Multi-unmanned aerial vehicle flight path planning method

Abstract

The invention discloses a multi-unmanned aerial vehicle flight path planning method, and belongs to the technical field of unmanned aerial vehicle intelligent control and collaborative decision, and the method comprises the steps: constructing a threat field model according to the distribution of threat sources in a task environment, and quantifying the threat cost of each flight path point on an unmanned aerial vehicle flight path; taking the weighted sum of the total length of the minimized unmanned aerial vehicle flight path and the total threat cost as a target function, and setting flight constraint conditions including the maximum rotation angle constraint and the maximum climbing angle constraint; and based on flight constraint conditions, solving the objective function by using an improved whale optimization algorithm fused with a genetic algorithm mechanism to obtain a collaborative optimization track with the minimum arrival time difference of the multiple unmanned aerial vehicles. According to the method, safe, smooth and efficient task flight path planning of multiple unmanned aerial vehicles in a complex environment can be realized.

Description

Technical Field

[0001] This invention relates to a multi-UAV trajectory planning method, belonging to the field of UAV intelligent control and collaborative decision-making technology. Background Technology

[0002] Multi-UAV trajectory planning is one of the important research tasks in the field of UAV cooperative control. It aims to generate flight paths for multiple UAVs that meet the requirements of obstacle avoidance, safety, smoothness and cooperative consistency, so that they can reach the target location efficiently. It is widely used in scenarios such as military reconnaissance, cooperative strike, disaster search and rescue and logistics transportation.

[0003] Traditional multi-UAV trajectory planning is largely based on extensions of single-UAV path planning methods, such as grid search, A* search, and randomized rapid tree (RRT), solving for each individual flight path separately. However, with the increase in the number of UAVs and the complexity of the environment, these methods generally suffer from low computational efficiency, difficulty in considering group cooperation, and lack of adaptability to dynamic obstacles. Furthermore, when modeling the problem as a multi-objective optimization, indices such as path length, safe obstacle avoidance, and time synchronization often conflict, leading to poor planning results.

[0004] In recent years, swarm intelligence optimization algorithms have been widely introduced into multi-UAV cooperative path planning to improve solution performance in high-dimensional optimization spaces. However, algorithms such as Particle Swarm Optimization (PSO) and Grey Wolf Optimization (GWO) still struggle to achieve a balance between global search capability and local exploitation capability, easily getting trapped in local optima and exhibiting unstable fitness convergence, especially underperforming in multi-UAV path coupling and dynamic environments.

[0005] Therefore, there is an urgent need to build an intelligent algorithm framework with stronger global exploration capabilities and local fine-grained development capabilities to achieve efficient, safe and coordinated multi-UAV trajectory planning. Summary of the Invention

[0006] The purpose of this invention is to provide a multi-UAV trajectory planning method that enables safe, smooth, and efficient mission trajectory planning for multiple UAVs in complex environments.

[0007] To achieve the above objectives, the present invention provides the following technical solution: In a first aspect, the present invention provides a multi-UAV trajectory planning method, comprising: Based on the distribution of threat sources in the mission environment, a threat field model is constructed to quantify the threat cost to each waypoint on the UAV's flight path. The objective function is to minimize the weighted sum of the total length of the UAV trajectory and the total threat cost, and flight constraints including maximum turn angle constraint and maximum climb angle constraint are set. Based on flight constraints, an improved whale optimization algorithm with a fusion genetic algorithm mechanism is used to solve the objective function, resulting in a collaboratively optimized trajectory that minimizes the arrival time difference among multiple UAVs.

[0008] Building upon the first aspect, further, based on the distribution of threat sources in the mission environment, a threat field model is constructed to quantify the threat costs experienced by each waypoint on the UAV's flight path, including: Based on the coordinates of each threat source in the mission environment and the coordinates of each track point on the UAV track, calculate the distance between each track point on the UAV track and each threat source in the mission environment. Based on the distance between each waypoint on the UAV's flight path and each threat source in the mission environment, the threat cost to each waypoint on the UAV's flight path is calculated using a distance attenuation model. The formula for calculating the distance between each waypoint on the UAV's flight path and each threat source in the mission environment is as follows: ; in, Indicates the first [unmanned aerial vehicle] flight path The first waypoint and mission environment The distance between the threat sources , These represent the first in the task environment. The horizontal and vertical axes of the threat sources , These represent the first and second digits on the drone's flight path, respectively. The horizontal and vertical coordinates of each waypoint; The formula for calculating the threat cost to each waypoint on the drone's flight path is as follows: ; in, Indicates the first [unmanned aerial vehicle] flight path The cost of threats to each waypoint Indicates the first in the task environment Threat intensity coefficient of each threat source.

[0009] Combining the first aspect, the objective function is further: ; in, Indicates the first [unmanned aerial vehicle] flight path The first waypoint and the first Euclidean distance between waypoints Indicates the first [unmanned aerial vehicle] flight path The cost of threats to each waypoint This represents the weighting factor used to balance the drone's flight path length with threat avoidance requirements. This indicates the total number of waypoints on the drone's flight path.

[0010] Building upon the first aspect, further, based on flight constraints, an improved whale optimization algorithm incorporating a genetic algorithm mechanism is used to solve the objective function, resulting in a collaboratively optimized flight path that minimizes the arrival time differences of multiple UAVs, including: An initial population is randomly generated within the solution space that satisfies the constraints, and each individual in the initial population represents a candidate trajectory scheme. The fitness of each individual in the initial population is calculated based on the objective function, and the initial population is divided into an elite subpopulation and a normal subpopulation according to the fitness, and the positions are updated accordingly. The improved whale optimization algorithm is used to update the position of each individual in the elite subgroup, and the genetic algorithm mechanism is used to update the position of each individual in the ordinary subgroup. Based on the current population diversity index, dynamically select whether to continue using the genetic algorithm mechanism or switch to the improved whale optimization algorithm to update the position of each individual in the ordinary subpopulation; For each individual after the location update, the validity of the track is verified, individuals that violate the constraints are repaired, and the repaired individuals are merged into the current population to obtain a new population; The fitness of each individual in the new population is calculated based on the objective function. The new population is then divided into a new elite subpopulation and a new ordinary subpopulation based on the fitness. The positions are updated again until the iteration termination condition is met. The individual with the best fitness in the latest population is then obtained as the optimal trajectory scheme.

