An unmanned aerial vehicle path planning method based on an improved artificial native animal optimizer

Abstract

The application discloses an unmanned aerial vehicle path planning method based on an improved artificial native animal optimizer, and belongs to the technical field of unmanned aerial vehicle path planning, and comprises the following steps: constructing an artificial native animal optimizer population, encoding the position of each individual in the population into a spherical vector, and the spherical vector corresponds to a candidate flight path, which comprises three components of a flight section length, an elevation angle and an azimuth angle; driving the population to perform iterative optimization, in each iteration, the individual updates its spherical vector based on the foraging behavior, dormancy behavior or reproduction behavior of each component of its current spherical vector; decoding the updated spherical vector, evaluating the quality of the candidate flight path corresponding to the updated spherical vector by using a cost function, and updating the historical optimal spherical vector of the individual in the population and the global optimal spherical vector; decoding the final global optimal spherical vector to obtain an optimal flight path. The method can improve the convergence speed, path quality and motion feasibility of unmanned aerial vehicle path planning in a complex environment.

Description

Technical Field

[0001] This invention relates to a method for UAV path planning based on an improved artificial protozoan optimizer, belonging to the field of UAV path planning technology. Background Technology

[0002] Unmanned aerial vehicle (UAV) path planning is the process of finding a feasible flight path from a starting point to a destination that satisfies flight constraints in complex environments with obstacles and threats. Traditional optimization algorithms, such as genetic algorithms and particle swarm optimization, have been widely used for this problem. However, when dealing with complex environments with high dimensions, nonlinearity, and multiple constraints, they often suffer from slow convergence speed, susceptibility to getting trapped in local optima, and the generation of paths that do not conform to the actual motion characteristics of the UAV.

[0003] The Artificial Protozoa Optimizer (APO) is a swarm intelligence optimization algorithm that simulates the foraging, hibernation, and reproductive behaviors of protozoa, possessing strong global exploration capabilities. However, the standard APO algorithm uses traditional Cartesian coordinate encoding, which cannot intuitively represent the kinematic constraints of UAVs. This results in generated paths that are often infeasible in terms of turning angles, climb angles, etc., requiring post-processing corrections, thus reducing planning efficiency and path quality. Summary of the Invention

[0004] The purpose of this invention is to provide a UAV path planning method based on an improved artificial protozoan optimizer, which can improve the convergence speed, path quality and motion feasibility of UAV path planning in complex environments.

[0005] To achieve the above objectives, the present invention provides the following technical solution: In a first aspect, the present invention provides a method for unmanned aerial vehicle (UAV) path planning based on an improved artificial protozoan optimizer, comprising: Obtain the starting point, target point, and environmental model of the drone to be planned in a flight environment containing threats; An artificial protozoan optimizer population is constructed, and the position of each protozoan individual in the artificial protozoan optimizer population is encoded into a spherical vector. Each spherical vector corresponds to a candidate flight path containing multiple waypoints, including three components: segment length, elevation angle, and azimuth angle. Based on the environmental model and flight constraints, a cost function is constructed to evaluate the quality of candidate flight paths; The artificial protozoan optimizer population is driven to perform iterative optimization. In each iteration, the protozoan individual updates its spherical vector by performing foraging, hibernation, or reproduction behaviors based on each component of its current spherical vector. The updated spherical vector is decoded based on the starting point and the target point to obtain the candidate flight path corresponding to the updated spherical vector; The quality of the candidate flight path corresponding to the updated spherical vector is evaluated using a cost function, and the historical best spherical vector and the global best spherical vector of the protozoan individual in the artificial protozoan optimizer population are updated based on the evaluation results. Until the iteration termination condition is met, the final global optimal spherical vector is decoded based on the starting point and the target point to obtain the optimal flight path.

[0006] In conjunction with the first aspect, further steps in constructing an artificial protozoan optimizer population include: Based on the heuristic information between the starting point and the target point, an elite solution is generated. The elite is decoded into an elite spherical vector, and by fixing the elevation angle of the elite spherical vector, the segment length and azimuth angle of the elite spherical vector are perturbed to generate an elite protozoan individual; The remaining protozoan individuals are randomly generated and together with the elite protozoan individuals, they form an artificial protozoan optimizer population.

[0007] In conjunction with the first aspect, further, the spherical vector of the protozoan individuals in the artificial protozoan optimizer population is: ; in, Indicating the first in the artificial protozoan optimizer population The spherical vector of the _th protozoan individual, corresponding to the _th Candidate flight paths, , , They represent The length, elevation angle, and azimuth of the flight path from the starting point to the first waypoint. , , They represent From the From the first waypoint to the second Segment length, elevation angle, and azimuth angle for each waypoint , , They represent From the The length, elevation angle, and azimuth angle of the flight path from each waypoint to the target point. express The number of waypoints included.

[0008] In conjunction with the first aspect, furthermore, the search range for the flight segment length is dynamically set based on the distance between the starting point and the target point and the number of flight segments; the search range for the elevation angle is set based on the maximum climb angle or maximum pitch angle of the UAV; and the search range for the azimuth angle is set based on the reference azimuth angle and maximum turning angle of the line connecting the starting point and the target point.

