Three-dimensional unmanned aerial vehicle path planning multi-objective optimization method, system, device and medium

Abstract

The application discloses a three-dimensional unmanned aerial vehicle path planning multi-objective optimization method, system, device and medium, and the method comprises the steps of acquiring three-dimensional environment data of an unmanned aerial vehicle flight task area and constructing a three-dimensional space cost map; initializing a plurality of three-dimensional candidate flight paths in the three-dimensional space cost map and mapping the three-dimensional candidate flight paths into an initial population in a multi-objective swarm intelligent optimizer; calculating multi-objective fitness of each candidate flight path in the initial population and screening out non-dominated flight paths; extracting distribution entropy of the flight path set, adaptively and dynamically adjusting a fractional order parameter according to the distribution entropy, and iteratively updating the position of a flight path point of the candidate flight path; in the iterative updating process, extracting a fractal dimension of the flight path set in a multi-dimensional flight performance evaluation space, and if falling into a local terrain trap, triggering an expansion recovery strategy; and outputting a three-dimensional flight path set with Pareto optimality after reaching a maximum number of iterations. The application can solve the multi-objective conflict and local trap problem under a complex terrain.

Description

Technical Field

[0001] This invention relates to a method, system, device, and medium for multi-objective optimization of path planning for three-dimensional unmanned aerial vehicles (UAVs), belonging to the technical fields of autonomous navigation, intelligent optimization algorithms, and multi-objective path planning for UAVs. Background Technology

[0002] In complex three-dimensional environments such as mountain patrols and emergency search and rescue, autonomous path planning for unmanned aerial vehicles (UAVs) faces extremely challenging multi-objective physical trade-offs. Specifically, UAVs encounter the following serious technical conflicts and shortcomings when flying in real-world environments:

[0003] 1) The extreme conflict between physical safety and flight energy consumption: When facing narrow canyons or multi-peak terrain, existing conventional path planning systems often generate "edge-grabbing" trajectories that closely follow the edges of terrain obstacles in order to pursue the absolute shortest path (reducing flight energy consumption). While this trajectories are effective in ideal simulations, in actual flight, encountering airflow disturbances or rotor power response delays can easily lead to the drone crashing into a mountain (i.e., the "reward hacking" phenomenon in algorithmic fields). Conversely, excessively increasing the safety distance can result in overly circuitous trajectories, causing the drone's battery to run out and preventing it from returning. Existing systems lack a mechanism that can achieve a stable and continuous trade-off between safety and energy consumption (i.e., maintain a high-quality Pareto front).

[0004] 2) Dynamic hysteresis and directional oscillations during complex terrain traversal: Existing swarm intelligence optimization systems, when guiding UAVs through narrow feasible corridors, typically rely solely on the local terrain gradient or instantaneous velocity at the current moment for position updates. Due to the lack of effective accumulation and memorization of historical flight trajectory trends, the generated waypoints exhibit severe left-right swaying and high-frequency inflection points within canyons. This not only severely violates the dynamic constraints of the UAV, such as its maximum turning angle and climb rate, but also causes significant mechanical losses and energy waste.

[0005] 3) False Convergence (Dead End) in Flight Path Planning under Complex Weather / Terrain: In complex 3D environments with multiple obstacles and threats, flight path planning systems are highly susceptible to getting trapped in "terrain traps" formed by local peaks or no-fly zones. Traditional collision avoidance or anti-stagnation mechanisms rely solely on distance determination or random variation, often failing to identify whether the current candidate flight path group has experienced "geometric spatial diversity collapse." This false convergence state, where the system appears to have converged but is actually stuck in a dead end, causes the UAV to repeatedly hover in local areas, ultimately leading to mission failure. Summary of the Invention

[0006] In view of this, the present invention provides a multi-objective optimization method, system, computer equipment and storage medium for three-dimensional UAV path planning. By deeply binding mathematical operators with the physical flight characteristics of UAVs, it can solve the multi-objective conflict and local trap problems in complex terrain, and can stably generate safe, smooth and short paths while maintaining Pareto diversity in complex three-dimensional environments.

[0007] The first objective of this invention is to provide a multi-objective optimization method for path planning of three-dimensional unmanned aerial vehicles (UAVs).

[0008] The second objective of this invention is to provide a three-dimensional unmanned aerial vehicle (UAV) path planning multi-objective optimization system.

[0009] A third objective of this invention is to provide a computer device.

[0010] A fourth objective of this invention is to provide a storage medium.

[0011] The first objective of this invention can be achieved by adopting the following technical solution:

[0012] A multi-objective optimization method for path planning of a three-dimensional unmanned aerial vehicle (UAV), the method comprising:

[0013] Acquire 3D environmental data of the UAV flight mission area, construct a 3D spatial cost map including terrain elevation and obstacles, and set dynamic constraints on maximum turning angle and climb rate according to the UAV model;

[0014] Multiple 3D candidate tracks are initialized within the 3D spatial cost map. Each candidate track is discretized into a sequence of waypoint coordinates and mapped to the initial population in the multi-objective swarm intelligent optimizer.

[0015] Based on path length, threat avoidance / safety, flight altitude constraints, and trajectory smoothness, the multi-objective fitness of each candidate trajectory in the initial population is calculated. Non-dominated trajectories are selected based on Pareto dominance and stored in the optimal non-dominated trajectory memory.

