accuracy and stability are improved, indicating the effectiveness of the improved strategy designed in the application.

[0232] Table 7 Path planning experimental results. Significant values are in bold.

[0233]

[0234] The application solves the problem of UAV path planning in complex environments based on a new global-local balanced whale optimization algorithm. A three-dimensional space model is constructed using DEM, and a total cost function is constructed in combination with task requirements and constraint conditions. For the standard WOA, a bubble net attack enhancement scheme is proposed, considering that the ability required for individuals to jump out of the current position is different in different stages, and the ability to escape from local optimum is improved through preset condition mutation operation. Secondly, a failure parameter inspection mutation mechanism is designed to accelerate the convergence speed of the algorithm, and in the later stage of the algorithm, a random gradient assisted optimization strategy is used to improve the global search ability of the algorithm. The optimization performance of GLBWOA is detected by CEC2017 function test set, and the performance of each index is better than that of the remaining 4 high-performance algorithms, indicating that the three strategies proposed can effectively balance the global and local search ability of the algorithm. In 4 benchmark scenarios, the algorithm generates path quality, and GLBWOA performs well in 4 scenarios, and under the condition of consistent algorithm parameter setting, the average flight total cost is lower, the algorithm convergence accuracy is higher and the convergence speed is faster. To better test the algorithm performance, in the follow-up research, the influence of various complex situations such as moving obstacles and weather changes on the solution of the UAV path planning problem can be further considered. And focus on deploying the algorithm in real UAVs to plan paths in real environments to verify the effectiveness of the algorithm.

Claims

1. A UAV path planning method based on a global-local equilibrium whale optimization algorithm, comprising: Step 1: Initialize the algorithm parameters and the positions of individuals in the population; initialize the leader position, leader score, and convergence curve; Traverse all individuals in the population, calculate the fitness value of each individual, store it in the fitness array, and set the maximum number of no improvements; It is characterized in that it also includes the following steps: Step 2: Get loop iteration parameters, including: (1) Coefficient vector ;in ; is the number of iterations; T is the maximum number of iterations; (2) Coefficient vector ; and is a random number in the range [0,1]; (3) To change the constant of the spiral shape, set it to 1; (4) yes A random number between (5) P is a random number in [0,1]; (6) rand is a random number in the range [0,1]; Step 3: Determine whether P <0.5, if yes, go to step 4, otherwise go to step 5; Step 4: Determine whether , then search for prey, update the position of the individual whale according to the following two formulas, and then go to step 6; in, t It is the present moment; represents the bracketing step length, and is the coefficient vector; is the current leader position; is the current position of the individual whale; is the updated position of the individual whale; Otherwise, the prey is captured and the position of the individual whale is updated according to the following two formulas; then go to step 6; in, t It is the present moment; represents the bracketing step length, is the position of a whale randomly selected from the current population; is the current position of the individual whale; is the updated position of the individual whale; Step 5: Determine whether rand >0.6, then the bubble net attacks and surrounds the prey, and the position of the individual whale is updated according to the following two formulas, and then go to step 6; Otherwise, the bubble attack is enhanced, and the mutation operation is performed according to the following formula, and then step 6 is entered; in, For the current leadership position; is a random number, is the current position of the individual whale; is the updated position of the individual whale; Step 6: Perform a boundary check on the updated whale individual positions obtained in step 4 or step 5, retain the position values ​​of those whale individuals within the boundary, and set the position values ​​outside the boundary to 0; traverse the positions of all current whale individuals, calculate the fitness value of each whale individual, and store it in the fitness array; for each whale individual, if its fitness value is less than the current leader's score, use the fitness value and its corresponding individual position to update the leader's score and position respectively, and reset the no improvement count counter; otherwise, it means that no better solution has been found, and the no improvement count is set to +1; then go to step 7; Step 7: Determine whether the preset conditions are met. If so, the mutation operation is triggered and a boundary check is performed. The position values ​​of individuals within the boundary are retained, and the position values ​​outside the boundary are set to 0. The fitness value of each whale individual is calculated and compared with the score of the current leader. If the fitness value of the current individual is less than the score of the current leader, the objective function value and position of the current individual are used to update the score and position of the leader respectively, and then go to step 8. If the preset conditions are not met, go directly to step 8. Step 8: Set the step size and get the new leader position based on the step size and the current leader position. X_new ; Go to step 9; Step 9, calculate the new leader position If the fitness value of is less than the current leader score, the new position is adopted Update the current leader position and go to step 10; otherwise, go directly to step 10; Step 10: Determine whether s < T , then let s = s +1, return to step 2; otherwise, output the current leader score, which is the optimal solution of the objective function, which is the comprehensive cost function; The formula of the comprehensive cost function is as follows: in, arrive They represent the voyage length cost, obstacle threat cost, navigation altitude cost and path smoothing cost respectively. is the weight coefficient corresponding to different costs.