[0009] Combining the first aspect, the cost function is further as follows: ; in, Represents the cost function, , , , These represent the path length cost, threat and obstacle avoidance cost, height restriction cost, and path smoothness cost, respectively. , , , They represent , , , Weighting coefficients; The cost function employs a soft penalty strategy for candidate flight paths that violate flight constraints, imposing finite and continuous penalty values. Flight constraints include flight altitude constraints, threat zone constraints, maximum turning angle constraints, and climb angle constraints.

[0010] In conjunction with the first aspect, further, foraging behavior includes autotrophic foraging and heterotrophic foraging; The update formula for the spherical surface corresponding to autotrophic foraging is: ; The update formula for the spherical surface corresponding to heterotrophic foraging is: ; in, Indicating the first in the artificial protozoan optimizer population The spherical vector of an individual protozoan. Indicating the first in the artificial protozoan optimizer population The updated spherical vector of each protozoan individual Indicates used for adjustment The fractal scaling vector of the update magnitude of each component, This indicates the use of dynamic control in foraging behavior. The mapping vector of the update dimension of each component, , Let represent the positional difference vectors for autotrophic foraging and heterotrophic foraging, respectively. Indicates foraging factors, Indicating the first in the artificial protozoan optimizer population The spherical vector of an individual protozoan. Indicates the population of artificial protozoa optimizers that is related to the first The spherical vector of the protozoan individual with the shortest Euclidean distance in the search space. , These represent the weighting factors for autotrophic foraging and heterotrophic foraging, respectively. , These represent the first and last two digits of the protozoan individual in the artificial protozoan optimizer population, sorted by cost function value. The spherical vector of an individual protozoan. , These represent the digits of the artificial protozoan population sorted by cost function value in the optimizer. The first and last moments of a protozoan individual The spherical vector of an individual protozoan. This represents the number of the first and last neighbor pairs of the current protozoan individual in the artificial protozoan optimizer population, sorted by cost function value. This represents the Hadamard product of element-wise multiplication.

[0011] In conjunction with the first aspect, further, It is dynamically generated based on the ranking of cost function values ​​of individual protozoa in the artificial protozoa optimizer population; The generation strategies include: The number of elements representing the update dimension decreases as the cost function value of the protozoan individual deteriorates.

[0012] In conjunction with the first aspect, furthermore, in heterotrophic foraging behavior, when updating the elevation angle of the spherical surface quantity, Introducing scaling factor , ,in, This represents the adjustment coefficient. This represents the average elevation angle of the current spherical surface. This indicates the maximum permissible elevation angle.

[0013] In conjunction with the first aspect, further, during the dormant behavior, the updated spherical vector of the protozoan individual in the artificial protozoan optimizer population is generated by applying a limited-amplitude random perturbation to the spherical vector of the protozoan individual with the best cost function value in the current artificial protozoan optimizer population under flight constraints.

[0014] In conjunction with the first aspect, the further update formula for the spherical quantity corresponding to reproductive behavior is: ; in, Indicating the first in the artificial protozoan optimizer population The spherical vector of an individual protozoan. Indicating the first in the artificial protozoan optimizer population The updated spherical vector of each protozoan individual Represents a random number. , These represent the maximum and minimum disturbance ranges, respectively. Indicating the use of control in reproductive behavior The mapping vector of the update dimension of each component, This represents the Hadamard product of element-wise multiplication.

[0015] Secondly, the present invention provides a UAV path planning system based on an improved artificial protozoan optimizer, comprising: The environmental modeling module is used to obtain the starting point, target point, and environmental model of the UAV to be planned in a flight environment containing threats; it constructs an artificial protozoan optimizer population, encoding the position of each protozoan individual in the artificial protozoan optimizer population into a spherical vector, and each spherical vector corresponds to a candidate flight path containing multiple waypoints, including three components: segment length, elevation angle, and azimuth angle; based on the environmental model and flight constraints, it constructs a cost function to evaluate the quality of the candidate flight paths; The iterative optimization module drives the artificial protozoan optimizer population to perform iterative optimization. In each iteration, the protozoan individual updates its spherical vector by performing foraging, hibernation, or reproduction behaviors based on the components of its current spherical vector. The updated spherical vector is decoded according to the starting point and the target point to obtain the candidate flight path corresponding to the updated spherical vector. The quality of the candidate flight path corresponding to the updated spherical vector is evaluated using a cost function, and the historical best spherical vector and the global best spherical vector of the protozoan individual in the artificial protozoan optimizer population are updated according to the evaluation results. Until the iteration termination condition is reached, the final global best spherical vector is decoded according to the starting point and the target point to obtain the optimal flight path.

[0016] Thirdly, the present invention provides a computer device, comprising: Storage medium: used to store computer programs; Processor: for executing the computer program to implement the UAV path planning method based on the improved artificial protozoan optimizer 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 UAV path planning method based on the improved artificial protozoan optimizer 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 UAV path planning method based on the improved artificial protozoan optimizer described in the first aspect.