[0016] Extract the distribution entropy of the track set in the optimal non-dominated track memory, adaptively and dynamically adjust the fractional-order parameters according to the distribution entropy, and iteratively update the waypoint positions of the candidate tracks in combination with the non-Markov fractional-order memory momentum.

[0017] During the iterative update process, the geometric complexity of the track set in the optimal non-dominated track memory in the multidimensional flight performance evaluation space is extracted, the corresponding fractal dimension is calculated, and the current track optimization is judged based on the fractal dimension to determine whether it is trapped in a local terrain trap. If it is trapped in a local terrain trap, the expansion recovery strategy is triggered to force the waypoints of the candidate track to jump out of the current local extreme value region. The multidimensional flight performance evaluation space consists of path length, threat avoidance / safety, flight altitude constraint and track smoothness.

[0018] After reaching the maximum number of iterations, output the Pareto optimal set of three-dimensional tracks from the optimal non-dominated track memory.

[0019] Furthermore, based on path length, threat avoidance / safety, flight altitude constraints, and trajectory smoothness, the multi-objective fitness of each candidate trajectory in the initial population is calculated, including:

[0020] The path length fitness is calculated by accumulating the three-dimensional Euclidean distances between adjacent waypoints.

[0021] Based on the spatial relationship between candidate tracks and threat areas, the threat avoidance and security adaptability are calculated.

[0022] The altitude cost is calculated based on the degree of deviation of the waypoint altitude from the permissible flight altitude range;

[0023] The track smoothness fitness is calculated based on the changes in turning and climb angles between adjacent track segments.

[0024] Furthermore, the step of extracting the distribution entropy of the track set in the optimal non-dominated track memory and adaptively and dynamically adjusting the fractional-order parameters based on the distribution entropy includes:

[0025] Extract the distribution entropy of the track set in the optimal non-dominated track memory within the target space grid to characterize the diversity level of the current track set;

[0026] After smoothing the distribution entropy, a mapping relationship between the distribution entropy and the fractional-order parameter is established, and the fractional-order parameter is continuously and adaptively adjusted with a preset reference diversity level as the mapping center.

[0027] When the distribution entropy decreases, the fractional-order parameter is reduced through the mapping relationship to enhance the long-range historical memory effect and global exploration capability;

[0028] When the distribution entropy increases, the fractional-order parameter is increased through the mapping relationship to enhance local exploitation capability and improve convergence efficiency.

[0029] Furthermore, the iterative update of waypoint positions for candidate paths using non-Markov fractional memory momentum includes:

[0030] Extract the incremental waypoint positions of the UAV during the optimization process of several generations in history;

[0031] Using the definition of discrete truncated fractional derivatives, the historical position increments are summed by fractional weights to construct a non-Markov fractional memory momentum.

[0032] The non-Markov fractional memory momentum is superimposed on the update direction vector of the current waypoint, and the random oscillations in a single iteration are offset by the accumulation of cross-generational terrain gradient information.

[0033] Furthermore, the step of extracting the geometric complexity of the set of tracks in the optimal non-dominated track memory in the multidimensional flight performance evaluation space and calculating the corresponding fractal dimension includes:

[0034] The box dimension method is used to estimate the geometric complexity of the Pareto front formed by the set of tracks in the optimal non-dominated track memory in the multidimensional flight performance evaluation space, and the corresponding fractal dimension is calculated.

[0035] Furthermore, the step of determining whether the current trajectory optimization is trapped in a local terrain trap based on the fractal dimension includes:

[0036] The fractal dimension is compared with the preset diversity safety threshold. If the fractal dimension is lower than the preset diversity safety threshold and the supervolume gain tends to stagnate for several consecutive generations, it is determined that the current trajectory optimization has fallen into a local terrain trap.

[0037] Furthermore, the triggering of the expansion recovery strategy, which forces the waypoints of candidate paths to jump out of the current local extreme value region, includes:

[0038] Apply Lévy flight perturbations to some waypoints of stagnant candidate tracks, or perform local resampling distribution within the global boundary constraints of the 3D spatial cost map, so that candidate tracks can re-cover a wider physical search area to restore the continuity and terrain coverage of the Pareto front.

[0039] The second objective of this invention can be achieved by adopting the following technical solution:

[0040] A three-dimensional unmanned aerial vehicle (UAV) path planning multi-objective optimization system, the system comprising:

[0041] The environment modeling module is used to acquire three-dimensional environmental data of the UAV flight mission area, construct a three-dimensional spatial cost map including terrain elevation and obstacles, and set dynamic constraints on the maximum turning angle and climb rate according to the UAV model.

[0042] The population mapping module is used to initialize multiple 3D candidate tracks within the 3D spatial cost map, discretize each candidate track into a sequence of waypoint coordinates, and map it into the initial population in the multi-objective swarm intelligent optimizer.

[0043] The fitness evaluation and archiving module is used to calculate the multi-objective fitness of each candidate trajectory in the initial population based on path length, threat avoidance / safety, flight altitude constraints and trajectory smoothness, select non-dominated trajectories based on Pareto dominance, and store them in the optimal non-dominated trajectory memory.

[0044] The fractional-order physics optimization module is used to extract the distribution entropy of the track set in the optimal non-dominated track memory, adaptively and dynamically adjust the fractional-order parameters according to the distribution entropy, and iteratively update the waypoint positions of the candidate tracks in combination with the non-Markov fractional-order memory momentum.