[0011] Building upon the first aspect, further updating the position of each individual in the elite subgroup using the improved whale optimization algorithm includes: Update the position of each individual in the elite subgroup based on the selection probability, choosing either the prey-encircling behavior or the spiral search behavior. The formula for updating the position of each individual in the elite subgroup by selecting the prey-surrounding behavior is: ; in, , They represent the first , The position vector of an individual at the next iteration. Indicates the first The position vector of the optimal individual at the nth iteration, i.e., the position vector of the i-th iteration. The position vector of the individual with the best fitness in the population at the next iteration. and Both are coefficient vectors. , , for Random vectors within the range The parameter decreases linearly from 2 to 0 with the number of iterations; The formula for updating the position of each individual in the elite subgroup using the spiral search behavior is: ; in, The constant for the spiral shape. for A random number within a given range.

[0012] In conjunction with the first aspect, further updating the position of each individual in the ordinary subpopulation using a genetic algorithm mechanism includes: A candidate pool is formed by randomly selecting several individuals from the ordinary subgroup, and the individual with the best fitness is selected from the candidate pool as the parent generation. Two random position indices are selected on the parent's gene coding sequence as crossover points. Gene coding segments between the crossover points are swapped to generate offspring. By applying a Gaussian-based random perturbation to a portion of the offspring's genes with an adaptively adjusted mutation rate, individuals with updated positions are obtained.

[0013] In conjunction with the first aspect, the formula for calculating the population diversity index is as follows: ; in, Indicators representing population diversity Indicates the size of the population. , They represent the first in the population. , The position vectors of each individual; When the diversity index of the population is less than the index threshold or the current iteration process is in the forced exploration phase, the position of each individual in the ordinary subpopulation is updated using the genetic algorithm mechanism; otherwise, the improved whale optimization algorithm is switched to update the position of each individual in the ordinary subpopulation.

[0014] In conjunction with the first aspect, further remediation of individuals who violate the constraints includes: The collision penalty term and the smoothness penalty term are integrated into the objective function to form a comprehensive optimization objective function: ; in, This indicates the total length of the drone's flight path. This indicates the penalty for a drone's flight path colliding with an obstacle. This indicates a penalty for the drone's flight path turning angle not meeting the smoothness requirement. Indicates the first [unmanned aerial vehicle] flight path The cost of threats to each waypoint This represents the weighting factor used to balance the drone's flight path length with threat avoidance requirements. This indicates the total number of waypoints on the drone's flight path; A heuristic method of regenerating waypoints along the direction from the start to the end is used to repair individuals that violate the constraints and generate new drone waypoints. The new drone tracks are sparsified by removing track points whose distance is less than a distance threshold.

[0015] Secondly, the present invention provides a multi-UAV trajectory planning system, comprising: The threat field construction module is used to build a threat field model based on the distribution of threat sources in the mission environment and quantify the threat cost to each waypoint on the UAV's flight path. The objective function construction module is used to minimize the weighted sum of the total length of the UAV trajectory and the total threat cost as the objective function, and to set flight constraints including the maximum turning angle constraint and the maximum climb angle constraint. The solution module is used to solve the objective function based on flight constraints and using an improved whale optimization algorithm that incorporates a genetic algorithm mechanism, so as to obtain a collaboratively optimized trajectory that minimizes the arrival time difference of multiple UAVs.

[0016] Thirdly, the present invention provides a computer device, comprising: Storage medium: used to store computer programs; Processor: Used to execute the computer program to implement the multi-UAV trajectory planning method described in the first aspect.

[0017] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the multi-UAV trajectory planning method described in the first aspect.

[0018] Fifthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the multi-UAV trajectory planning method described in the first aspect.

[0019] Compared with the prior art, the beneficial effects of the present invention are: This invention provides a multi-UAV trajectory planning method that, by constructing a threat field model, establishing a trajectory optimization objective function, and introducing an improved whale optimization algorithm that incorporates a genetic algorithm mechanism, achieves safe, smooth, and efficient mission trajectory planning for multiple UAVs in complex environments. By setting a maximum turning angle constraint, the smoothness and flight stability of the UAV trajectory are ensured, preventing sudden changes in heading that could lead to loss of control. A maximum climb angle constraint ensures flight safety and meets the aerodynamic requirements of the aircraft. Collision fusion penalty terms and smoothness penalty terms are integrated to improve UAV flight stability and control performance. A grouping strategy of elite and ordinary subgroups is constructed, combining prey encirclement behavior with selection, crossover, and mutation operations to achieve a dynamic balance between global search and local exploitation. Adaptive diversity monitoring and Gaussian perturbation mutation enhance the ability to escape local optima. Real-time collision avoidance control between multiple UAVs and with environmental obstacles is achieved based on path validity repair and penalty mechanisms, effectively improving solution quality and convergence efficiency. The spiral search mechanism can enhance the local search capability of the neighborhood of the optimal solution, the random perturbation strategy can maintain the diversity of the population and improve the ability to escape local optima, and the arrival time difference of multiple UAVs can be minimized by the cooperative constraint control, thus achieving formation consistency. Attached Figure Description