[0019] Compared with the prior art, the beneficial effects of the present invention are: The UAV path planning method based on an improved artificial protozoan optimizer provided by this invention embeds a spherical vector encoding mechanism into the artificial protozoan optimizer, so that the search space of the APO algorithm is naturally aligned with the UAV's kinematic space, enabling efficient searching directly within a configuration space that meets flight constraints. The APO algorithm improved based on the spherical vector encoding mechanism, while maintaining global optimization capabilities, enhances path smoothness, safety, and practical flyability, outperforming traditional optimization methods in terms of convergence speed and planning success rate. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the paths generated by the algorithm of APO variant and spherical vector encoding provided in the embodiments of the present invention in scenarios 1 to 4, wherein (a) to (d) correspond to scenarios 1 to 4 respectively; Figure 2 This is a schematic diagram of the paths generated by the algorithm of APO variant and spherical vector encoding provided in the embodiments of the present invention in scenarios 5 to 8, wherein (a) to (d) correspond to scenarios 5 to 8 respectively; Figure 3 This is a schematic diagram of the optimal cost function value of the algorithm provided by the APO variant and spherical vector encoding in the iteration process of scenario 1 to scenario 4, provided by the embodiment of the present invention, wherein (a) to (d) correspond to scenario 1 to scenario 4 respectively; Figure 4 This is a schematic diagram of the optimal cost function value of the algorithm provided by the APO variant and spherical vector encoding in the iteration process of scenario 5 to scenario 8, provided by the embodiment of the present invention, wherein (a) to (d) correspond to scenario 5 to scenario 8 respectively; Figure 5 This is a schematic diagram of the paths generated by the SAPO algorithm and other metaheuristic algorithms provided in this embodiment of the invention in scenarios 1 to 4, wherein (a) to (d) correspond to scenarios 1 to 4 respectively; Figure 6 This is a schematic diagram of the paths generated by the SAPO algorithm and other metaheuristic algorithms provided in this embodiment of the invention in scenarios 5 to 8, wherein (a) to (d) correspond to scenarios 5 to 8 respectively; Figure 7 This is a schematic diagram of the optimal cost function values ​​of the SAPO algorithm and other metaheuristic algorithms provided in the embodiments of the present invention during the iteration process of scenarios 1 to 4, wherein (a) to (d) correspond to scenarios 1 to 4 respectively; Figure 8 This is a schematic diagram of the optimal cost function values ​​of the SAPO algorithm and other metaheuristic algorithms provided in the embodiments of the present invention during the iteration process of scenarios 5 to 8, wherein (a) to (d) correspond to scenarios 5 to 8 respectively. 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 method for UAV path planning based on an improved artificial protozoan optimizer, comprising: Obtain the starting point, target point, and environmental model of the drone to be planned in a flight environment containing threats; An artificial protozoan optimizer population is constructed, and the position of each protozoan individual in the artificial protozoan optimizer population is encoded into a spherical vector. Each spherical vector corresponds to a candidate flight path containing multiple waypoints, including three components: segment length, elevation angle, and azimuth angle. Based on the environmental model and flight constraints, a cost function is constructed to evaluate the quality of candidate flight paths; The artificial protozoan optimizer population is driven to perform iterative optimization. In each iteration, the protozoan individual updates its spherical vector by performing foraging, hibernation, or reproduction behaviors based on each component of its current spherical vector. The updated spherical vector is decoded based on the starting point and the target point to obtain the candidate flight path corresponding to the updated spherical vector; The quality of the candidate flight path corresponding to the updated spherical vector is evaluated using a cost function, and the historical best spherical vector and the global best spherical vector of the protozoan individual in the artificial protozoan optimizer population are updated based on the evaluation results. Until the iteration termination condition is met, the final global optimal spherical vector is decoded based on the starting point and the target point to obtain the optimal flight path.

[0024] The UAV path planning method based on the improved artificial protozoan optimizer provided in this invention embeds spherical vector encoding into the APO algorithm, making the search process naturally compatible with the UAV's motion characteristics. While inheriting the global search capability of the APO algorithm, it can improve path quality, convergence speed and actual flyability, and is suitable for UAV autonomous trajectory planning and multi-UAV collaborative tasks in complex threat environments.

[0025] The UAV path planning method based on the improved artificial protozoan optimizer provided in this embodiment can be applied to a terminal and can be executed by a UAV path planning system based on the improved artificial protozoan optimizer. The 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 function.

[0026] In one possible embodiment, constructing an artificial protozoan optimizer population specifically includes the following steps: Step 1: Generate an elite solution based on the heuristic information between the starting point and the target point; Step 2: Decode the elite into an elite spherical vector, and by fixing the elevation angle of the elite spherical vector, perturb the segment length and azimuth angle of the elite spherical vector to generate an elite protozoan individual; Step 3: Randomly generate the remaining protozoan individuals, which together with the elite protozoan individuals form the artificial protozoan optimizer population.

[0027] In this embodiment, during the population initialization phase, a hybrid strategy of elite embedding is adopted. First, an elite solution based on heuristic information between the starting point and the target point is generated. Then, by perturbing its flight segment length and azimuth angle while fixing its elevation angle to maintain feasibility, elite individuals are generated. These individuals are then combined with other randomly generated individuals to form the initial population.

[0028] The hybrid strategy of elite embedding guides the search direction by directional perturbation of segment length and azimuth during the initialization phase, and fixes the elevation angle to maintain path feasibility, thus providing a high-quality and highly guiding initial starting point for the APO algorithm.