[0045] The fractal dimension anti-collision module is used to extract the geometric complexity of the set of tracks in the optimal non-dominated track memory in the multi-dimensional flight performance evaluation space during the iterative update process, calculate the corresponding fractal dimension, and determine whether the current track optimization is trapped in a local terrain trap based on the fractal dimension. If it is trapped in a local terrain trap, the expansion recovery strategy is triggered to force the waypoints of the candidate track to jump out of the current local extreme value region. The multi-dimensional flight performance evaluation space consists of path length, threat avoidance / safety, flight altitude constraint and track smoothness.

[0046] The output module is used to output the Pareto optimal set of three-dimensional tracks from the optimal non-dominated track memory after reaching the maximum number of iterations.

[0047] The third objective of this invention can be achieved by adopting the following technical solution:

[0048] A computer device includes a processor and a memory for storing processor-executable programs, wherein when the processor executes the programs stored in the memory, it implements the above-described multi-objective optimization method for three-dimensional UAV path planning.

[0049] The fourth objective of this invention can be achieved by adopting the following technical solution:

[0050] A storage medium storing a program that, when executed by a processor, implements the aforementioned multi-objective optimization method for three-dimensional UAV path planning.

[0051] The present invention has the following advantages over the prior art:

[0052] 1. This invention adopts an entropy-driven adaptive fractional order mechanism, which dynamically adjusts the fractional order parameters according to the distribution entropy of the solutions in the external archive, enabling the search to adaptively switch between "exploration and development"; when diversity decreases, the fractional order memory effect is enhanced, which helps to escape local extrema; when diversity is sufficient, the search tends to converge faster.

[0053] 2. This invention combines non-Markov fractional memory momentum to iteratively update the waypoint positions of candidate paths, and introduces the search increments of several generations in the form of fractional convolution into the update direction, so that the current position update no longer depends solely on the information of the current generation, thereby improving directional stability, the ability to traverse narrow feasible corridors, and the ability to escape in complex terrain.

[0054] 3. This invention employs a fractal dimension-guided stagnation control mechanism to estimate the geometric complexity of the non-dominated solution set in the target space using fractal dimension estimation, and combines the hypervolume change to determine whether frontier collapse or search stagnation has occurred; when diversity collapse is detected, an expansion strategy is automatically triggered to re-inject exploration capabilities. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0056] Figure 1 This is a general framework diagram of the three-dimensional UAV path planning multi-objective optimization method of Embodiment 1 of the present invention.

[0057] Figure 2 This is a simplified flowchart of the three-dimensional UAV path planning multi-objective optimization method of Embodiment 1 of the present invention.

[0058] Figure 3 This is a flowchart illustrating the multi-objective optimization method for three-dimensional UAV path planning in Embodiment 1 of the present invention.

[0059] Figure 4 This is a diagram of the entropy-driven fractional-order cooling and step-size modulation mechanism in Embodiment 1 of the present invention.

[0060] Figure 5 This is a schematic diagram of the non-Markov fractional memory momentum of Embodiment 1 of the present invention.

[0061] Figure 6 This is a schematic diagram of the fractal dimension monitoring and strategy switching mechanism in Embodiment 1 of the present invention.

[0062] Figure 7This is a structural block diagram of the three-dimensional UAV path planning multi-objective optimization system of Embodiment 2 of the present invention.

[0063] Figure 8 This is a structural block diagram of the computer device according to Embodiment 3 of the present invention. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0065] Example 1:

[0066] To overcome the shortcomings of existing algorithms in terms of convergence accuracy, search robustness, front cover, and stagnation recovery, this embodiment provides a multi-objective optimization method for 3D UAV path planning. This method is guided by fractional-order and fractal-dimensional principles and is denoted as FOFD-MOETO. Figures 1-3 As shown, it includes the following steps:

[0067] S301. Acquire three-dimensional environmental data of the UAV flight mission area, construct a three-dimensional spatial cost map including terrain elevation and obstacles, and set dynamic constraints on the maximum turning angle and climb rate according to the UAV model.

[0068] The three-dimensional environmental data in this embodiment includes at least the terrain elevation data of the mission area, the spatial location and geometric dimensions of obstacles, the coordinates of the starting point and the target point, the boundary data of the mission area, and the no-fly zone / threat zone data. The UAV dynamics constraint parameters include the maximum turning angle, the maximum rate of climb, the speed range, and the safety margin.

[0069] In this embodiment, dynamic constraints on the maximum turning angle and climb rate are set according to the UAV model. Specifically, this includes: a maximum turning angle threshold, denoted as theta_max, is preset based on the UAV model's lateral maneuverability. When the angle between adjacent track segments exceeds this threshold, the candidate track is determined to not meet the dynamic constraints, and is penalized or corrected. A maximum climb rate threshold, denoted as r_max, is preset based on the UAV model's vertical maneuverability. If the rate of change of altitude between adjacent track points exceeds this threshold, the candidate track is determined to not meet the dynamic constraints. The maximum turning angle threshold theta_max and the maximum climb rate threshold r_max are preset based on the UAV model. For any three consecutive track points in the candidate track, the angle theta_m between two adjacent track segments is calculated, and theta_m is constrained not to be greater than theta_max. For any two adjacent track points, the ratio r_m of their altitude change to horizontal displacement is calculated, and r_m is constrained. Not greater than r_max; when a candidate trajectory violates any of the above constraints, a penalty, repair or boundary projection process is applied to the corresponding candidate solution to ensure that the obtained trajectory meets the UAV dynamics executability requirements.