[0020] Figure 1 This is a flowchart of the multi-UAV trajectory planning method provided in the embodiments of the present invention; Figure 2 This is a flowchart of the improved whale optimization algorithm that incorporates a genetic algorithm mechanism, provided in an embodiment of the present invention. Figure 3 This is a schematic diagram of the convergence curves of the improved whale optimization algorithm and the comparison algorithm with the genetic algorithm mechanism provided in the embodiments of the present invention on the standard test function, wherein (a) corresponds to the Sphere function, (b) corresponds to the Rastrigin function, (c) corresponds to the Ackley function, and (d) corresponds to the Rosenbrock function; Figure 4 This is a line graph comparing WOA and GA-WOA in terms of average optimal cost and average running time, provided in the embodiments of the present invention. Figure 5 This is a schematic diagram of the trajectory planning results of each algorithm provided in the embodiments of the present invention, wherein (a) corresponds to the PSO algorithm, (b) corresponds to the ACO algorithm, (c) corresponds to the GA algorithm, (d) corresponds to the DE algorithm, (e) corresponds to the WOA algorithm, and (f) corresponds to the GA-WOA algorithm; Figure 6 This is a schematic diagram comparing the performance of multiple UAV algorithms provided in an embodiment of the present invention. Detailed Implementation

[0021] The technical solution of the present invention will be further described in detail below with reference to specific embodiments.

[0022] Embodiments of the present invention are described in detail below. Examples of these embodiments are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention. Unless otherwise specified, embodiments of the present invention and the technical features thereof can be combined with each other.

[0023] This invention provides a multi-UAV trajectory planning method, comprising: Based on the distribution of threat sources in the mission environment, a threat field model is constructed to quantify the threat cost to each waypoint on the UAV's flight path. The objective function is to minimize the weighted sum of the total length of the UAV trajectory and the total threat cost, and flight constraints including maximum turn angle constraint and maximum climb angle constraint are set. Based on flight constraints, an improved whale optimization algorithm with a fusion genetic algorithm mechanism is used to solve the objective function, resulting in a collaboratively optimized trajectory that minimizes the arrival time difference among multiple UAVs.

[0024] The multi-UAV trajectory planning method provided in this invention obtains trajectories through a unified optimization framework, reduces the difference in arrival time, maintains consistency in cooperative behavior, generates trajectories with significant threat avoidance effects, has smooth paths, high execution feasibility, and an optimization convergence speed superior to traditional methods, thus showing good prospects for engineering applications.

[0025] Figure 1 This is a flowchart of the multi-UAV trajectory planning method provided in this embodiment. This flowchart only shows the logical order of the method in this embodiment. Provided there are no conflicts, different methods can be used. Figure 1 Complete the steps shown or described in the order indicated.

[0026] The multi-UAV trajectory planning method provided in this embodiment can be applied to a terminal and can be executed by a multi-UAV trajectory planning system. This system can be implemented by software and / or hardware and can be integrated into the terminal, such as any tablet computer or computer device with communication functions.

[0027] This invention provides a method for planning the flight paths of multiple unmanned aerial vehicles (UAVs), which specifically includes the following steps: Step 1: Based on the distribution of threat sources in the mission environment, construct a threat field model and quantify the threat cost to each waypoint on the UAV's flight path; In this embodiment, based on the distribution of threat sources in the mission environment, a threat field model is constructed, and the threat cost of each waypoint on the UAV's flight path is quantified. Specifically, the steps include: Step 1: Based on the coordinates of each threat source in the mission environment and the coordinates of each track point on the UAV track, calculate the distance between each track point on the UAV track and each threat source in the mission environment; Specifically, the formula for calculating the distance between each waypoint on the UAV's flight path and each threat source in the mission environment is as follows: ; in, Indicates the first [unmanned aerial vehicle] flight path The first waypoint and mission environment The distance between the threat sources , These represent the first in the task environment. The horizontal and vertical axes of the threat sources , These represent the first and second digits on the drone's flight path, respectively. The horizontal and vertical coordinates of each track point.

[0028] The distribution of threat sources is calculated comprehensively through overlay to reflect the risks in a multi-threat environment.

[0029] Step 2: Based on the distance between each waypoint on the UAV's flight path and each threat source in the mission environment, calculate the threat cost to each waypoint on the UAV's flight path using the distance attenuation model.

[0030] Specifically, the formula for calculating the threat cost to each waypoint on the drone's flight path is as follows: ; in, Indicates the first [unmanned aerial vehicle] flight path The cost of threats to each waypoint Indicates the first in the task environment Threat intensity coefficient of each threat source.

[0031] when When reduced to near zero, Increase the penalty value to a high level for threat avoidance.

[0032] Step 2: Use the weighted sum of minimizing the total length of the UAV trajectory and the total threat cost as the objective function, and set flight constraints including maximum turning angle constraints and maximum climb angle constraints; In this embodiment, the objective function is: ; in, Indicates the first [unmanned aerial vehicle] flight path The first waypoint and the first Euclidean distance between waypoints Indicates the first [unmanned aerial vehicle] flight path The cost of threats to each waypoint This represents the weighting factor used to balance the drone's flight path length with threat avoidance requirements. This indicates the total number of waypoints on the drone's flight path.

[0033] Step 3: Based on flight constraints, the improved whale optimization algorithm with a fusion genetic algorithm mechanism is used to solve the objective function, and a collaborative optimization trajectory that minimizes the arrival time difference of multiple UAVs is obtained.

[0034] In this embodiment, based on flight constraints, the improved whale optimization algorithm, which incorporates a genetic algorithm mechanism, is used to solve the objective function to obtain a collaboratively optimized flight path that minimizes the arrival time difference among multiple UAVs. Specifically, the steps include the following: Step 1: Randomly generate an initial population within the solution space that satisfies the constraints. Each individual in the initial population represents a candidate trajectory scheme. Step 2: Calculate the fitness of each individual in the initial population based on the objective function, and divide the initial population into an elite subpopulation and a normal subpopulation according to the fitness, then update the positions: Step 2.1: Update the position of each individual in the elite subgroup using the improved whale optimization algorithm, and update the position of each individual in the ordinary subgroup using the genetic algorithm mechanism; In this embodiment, updating the position of each individual in the elite subgroup using the improved whale optimization algorithm specifically includes: updating the position of each individual in the elite subgroup by selecting either the prey encirclement behavior or the spiral search behavior based on the selection probability.