[0029] In one possible embodiment, the spherical vector of the protozoan individuals in the artificial protozoan optimizer population is: ; in, Indicating the first in the artificial protozoan optimizer population The spherical vector of the _th protozoan individual, corresponding to the _th Candidate flight paths, , , They represent The length, elevation angle, and azimuth of the flight path from the starting point to the first waypoint. , , They represent From the From the first waypoint to the second Segment length, elevation angle, and azimuth angle for each waypoint , , They represent From the The length, elevation angle, and azimuth angle of the flight path from each waypoint to the target point. express The number of waypoints included.

[0030] In this embodiment, a spherical vector encoding mechanism is introduced to improve the core of the APO algorithm framework, making it more suitable for UAV trajectory optimization problems. The position vector in the traditional APO algorithm is redefined as a spherical vector, using the segment length... Angle of elevation and azimuth Three components are used to encode the drone's operational state. For a given... The flight path consists of several intermediate waypoints, using The algorithm encodes the motion vector using spherical vectors, with each three consecutive dimensions representing the segment length, elevation angle, and azimuth angle of the motion vector from one waypoint to the next in spherical coordinates. This encoding method allows the search space of the APO algorithm to be directly mapped to the kinematic configuration space of the UAV, achieving a natural unification of problem representation and physical constraints.

[0031] Specifically, the search range for the flight segment length is dynamically set based on the distance between the starting point and the target point and the number of flight segments. The elevation angle corresponds to the climb angle or pitch angle, and the search range for the elevation angle is set based on the maximum climb angle or maximum pitch angle constraint of the UAV. The azimuth angle corresponds to the horizontal turning angle, and the search range for the azimuth angle is set based on the reference azimuth angle and maximum turning angle constraint of the line connecting the starting point and the target point.

[0032] In one possible embodiment, the cost function is: ; in, Represents the cost function, , , , These represent the path length cost, threat and obstacle avoidance cost, height restriction cost, and path smoothness cost, respectively. , , , They represent , , , The weighting coefficients.

[0033] The quality of the candidate flight paths corresponding to the updated spherical vectors is evaluated using a cost function. Based on the evaluation results, the historical best spherical vectors and global best spherical vectors of individual protozoa in the artificial protozoa optimizer population are updated according to the greedy criterion.

[0034] The cost function employs a soft penalty strategy for candidate flight paths that violate flight constraints, imposing finite and continuous penalty values.

[0035] Specifically, flight constraints include flight altitude constraints, threat zone constraints, maximum turning angle constraints, and climb angle constraints.

[0036] In this embodiment, the cost function comprises four sub-costs: path length cost, threat and obstacle avoidance cost, altitude restriction cost, and path smoothness cost. Each sub-cost adjusts the importance of different optimization objectives through weighting, thereby achieving a trade-off between path length, safety, and flight performance. Regarding constraint handling, traditional methods typically impose infinite penalties on paths that violate constraints such as flight altitude, threat zone, maximum turning angle, and climb angle. This leads to discontinuities and numerical divergence in the cost function, hindering the stable convergence of intelligent optimization algorithms. Therefore, this embodiment introduces a soft-penalty strategy, rewriting hard constraints into soft-constraint forms and imposing finite and continuous penalty values ​​on violations. This soft-penalty approach maintains good smoothness of the cost function in the solution space, improving the convergence stability of swarm intelligence algorithms such as particle swarm optimization and enhancing the algorithm's tolerance to minor constraint violations, thus facilitating the acquisition of better feasible path solutions under complex constraints.

[0037] In one possible embodiment, foraging behavior includes autotrophic foraging and heterotrophic foraging.

[0038] The update formula for the spherical surface corresponding to autotrophic foraging is: ; The update formula for the spherical surface corresponding to heterotrophic foraging is: ; in, Indicating the first in the artificial protozoan optimizer population The spherical vector of an individual protozoan. Indicating the first in the artificial protozoan optimizer population The updated spherical vector of each protozoan individual Indicates used for adjustment The fractal scaling vector of the update magnitude of each component, Each component is uniformly distributed in the range [0,1]. This indicates the use of dynamic control in foraging behavior. The mapping vector of the update dimension of each component, , Let represent the positional difference vectors for autotrophic foraging and heterotrophic foraging, respectively. This represents a foraging factor used to regulate the update step size of spherical surface area. Indicating the first in the artificial protozoan optimizer population The spherical vector of an individual protozoan. Indicates the population of artificial protozoa optimizers that is related to the first The spherical vector of the protozoan individual with the shortest Euclidean distance in the search space. , These represent the weighting factors for autotrophic foraging and heterotrophic foraging, respectively, used to adjust for the contribution of neighbors to the difference. , These represent the first and last two digits of the protozoan individual in the artificial protozoan optimizer population, sorted by cost function value. The spherical vector of an individual protozoan. , These represent the digits of the artificial protozoan population sorted by cost function value in the optimizer. The first and last moments of a protozoan individual The spherical vector of an individual protozoan. This represents the number of the first and last neighbor pairs of the current protozoan individual in the artificial protozoan optimizer population, sorted by cost function value. This represents the Hadamard product of element-wise multiplication.

[0039] In this embodiment, It is dynamically generated based on the ranking of cost function values ​​of individual protozoa in the artificial protozoa optimizer population.

