Multi-unmanned aerial vehicle cooperative path planning method based on improved multi-target Swane algorithm

Abstract

The invention provides a multi-unmanned aerial vehicle cooperative path planning method based on an improved multi-target Swane algorithm. The multi-unmanned aerial vehicle cooperative path planning method comprises the following steps: constructing a three-dimensional terrain scene containing obstacles; constructing a multi-objective optimization function; the method comprises the following steps: providing an improved Schwander algorithm, improving population initialization quality through quasi-opposition learning, dynamically regulating and controlling switching between an exploration stage and a development stage by utilizing reinforcement learning Qlearning, implementing grouping difference position updating according to individual fitness in the exploration stage, and implementing grouping difference position updating according to a sine learning mechanism and a self-adaptive mutation mechanism based on von Mises distribution in the development stage. The global search and local development capabilities are balanced; optimizing the path point position of the unmanned aerial vehicle based on an improved South goose algorithm, and obtaining a Pareto optimal solution set; and finally, selecting a final cooperative flight path from the solution set according to the actual task preference and the priority. According to the method, the problems that a traditional algorithm is prone to falling into local optimum under complex constraints and the convergence speed is low are effectively solved, and a safe, smooth and efficient flight path meeting the cooperation requirement can be planned for a multi-unmanned-aerial-vehicle system.

Description

Technical Field

[0001] This invention belongs to the field of UAV path planning technology, and particularly relates to a multi-UAV cooperative path planning method based on an improved multi-objective snow goose algorithm. Background Technology

[0002] Multi-UAV cooperative path planning, as a multi-constraint optimization problem in complex environments, requires achieving global optimum for multiple UAV paths under constraints such as path length, energy consumption, and collision avoidance. With the large-scale application of UAVs in dynamic scenarios such as disaster relief and swarm logistics, traditional single-objective optimization algorithms are prone to getting trapped in local optima due to their difficulty in balancing the conflicts between multiple objectives, leading to planning failure. To address this problem, researchers have proposed multi-objective optimization algorithms, such as Multi-Objective Particle Swarm Optimization (MOPSO) and Non-Dominated Sorting Genetic Algorithm, which introduce Pareto optimal solution sets to weigh multiple objectives. For complex 3D spatial path planning problems, heuristic algorithms such as Multi-Objective Gray Wolf Optimization (MOGWO) and Multi-Objective Whale Optimization (MOWOA) have also demonstrated excellent global search performance. However, with the increasing complexity of real-world problems and the limitations of existing methods due to the specificity of scenarios, there is still no universally applicable solution, driving the continuous exploration of new optimization algorithms.

[0003] In 2024, Tian et al. proposed the Snow Geese algorithm (SGA), which can be found in Tian, ​​AQ, Liu, FF, & Lv, HX (2024). Snow Geese Algorithm: A novel migration-inspired meta-heuristic algorithm for constrained engineering optimization problems. Applied Mathematical Modelling, 126, 327-347. It outperforms classic algorithms such as particle swarm optimization and differential evolution in both solution accuracy and convergence speed for benchmark optimization problems, and has been successfully applied to practical engineering problems such as pipe column design, piston rod optimization, reinforced concrete beam design, and vehicle side-impact design. However, when applied to multi-UAV cooperative path planning, the Snow Geese algorithm exhibits a significant imbalance between its global exploration capability and local exploitation capability. This imbalance leads to a rapid shrinking of the effective search space, premature convergence, and the estimation of motion parameters getting trapped in local optima. Summary of the Invention

[0004] The purpose of this invention is to solve the problems of defects in existing obstacle avoidance technology, lack of dynamic prompts of collision risk direction in the obstacle avoidance system interface, and complex processing of multi-path visual data.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: A multi-UAV cooperative path planning method based on an improved multi-objective snow goose algorithm includes the following steps: S1. Construct a 3D terrain scene containing obstacles using a digital elevation model; S2. Construct a constrained multi-objective optimization function for UAV collaborative path planning; the constrained multi-objective optimization function includes a fitness function and constraints. The fitness function includes path length, flight altitude, no-fly zones, and terrain threats; the constraints include path smoothness and multi-UAV collaborative constraints. S3. Construct an improved multi-objective snow goose algorithm RL-MOSGA, use this algorithm to optimize the path point positions of multiple UAVs, and obtain the Pareto optimal solution set according to the constrained multi-objective optimization function; S4. Based on actual preferences and priorities, obtain the final path from the Pareto optimal solution set.

[0006] Furthermore, the UAV path for the 3D terrain scene in step S1 is as follows: For a given task, each drone starts flying from a different starting point S = (x0, y0, z0) and ends at a destination E = (x0, y0, z0). e y e z e The drone can reach its destination; between these two points, the drone can take n positions (x, y) in space during its flight. n , y n , z n ) as path points; every two adjacent connection points (x k , y k , z k ) and (x k+1 , y k+1 , z k+1 This constitutes a path segment L. i After the flight ends, the path taken by a single drone is as follows: All drone waypoints are encoded as a single d-dimensional decision vector.