[0035] Specifically, the formula for updating the position of each individual in the elite subgroup by selecting the prey-surrounding behavior is: ; in, , They represent the first , The position vector of an individual at the next iteration. Indicates the first The position vector of the optimal individual at the nth iteration, i.e., the position vector of the i-th iteration. The position vector of the individual with the best fitness in the population at the next iteration. and Both are coefficient vectors. , , for Random vectors within the range The parameter is linearly decreased from 2 to 0 with the number of iterations. It is used to transition from global search to local search, so that the algorithm has global search capability in the early stage and enhances local search capability in the later stage, thereby improving the accuracy and stability of trajectory optimization.

[0036] The formula for updating the position of each individual in the elite subgroup using the spiral search behavior is: ; in, The constant for the spiral shape. for A random number within a given range.

[0037] In this embodiment, updating the position of each individual in the ordinary subpopulation using a genetic algorithm mechanism specifically includes the following steps: Step ①: Randomly select several individuals from the ordinary subgroup to form a candidate pool, and select the individual with the best fitness from the candidate pool as the parent generation; Step 2: Randomly select two position indices on the parent's gene coding sequence as crossover points, swap the gene coding segments between the crossover points, and generate offspring; Step 3: Apply a Gaussian-based random perturbation to a portion of the offspring's genes with an adaptively adjusted mutation rate to obtain individuals with updated positions.

[0038] Step 2.2: Dynamically select whether to continue using the genetic algorithm mechanism or switch to the improved whale optimization algorithm to update the position of each individual in the ordinary subpopulation based on the diversity index of the current population; In this embodiment, the formula for calculating the population diversity index is: ; in, Indicators representing population diversity Indicates the size of the population. , They represent the first in the population. , The position vector of each individual.

[0039] Specifically, when the diversity index of the population is less than the index threshold or the current iteration process is in the forced exploration phase, the position of each individual in the ordinary subpopulation is updated using the genetic algorithm mechanism; otherwise, the improved whale optimization algorithm is switched to update the position of each individual in the ordinary subpopulation.

[0040] Step 3: Verify the validity of the track for each individual after the position update, repair individuals that violate the constraints, and merge the repaired individuals into the current population to obtain a new population; In this embodiment, the repair of individuals that violate the constraints specifically includes the following steps: Step ①: Integrate the collision penalty term and the smoothness penalty term into the objective function to form a comprehensive optimization objective function: ; in, This indicates the total length of the drone's flight path. This indicates the penalty for a drone's flight path colliding with an obstacle. This indicates a penalty for the drone's flight path turning angle not meeting the smoothness requirement. Indicates the first [unmanned aerial vehicle] flight path The cost of threats to each waypoint This represents the weighting factor used to balance the drone's flight path length with threat avoidance requirements. This indicates the total number of waypoints on the drone's flight path; Step 2: Use the heuristic method of regenerating waypoints along the direction from the start point to the end point to repair individuals that violate the constraints and generate new drone waypoints; Step 3: Sparsify the new drone tracks by removing track points whose distance is less than the distance threshold.

[0041] Step 4: Calculate the fitness of each individual in the new population based on the objective function, and divide the new population into a new elite subpopulation and a new ordinary subpopulation according to the fitness. Update the position again until the iteration termination condition is met, and obtain the individual with the best fitness in the latest population as the optimal trajectory scheme.

[0042] In one possible embodiment, the multi-UAV trajectory planning problem is constructed in a three-dimensional mission space. The UAV swarm consists of several homogeneous or heterogeneous UAVs, and each UAV is given a controllable pose and motion state at the planning time. This embodiment minimizes the total cost of all UAV trajectories while satisfying the constraints of safe flight, global cooperation, and mission objectives. The constrained optimization problem is solved based on the Improved Whale Optimization Algorithm (IWOA) to obtain the optimal cooperative trajectory of the swarm of UAVs.

[0043] First, to perform trajectory planning, the mission environment needs to be modeled. The Whale Optimization Algorithm (WOA) constructs its framework by simulating the unique hunting behavior of humpback whales. As a metaheuristic algorithm, its search process begins with a randomly initialized solution set. The algorithm comprises three core phases: the prey encirclement phase, the bubble-net attack phase, and the prey search phase. In the algorithm implementation, each individual whale corresponds to a feasible solution. Through the synergistic effect of the three strategies mentioned above, the algorithm dynamically adjusts its exploration and development capabilities, thereby affecting its convergence performance. When the search process meets the preset termination condition, the algorithm terminates and outputs the final optimization result. The Whale Optimization Algorithm, with its simple structure, convenient implementation, and high convergence efficiency, demonstrates significant application potential in solving complex optimization problems.

[0044] During the encirclement and hunting phase, humpback whales surround their prey after identifying its location. In the whale optimization algorithm, it's assumed that the current best solution is the optimal solution, as this requires continuous exploration to determine. Once the optimal position is found, other individuals update their own positions based on the location of the best individual. In the algorithm, whales select target prey by locating its prey. Specifically, after the best search agent determines its position, other search agents update their own positions based on the best agent's location. This process occurs iteratively (during the exploration and development phases). The linear decrease from 2 to 0 The range is Two methods were designed to biomimeticly model whale behavior and form formulas during the bubble net attack phase.

[0045] (1) Contraction and encirclement mechanism: This behavior is achieved by reducing... It is achieved through values. The number of iterations reduces the number of elements from 2 to 0. It is a range Any value in the range, and any new position of any whale is any position within the distance from its original position to the current best whale position.