[0040] In the standard APO algorithm, the design of the mapping vector typically follows this principle: individuals with poor fitness values ​​have fewer update dimensions, while individuals with good fitness values ​​have more update dimensions. However, in the spherical vector encoding framework used in this embodiment, the path has a special cumulative property: the Cartesian coordinate position of each waypoint is determined by the cumulative relationship between the previous waypoint and the components of the current spherical vector. ; in, , They represent the first , Cartesian coordinates of each waypoint , , They represent the first From the first waypoint to the second The segment length, elevation angle, and azimuth angle of each waypoint.

[0041] This cumulative property means that updating any edge in the path, i.e., a spherical vector component, will directly affect the spatial position of all its subsequent nodes.

[0042] Based on the cumulative relationship, The generation strategies include: The number of elements representing the update dimension decreases as the cost function value of the protozoan individual deteriorates.

[0043] Specifically, The element representing the update dimension has a value of 1 if it is not 0 otherwise. Protozoan individuals with poor cost function values ​​are assigned fewer update dimensions. The system contains a large number of elements with values ​​of 0 to avoid excessive perturbation to the path structure and promote development; protozoan individuals with better cost function values ​​are assigned more update dimensions, i.e. The system contains a large number of elements with a value of 1, allowing for fine-tuning of the path and promoting exploration.

[0044] For protozoan individuals with poor cost function values, fewer edges are updated, meaning fewer dimensions are updated. Since updating each edge causes changes in the positions of all subsequent edges, reducing the number of updated edges avoids excessive disturbance to the overall path shape, maintains a relatively stable path structure, facilitates global exploration, and prevents the path from becoming infeasible due to simultaneous adjustments in multiple locations.

[0045] For protozoan individuals with better cost function values, more edges are updated, meaning more dimensions are updated. This allows the APO algorithm to fine-tune the path based on the found good path, optimize local details, fine-tune multiple key turning points, further improve path quality, maintain the continuity of the overall path shape, and avoid drastic changes.

[0046] In this embodiment, during heterotrophic foraging behavior, when updating the elevation angle of the spherical surface quantity, Introducing scaling factor Adjust the update step size of the elevation angle to adaptively balance exploration and development in the vertical direction. ,in, This represents the adjustment coefficient. This represents the average elevation angle of the current spherical surface. This indicates the maximum permissible elevation angle.

[0047] In one possible embodiment, during the dormant behavior, the updated spherical vector of the protozoan individual in the artificial protozoan optimizer population is generated by applying a limited-amplitude random perturbation to the spherical vector of the protozoan individual with the best cost function value in the current artificial protozoan optimizer population under flight constraints.

[0048] In this embodiment, an elite-guided directional regeneration strategy is adopted. Instead of resetting the solution to a completely random one, the solution is represented by its corresponding spherical vector and a random perturbation of a limited magnitude is applied to construct a new feasible solution in the neighborhood of the elite solution.

[0049] Specifically, when a protozoan individual is determined to have entered a dormant state, its current spherical vector is replaced with a newly generated spherical vector. The newly generated spherical vector is generated by superimposing a random perturbation of a limited amplitude on the spherical vector of the protozoan individual with the best cost function value in the current artificial protozoan optimizer population, and satisfies the flight constraint.

[0050] In one possible embodiment, the update formula for the spherical vector corresponding to the reproductive behavior is: ; in, Indicating the first in the artificial protozoan optimizer population The spherical vector of an individual protozoan. Indicating the first in the artificial protozoan optimizer population The updated spherical vector of each protozoan individual This represents a random number, specifically a random number uniformly distributed within the range [0,1]. , These represent the maximum and minimum disturbance ranges, respectively. Indicating the use of control in reproductive behavior The mapping vector of the update dimension of each component, This represents the Hadamard product of element-wise multiplication.

[0051] Specifically, when a protozoan is determined to be performing reproductive behavior, a random perturbation is superimposed on its current spherical vector to generate a new spherical vector. The magnitude and direction of the random perturbation are restricted by flight constraints.

[0052] In one possible embodiment, the UAV path planning algorithm based on spherical vector encoding for improving APO specifically includes the following steps: Step 1: Initialize the environment model to obtain the starting point, target point, threat distribution, and flight constraints; Step 2: Set algorithm parameters, including population size, maximum number of iterations, mapping vector parameters, etc.; Step 3: Generate the initial population using a hybrid initialization strategy of elite de-embedding; Step 4: Evaluate the cost function value for each individual in the initial population; Step 5: Enter the main loop. For each generation of individuals: Step ①: Sort the population according to fitness; Step 2: Calculate the foraging factor and probability parameters; Step 3: Perform foraging, hibernation, or reproduction behaviors on each individual; Step 4: Update the individual's spherical vector position; Step 5: Assess the fitness of the new location; Step 6: Update the individual optimal and global optimal solutions; Step 6: Determine the termination condition. If it is met, output the flight path corresponding to the global optimal solution; otherwise, return to step 5 to continue iterating.

[0053] To verify the effectiveness of the UAV path planning method based on the improved artificial protozoan optimizer provided in this embodiment of the invention, simulation experiments were conducted on a hardware platform using simulation software. Eight test scenarios with different complexities were constructed based on real digital elevation model data. Four test scenarios with different threat distributions and terrain features were constructed using real terrain data, with threats represented by red cylinders. The comprehensive cost function value was used as the main evaluation index, while the convergence speed and smoothness of the generated paths were also recorded. The number of path nodes was set to 12, corresponding to 10 flight segments.