[0070] S302. Initialize multiple 3D candidate tracks within the 3D spatial cost map, discretize each candidate track into a sequence of waypoint coordinates, and map it to the initial population in the multi-objective swarm intelligent optimizer.

[0071] The multi-objective swarm intelligent optimizer used in this embodiment is the Multi-Objective Exponential-Triangular Optimizer (MOETO). The optimization objectives include at least: path length, track smoothness, climb / altitude stability, and safety constraint satisfaction. In multi-aircraft collaborative tasks, objectives such as coverage, communication overlap, and conflict avoidance can be further added.

[0072] In this embodiment, the starting point, ending point, and several intermediate control points are used as trajectory parameterization nodes in the three-dimensional spatial cost map. The decision vector corresponding to the candidate trajectory is constructed by the coordinates or offsets of the intermediate control points. Multiple decision vectors are randomly generated within the boundary constraints as the initial population. The corresponding control points of each decision vector are recovered, and continuous three-dimensional candidate trajectories are generated by spline interpolation. The continuous three-dimensional candidate trajectories are then discretized into a waypoint coordinate sequence, which serves as candidate individuals in the multi-objective swarm intelligent optimizer.

[0073] S303. Based on path length, threat avoidance / safety, flight altitude constraints and track smoothness, calculate the multi-objective fitness of each candidate track in the initial population, select non-dominated tracks based on Pareto dominance, and store them in the optimal non-dominated track memory.

[0074] In this embodiment, the multi-objective fitness of each candidate trajectory in the initial population is calculated based on path length, threat avoidance / safety, flight altitude constraints, and trajectory smoothness. This includes: calculating path length fitness based on the sum of the three-dimensional Euclidean distances between adjacent waypoints; calculating threat avoidance and safety fitness based on the spatial relationship between candidate trajectories and threat areas; calculating altitude cost based on the deviation of the trajectory point altitude from the allowable flight altitude range; and calculating trajectory smoothness fitness based on the changes in turning and climb angles between adjacent trajectory segments.

[0075] In this embodiment, non-dominated tracks are selected based on Pareto dominance and stored in the optimal non-dominated track memory. Specifically, this includes: comparing each candidate track pairwise using Pareto dominance based on the multi-objective function values ​​corresponding to each candidate track; if a candidate track is not inferior to another candidate track in all objectives and is superior to another candidate track in at least one objective, then the candidate track is determined to dominate the other candidate track; candidate tracks not dominated by any other candidate tracks are identified as non-dominated tracks and stored in the optimal non-dominated track memory; the non-dominated tracks obtained in the current iteration are merged with the tracks in the historical optimal non-dominated track memory, and Pareto selection is performed again to obtain the updated optimal non-dominated track memory.

[0076] S304. Extract the distribution entropy of the track set in the optimal non-dominated track memory, adaptively and dynamically adjust the fractional-order parameters according to the distribution entropy, and iteratively update the waypoint positions of the candidate tracks in combination with the non-Markov fractional-order memory momentum.

[0077] In this embodiment, the distribution entropy of the track set in the optimal non-dominated track memory within the target space grid is extracted to characterize the diversity level of the current track set. After smoothing the distribution entropy, a mapping relationship between the distribution entropy and the fractional-order parameter is established, and the fractional-order parameter is continuously and adaptively adjusted using a preset reference diversity level as the mapping center. When the distribution entropy decreases, i.e., the diversity level decreases, the fractional-order parameter is reduced through the mapping relationship to enhance the long-range historical memory effect and global exploration capability. When the distribution entropy increases, i.e., the diversity level increases, the fractional-order parameter is increased through the mapping relationship to enhance local exploitation capability and improve convergence efficiency. The fractional-order parameter is used to modulate the fractional-order cooling term and step-size shaping term in the MOETO algorithm.

[0078] Furthermore, in the process of multi-objective optimization, in order to balance the UAV's ability to explore terrain obstacles and its ability to develop stable flight, such as... Figure 4As shown, this embodiment extracts the distribution entropy H(t) of the set of non-dominated tracks in the optimal non-dominated track memory, i.e., the external archive, within the target space grid. Specifically, the multidimensional flight performance evaluation space is divided into K grids, and the track distribution probability p_k(t) in each grid is calculated. The distribution entropy is then:

[0079] ;

[0080] Where ε is a tiny constant to avoid the singularity of logarithmic operations.

[0081] Furthermore, by smoothing the distribution entropy, we obtain:

[0082] ;

[0083] Where ρ is the smoothing coefficient.

[0084] Subsequently, a mapping function between the smooth distribution entropy and the fractional parameter α(t) is established:

[0085] ;

[0086] Where σ(·) is the Logistic mapping function, α_min and α_max are the lower and upper limits of the fractional-order parameter, respectively, κ is the sensitivity adjustment coefficient, and H_ref is the reference diversity level.

[0087] When the smooth distribution entropy is small, it indicates that the distribution of the non-dominated track set in the target space tends to be concentrated and the diversity decreases. At this time, the mapping yields a smaller fractional-order parameter to enhance the long-range historical memory effect and global exploration capability. When the smooth distribution entropy is large, it indicates that the distribution of the non-dominated track set in the target space is relatively uniform and the diversity is high. At this time, the mapping yields a larger fractional-order parameter to enhance local development capability and improve convergence efficiency.