[0046] (2) Spiral update position: calculate and The gap distance between them, that is, the distance between the whale and its prey, is used to create a spiral motion to simulate the actual movement of a whale. It is the distance from the whale to its prey. It is a spiral shape constant, a random number. The range is Whales have two swimming patterns: circling prey or following a given spiral path. Both patterns are modeled simultaneously, with a 50% probability of choosing one over the other to update the whale's position during optimization. In the random location search phase, the whale randomly scans for prey based on its current location. In this phase, unlike the development phase, the whale's location search is refreshed by randomly selected whales, not the currently best available whale. Therefore, the conditions for this phase become... This forces the search agent to emphasize exploration, moving away from the reference whale to perform a global search.

[0047] The Whale Optimization Algorithm (WOA) starts with a set of randomly generated locations representing potential solutions to the problem, and then uses biomimetic principles to gradually approach the global optimum. In each iteration, the global optimum is updated based on fitness evaluation until a preset number of iterations is reached or a specific stopping condition is met.

[0048] Although the traditional whale optimization algorithm is widely used due to its simple parameters and ease of implementation, it still suffers from slow convergence, susceptibility to local optima, and weak constraint handling capabilities when solving complex, multi-constraint problems such as UAV path planning. Therefore, as Figure 2 As shown in the figure, this embodiment proposes an improved whale optimization algorithm (GA-WOA) that combines the advantages of genetic algorithms. This method constructs a path planning solution framework that is both efficient and stable by introducing a population hierarchical evolution mechanism, a dynamic adaptive transformation strategy, improved genetic operation operators, and enhanced convergence control measures.

[0049] The GA-WOA algorithm introduces an innovative elite-preservation strategy, dividing the population into two distinct tiers: an elite tier and a general tier. This hierarchical design not only maintains the advantages of traditional evolutionary algorithms in global exploration but also significantly improves the performance of local search by specifically optimizing the elite tier.

[0050] In practical applications, this embodiment has found through numerous experiments that when When the value is between 0.2 and 0.4, the algorithm can achieve the best balance: too high a proportion of elites will lead to a decrease in population diversity, while too low a proportion will affect the convergence speed.

[0051] The ordinary group is evolved using an improved genetic algorithm. First, the algorithm selects high-quality parents from the candidate pool through a tournament selection mechanism. This selection mechanism ensures both selection pressure and population diversity. To guarantee the integrity of path points, the crossover operation is always performed on complete coordinate pairs, avoiding invalid solutions. Experiments show that this crossover method effectively preserves high-quality path segments.

[0052] In the design process of algorithm optimization, the key is to effectively balance global exploration and local mining. The GA-WOA algorithm proposed in this embodiment achieves adaptive control of these two search strategies by introducing a metric to measure diversity and a dynamic switching mechanism.

[0053] Population diversity indices reflect the dispersion of the distribution of individuals within a population. When When the threshold is high, it indicates low population diversity, and the algorithm automatically switches to WOA (Wide Area of ​​Analysis) development mode; otherwise, it maintains GA (General Analysis) exploration mode. This threshold was determined through extensive experiments and achieves a good balance in most cases.

[0054] To ensure the algorithm has sufficient exploratory power in the early stages, this embodiment includes a forced exploration phase, which mandates the use of the GA strategy for the first 10% of the total iterations. This effectively prevents the algorithm from converging to a suboptimal solution prematurely. Simultaneously, the Gaussian perturbation standard deviation in the algorithm employs a linear decay strategy. This dynamic adjustment mechanism allows the algorithm to perform a wide-ranging search in the early stages, followed by fine-tuning in the later stages.

[0055] To address the unique challenges of UAV path planning, the GA-WOA algorithm incorporates several improvements over traditional genetic operations, significantly enhancing its performance and reliability.

[0056] In terms of mutation operations, the algorithm employs a Gaussian distribution-based directed mutation strategy to control the dimensionality of mutations. The mutation rate uses a three-stage adaptive strategy; this design allows the algorithm to maintain strong exploratory capabilities in the early stages while focusing on local optimization in the later stages.

[0057] Considering the constrained nature of the path planning problem, the algorithm introduces a strict validity verification mechanism. For individuals that do not meet the constraints, the algorithm adopts a heuristic repair strategy to regenerate path points along the direction from the starting point to the destination. This repair method ensures the feasibility of the path while maintaining a certain degree of randomness.

[0058] In addition, the algorithm introduces a path smoothness penalty, which effectively avoids overly sharp turns in the path.

[0059] To prevent the algorithm from falling into premature convergence or over-optimization, GA-WOA employs a complete convergence control strategy.

[0060] The historical best monitoring mechanism continuously tracks changes in the optimal solution. When the improvement amount is less than a threshold for 50 consecutive generations, the algorithm terminates prematurely. This mechanism not only saves computational resources but also prevents meaningless over-optimization.

[0061] Path sparsification is another important innovation, which can eliminate redundant path points and improve the practicality of the solution.

[0062] To verify the effectiveness of the improved algorithm, this embodiment constructs a multidimensional optimization problem based on the standard test function set and conducts a comparative experiment between the optimized WOA algorithm and the standard WOA algorithm.

[0063] like Figure 3 As shown, the test function set includes four typical optimization functions: Sphere, Rastrigin, Ackley, and Rosenbrock.

[0064] The Sphere function is a continuous unimodal function with the global optimum located at the origin. Its surface exhibits a smooth, symmetrical distribution, and it is often used to verify the local exploitation capabilities of algorithms. Its simple geometric characteristics can easily lead to premature convergence, making it a good indicator of an algorithm's convergence speed and solution accuracy.

[0065] The Rastrigin function is a multimodal function with highly oscillating characteristics, where the global optimum is surrounded by numerous local extrema. This function exhibits a "honeycomb" structure in the search space, providing a strong test of the algorithm's global exploration capability and its ability to escape local optima.