[0054] To systematically evaluate the performance of the improved APO algorithm, this embodiment designs comparative experiments around the core related algorithms. The APO algorithm based on spherical vector encoding (denoted as SAPO algorithm) provided in this embodiment is compared with the standard APO algorithm, the PSO algorithm which also uses spherical vector encoding (denoted as SPSO algorithm), and the APO variant algorithm based on membrane structures (denoted as MAAPO algorithm), in order to explore in depth the effect of combining spherical vector encoding with different optimization frameworks.

[0055] Furthermore, to provide a more complete reference context, this embodiment also compares with a series of classic metaheuristic algorithms. To ensure that each comparison algorithm achieves sufficient convergence in the experiments, this embodiment adopts differentiated iteration count settings based on the convergence characteristics of different algorithms. Considering that the Differential Evolution (DE), Grey Wolf Optimizer (GWO), and Genetic Algorithm (GA) converge relatively slowly in the tests, their maximum iteration count is set to 1000; the remaining algorithms have shown a good convergence trend within 500 iterations, so their maximum iteration count is uniformly set to 500. This parameter setting aims to balance the algorithm's convergence depth and computational cost, providing each algorithm with sufficient convergence opportunities as much as possible.

[0056] To objectively assess the statistical significance of the performance differences between the algorithms, this embodiment conducted paired t-tests on the SAPO algorithm and each comparison algorithm in various scenarios, with a significance level of α=0.05, to determine whether there are significant differences in the mean path costs obtained by the two algorithms in multiple independent runs, thereby statistically supporting the conclusions of the performance comparison and enhancing the credibility and rigor of the results.

[0057] The test results are shown in Tables 1 and 2. The T-test results in Tables 1 and 2 are labeled as follows: "NA" indicates that no test is performed when compared with itself; "N" indicates that the difference is not significant; "D+" indicates that SAPO is significantly better than the comparison algorithm; "D-" indicates that SAPO is significantly worse than the comparison algorithm.

[0058] Table 1: Cost function values ​​of 10 line segment paths generated by the APO variant and spherical vector encoding algorithm .

[0059] Table 2: Fitness values ​​of 10 line segment paths generated by the SAPO algorithm and other metaheuristic algorithms .

[0060] The paths generated by the APO variant and spherical vector encoding algorithm in scenes 1 to 4 are as follows: Figure 1 As shown, the paths generated by the APO variant and spherical vector encoding algorithm in scenes 5 to 8 are as follows: Figure 2 As shown. The paths generated by the SAPO algorithm and other metaheuristic algorithms in scenarios 1 to 4 are as follows: Figure 5 As shown, the paths generated by the SAPO algorithm and other metaheuristic algorithms in scenarios 5 to 8 are as follows: Figure 6 As shown.

[0061] From the path planning results, all algorithms can effectively avoid obstacles and generate feasible paths, but their performance differences lead to variations in the quality of the generated paths. In relatively simple scenarios, both the SPSO and SAPO algorithms can plan near-optimal flight paths, demonstrating the overall effectiveness of spherical vector optimization algorithms. In scenarios with more complex obstacle distributions, the SAPO algorithm generates significantly better paths than the SPSO algorithm, although the SPSO algorithm's paths still structurally conform to actual flight requirements. In contrast, other algorithms can generate reasonable paths in simple scenarios, but in complex obstacle environments, they exhibit problems such as paths deviating from reality and having unreasonable structures, further confirming the advantages of spherical vector encoding in UAV motion constraints.

[0062] It is worth noting that although the optimal path does not account for the highest percentage of the score in the weighted function evaluation, the SAPO algorithm is still able to select the optimal path. Other algorithms, however, tend to produce less efficient paths in complex scenarios.

[0063] The optimal cost function values ​​of the algorithm using APO variants and spherical vector encoding during the iterations from scenario 1 to scenario 4 are as follows: Figure 3 As shown, the optimal cost function values ​​of the algorithm using the APO variant and spherical vector encoding during the iteration process from scene 5 to scene 8 are as follows: Figure 4 As shown. The optimal cost function values ​​of the SAPO algorithm and other metaheuristic algorithms during the iteration process of scenarios 1 to 4 are as follows. Figure 7 As shown, the optimal cost function values ​​of the SAPO algorithm and other metaheuristic algorithms during the iteration process from scenario 5 to scenario 8 are as follows: Figure 8 As shown.

[0064] Analysis of the convergence characteristic curves shows that the optimal cost function values ​​obtained by the SAPO and SPSO algorithms in the early stages of iteration are significantly better than those of other comparative algorithms. This indicates that both algorithms can locate superior solution regions during the initialization phase. This is attributed to the fact that spherical vector encoding can naturally align with the UAV kinematic model, making the search process more focused on the high-potential solution space. In terms of convergence efficiency, the SAPO algorithm exhibits the fastest convergence speed in most test scenarios, and its curve decline trend is significantly better than that of traditional algorithms. Although it is close to the SPSO algorithm in some scenarios, it still shows better convergence stability and iterative efficiency overall.