[0088] In this embodiment, the waypoint positions of candidate paths are iteratively updated using non-Markov fractional memory momentum to guide the paths through narrow terrain in a 3D spatial cost map. This includes: extracting the waypoint position increments of the UAV during several generations of optimization; using the definition of discrete truncated fractional derivatives, performing fractional weighted summation of the historical position increments to construct non-Markov fractional memory momentum; and superimposing the non-Markov fractional memory momentum into the update direction vector of the current waypoint, using the accumulated terrain gradient information across generations to offset random oscillations in a single iteration, thereby improving the smoothness and directional stability of the path.

[0089] Furthermore, because existing methods rely solely on the current generation's velocity for waypoint updates, high-frequency inflection point oscillations occur when traversing narrow corridors, such as... Figure 5As shown, this embodiment utilizes the Grünwald-Letnikov (GL) fractional derivative definition to extract the historical position increments of the past L generations, constructing a non-Markov fractional memory momentum. :

[0090] ;

[0091] in, For the i-th candidate track in history Location of waypoints in the era For the Gamma function, This is the position increment.

[0092] Finally, this momentum is added to the current waypoint update formula:

[0093] ;

[0094] in, The momentum weighting coefficient is equivalent to giving the UAV "physical inertia with long-range memory", which enables the trajectory planning in narrow terrain to effectively offset random oscillations and generate a smooth trajectory that conforms to the dynamic constraints of the UAV.

[0095] S305. During the iterative update process, extract the geometric complexity of the track set in the optimal non-dominated track memory in the multidimensional flight performance evaluation space, calculate the corresponding fractal dimension, and determine whether the current track optimization is trapped in a local terrain trap based on the fractal dimension. If it is trapped in a local terrain trap, trigger the expansion recovery strategy to force the waypoints of the candidate track to jump out of the current local extreme value region.

[0096] In this embodiment, the geometric complexity of the track set in the optimal non-dominated track memory in the multidimensional flight performance evaluation space is extracted, and the corresponding fractal dimension is calculated. This includes: estimating the geometric complexity of the Pareto front formed by the track set in the optimal non-dominated track memory in the multidimensional flight performance evaluation space using the box-counting dimension method, and calculating the corresponding fractal dimension; comparing the fractal dimension with a preset diversity safety threshold; if the fractal dimension is lower than the preset diversity safety threshold, and the hypervolume gain tends to stagnate for several consecutive generations, it is determined that the current track optimization has fallen into a local terrain trap; wherein, the multidimensional flight performance evaluation space consists of path length, threat avoidance / safety, flight altitude constraints, and track smoothness.

[0097] Furthermore, to accurately identify the "false convergence" state, such as Figure 6As shown, this embodiment uses the box-counting dimension method to calculate the fractal dimension of the Pareto front formed by the optimal non-dominated track set in the multidimensional performance space. :

[0098] ;

[0099] in, To define the grid side lengths for dividing the evaluation space, The number of grids containing at least one non-dominant path, the stagnation criterion: when the fractal dimension D is satisfied for consecutive generations T. f <D threshold When the rate of change of the hypervolume (HV) is less than δ (the gain tends to stagnate), the track group is determined to be trapped in a local terrain trap, and the expansion strategy is triggered.

[0100] The expansion recovery strategy in this embodiment includes: applying Lévy flight perturbations to some waypoints of the candidate track that have stalled, or performing local resampling distribution within the global boundary constraints of the three-dimensional spatial cost map, so that the candidate track can re-cover a wider physical search area to restore the continuity and terrain coverage of the Pareto front.

[0101] S306. After reaching the maximum number of iterations, output the Pareto optimal set of three-dimensional tracks from the optimal non-dominated track memory.

[0102] After outputting the Pareto optimal set of three-dimensional tracks, this embodiment can select a target track from the Pareto optimal set of three-dimensional tracks according to mission preferences, and convert the waypoint sequence of the target track into flight control commands and send them to the UAV actuators.

[0103] In this embodiment, the multi-objective optimization method for 3D UAV path planning inputs the start and end points into the system for single-UAV 3D path planning. After constructing 3D terrain constraints, FOFD-MOETO optimization is performed. The algorithm outputs a set of Pareto candidate paths, each corresponding to different trade-offs in path length, smoothness, and safety redundancy. Ultimately, the shortest path or a smoother, safer path can be selected based on task preferences. In multi-UAV collaborative path planning, multiple UAV mission objectives, no-fly zones, collision constraints, and coverage requirements are incorporated into the same optimization framework. The algorithm retains diverse candidate solutions through external archives and dynamically adjusts the search intensity based on fractal dimension and hypervolume signal, thereby obtaining dense, collision-free, and high-coverage collaborative trajectories. In remote sensing mission evaluation, the path planning results are substituted into remote sensing mission indicators for secondary evaluation, such as terrain visibility, coverage integrity, and trajectory overlap redundancy. Experiments show that the method can effectively balance mission coverage and observation quality while maintaining flight safety.

[0104] To verify the physical effectiveness of the 3D UAV path planning multi-objective optimization method of this embodiment in a real complex 3D environment, a comparative test was conducted on a complex terrain model containing 50 dense Gaussian peaks and 3 dynamic no-fly zones. The method of this embodiment was compared with classic basic algorithms (such as standard MOETO and NSGA-II). The quantitative experimental data are as follows:

[0105] 1) Multi-objective comprehensive performance coverage: After introducing fractal dimension guidance and fractional order mechanism, the hypervolume (HV) index of the Pareto front generated by the system of this invention reached 0.875, which is an absolute improvement of 10.4% compared with the standard MOETO (0.792) and an improvement of 18.2% compared with NSGA-II. This shows that the method of this embodiment can provide more and better trade-offs between path length, smoothness and safety.