[0007] Furthermore, the fitness function and constraints in step S2 are as follows: (1) Fitness function: The path length fitness function for a UAV is defined as follows: In the formula, Let be the coordinates of the k-th path point in the UAV path, and let be the number of path points. The flight altitude constraint for the drone's path is defined as: In the formula: Let p be the height of the path point. Let k be the height at path point k. H represents the altitude cost of all waypoints for the drone, and H represents the altitude cost of a single waypoint. The fitness function for a no-fly zone for drones is defined as follows: In the formula: o represents the number of no-fly zones. Let be the distances between the center of the i-th no-fly zone and the starting, 1 / 4, 1 / 2, 3 / 4, and ending positions of the path segment, respectively, and let be the radius of the no-fly zone. The fitness function for a drone to be threatened by terrain is defined as: If the pathpoint does not collide with the terrain, the constraint cost is 0; otherwise, the cost is... ; (2) The constraints include: The pitch and yaw angle constraints for the UAV are as follows: In the formula: and These are the heading angle and the pitch angle, respectively. Maximum heading angle, Maximum pitch angle; The fitness function for path smoothing is defined as follows: In the formula: and These represent the changes in heading angle and pitch angle between the current path point k and the next path point k+1, respectively. Cooperative Constraints: In multi-UAV cooperative path planning, spatial constraints require that the distance between each UAV be within a safe range; assuming... Let UAV be the position of UAV at time t. Then the distance between UAVs should satisfy: In the formula, For a safe distance.

[0008] Furthermore, the constrained multi-objective optimization function is as follows: The total path cost for a single UAV is: In the formula: w1, w2, w3, and w4 are the weighting coefficients for no-fly zone, path length, altitude, and path smoothness, respectively; We construct a decomposition-based constrained multi-objective optimization function by weighted summing of the path costs of each UAV, which serves as the optimization objective function for a single UAV. Where x is a d-dimensional decision vector that encodes the path points of all UAVs; The decision space refers to the range of values ​​for the coordinates of the control path points. for DN The objective function vector of each objective contains DN The optimization objective function for a single drone; These are constraints.

[0009] Furthermore, the improved Snow Goose Algorithm RL-MOSGA in step S3 includes the following steps: (1) Quasi-oppositional learning (QOBL) is used for population initialization; (2) Use reinforcement learning Q-learning to dynamically adjust the switching parameters between the exploration and development phases; (3) During the exploration phase, the snow geese were divided into the first fifth, the last fifth and the middle group according to their individual fitness, and different position update strategies were adopted for each group. (4) In the development phase, a two-stage evolutionary strategy consisting of a sinusoidal learning mechanism based on von Mises distribution and an adaptive mutation mechanism is introduced.

[0010] Furthermore, quasi-oppositional learning is used for population initialization: Quasi-oppositional learning uses stochastic iterators to generate candidate solutions; it calculates the average solution based on the boundary conditions and finds the opposite solution: (14) (15) in It was exported from OBL. The j-th column of the candidate solution of dimension; rand () represents a variable randomly generated between [0,1]; The lower realm The upper boundary; Candidate solutions generated by quasi-oppositional learning.

[0011] Furthermore, reinforcement learning Q-learning specifically includes: Construct a Q-table, which consists of states and actions. The current stage is taken as the state, and the transition between stages is taken as the action. The value corresponding to each state and action in the table is the q-value. Each individual snow goose selects its action by determining the largest q value in its own Q-table; and updates the q value in the Q-table according to the immediate reinforcement reward mechanism: in, This is the current state. The next state is... This is the current action. It is a discount parameter. It's the learning rate. It is execution exist Instant enhancement rewards obtained at that time It is in state Next action The estimated q value at that time; Learning rate The calculation formula is as follows: In the formula, express initial value, express The final value, t is defined as the current iteration number. Defined as the maximum number of iterations; The instant enhancement reward mechanism is as follows: (19) Where t represents the t-th stage; ω is the adjustment factor; Let be the optimal fitness value at stage t; This represents the optimal fitness value at stage t+1.

[0012] Furthermore, the exploration phase specifically includes: The formula for the dynamic change of velocity is as follows: in , The first Subsequent The speed value of the next iteration; This is the current iteration metric, representing the algorithm's progress to the current stage; M is the predefined total number of iterations for the algorithm. The weighting factors in the speed update formula; acceleration parameters for: In the formula, This represents the optimal position in the it-th iteration. Let i be the position of the i-th individual snow goose in the it-th iteration. Let be the velocity of the i-th individual snow goose in the it-th iteration; In a V-formation flock of geese, the update formula for the top fifth of snow geese in terms of fitness values ​​is as follows: In the formula, For the first At the +1st iteration, the... The location of each individual snow goose; For the remaining fifth of snow geese, including the weaker, unwell, or incapacitated individuals, the updated formula is as follows: In the formula, Indicates the position of the central particle within the group; For the remaining snow geese in the population, the position update formula is: b, d, and e are weighting coefficients. Indicates the position of the central particle within the group. The fitness value associated with the central particle. ; This indicates that it corresponds to a candidate solution.