[0065] Statistical results from repeated experiments show that the SAPO algorithm achieved the best average path cost in all scenarios, indicating its superior comprehensive planning performance. Furthermore, the standard deviation of its cost function value was generally lower than other algorithms in most scenarios, demonstrating that the SAPO algorithm maintains stable output quality under different random initial conditions, exhibiting good robustness and reliability. This statistical advantage further confirms that the SAPO algorithm possesses significant repeatability and stability in multiple runs, making it suitable for practical applications requiring high consistency of results.

[0066] To further verify the statistical significance of the performance differences between the algorithms, this embodiment conducted a paired-samples t-test on the results for each scenario, with a significance level of α=0.05. The test showed that in the vast majority of scenarios, the SAPO algorithm and the comparison algorithms had statistically significant differences in path cost. This further confirms from a statistical inference perspective that the SAPO algorithm can stably generate high-quality paths in multiple repeated experiments, demonstrating good repeatability and robustness, and is suitable for practical scenarios with high requirements for result consistency.

[0067] The UAV path planning method based on an improved artificial protozoan optimizer provided in this invention achieves alignment between the search space and the UAV kinematic space by embedding a spherical vector encoding mechanism into the APO algorithm. Experimental results show that this method outperforms traditional optimization algorithms in terms of path quality, convergence speed, and actual flyability, and can effectively solve the UAV path planning problem in complex threat environments.

[0068] The UAV path planning method based on an improved artificial protozoan optimizer provided in this invention is specifically designed for 3D UAV path planning and can be integrated into UAV autonomous navigation systems. This method significantly improves the convergence speed and solution quality of path planning in complex terrains through spherical coordinate modeling and an elite-guided initialization strategy. It can be applied to real-time or offline trajectory planning for single UAVs in complex environments with terrain undulations and threat distribution, and is particularly suitable for practical applications such as military reconnaissance, disaster relief, and power line inspection, demonstrating significant engineering practical value and broad application prospects.

[0069] This invention provides a UAV path planning system based on an improved artificial protozoan optimizer, comprising: The environmental modeling module is used to obtain the starting point, target point, and environmental model of the UAV to be planned in a flight environment containing threats; it constructs an artificial protozoan optimizer population, encoding the position of each protozoan individual in the artificial protozoan optimizer population into a spherical vector, and each spherical vector corresponds to a candidate flight path containing multiple waypoints, including three components: segment length, elevation angle, and azimuth angle; based on the environmental model and flight constraints, it constructs a cost function to evaluate the quality of the candidate flight paths; The iterative optimization module drives the artificial protozoan optimizer population to perform iterative optimization. In each iteration, the protozoan individual updates its spherical vector by performing foraging, hibernation, or reproduction behaviors based on the components of its current spherical vector. The updated spherical vector is decoded according to the starting point and the target point to obtain the candidate flight path corresponding to the updated spherical vector. The quality of the candidate flight path corresponding to the updated spherical vector is evaluated using a cost function, and the historical best spherical vector and the global best spherical vector of the protozoan individual in the artificial protozoan optimizer population are updated according to the evaluation results. Until the iteration termination condition is reached, the final global best spherical vector is decoded according to the starting point and the target point to obtain the optimal flight path.

[0070] The UAV path planning system based on the improved artificial protozoan optimizer provided in this embodiment of the invention can execute the UAV path planning method based on the improved artificial protozoan optimizer provided in this embodiment of the invention, and has the corresponding functional modules and beneficial effects of the execution method.

[0071] This invention provides a computer device, comprising: Storage medium: used to store computer programs; Processor: Used to execute computer programs to implement the UAV path planning method based on an improved artificial protozoan optimizer provided in the embodiments of the present invention.

[0072] This invention provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the UAV path planning method based on an improved artificial protozoan optimizer provided in this invention.

[0073] This invention provides a computer program product, including a computer program that, when executed by a processor, implements the UAV path planning method based on an improved artificial protozoan optimizer provided in this invention.

[0074] 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.

[0075] 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.

[0076] 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.

[0077] 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.

[0078] 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 method for UAV path planning based on an improved artificial protozoan optimizer, characterized in that, include: Obtain the starting point, target point, and environmental model of the drone to be planned in a flight environment containing threats; An artificial protozoan optimizer population is constructed, and the position of each protozoan individual in the artificial protozoan optimizer population is encoded into a spherical vector. Each spherical vector corresponds to a candidate flight path containing multiple waypoints, including three components: segment length, elevation angle, and azimuth angle. Based on the environmental model and flight constraints, a cost function is constructed to evaluate the quality of candidate flight paths; The artificial protozoan optimizer population is driven to perform iterative optimization. In each iteration, the protozoan individual updates its spherical vector by performing foraging, hibernation, or reproduction behaviors based on each component of its current spherical vector. The updated spherical vector is decoded based on the starting point and the target point to obtain the candidate flight path corresponding to the updated spherical vector; The quality of the candidate flight path corresponding to the updated spherical vector is evaluated using a cost function, and the historical best spherical vector and the global best spherical vector of the protozoan individual in the artificial protozoan optimizer population are updated based on the evaluation results. Until the iteration termination condition is met, the final global optimal spherical vector is decoded based on the starting point and the target point to obtain the optimal flight path.

