Three-dimensional path planning method for land-sea-air cross-domain unmanned system

Abstract

This invention discloses a three-dimensional path planning method for cross-domain unmanned systems operating across land, sea, and air, belonging to the technical field of path planning for cross-domain unmanned systems. This invention aims to solve the problems of low planning success rate and high path cost in existing path planning methods in complex cross-domain environments due to inconsistent environmental modeling and the difficulty of balancing exploration and development with a single intelligent optimization algorithm. The key technical solution lies in constructing a unified environmental model that integrates land, sea, and air geographic information and multi-dimensional adversarial threats, and proposing a hybrid intelligent optimization algorithm for three-dimensional path planning. This algorithm uses particle swarm optimization as its main framework and dynamically integrates the global exploration operator of the cuckoo search algorithm and the local development operator of the whale optimization algorithm through an adaptive probabilistic strategy. This invention can effectively improve the path planning success rate and mission execution efficiency of cross-domain unmanned systems in complex adversarial environments.

Description

Technical Field

[0001] This invention belongs to the field of path planning technology for cross-domain unmanned systems, and particularly relates to a three-dimensional path planning method for cross-domain unmanned systems involving land, sea and air. Background Technology

[0002] With the maturation of artificial intelligence and unmanned systems technologies, intelligent platforms such as drones and unmanned surface vessels (USVs) have played a crucial role in complex missions such as ocean exploration, disaster relief, and border patrol. However, single-type unmanned platforms are limited by their physical domains, exhibiting inherent limitations in perception range, maneuverability, and endurance, making it difficult to independently adapt to large-scale, multi-factor complex mission scenarios. Against this backdrop, cross-domain unmanned systems have emerged. By integrating unmanned platforms from different domains such as air, surface, underwater, and land, they aim to achieve information sharing and mission collaboration, thereby addressing multiple challenges in complex environments.

[0003] As a core enabling technology for collaboration in cross-domain unmanned systems, path planning faces severe challenges. First, the environment is complex, requiring unified processing of multi-dimensional geographic information and heterogeneous threats across a continuous three-dimensional space encompassing land, sea, and air. Second, constraints are diverse, with complex energy consumption models resulting from different media, necessitating the establishment of a unified cost model. Finally, collaboration is rigorous, requiring paths to meet the spatiotemporal coordination requirements of multiple platforms. Especially in time-sensitive tasks such as disaster relief, maximizing efficiency and minimizing costs simultaneously while ensuring safety is paramount.

[0004] Existing research on cross-domain path planning mainly focuses on two aspects: platform collaborative control and environment modeling and path generation. Regarding environment modeling and path generation, directly related research is relatively limited. Existing methods, such as hierarchical planning, plan paths separately for platforms in different domains before coordinating them. This approach disrupts spatial continuity and makes it difficult to obtain globally optimal cross-domain paths. In terms of unified modeling of multi-domain threats, most existing typical threat models are relatively simple and fail to fully simulate the complex scenarios of heterogeneous threats such as radar and air defense firepower coexisting in real cross-domain environments. Regarding path planning algorithms, traditional graph search-based algorithms can guarantee finding the optimal solution in discrete spaces, but they suffer from the curse of dimensionality and are difficult to apply to high-dimensional continuous spaces. Random sampling-based algorithms are suitable for high-dimensional spaces, but the planned paths are highly random and lack optimality guarantees. While metaheuristic intelligent optimization algorithms such as particle swarm optimization, cuckoo search, and whale optimization are widely used in path planning, these algorithms are mainly applied to robot path planning within a single domain. When dealing with high-dimensional, multi-constrained cross-domain problems, single algorithms are prone to getting trapped in local optima, exhibiting low convergence accuracy, and possessing an inherent flaw of unbalanced exploration and development capabilities. Existing research on algorithm fusion mostly focuses on pairwise combinations, failing to fully explore the complementary potential of multiple algorithms and lacking optimization designs for special constraints such as cross-domain medium switching and energy consumption differences. Therefore, existing methods suffer from core technical bottlenecks in addressing real-world land, sea, and air cross-domain collaborative tasks, including insufficient environmental modeling capabilities and limited overall algorithm performance. This results in planned paths that fail to meet practical application requirements in terms of safety, optimality, and reliability. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a three-dimensional path planning method for a land-sea-air cross-domain unmanned system, thereby resolving the issues present in the existing technologies.

[0006] Firstly, to achieve the above objectives, the present invention provides a three-dimensional path planning method for a land-sea-air cross-domain unmanned system, comprising the following steps: Obtain geographic information and threat source information for the task area; Based on the aforementioned geographic information and threat source information, a unified three-dimensional environment model is constructed; Based on the hybrid intelligent optimization algorithm, a collision-free three-dimensional path is planned from the starting point to the end point for the unmanned system in the unified three-dimensional environment model. The hybrid intelligent optimization algorithm takes the particle swarm optimization algorithm (PSO) as the main framework and selects to execute the exploration operator of the Cuckoo Search algorithm (CS) or the development operator of the Whale Optimization algorithm (WOA) according to the adaptive probability strategy during the iteration process. Output the planned 3D path.