[0013] Furthermore, the sinusoidal learning mechanism based on the von Mises distribution is as follows: in , The first and the In the nth iteration The location of an individual snow goose For the first The optimal position in the next iteration Indicates the first During the nth iteration The learning phase factor of an individual snow goose. Obtained through VMD preferred direction ,parameter heading angle for: ; The adaptive mutation mechanism is as follows: Where TDR represents the travel distance rate, This indicates the (it + 1)th iteration. The adaptive factor for each individual.

[0014] Furthermore, the improved position update formula for the development phase after the two-stage evolution strategy is as follows: In the formula, A random number between 0 and 1.

[0015] The beneficial effects of this invention are as follows: 1. Drone path planning has multiple constraints and complex optimization parameters. Traditional algorithms are difficult to converge in drone path planning and are prone to getting trapped in local optima, thus failing to optimize the drone's flight path quickly and accurately.

[0016] 2. This paper proposes a multi-objective Snow Goose algorithm based on improved reinforcement learning. Through quasi-oppositional learning and the generation mechanism of quasi-oppositional points, it strategically generates higher-quality and more diverse candidate solutions during the initialization process, thereby improving the overall performance of the optimization algorithm. This ensures a wider and more uniform distribution of solutions in the search space, preventing the population from prematurely concentrating in a small area and laying a better foundation for global search. Q-learning algorithms are mainly used to adjust parameters in optimization algorithms to improve the optimization effect. Q-learning algorithms in reinforcement learning can learn through continuous interaction with the environment and make the most advantageous behavior based on the state. Therefore, the idea of ​​Q-learning algorithm is applied to dynamically adjust the optimization strategy of SGA. Dynamically selecting search strategies for different stages of the problem ensures maximum benefit at each stage, effectively balancing and utilizing the exploration and development stages. Furthermore, the two-stage evolutionary strategy (TSE) includes a sinusoidal learning mechanism (SLM) based on the von Mises distribution for dynamic learning from the optimal solution; simultaneously, an adaptive mutation mechanism (AMM) is used to avoid local optima, effectively accelerating the algorithm's convergence speed while avoiding getting trapped in local optima. Attached Figure Description

[0017] Figure 1 This is a flowchart of the improved Snow Goose algorithm provided by the present invention; Figure 2This is a flowchart of the UAV collaborative path planning provided by the present invention; Figure 3 This is a 3D diagram of the collaborative path planning results of two UAVs in a simple scenario provided by the present invention; Figure 4 This is a two-dimensional top view of the collaborative path planning results of two UAVs in a simple scenario provided by the present invention; Figure 5 This is a 3D diagram of the collaborative path planning results of two UAVs in a complex scenario provided by the present invention; Figure 6 This is a two-dimensional top view of the collaborative path planning results of two UAVs in a complex scenario provided by the present invention; Figure 7 This is a Pareto front distribution map in a simple scenario provided by the present invention; Figure 8 This is a Pareto front distribution map for complex scenarios provided by the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0019] The application principle of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0020] Please refer to Figure 1 A multi-UAV cooperative path planning method based on an improved multi-objective snow goose algorithm includes the following steps: S1. Construct a 3D terrain scene containing obstacles using a DEM.

[0021] Spatial Model: The scenarios used for evaluation are based on real digital elevation model (DEM) maps derived from LiDAR sensors. Two baseline scenarios were generated by expanding the topographic structure of Christmas Island, Australia, using a selected region. Mathematically, the environment map takes the following form:

[0022] in , and These represent the mapping limits of the DEM on the X, Y, and Z axes, respectively. In reality, the environment is far more complex, containing numerous threats and obstacles. Both pose a risk to the physical safety of the drone. Therefore, the drone must avoid colliding with them and entering their areas. For a given mission, each drone starts from a different point in time. Begin flight, at the destination Reaching the destination. Between the starting point and the destination, the drone can take n positions in space during its flight. As path points. Each pair of adjacent connection points. and Form a path segment After the flight, the path taken by a single drone is as follows:

[0023] In addition, all drone path points are encoded into a single d-dimensional decision vector (dimensional d = 3·DN·CN, where DN is the number of drones, CN is the number of path points per drone, and 3 represents the corresponding x, y, z three-dimensional coordinates).

[0024] In this application, a terrain scene is constructed to simulate a real scene. In the simulation experiments in steps S3 and S4, the output UAV flight path is based on the constructed terrain scene, and some parameters of the objective function in S2 (terrain height, no-fly zone) are set from the terrain scene.

[0025] S2. Construct a constrained multi-objective optimization function for UAV cooperative path planning and obtain the fitness value.