[0066] The Ackley function is also a multimodal function, with its global optimum located in a flat region and dense suboptimal solutions on the periphery. Because its gradient changes gently but its local extrema are widely distributed, the algorithm can easily get stuck in a "plateau" situation, making the choice of search direction a challenge.

[0067] The Rosenbrock function is a non-convex function, and its global optimum is located at the bottom of a narrow parabolic valley. The gradient direction deviates significantly from the optimal solution direction, which poses a challenge to the algorithm's path-following ability and dynamic adjustment mechanism.

[0068] The 3D curves of the above four functions are as follows: Figure 3 As shown.

[0069] The results of WOA and GA-WOA on each test function are shown in Table 1.

[0070] Table 1: Performance Comparison Results .

[0071] To more intuitively demonstrate the performance of the two algorithms on each test function, Figure 4 Line graphs comparing the average optimal cost and average running time of the two algorithms were plotted.

[0072] As shown in the charts, the GA-WOA algorithm exhibits a significant accuracy advantage across all test functions. Taking the Rastrigin function as an example, the average optimal cost of GA-WOA is 10.96, only 23% of that of WOA (47.78). This demonstrates that the crossover and mutation mechanisms in the genetic algorithm effectively enhance global search capabilities and overcome the problem of traditional WOA methods easily getting trapped in local optima. Similarly, when dealing with the complex Rosenbrock function, GA-WOA reduces the average optimal cost from 49.11 to 13.25, a reduction of 73%, further confirming the efficiency and adaptability of this hybrid strategy in solving non-convex, high-dimensional problems.

[0073] While GA-WOA demonstrates superior accuracy, its average execution time is significantly longer than the WOA algorithm. For example, in the Sphere function, GA-WOA takes 8.77 seconds to complete the task, compared to WOA's 0.42 seconds. This additional time consumption is primarily attributed to the population iteration and fitness calculation processes within the genetic algorithm. However, when handling the Ackley function, GA-WOA exhibits a good balance between time and accuracy, indicating that the improved algorithm is more efficient in solving multilocal extremum problems in noisy environments.

[0074] In summary, while the GA-WOA algorithm consumes fewer computational resources than the unmodified WOA algorithm, the improved algorithm offers significant improvements in adaptability and solution quality. Therefore, GA-WOA is highly suitable for scenarios where timeliness is not critical, but the quality of the solution is extremely important, such as in the case of drones where safety is paramount. This embodiment is developed based on the Python 3.9 platform, mainly using NumPy for matrix operations and Matplotlib for visualization. The hardware platform uses an Intel i7-11800H processor with 32GB of memory, and all tests were completed under the Windows 10 operating system.

[0075] In the design of the WOA-GA algorithm, the specific configuration of parameters directly affects the algorithm's exploration ability, convergence speed, and stability. By scientifically and rationally setting the parameters, the algorithm can efficiently find the optimal solution when performing UAV path planning tasks, achieving a good balance between computational efficiency and search accuracy. A population size of 300 individuals is chosen; a larger population size improves exploration ability but also increases computational cost. 300 individuals strike a balance between exploration ability and computational efficiency. The number of iterations is set to 300 to ensure the algorithm has sufficient time for a comprehensive search, avoiding premature convergence. 300 iterations increase the probability of finding the global optimum while avoiding overcomputation. A crossover probability of 0.8 improves population diversity and optimization ability, ensuring the algorithm makes sufficient combination attempts. A mutation probability of 0.05 maintains population stability while improving exploration ability to some extent, avoiding getting trapped in local optima. An initial spiral coefficient of 1 balances local search and global exploration, ensuring the algorithm can meticulously explore local optima while searching for the global optimum. The initial coefficient is set to 2, providing a larger exploration range in the initial stage and improving search capability. The final coefficient is set to 0, providing a large exploration range initially, which is gradually reduced to enhance convergence performance. The serpentine search probability is set to 0.8, helping the algorithm avoid lingering near local optima and improving search diversity. The convergence rate adjustment factor is set to 0.2, improving convergence speed in the later stages of the search process while maintaining a certain level of exploration capability. The precision threshold is set to 0.001, terminating the iteration when satisfactory precision is achieved, thus saving computational resources.

[0076] The simulation environment is set as a 100×100 two-dimensional grid map, containing one common starting point, six UAV target points, and multiple static circular obstacles. The starting point is located at (10,10); the specific distribution of the target points is as follows: target point 1 is located at (70,85), target point 2 is located at (80,70), target point 3 is located at (90,50), target point 4 is located at (20,95), target point 5 is located at (30,65), and target point 6 is located at (40,20); the specific distribution of obstacles is as follows: obstacle 1 is located at (30,40) with a radius of 14; obstacle 2 is located at (60,30) with a radius of 9; obstacle 3 is located at (50,70) with a radius of 11; and obstacle 4 is located at (20,80) with a radius of 7.

[0077] The goal of drone path planning is to find a path from the starting point to the destination while minimizing the path cost. The path cost includes path length, collision penalty, and path smoothness penalty.

[0078] This embodiment applies six different algorithms (PSO, ACO, DE, GA, WOA, and the improved GA-WOA) to multi-UAV path planning. These algorithms are used to find the optimal path from the starting point to the destination. To visually demonstrate the planning characteristics of different algorithms, Figure 5 The trajectory planning results of each algorithm in the environment set in this study are presented. Figure 5 It can be seen that the PSO algorithm can successfully plan obstacle avoidance paths for UAVs, enabling them to bypass obstacle areas of different sizes. However, some UAV paths are quite tortuous, which may affect flight efficiency. The ACO and DE algorithms failed to effectively plan obstacle avoidance paths, resulting in some collisions, and some UAV paths had obvious turns. The GA algorithm failed completely in obstacle avoidance, sacrificing safety for a shorter path. The WOA algorithm can guide UAVs to effectively avoid obstacles, achieving planning from the start point to the destination, and can help UAVs find feasible paths when dealing with multiple obstacles of different sizes. The GA-WOA algorithm, combining the advantages of whale optimization and genetic algorithms, performs well in obstacle avoidance and can effectively guide UAVs to avoid obstacles. Moreover, compared to a single algorithm, the GA-WOA algorithm's path planning is relatively better, with some paths being smoother and more efficient.