2. The UAV path planning method based on an improved artificial protozoan optimizer according to claim 1, characterized in that, Constructing an artificial protozoan optimizer population includes: Based on the heuristic information between the starting point and the target point, an elite solution is generated. The elite is decoded into an elite spherical vector, and by fixing the elevation angle of the elite spherical vector, the segment length and azimuth angle of the elite spherical vector are perturbed to generate an elite protozoan individual; The remaining protozoan individuals are randomly generated and together with the elite protozoan individuals, they form an artificial protozoan optimizer population.

3. The UAV path planning method based on an improved artificial protozoan optimizer according to claim 1, characterized in that, The spherical vector of each protozoan individual in the artificial protozoan optimizer population is: ； in, Indicating the first in the artificial protozoan optimizer population The spherical vector of the _th protozoan individual, corresponding to the _th Candidate flight paths, , , They represent The length, elevation angle, and azimuth of the flight path from the starting point to the first waypoint. , , They represent From the From the first waypoint to the second Segment length, elevation angle, and azimuth angle for each waypoint , , They represent From the The length, elevation angle, and azimuth angle of the flight path from each waypoint to the target point. express The number of waypoints included.

4. The UAV path planning method based on an improved artificial protozoan optimizer according to claim 1, characterized in that, The search range for the flight segment length is dynamically set based on the distance between the starting point and the target point and the number of flight segments. The search range for the elevation angle is set based on the maximum climb angle or maximum pitch angle of the UAV. The search range for the azimuth angle is set based on the reference azimuth angle and maximum turning angle of the line connecting the starting point and the target point.

5. The UAV path planning method based on an improved artificial protozoan optimizer according to claim 1, characterized in that, The cost function is: ； in, Represents the cost function, , , , These represent the path length cost, threat and obstacle avoidance cost, height restriction cost, and path smoothness cost, respectively. , , , They represent , , , Weighting coefficients; The cost function employs a soft penalty strategy for candidate flight paths that violate flight constraints, imposing finite and continuous penalty values. Flight constraints include flight altitude constraints, threat zone constraints, maximum turning angle constraints, and climb angle constraints.

6. The UAV path planning method based on an improved artificial protozoan optimizer according to claim 1, characterized in that, Foraging behaviors include autotrophic foraging and heterotrophic foraging; The update formula for the spherical surface corresponding to autotrophic foraging is: ； The update formula for the spherical surface corresponding to heterotrophic foraging is: ； in, Indicating the first in the artificial protozoan optimizer population The spherical vector of an individual protozoan. Indicating the first in the artificial protozoan optimizer population The updated spherical vector of each protozoan individual Indicates used for adjustment The fractal scaling vector of the update magnitude of each component, This indicates the use of dynamic control in foraging behavior. The mapping vector of the update dimension of each component, , Let represent the positional difference vectors for autotrophic foraging and heterotrophic foraging, respectively. Indicates foraging factors, Indicating the first in the artificial protozoan optimizer population The spherical vector of an individual protozoan. Indicates the population of artificial protozoa optimizers that is related to the first The spherical vector of the protozoan individual with the shortest Euclidean distance in the search space. , These represent the weighting factors for autotrophic foraging and heterotrophic foraging, respectively. , These represent the first and last two digits of the protozoan individual in the artificial protozoan optimizer population, sorted by cost function value. The spherical vector of an individual protozoan. , These represent the digits of the artificial protozoan population sorted by cost function value in the optimizer. The first and last moments of a protozoan individual The spherical vector of an individual protozoan. This represents the number of the first and last neighbor pairs of the current protozoan individual in the artificial protozoan optimizer population, sorted by cost function value. This represents the Hadamard product of element-wise multiplication.

7. The UAV path planning method based on an improved artificial protozoan optimizer according to claim 6, characterized in that, It is dynamically generated based on the ranking of cost function values ​​of individual protozoa in the artificial protozoa optimizer population; The generation strategies include: The number of elements representing the update dimension decreases as the cost function value of the protozoan individual deteriorates.

8. The UAV path planning method based on the improved artificial protozoan optimizer according to claim 6, characterized in that, In heterotrophic foraging behavior, when updating the elevation angle of the spherical surface, Introducing scaling factor , ,in, This represents the adjustment coefficient. This represents the average elevation angle of the current spherical surface. This indicates the maximum permissible elevation angle.

9. The UAV path planning method based on an improved artificial protozoan optimizer according to claim 1, characterized in that, During dormancy, the updated spherical vector of protozoan individuals in the artificial protozoan optimizer population is generated by applying a limited-amplitude random perturbation to the spherical vector of the protozoan individual with the best cost function value in the current artificial protozoan optimizer population under flight constraints.

10. The UAV path planning method based on an improved artificial protozoan optimizer according to claim 1, characterized in that, The update formula for the spherical quantity corresponding to reproductive behavior is: ； in, Indicating the first in the artificial protozoan optimizer population The spherical vector of an individual protozoan. Indicating the first in the artificial protozoan optimizer population The updated spherical vector of each protozoan individual Represents a random number. , These represent the maximum and minimum disturbance ranges, respectively. Indicating the use of control in reproductive behavior The mapping vector of the update dimension of each component, This represents the Hadamard product of element-wise multiplication.

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