[0026] To plan a high-quality path for unmanned aerial vehicles (UAVs), it is necessary to establish a suitable fitness function and consider various flight constraints in static three-dimensional global path planning. This results in the construction of a constrained multi-objective optimization function for UAV collaborative path planning, which mainly consists of two parts: the first part is the fitness function; the other part consists of various constraints, such as yaw angle, pitch angle, and safety distance.

[0027] S201. Constructing the fitness function The fitness functions include fitness functions for path length, flight altitude, no-fly zones, and terrain threat. Details are as follows:

[0028] (1) Path length and flight altitude: The path length consists of a series of waypoints. The path length fitness function of a UAV is defined as: (1) In the formula: Let be the coordinates of the k-th path point in the UAV path, and be the number of path points.

[0029] When traversing a battlefield environment, UAVs can utilize terrain as cover to reduce the probability of being detected by air defense systems. Integrating flight altitude causes UAVs to tend towards low-altitude routes; the flight altitude constraint for a UAV's path is defined as follows: (2) (3) In the formula: Let p be the height of the path point. Let k be the height at path point k. H represents the altitude cost of all waypoints for the drone, while H represents the altitude cost of a single waypoint.

[0030] (2) Threats from no-fly zones and terrain In a battlefield environment, a no-fly zone can be represented as an area covered by radar, missiles, artillery, etc. Cylinders of varying radii are used to represent no-fly zones, and the fitness function for a UAV no-fly zone is defined as follows: (4) In the formula: The number of no-fly zones, Let be the distances between the center of the i-th no-fly zone and the starting, quarter, half, three-quarter, and ending positions of the path segment, respectively, and let be the radius of the no-fly zone. The cost of the UAV traversing the path segment is calculated using five reference points on the segment, including the starting, quarter, half, three-quarter, and ending positions.

[0031] The cost of a UAV colliding with terrain is extremely high. The fitness function for a UAV threatened by terrain is defined as follows:

[0032] (5) (6) If the pathpoint does not collide with the terrain, the constraint cost is 0; otherwise, the cost is... In this article The value is 10 4 .

[0033] S202, Constructing Constraints The constraints include path smoothing and collaborative constraints, as detailed below: (1) Path smoothing Due to the inherent limitations of UAV performance, pitch and yaw angles need to be restricted. When the UAV's flight attitude changes, its energy consumption increases significantly. To reduce energy loss, the pitch and yaw angles of the UAV are constrained as follows:

[0034] (7) (8) In the formula: and These are the heading angle and the pitch angle, respectively. Maximum heading angle, The maximum pitch angle is given. The fitness function for path smoothing is defined as follows:

[0035] (9) In the formula: and These represent the changes in heading and pitch angles between the current path point k and the next path point k+1, respectively. Taking the heading angle as an example, the angle change between path point k and path point k+1 is... ,like Figure 2 As shown, and The smaller the change range, the smaller the path change range, the higher the smoothness of the planned path, and the smaller the fluctuation.

[0036] (2) Collaborative constraints In multi-UAV cooperative path planning, spatial constraints require that the distance between each UAV be within a safe range. Assume... Let UAV be the position of UAV at time t. Then the distance between UAVs should satisfy:

[0037] (10) In the formula, For a safe distance.

[0038] Multi-UAV collaboration means that the time required for each UAV to reach the target point must meet certain conditions. Assuming that each UAV arrives at the target point simultaneously, this means that after considering the speed variation range and flight distance of each UAV, each UAV can arrive simultaneously. Let's assume the i-th UAV... i The speed is The path length is L i The jth UAV j The speed is The path length is L j Then UAV i and UAV j The arrival time can be calculated as follows:

[0039] (11) This indicates that multi-UAV collaboration can only be achieved when the arrival time intervals of each UAV overlap.

[0040] S203, The total path cost for a single UAV is: (12) In the formula, w1, w2, w3, and w4 are the weighting coefficients for the no-fly zone, path length, altitude, and path smoothness, respectively. The weighted summation of the path costs for each UAV is used to construct a decomposition-based constrained multi-objective optimization function, which serves as the optimization objective function for a single UAV.

[0041] The above "environment-path-objective-constraints" are integrated into a unified constrained multi-objective optimization problem model, in the following form: (13) Where x is a d-dimensional decision vector that encodes the path points of all UAVs (d=3·DN·cn, where 3 is the x / y / z three-dimensional vector, DN is the number of UAVs, and cn is the number of control points for each UAV). The decision space refers to the range of values ​​for the coordinates of the control path points. for DN The objective function vector of each objective contains DN The objective function for optimizing a single drone. The constraints are that all UAV paths must satisfy the time and space constraints of formulas (10) and (11). The fitness value is determined by... Obtain.

[0042] S3. Construct the improved Snow Goose Algorithm (RL-MOSGA Algorithm) and obtain the optimal path.

[0043] The improved Xueyan algorithm (RL-MOSGA algorithm) includes using quasi-oppositional learning (QOBL) for population initialization, replacing the behavioral transition factor in the Xueyan algorithm with reinforcement learning (Q-learning), and adopting a two-stage evolutionary strategy based on a sinusoidal learning mechanism and an adaptive mutation mechanism based on the von Mises distribution. This accelerates the convergence speed of the algorithm while ensuring the diversity of the population.