[0079] This embodiment focuses on three key metrics: total path length, computation time, and collision penalty. Based on experimental results, a comprehensive evaluation is conducted, and the performance of six algorithms in multi-UAV path planning is analyzed in detail. The experimental results for each algorithm are as follows: Figure 6 As shown.

[0080] Total path length is a core metric for evaluating path quality. Figure 6 As can be seen, the GA algorithm ranks first with a path length of 468.19 units, which is 1.3% shorter than the second-place GA-WOA (474.21). However, its shorter path comes at the cost of safety, with a collision penalty as high as 12321.66. The remaining path lengths are ranked as follows: WOA, PSO, DE, and ACO, which are 2.7%, 14.62%, 22.73%, and 26.45% longer than GA-WOA, respectively.

[0081] The computation time reflects the running efficiency of each algorithm. The GA algorithm has the shortest computation time, at 12.42 seconds, but its path planning effect is not ideal, failing to effectively avoid obstacles despite its short computation time. DE and PSO take 45.95 seconds and 57.67 seconds respectively, which are more efficient than other algorithms, but their path planning effect is among the lowest. ACO has an extremely high computation time (1126.50 seconds) due to its pheromone update mechanism, making it unsuitable for real-time UAV path planning scenarios. GA-WOA takes 314.14 seconds, which is in the middle range of computation time among the algorithms, 54.5% faster than the original WOA (689.52 seconds), while also shortening the path length to some extent, demonstrating the advantages of hybrid algorithms and the effectiveness of the improved algorithm studied in this embodiment.

[0082] Collision penalty is a key factor in evaluating path safety. In the experiments, the GA algorithm showed the lowest safety performance, with a total collision penalty value of 12321.66; the ACO and DE algorithms also exhibited varying degrees of collisions, with corresponding penalty values ​​of 3731.1 and 5098.02, respectively. In contrast, the PSO, WOA, and GA-WOA algorithms did not experience any collisions throughout the entire test, demonstrating extremely high reliability.

[0083] Comprehensive evaluation shows that the GA-WOA algorithm, with its unique dynamic adaptive switching strategy and improved design, demonstrates superior overall performance in multi-UAV path planning scenarios. This algorithm fully meets obstacle avoidance requirements while ensuring the shortest path, achieving a perfect balance between safety and economy. Although its computation time is relatively longer, it is significantly shorter than the original WOA algorithm and yields higher-quality planned paths. The design, which integrates the global search capability of the whale optimization algorithm and the local optimization characteristics of the genetic algorithm, effectively overcomes the weakness of single algorithms that are prone to getting trapped in local optima, making it particularly outstanding in complex environments with multiple obstacles. Overall, the GA-WOA algorithm has achieved leading levels in all relevant indicators of multi-UAV path planning, strongly demonstrating the effectiveness of the improved WOA algorithm in this embodiment.

[0084] This invention provides a multi-UAV trajectory planning system, comprising: The threat field construction module is used to build a threat field model based on the distribution of threat sources in the mission environment and quantify the threat cost to each waypoint on the UAV's flight path. The objective function construction module is used to minimize the weighted sum of the total length of the UAV trajectory and the total threat cost as the objective function, and to set flight constraints including the maximum turning angle constraint and the maximum climb angle constraint. The solution module is used to solve the objective function based on flight constraints and using an improved whale optimization algorithm that incorporates a genetic algorithm mechanism, so as to obtain a collaboratively optimized trajectory that minimizes the arrival time difference of multiple UAVs.

[0085] The multi-UAV trajectory planning system provided in this embodiment of the invention can execute the multi-UAV trajectory planning method provided in this embodiment of the invention, and has the corresponding functional modules and beneficial effects of the execution method.

[0086] This invention provides a computer device, comprising: Storage medium: used to store computer programs; Processor: Used to execute computer programs to implement the multi-UAV trajectory planning method provided in the embodiments of the present invention.

[0087] This invention provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the multi-UAV trajectory planning method provided in this invention.

[0088] This invention provides a computer program product, including a computer program that, when executed by a processor, implements the multi-UAV trajectory planning method provided in this invention.

[0089] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0090] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart. Figure 1 One or more processes and / or boxes Figure 1 A system that specifies functions in one or more boxes.

[0091] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including an instruction set implemented in a process. Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0092] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0093] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A multi-UAV trajectory planning method, characterized in that, include: Based on the distribution of threat sources in the mission environment, a threat field model is constructed to quantify the threat cost to each waypoint on the UAV's flight path. The objective function is to minimize the weighted sum of the total length of the UAV trajectory and the total threat cost, and flight constraints including maximum turn angle constraint and maximum climb angle constraint are set. Based on flight constraints, an improved whale optimization algorithm with a fusion genetic algorithm mechanism is used to solve the objective function, resulting in a collaboratively optimized trajectory that minimizes the arrival time difference among multiple UAVs.

2. The multi-UAV trajectory planning method according to claim 1, characterized in that, Based on the distribution of threat sources in the mission environment, a threat field model is constructed to quantify the threat cost to each waypoint on the UAV's flight path, including: Based on the coordinates of each threat source in the mission environment and the coordinates of each track point on the UAV track, calculate the distance between each track point on the UAV track and each threat source in the mission environment. Based on the distance between each waypoint on the UAV's flight path and each threat source in the mission environment, the threat cost to each waypoint on the UAV's flight path is calculated using a distance attenuation model. The formula for calculating the distance between each waypoint on the UAV's flight path and each threat source in the mission environment is as follows: ； in, Indicates the first [unmanned aerial vehicle] flight path The first waypoint and mission environment The distance between the threat sources , These represent the first in the task environment. The horizontal and vertical axes of the threat sources , These represent the first and second digits on the drone's flight path, respectively. The horizontal and vertical coordinates of each waypoint; The formula for calculating the threat cost to each waypoint on the drone's flight path is as follows: ； in, Indicates the first [unmanned aerial vehicle] flight path The cost of threats to each waypoint Indicates the first in the task environment Threat intensity coefficient of each threat source.