[0106] 2) Physical safety and crash prevention indicators (success condition indicators): In the simulation of crossing extremely narrow canyons, traditional algorithms, due to the lack of long-range memory momentum, frequently exceed the dynamic limits of the UAV due to the turning angle of the generated track (leading to simulated crashes), and their "safe arrival rate in real physical environment" is only 82%. However, the method in this embodiment benefits from the effective suppression of track oscillation by non-Markov fractional memory momentum, which greatly improves the track smoothness. Under the same energy consumption constraints, the physical safety arrival rate of the UAV is increased to 99.2%, and the collision rate (crash rate) in real environment is reduced to below 1%.

[0107] 3) Local extremum escape capability: When facing multi-peak terrain traps, thanks to the precise collapse monitoring and expansion recovery mechanism of fractal dimension, the probability of the method in this embodiment getting stuck in a local dead end and causing planning failure is significantly reduced from 14.5% of the traditional algorithm to 2.3%.

[0108] It should be noted that although the method operations of the above embodiments are described in a specific order, this does not require or imply that these operations must be performed in that specific order, or that all the operations shown must be performed to achieve the desired result. On the contrary, the described steps may be performed in a different order. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

[0109] Example 4:

[0110] like Figure 7As shown, this embodiment provides a three-dimensional UAV path planning multi-objective optimization system. The system includes an environment modeling module 701, a population mapping module 702, a fitness evaluation and archiving module 703, a fractional-order physics optimization module 704, a fractal-dimensional collision avoidance module 705, and an output module 706. Specific descriptions of each module are as follows:

[0111] The environment modeling module 701 is used to acquire three-dimensional environmental data of the UAV flight mission area, construct a three-dimensional spatial cost map including terrain elevation and obstacles, and set dynamic constraints on the maximum turning angle and climb rate according to the UAV model.

[0112] The population mapping module 702 is used to initialize multiple three-dimensional candidate trajectories in the three-dimensional spatial cost map, discretize each candidate trajectories into a sequence of waypoint coordinates, and map them into the initial population in the multi-objective swarm intelligent optimizer.

[0113] The fitness evaluation and archiving module 703 is used to calculate the multi-objective fitness of each candidate trajectory in the initial population based on path length, threat avoidance / safety, flight altitude constraints and trajectory smoothness, select non-dominated trajectories based on Pareto dominance, and store them in the optimal non-dominated trajectory memory.

[0114] The fractional-order physics optimization module 704 is used to extract the distribution entropy of the track set in the optimal non-dominated track memory, adaptively and dynamically adjust the fractional-order parameters according to the distribution entropy, and iteratively update the waypoint positions of the candidate tracks in combination with the non-Markov fractional-order memory momentum.

[0115] The fractal dimension anti-collision module 705 is used to extract the geometric complexity of the set of tracks in the optimal non-dominated track memory in the multi-dimensional flight performance evaluation space during the iterative update process, calculate the corresponding fractal dimension, and determine whether the current track optimization is trapped in a local terrain trap based on the fractal dimension. If it is trapped in a local terrain trap, it triggers an expansion recovery strategy to force the waypoints of the candidate track to jump out of the current local extreme value region. The multi-dimensional flight performance evaluation space is composed of the path length, threat avoidance / safety, flight altitude constraint and track smoothness.

[0116] Output module 706 is used to output the Pareto optimal set of three-dimensional tracks from the optimal non-dominated track memory after reaching the maximum number of iterations.

[0117] It should be noted that the system provided in this embodiment is only an example of the above-described division of functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure can be divided into different functional modules to complete all or part of the functions described above.

[0118] Example 3:

[0119] This embodiment provides a computer device, such as... Figure 8 As shown, it includes a processor 802, a memory, an input device 803, a display device 804, and a network interface 805 connected via a system bus 801. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium 806 and internal memory 807. The non-volatile storage medium 806 stores an operating system, computer programs, and a database. The internal memory 807 provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. When the processor 802 executes the computer programs stored in the memory, it implements the three-dimensional UAV path planning multi-objective optimization method of Embodiment 1 described above, as follows:

[0120] Acquire 3D environmental data of the UAV flight mission area, construct a 3D spatial cost map including terrain elevation and obstacles, and set dynamic constraints on maximum turning angle and climb rate according to the UAV model; initialize multiple 3D candidate tracks within the 3D spatial cost map, discretize each candidate track into a waypoint coordinate sequence, and map it to the initial population in a multi-objective swarm intelligent optimizer; calculate the multi-objective fitness of each candidate track in the initial population based on path length, threat avoidance / safety, flight altitude constraints, and track smoothness, select non-dominated tracks based on Pareto dominance, and store them in the optimal non-dominated track memory; extract the distribution entropy of the track set in the optimal non-dominated track memory, and adaptively and dynamically adjust the track set according to the distribution entropy. The system iteratively updates the waypoint positions of candidate paths using fractional-order parameters and non-Markov fractional-order memory momentum. During the iterative update process, it extracts the geometric complexity of the path set in the optimal non-dominated path memory within the multidimensional flight performance evaluation space, calculates the corresponding fractal dimension, and determines whether the current path optimization is trapped in a local terrain trap based on the fractal dimension. If trapped, it triggers an expansion recovery strategy to force the waypoints of candidate paths to escape the current local extreme value region. The multidimensional flight performance evaluation space consists of path length, threat avoidance / safety, flight altitude constraints, and path smoothness. After reaching the maximum number of iterations, it outputs the Pareto optimal three-dimensional path set from the optimal non-dominated path memory.