[0044] S301. Constructing an improved Snow Goose algorithm (RL-MOSGA algorithm) (1) Initialization phase: The initialization phase of the standard Snow Goose algorithm is crucial for establishing a diverse and effective initial population. Each initial candidate solution (i.e., the position of a Snow Goose individual) is randomly generated within the search area defined by the lower bound LB and the upper bound UB, resulting in high randomness and insufficient solution space coverage. To improve diversity, the improved Snow Goose algorithm RL-MOSGA uses Quasi-Opposite Learning (QOBL) for population initialization. In QOBL, in addition to finding the opposite solution (i.e., the opposite part of the search domain) through back learning, the average solution is further calculated based on the boundary to obtain the quasi-opposite point between the current solution and the opposite solution. This allows for the exploration of more potential useful areas in the search space, which is closer to the global optimum than random solutions (random solutions are solutions randomly generated within the search area defined by the lower bound LB and the upper bound UB).

[0045] (14) (14) Among them, 𝑥 𝑗 OBL It is the j-th column of the candidate solution of the 𝑗th dimension derived from OBL. rand () represents a variable that is randomly generated between [0,1]. The lower realm The upper bound is determined by evaluating 𝑥 𝑗 OBL The fitness value is used to include the solution with the best fitness in the initial population; Candidate solutions are generated for quasi-oppositional learning. This method ensures that the initial population is diverse and uniformly distributed, thereby enhancing the algorithm's exploration capabilities.

[0046] (2) Stage switching: The standard snow goose algorithm (the unmodified snow goose algorithm) uses the heading angle of the snow goose migration process. This indicates the transition of the snow goose population from the exploration phase to the development phase. When the value is ≤π, the algorithm selects the exploration phase; otherwise, it enters the development phase. However, because the Xueyan algorithm only switches between the exploration and development phases based on the current iteration count, it cannot dynamically adjust its strategy based on real-time feedback such as the quality of the current solution, population diversity, or convergence progress. This can lead to prematurely entering the development phase before fully exploring the solution space, resulting in getting trapped in local optima; or it may continue inefficient exploration even after finding a high-quality region, wasting computational resources. This reduces the algorithm's robustness, makes its performance unstable, and makes it difficult to balance exploration and development. Furthermore, all individuals are forced to perform the same behavior, without considering the characteristics of each individual, uniformly applying exploration or development tasks to the entire population. Therefore, reinforcement learning Q-learning is used to optimize the hyperparameters used to dynamically control the transition between the two phases in the Xueyan algorithm.

[0047] In RL-MOSGA, individual snow geese are treated as training agents in reinforcement learning, and the search space is considered an interactive environment. The core idea of ​​Q-learning is to construct a Q-table, which consists of states and actions. The current stage is considered the state, and stage transitions are considered actions. Each state and action in the table corresponds to a q-value. The snow goose individual selects the action to execute (i.e., stage transition) by determining the maximum q-value in its own Q-table. Based on accumulated performance, the snow goose individual adaptively switches stages (states). The q-value in the Q-table is updated according to an immediate reinforcement reward mechanism. If the action leads to better performance, a positive reward is given; otherwise, a negative reward is given as a penalty, thus updating the q-value in the Q-table. The calculation formula is as follows:

[0048] (15) in, This is the current state. The next state is... This is the current action. It is a discount parameter. It's the learning rate. It is execution exist Instant enhancement rewards obtained at that time It is in state Next action The estimated q value at that time.

[0049] In the Q-learning algorithm, when the learning rate As the q-value approaches 1, newly acquired information becomes more valuable for updating the q-value in the Q-table. When given a smaller q-value... When a value is reached, existing information is not ignored. To maximize learning from the search space, a higher value can be adaptively reduced during iteration. The calculation formula is as follows:

[0050] (16) In the formula, express initial value, express The final value, t is defined as the current iteration number. Defined as the maximum number of iterations.

[0051] The instant enhancement reward mechanism is as follows: (17) Where t represents the t-th stage; For adjustment factors; Let be the optimal fitness value at stage t; This represents the optimal fitness value at stage t+1.

[0052] (3) Exploration Phase: Throughout the migration, the energy level of the snow goose population continuously changes due to factors such as aerodynamic drag and metabolic energy consumption. In RL-MOSGA, the dynamic change formula for velocity is as follows:

[0053] (18) in , The first Subsequent The speed value of the next iteration; The current iteration metric represents the algorithm's progress at the current stage; parameters The impact of the current velocity of the snow goose population on its offspring was quantified in the RL-MOSGA algorithm. The determination was based on energy dynamics observed during the migratory flight of snow geese. Initially, the collective energy showed a marginal increase; however, as the flight time increased, The value shows a gradual downward trend.

[0054] (19) In the formula, M is the total number of iterations predefined by the algorithm. The weighting factors in the speed update formula.