2. The UAV path planning method based on the global-local equilibrium whale optimization algorithm according to claim 1 is characterized in that: Step 1 is as follows: Call the initialization function, according to the given upper bound ub , Nether lb , the number N and dimension dim of individuals in the population, initialize the position of individuals in the population; Set the initial value of the leader position Leader_pos to an all-zero vector with dimension dim; set the initial value of the leader score Leader_score to infinity; create a zero vector GLBWOA_Convergence_curve with length iter; Traverse all individuals. For each individual, use the fobj function to calculate its fitness value and store it in the i-th element of the fitness array; use Positions(i, :) to represent the position of the i-th individual; set the maximum number of no improvements to 5 and initialize the no improvement counter to 0.

3. The UAV path planning method based on the global-local equilibrium whale optimization algorithm according to claim 2 is characterized in that: In step 7, the mutation operation includes: According to the current iteration number and the maximum number of iterations T The formula for calculating the variable step length is as follows: ； Calculate the mutation vector, the formula is as follows: in, is the mutation vector; ; Generate a random number matrix with 1 row and dim column; The mutation vector is applied to update the position of the individual whale, and the formula is as follows: 。 4. The UAV path planning method based on the global-local equilibrium whale optimization algorithm according to claim 1 is characterized in that: Step 8 includes the following sub-steps: Step 81, randomly generate a step size in the range [0, 0.01] and calculate the gradient at the current leader's position according to the following formula: in, represents the gradient at the current leader position; f is the objective function; is a set of unit orthogonal vectors, Dim represents the dimension of the optimization problem being solved; is the current position of the individual whale in the i-th dimension; in, is the current leader position of the i-th dimension; Is a small positive number, set to 10 -6 ; Step 82: Calculate new variables X1 and X2 for representing the updated position of the individual using the following two formulas, and calculate the fitness values ​​f1 and f2 of X1 and X2 respectively; The updated step size is obtained based on the fitness values ​​f1 and f2. The formula is as follows: in, is a scale factor, set to 1.8; is the current step length; is the updated step size; Step 83, calculate the new leader position X_new according to the updated step size and the current leader position using the following formula; then proceed to step 9; 。 5. The UAV path planning method based on the global-local equilibrium whale optimization algorithm according to claim 1 is characterized in that: In step 10, , , , .

6. The UAV path planning method based on the global-local equilibrium whale optimization algorithm according to claim 1, characterized in that: In step 10: 1) Flight length cost function : in, is the coordinate of the voyage point; n is the number of voyage points; 2) Threat Cost Function : ， in, is the set of all threats. The threat caused by obstacles is a cylinder, and its projection center coordinates are , the radius is , Q is the diameter of the UAV, is the length of the safety buffer zone, the path formed directly between every two flight points during the flight of the UAV The distance from the center coordinate is ; 3) Altitude cost function : in, is the j-th journey point of path i, The maximum flight altitude is limited. The minimum flight altitude is restricted; 4) Smoothing costs : in, and denote the cost coefficients of the turning angle and the climbing angle respectively; is the climb angle at point j on path i, is the climb angle at the j-1th leg of path i; is the turning angle between two adjacent path segments on path i; for The unit vector in the direction of the coordinate axis is Expressed as: in, is the path vector The path formed; in, is the coordinate of the route point The projection point on the plane formed by the x-axis and the y-axis, yes The projection point on the plane formed by the x-axis and the y-axis, yes and The path vector formed by the two points, yes The x-axis and y-axis form a projection point on the plane, yes and The path vector formed by the two points.

7. The UAV path planning method based on the global-local equilibrium whale optimization algorithm according to claim 6 is characterized in that: Set to 200, Set to 100.

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