[0121] Example 4:

[0122] This embodiment provides a storage medium, which is a computer-readable storage medium, storing a computer program. When the computer program is executed by a processor, it implements the three-dimensional UAV path planning multi-objective optimization method of Embodiment 1 above, as follows:

[0123] Acquire 3D environmental data of the UAV flight mission area, construct a 3D spatial cost map including terrain elevation and obstacles, and set dynamic constraints on maximum turning angle and climb rate according to the UAV model; initialize multiple 3D candidate tracks within the 3D spatial cost map, discretize each candidate track into a waypoint coordinate sequence, and map it to the initial population in a multi-objective swarm intelligent optimizer; calculate the multi-objective fitness of each candidate track in the initial population based on path length, threat avoidance / safety, flight altitude constraints, and track smoothness, select non-dominated tracks based on Pareto dominance, and store them in the optimal non-dominated track memory; extract the distribution entropy of the track set in the optimal non-dominated track memory, and adaptively and dynamically adjust the track set according to the distribution entropy. The system iteratively updates the waypoint positions of candidate paths using fractional-order parameters and non-Markov fractional-order memory momentum. During the iterative update process, it extracts the geometric complexity of the path set in the optimal non-dominated path memory within the multidimensional flight performance evaluation space, calculates the corresponding fractal dimension, and determines whether the current path optimization is trapped in a local terrain trap based on the fractal dimension. If trapped, it triggers an expansion recovery strategy to force the waypoints of candidate paths to escape the current local extreme value region. The multidimensional flight performance evaluation space consists of path length, threat avoidance / safety, flight altitude constraints, and path smoothness. After reaching the maximum number of iterations, it outputs the Pareto optimal three-dimensional path set from the optimal non-dominated path memory.

[0124] It should be noted that the computer-readable storage medium in this embodiment can be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof.

[0125] In this embodiment, the computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in connection with an instruction execution system, apparatus, or device. In this embodiment, the computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, carrying a computer-readable program. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. The computer-readable signal medium can also be any computer-readable storage medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The computer program contained on the computer-readable storage medium can be transmitted using any suitable medium, including but not limited to: wires, optical cables, RF (radio frequency), etc., or any suitable combination thereof.

[0126] The computer-readable storage medium described above can be used to write computer programs for executing this embodiment in one or more programming languages ​​or combinations thereof. These programming languages ​​include object-oriented programming languages—such as Java, Python, and C++—and conventional procedural programming languages—such as C or similar programming languages. The program can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0127] In summary, this invention achieves stable approximation of the Pareto front in complex scenarios through fractional-order historical memory enhancement, fractal dimension stagnation identification, and adaptive expansion recovery, demonstrating strong novelty, inventiveness, and engineering application value. This invention does not simply superimpose existing optimizers, but establishes a coupled mapping relationship between entropy, fractional order, and fractal dimension. The fractional-order parameter is not arbitrarily set but adaptively generated by the diversity of the archives. Stagnation control is not a fixed-period restart but is jointly triggered by the fractal dimension and the hypervolume, exhibiting clear technical connections, synergistic effects, and irreplaceability.

[0128] The above description is merely a preferred embodiment of the present invention. It will be apparent to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects. The scope of the present invention is defined by the appended claims rather than the foregoing description, and thus all variations falling within the meaning and scope of the equivalents of the claims are intended to be included within the present invention.

Claims

1. A multi-objective optimization method for path planning of a three-dimensional unmanned aerial vehicle (UAV), characterized in that, The method includes: Acquire 3D environmental data of the UAV flight mission area, construct a 3D spatial cost map including terrain elevation and obstacles, and set dynamic constraints on maximum turning angle and climb rate according to the UAV model; Multiple 3D candidate tracks are initialized within the 3D spatial cost map. Each candidate track is discretized into a sequence of waypoint coordinates and mapped to the initial population in the multi-objective swarm intelligent optimizer. Based on path length, threat avoidance / safety, flight altitude constraints, and trajectory smoothness, the multi-objective fitness of each candidate trajectory in the initial population is calculated. Non-dominated trajectories are selected based on Pareto dominance and stored in the optimal non-dominated trajectory memory. Extract the distribution entropy of the track set in the optimal non-dominated track memory, adaptively and dynamically adjust the fractional-order parameters according to the distribution entropy, and iteratively update the waypoint positions of the candidate tracks in combination with the non-Markov fractional-order memory momentum. During the iterative update process, the geometric complexity of the track set in the optimal non-dominated track memory in the multidimensional flight performance evaluation space is extracted, the corresponding fractal dimension is calculated, and the current track optimization is judged based on the fractal dimension to determine whether it is trapped in a local terrain trap. If it is trapped in a local terrain trap, the expansion recovery strategy is triggered to force the waypoints of the candidate track to jump out of the current local extreme value region. The multidimensional flight performance evaluation space consists of path length, threat avoidance / safety, flight altitude constraint and track smoothness. After reaching the maximum number of iterations, output the Pareto optimal set of three-dimensional tracks from the optimal non-dominated track memory.