[0055] Velocity changes are further affected by acceleration parameters The impact of aerodynamics. In the RL-MOSGA algorithm, aerodynamic considerations are integrated into... The formula consists of three distinct components: the first reflects the optimal position within the entire population, the second corresponds to the current position of an individual snow goose, and the third takes into account the effects of aerodynamic drag.

[0056] (20) In the formula, This represents the optimal position in the it-th iteration. Let be the position of the i-th individual in the it-th iteration. Let be the velocity of the i-th individual in the it-th iteration.

[0057] In the V-formation of a flock of geese, the spatial layout reflects a hierarchical structure based on the fitness and survival conditions of individual snow geese. For the top fifth of snow goose individuals exhibiting the highest fitness values, the update formula is as follows: (twenty one) In the formula, For the first At the +1st iteration, the... The location of an individual snow goose.

[0058] For the remaining fifth of snow geese, including the weaker, unwell, or incapacitated individuals, the updated formula is as follows: (twenty two) In the formula, This indicates the position of the central particle within the group.

[0059] For the remaining snow geese in the population, position updates are performed using formula (22). These different equations enable the adjustment of snow geese positions based on individual fitness levels, ensuring that the optimization process can adapt to snow geese with different abilities and conditions within the population.

[0060] (twenty three) (twenty four) (25) (26) (27) Different types of snow geese are updated using different formulas to modify their positions. It is worth noting that each component requires a weighting coefficient to represent its contribution to the overall formula. In RL-MOSGA, the weighting coefficients are b, d, and e. The values ​​of variables b, d, and e correspond to empirical values ​​obtained from experiments. This indicates the position of the central particle within the group, while The fitness value associated with the central particle. . This indicates a candidate solution, which represents the position of the lowest-ranking snow goose after group classification.

[0061] (4) Development stage: In the later iterations of the SGA algorithm, all individual snow geese will be located in the optimal positions around them and then fixated on the position of the current optimal solution, which can easily get stuck in local optima. In order to improve the global search capability of the algorithm in the later iterations, this paper adopts a two-stage evolutionary strategy (TSE) to overcome the above problems.

[0062] a. Sinusoidal learning mechanism based on von Mises distribution To accelerate convergence, an optimal learning scheme is advantageous. Such a scheme not only supports efficient evolutionary search for dominant solutions but also maintains population diversity throughout the evolutionary process. To meet this requirement, a sinusoidal learning mechanism based on the von Mises distribution (SLM) is adopted. SLM is applied to the development phase. In this SLM framework, each individual snow goose is designed to learn from the optimal solution through a sinusoidal function. The angle in this sinusoidal function... Derived from VMD, and based on during the evolution process Dynamic adjustments are made. The proposed mechanism can be represented as:

[0063] (28) in , The first and the In the nth iteration The location of an individual snow goose For the first The optimal position in the next iteration Indicates the first During the nth iteration The learning phase factor of an individual snow goose. Obtained through VMD preferred direction ,parameter heading angle for: (29) b. Adaptive mutation mechanism During the iteration process, population diversity decreases. To obtain the global optimum of the SGA (Snow Goose Algorithm) and overcome local optima, this mutation mechanism helps increase the population diversity of the SGA. In the SGA, the excessive randomness of Brownian motion can interfere with searching the region near the optimal solution. Its random step size lacks directional guidance, which may cause the population to wander around the optimal solution or even move far away from it, thus significantly slowing down the convergence speed. Here, an adaptive mutation mechanism (AMM) is introduced to solve this problem, which can be expressed as:

[0064] (30) Here, TDR represents the travel distance rate, which can be adaptively adjusted and is related to the number of iterations. This indicates the (it + 1)th iteration. The adaptive factor for each individual variable can adaptively adjust the mutation scale, thereby balancing the algorithm's exploration and search capabilities. TDR and The value of can be calculated using the following formula:

[0065] (31) (32) To prevent the divisor from being zero, Set as , Let be a constant, set to 0.3.

[0066] Based on the above, the improved position update formula for the development phase of the two-stage evolutionary strategy is as follows: (33) In the formula, A random number between 0 and 1.

[0067] S302. Improve the Xueyan algorithm to optimize the path point positions of multiple UAVs, and obtain the Pareto optimal solution set according to the constrained multi-objective optimization function.

[0068] The path points of the UAVs in S1 are used as decision vectors (to encode the path points of all UAVs in S203), and each path set ( The candidate solution is the set of all UAV pathpoints. The evaluation index is the objective function of formula (12). The improved Xueyan algorithm is used to iteratively optimize the candidate solution so that the objective function value of the candidate solution is equal to that of formula (13). The smaller the value, the better the optimization effect. All non-dominated solutions will be stored in the archive. The iteration will terminate after a certain number of iterations or when further optimization is not possible. The final output set of optimal solutions is the Pareto front, and each solution is the Pareto optimal solution.