3. The multi-UAV trajectory planning method according to claim 1, characterized in that, The objective function is: ； in, Indicates the first [unmanned aerial vehicle] flight path The first waypoint and the first Euclidean distance between waypoints Indicates the first [unmanned aerial vehicle] flight path The cost of threats to each waypoint This represents the weighting factor used to balance the drone's flight path length with threat avoidance requirements. This indicates the total number of waypoints on the drone's flight path.

4. The multi-UAV trajectory planning method according to claim 1, characterized in that, Based on flight constraints, an improved whale optimization algorithm incorporating a genetic algorithm mechanism is used to solve the objective function, resulting in collaboratively optimized trajectories that minimize the arrival time differences of multiple UAVs, including: An initial population is randomly generated within the solution space that satisfies the constraints, and each individual in the initial population represents a candidate trajectory scheme. The fitness of each individual in the initial population is calculated based on the objective function, and the initial population is divided into an elite subpopulation and a normal subpopulation according to the fitness, and the positions are updated accordingly. The improved whale optimization algorithm is used to update the position of each individual in the elite subgroup, and the genetic algorithm mechanism is used to update the position of each individual in the ordinary subgroup. Based on the current population diversity index, dynamically select whether to continue using the genetic algorithm mechanism or switch to the improved whale optimization algorithm to update the position of each individual in the ordinary subpopulation; For each individual after the location update, the validity of the track is verified, individuals that violate the constraints are repaired, and the repaired individuals are merged into the current population to obtain a new population; The fitness of each individual in the new population is calculated based on the objective function. The new population is then divided into a new elite subpopulation and a new ordinary subpopulation based on the fitness. The positions are updated again until the iteration termination condition is met. The individual with the best fitness in the latest population is then obtained as the optimal trajectory scheme.

5. The multi-UAV trajectory planning method according to claim 4, characterized in that, Updating the position of each individual in the elite subpopulation using the improved whale optimization algorithm includes: Update the position of each individual in the elite subgroup based on the selection probability, choosing either the prey-encircling behavior or the spiral search behavior. The formula for updating the position of each individual in the elite subgroup by selecting the prey-surrounding behavior is: ； in, , They represent the first , The position vector of an individual at the next iteration. Indicates the first The position vector of the optimal individual at the nth iteration, i.e., the position vector of the i-th iteration. The position vector of the individual with the best fitness in the population at the next iteration. and Both are coefficient vectors. , , for Random vectors within the range The parameter decreases linearly from 2 to 0 with the number of iterations; The formula for updating the position of each individual in the elite subgroup using the spiral search behavior is: ； in, The constant for the spiral shape. for A random number within a given range.

6. The multi-UAV trajectory planning method according to claim 4, characterized in that, Updating the position of each individual in a normal subpopulation using a genetic algorithm mechanism includes: A candidate pool is formed by randomly selecting several individuals from the ordinary subgroup, and the individual with the best fitness is selected from the candidate pool as the parent generation. Two random position indices are selected on the parent's gene coding sequence as crossover points. Gene coding segments between the crossover points are swapped to generate offspring. By applying a Gaussian-based random perturbation to a portion of the offspring's genes with an adaptively adjusted mutation rate, individuals with updated positions are obtained.

7. The multi-UAV trajectory planning method according to claim 4, characterized in that, The formula for calculating the population diversity index is: ； in, Indicators representing population diversity Indicates the size of the population. , They represent the first in the population. , The position vectors of each individual; When the diversity index of the population is less than the index threshold or the current iteration process is in the forced exploration phase, the position of each individual in the ordinary subpopulation is updated using the genetic algorithm mechanism; otherwise, the improved whale optimization algorithm is switched to update the position of each individual in the ordinary subpopulation.

8. The multi-UAV trajectory planning method according to claim 4, characterized in that, Repairing individuals who violate constraints includes: The collision penalty term and the smoothness penalty term are integrated into the objective function to form a comprehensive optimization objective function: ； in, This indicates the total length of the drone's flight path. This indicates the penalty for a drone's flight path colliding with an obstacle. This indicates a penalty for the drone's flight path turning angle not meeting the smoothness requirement. Indicates the first [unmanned aerial vehicle] flight path The cost of threats to each waypoint This represents the weighting factor used to balance the drone's flight path length with threat avoidance requirements. This indicates the total number of waypoints on the drone's flight path; A heuristic method of regenerating waypoints along the direction from the start to the end is used to repair individuals that violate the constraints and generate new drone waypoints. The new drone tracks are sparsified by removing track points whose distance is less than a distance threshold.

9. A multi-UAV trajectory planning system, characterized in that, include: The threat field construction module is used to build a threat field model based on the distribution of threat sources in the mission environment and quantify the threat cost to each waypoint on the UAV's flight path. The objective function construction module is used to minimize the weighted sum of the total length of the UAV trajectory and the total threat cost as the objective function, and to set flight constraints including the maximum turning angle constraint and the maximum climb angle constraint. The solution module is used to solve the objective function based on flight constraints and using an improved whale optimization algorithm that incorporates a genetic algorithm mechanism, so as to obtain a collaboratively optimized trajectory that minimizes the arrival time difference of multiple UAVs.

10. A computer device, characterized in that, include: Storage medium: used to store computer programs; Processor: for executing the computer program to implement the multi-UAV trajectory planning method according to any one of claims 1 to 8.

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