2. The multi-objective optimization method for three-dimensional UAV path planning according to claim 1, characterized in that, Based on path length, threat avoidance / safety, flight altitude constraints, and trajectory smoothness, the multi-objective fitness of each candidate trajectory in the initial population is calculated, including: The path length fitness is calculated by accumulating the three-dimensional Euclidean distances between adjacent waypoints. Based on the spatial relationship between candidate tracks and threat areas, the threat avoidance and security adaptability are calculated. The altitude cost is calculated based on the degree of deviation of the waypoint altitude from the permissible flight altitude range; The track smoothness fitness is calculated based on the changes in turning and climb angles between adjacent track segments.

3. The multi-objective optimization method for three-dimensional UAV path planning according to claim 1, characterized in that, The step of extracting the distribution entropy of the track set in the optimal non-dominated track memory and adaptively and dynamically adjusting the fractional-order parameters based on the distribution entropy includes: Extract the distribution entropy of the track set in the optimal non-dominated track memory within the target space grid to characterize the diversity level of the current track set; After smoothing the distribution entropy, a mapping relationship between the distribution entropy and the fractional-order parameter is established, and the fractional-order parameter is continuously and adaptively adjusted with a preset reference diversity level as the mapping center. When the distribution entropy decreases, the fractional-order parameter is reduced through the mapping relationship to enhance the long-range historical memory effect and global exploration capability; When the distribution entropy increases, the fractional-order parameter is increased through the mapping relationship to enhance local exploitation capability and improve convergence efficiency.

4. The multi-objective optimization method for three-dimensional UAV path planning according to claim 1, characterized in that, The iterative update of waypoint positions for candidate paths using non-Markov fractional memory momentum includes: Extract the incremental waypoint positions of the UAV during the optimization process of several generations in history; Using the definition of discrete truncated fractional derivatives, the historical position increments are summed by fractional weights to construct a non-Markov fractional memory momentum. The non-Markov fractional memory momentum is superimposed on the update direction vector of the current waypoint, and the random oscillations in a single iteration are offset by the accumulation of cross-generational terrain gradient information.

5. The multi-objective optimization method for three-dimensional UAV path planning according to claim 1, characterized in that, The step of extracting the geometric complexity of the set of tracks in the optimal non-dominated track memory in the multidimensional flight performance evaluation space and calculating the corresponding fractal dimension includes: The box dimension method is used to estimate the geometric complexity of the Pareto front formed by the set of tracks in the optimal non-dominated track memory in the multidimensional flight performance evaluation space, and the corresponding fractal dimension is calculated.

6. The multi-objective optimization method for three-dimensional UAV path planning according to claim 1, characterized in that, The step of determining whether the current trajectory optimization is trapped in a local terrain trap based on the fractal dimension includes: The fractal dimension is compared with the preset diversity safety threshold. If the fractal dimension is lower than the preset diversity safety threshold and the supervolume gain tends to stagnate for several consecutive generations, it is determined that the current trajectory optimization has fallen into a local terrain trap.

7. The multi-objective optimization method for three-dimensional UAV path planning according to claim 1, characterized in that, The triggered expansion recovery strategy forces the waypoints of candidate paths to jump out of the current local extreme value region, including: Apply Lévy flight perturbations to some waypoints of stagnant candidate tracks, or perform local resampling distribution within the global boundary constraints of the 3D spatial cost map, so that candidate tracks can re-cover a wider physical search area to restore the continuity and terrain coverage of the Pareto front.

8. A three-dimensional unmanned aerial vehicle (UAV) path planning multi-objective optimization system, characterized in that, The system includes: The environment modeling module is used to acquire three-dimensional environmental data of the UAV flight mission area, construct a three-dimensional spatial cost map including terrain elevation and obstacles, and set dynamic constraints on the maximum turning angle and climb rate according to the UAV model. The population mapping module is used to initialize multiple 3D candidate tracks within the 3D spatial cost map, discretize each candidate track into a sequence of waypoint coordinates, and map it into the initial population in the multi-objective swarm intelligent optimizer. The fitness evaluation and archiving module is used to calculate the multi-objective fitness of each candidate trajectory in the initial population based on path length, threat avoidance / safety, flight altitude constraints and trajectory smoothness, select non-dominated trajectories based on Pareto dominance, and store them in the optimal non-dominated trajectory memory. The fractional-order physics optimization module is used to extract the distribution entropy of the track set in the optimal non-dominated track memory, adaptively and dynamically adjust the fractional-order parameters according to the distribution entropy, and iteratively update the waypoint positions of the candidate tracks in combination with the non-Markov fractional-order memory momentum. The fractal dimension anti-collision module is used to extract the geometric complexity of the set of tracks in the optimal non-dominated track memory in the multi-dimensional flight performance evaluation space during the iterative update process, calculate the corresponding fractal dimension, and determine whether the current track optimization is trapped in a local terrain trap based on the fractal dimension. If it is trapped in a local terrain trap, the expansion recovery strategy is triggered to force the waypoints of the candidate track to jump out of the current local extreme value region. The multi-dimensional flight performance evaluation space consists of path length, threat avoidance / safety, flight altitude constraint and track smoothness. The output module is used to output the Pareto optimal set of three-dimensional tracks from the optimal non-dominated track memory after reaching the maximum number of iterations.

9. A computer device comprising a processor and a memory for storing a processor-executable program, characterized in that, When the processor executes the program stored in the memory, it implements the three-dimensional UAV path planning multi-objective optimization method according to any one of claims 1-7.

10. A computer-readable storage medium storing a program, characterized in that, When the program is executed by the processor, it implements the three-dimensional UAV path planning multi-objective optimization method according to any one of claims 1-7.

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