[0069] S4. Based on actual preferences and priorities, select the most suitable solution from the Pareto optimal solution and output the generated path.

[0070] The selection can be based on the importance of the drone; if a drone with high priority exists, its suitability should be chosen. middle The lowest Pareto optimal solution is selected; if no higher priority solution is available, a random solution is chosen.

[0071] Example 2: Simulation experiments using RL-MOSGA in simple and complex environments were conducted to demonstrate that RL-MOSGA effectively improves the efficiency and robustness of collaborative tasks in both simple and complex environments. RL-MOSGA population size: 100 (50 individuals per drone); maximum iterations: 50; external archive size: 100; grid size: 20; objective function weights: path length (0.3), safety (0.6), smoothness (0.1). Two types of 3D flight environments were designed: simple and complex. Threat regions were represented by cylinders. The simple environment contained 3 threat regions; the complex environment contained 6 threat regions. Drone task settings: Drone A had a start point (400, 100, 150) and an end point (1000, 400, 150); Drone B had a start point (200, 300, 150) and an end point (800, 700, 150).

[0072] Experimental results show that the multi-objective optimization function constructed in this application can effectively plan flight paths for multi-UAV systems that combine high efficiency, safety, and cooperation. Figures 3 to 6 It is evident that the generated cooperative flight paths strictly adhere to the UAV's maneuverability constraints. All paths corresponding to non-dominated solutions achieve collision-free obstacle avoidance and precise flight altitude control, and the path point spacing meets the requirements of actual flight missions. Furthermore, Figure 7 and Figure 8The Pareto front distributions of the RL-MOSGA algorithm in simple and complex environments are presented respectively. The results show that the algorithm can stably generate high-quality solution sets in different scenarios without premature convergence. Thanks to its introduced grid partitioning strategy and external archiving mechanism, the algorithm can quickly approximate the real Pareto front within 50 iterations, verifying the strong robustness and excellent multi-objective collaborative optimization capabilities of RL-MOSGA in high-dimensional complex path planning scenarios.

[0073] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-UAV cooperative path planning method based on an improved multi-objective snow goose algorithm, characterized in that, Includes the following steps: S1. Construct a 3D terrain scene containing obstacles using a digital elevation model; S2. Construct a constrained multi-objective optimization function for UAV collaborative path planning; the constrained multi-objective optimization function includes a fitness function and constraints. The fitness function includes path length, flight altitude, no-fly zones, and terrain threats; the constraints include path smoothness and multi-UAV collaborative constraints. S3. Construct an improved multi-objective snow goose algorithm RL-MOSGA, use this algorithm to optimize the path point positions of multiple UAVs, and obtain the Pareto optimal solution set according to the constrained multi-objective optimization function; S4. Based on actual preferences and priorities, obtain the final path from the Pareto optimal solution set.

2. The multi-UAV cooperative path planning method based on the improved multi-objective snow goose algorithm according to claim 1, characterized in that, The UAV path for the 3D terrain scene in step S1 is as follows: For a given task, each drone starts flying from a different starting point S = (x0, y0, z0) and ends at a destination E = (x0, y0, z0). e y e z e The drone can reach its destination; between these two points, the drone can take n positions (x, y) in space during its flight. n , y n , z n ) as path points; every two adjacent connection points (x k , y k , z k ) and (x k+1 , y k+1 , z k+1 This constitutes a path segment L. i After the flight, the path taken by a single drone is as follows: All drone waypoints are encoded as a single d-dimensional decision vector.

3. The multi-UAV cooperative path planning method based on the improved multi-objective snow goose algorithm according to claim 1, characterized in that, The fitness function and constraints in step S2 are as follows: (1) Fitness function: The path length fitness function for a drone is defined as follows: In the formula, Let be the coordinates of the k-th path point in the UAV path, and let be the number of path points. The flight altitude constraint for the drone's path is defined as: In the formula: Let p be the height of the path point. Let k be the height at path point k. H represents the altitude cost of all waypoints for the drone, and H represents the altitude cost of a single waypoint. The fitness function for a no-fly zone for drones is defined as follows: In the formula: o represents the number of no-fly zones. Let be the distances between the center of the i-th no-fly zone and the starting, 1 / 4, 1 / 2, 3 / 4, and ending positions of the path segment, respectively, and let be the radius of the no-fly zone. The fitness function for a drone to be threatened by terrain is defined as: If the pathpoint does not collide with the terrain, the constraint cost is 0; otherwise, the cost is... ; (2) The constraints include: The pitch and yaw angle constraints for the UAV are as follows: In the formula: and These are the heading angle and the pitch angle, respectively. Maximum heading angle, Maximum pitch angle; The fitness function for path smoothing is defined as follows: In the formula: and These represent the changes in heading angle and pitch angle between the current path point k and the next path point k+1, respectively. Cooperative Constraints: In multi-UAV cooperative path planning, spatial constraints require that the distance between each UAV be within a safe range; assuming... Let UAV be the position of UAV at time t. Then the distance between UAVs should satisfy: In the formula, For a safe distance.

4. The multi-UAV cooperative path planning method based on the improved multi-objective snow goose algorithm according to claim 3, characterized in that, The specific constrained multi-objective optimization function is as follows: The total path cost for a single UAV is: In the formula: w1, w2, w3, and w4 are the weighting coefficients for no-fly zone, path length, altitude, and path smoothness, respectively; We construct a decomposition-based constrained multi-objective optimization function by weighted summing of the path costs of each UAV, which serves as the optimization objective function for a single UAV. Where x is a d-dimensional decision vector that encodes the path points of all UAVs; The decision space refers to the range of values ​​for the coordinates of the control path points. for DN The objective function vector of each objective contains DN The optimization objective function for a single drone; These are constraints.

5. The multi-UAV cooperative path planning method based on the improved multi-objective snow goose algorithm according to claim 1, characterized in that, Step S3, the improved Snow Goose Algorithm RL-MOSGA, includes the following steps: (1) Quasi-oppositional learning (QOBL) is used for population initialization; (2) Use reinforcement learning Q-learning to dynamically adjust the switching parameters between the exploration and development phases; (3) During the exploration phase, the snow geese were divided into the first fifth, the last fifth and the middle group according to their individual fitness, and different position update strategies were adopted for each group. (4) In the development phase, a two-stage evolutionary strategy consisting of a sinusoidal learning mechanism based on von Mises distribution and an adaptive mutation mechanism is introduced.

6. The multi-UAV cooperative path planning method based on the improved multi-objective snow goose algorithm according to claim 5, characterized in that, Quasi-oppositional learning for population initialization: Quasi-oppositional learning uses stochastic iterators to generate candidate solutions; it calculates the average solution based on the boundary conditions and finds the opposite solution: (14) (15) in It was exported from OBL. The j-th column of the candidate solution of dimension; rand () represents a variable randomly generated between [0,1]; The lower realm The upper boundary; Candidate solutions generated by quasi-oppositional learning.

7. The multi-UAV cooperative path planning method based on the improved multi-objective snow goose algorithm according to claim 5, characterized in that, Q-learning in reinforcement learning specifically refers to: Construct a Q-table, which consists of states and actions. The current stage is taken as the state, and the transition between stages is taken as the action. The value corresponding to each state and action in the table is the q-value. Each individual snow goose selects the action to perform by determining the largest q value in its own Q table; And update the q value in the Q table according to the real-time enhancement reward mechanism: in, This is the current state. The next state is... This is the current action. It is a discount parameter. It's the learning rate. It is execution exist Instant enhancement rewards obtained at that time It is in state Next action The estimated q value at that time; Learning rate The calculation formula is as follows: In the formula, express initial value, express The final value, t is defined as the current iteration number. Defined as the maximum number of iterations; The instant enhancement reward mechanism is as follows: (19) Where t represents the t-th stage; ω is the adjustment factor; Let be the optimal fitness value at stage t; This represents the optimal fitness value at stage t+1.

8. The multi-UAV cooperative path planning method based on the improved multi-objective snow goose algorithm according to claim 5, characterized in that, The exploration phase specifically includes: The formula for the dynamic change of velocity is as follows: in , The first Subsequent The speed value of the next iteration; This is the current iteration metric, representing the algorithm's progress to the current stage; M is the predefined total number of iterations for the algorithm. The weighting factors in the speed update formula; acceleration parameters for: In the formula, This represents the optimal position in the it-th iteration. Let be the position of the i-th individual snow goose in the it-th iteration. Let be the velocity of the i-th individual snow goose in the it-th iteration; In a V-formation flock of geese, the update formula for the top fifth of snow geese in terms of fitness values ​​is as follows: In the formula, For the first At the +1st iteration, the... The location of each individual snow goose; For the remaining fifth of snow geese, including the weaker, unwell, or incapacitated individuals, the updated formula is as follows: In the formula, Indicates the position of the central particle within the group; For the remaining snow geese in the population, the position update formula is: b, d, and e are weighting coefficients. Indicates the position of the central particle within the group. The fitness value 𝑖𝑡 associated with the central particle; This indicates that it corresponds to a candidate solution.

9. The multi-UAV cooperative path planning method based on the improved multi-objective snow goose algorithm according to claim 5, characterized in that, The sinusoidal learning mechanism based on the von Mises distribution is as follows: in , The first and the In the nth iteration The location of an individual snow goose For the first The optimal position in the next iteration Indicates the first During the nth iteration The learning phase factor of an individual snow goose. Obtained through VMD preferred direction ,parameter heading angle for: ; The adaptive mutation mechanism is as follows: Where TDR represents the travel distance rate, This indicates the (it + 1)th iteration. The adaptive factor for each individual.

10. The multi-UAV cooperative path planning method based on the improved multi-objective snow goose algorithm according to claim 9, characterized in that, The improved development phase position update formula after the two-stage evolution strategy is as follows: In the formula, A random number between 0 and 1.

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