[0007] Optionally, the process of building a unified 3D environment model includes: The land terrain undulations of the task area were simulated based on the superposition of Gaussian peak functions. By setting an ocean depth threshold, the three-dimensional environment model is divided into an underwater domain and an above-water domain. The threat areas of radar and anti-aircraft artillery are modeled as hemispherical or cylindrical spaces, and terrain obstacles are modeled as impassable areas.

[0008] Optionally, when planning a path based on a hybrid intelligent optimization algorithm, the quality of the path is evaluated using a fitness function, which is a piecewise function, and its construction process includes: Detect whether the path collides with a threat area or terrain; If a collision occurs, a penalty coefficient is applied to the path length to calculate the fitness value; If no collision occurs, the fitness value is calculated based on the physical length of the underwater and above-water portions of the path, combined with the corresponding energy consumption coefficient.

[0009] Optionally, the hybrid intelligent optimization algorithm performs the following process for each individual in the population in each iteration: Generate random numbers; If the random number is less than the first adaptive probability, then the update operator of the Whale Optimization Algorithm (WOA) is executed; If the random number is not less than the first adaptive probability and is less than the sum of the first adaptive probability and the second adaptive probability, then the update operator of the Cuckoo Search Algorithm CS is executed. Otherwise, execute the velocity and position update operators of the Particle Swarm Optimization (PSO) algorithm.

[0010] Optionally, the first adaptive probability and the second adaptive probability are dynamically adjusted according to the iteration process, and the adjustment strategy is as follows: In the early stages of the iteration, a higher second adaptive probability is set; As the iteration proceeds, the second adaptive probability is linearly decreased, while the first adaptive probability is increased.

[0011] Optionally, the process of executing the update operator of the Cuckoo Search Algorithm CS is a Lévy flight mechanism, including: Calculate the random step size that follows a Lévy distribution; A new individual position is generated based on the random step size and the current individual position.

[0012] Optionally, the process of executing the update operator of the Whale Optimization Algorithm (WOA) includes: Determine the current behavior pattern based on random numbers and parameters; If it is in the prey encirclement mode, the individual will move to the current global optimal position; If it is a bubble net attack mode, the individual will move along a spiral path towards the current global optimal position.

[0013] Optionally, a path post-processing procedure is also included before outputting the 3D path: The planned path point sequence is smoothed using cubic spline interpolation to generate a continuous and smooth flight trajectory.

[0014] Secondly, the present invention also provides a computer terminal device, comprising: One or more processors; A memory, coupled to the processor, for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the steps of the three-dimensional path planning method for the land, sea and air cross-domain unmanned system in the first aspect above.

[0015] Thirdly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the steps of the three-dimensional path planning method for the land, sea and air cross-domain unmanned system described in the first aspect above.

[0016] Compared with the prior art, the present invention has the following advantages and technical effects: This invention provides a three-dimensional path planning method for cross-domain unmanned systems operating across land, sea, and air, effectively overcoming the technical shortcomings of existing methods in this area. Through the constructed unified environment model, it can more realistically simulate complex cross-domain geographical and multi-dimensional threat scenarios, providing a precise input basis for path planning. The proposed hybrid intelligent optimization algorithm organically integrates the core advantages of different algorithms through an adaptive strategy, significantly improving the balance between global exploration and local development capabilities, thereby effectively avoiding premature convergence. This method can plan safe and collision-free paths in test environments of varying complexity, fundamentally guaranteeing its success rate. The planned paths demonstrate superiority in length, smoothness, and comprehensive threat avoidance capabilities. Ultimately, this invention significantly improves the overall efficiency and path planning reliability of cross-domain unmanned systems in complex adversarial environments. Attached Figure Description

[0017] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a schematic diagram of the Env-A smooth and sparse environment according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a moderately complex environment in Env-B according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the Env-C peak sparse environment according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the Env-D multi-peak dense environment according to an embodiment of the present invention; Figure 5 This is a flowchart of the Hybrid Intelligent Optimization Algorithm (PWCS) according to an embodiment of the present invention; Figure 6 This is a schematic diagram comparing the three-dimensional paths of various algorithms in the embodiment of the present invention in the Env-B environment; Figure 7 This is a schematic diagram comparing the two-dimensional paths of various algorithms in the Env-B environment according to embodiments of the present invention; Figure 8 This is a schematic diagram of the path planning results of each algorithm in the embodiment of the present invention in the Env-D environment; Figure 9 This is a schematic diagram comparing the convergence curves of various algorithms in the embodiment of the present invention under the Env-D environment; Figure 10 This is a schematic diagram comparing the three-dimensional paths of various algorithm variants in the Env-D environment according to embodiments of the present invention; Figure 11 This is a schematic diagram comparing the convergence curves of various algorithm variants in the Env-D environment according to embodiments of the present invention. Detailed Implementation

[0018] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0019] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0020] Example 1 like Figure 5 As shown, this embodiment provides a three-dimensional path planning method for a land-sea-air cross-domain unmanned system, including: Obtain geographic information and threat source information for the task area; Based on the aforementioned geographic information and threat source information, a unified three-dimensional environment model is constructed; Based on the hybrid intelligent optimization algorithm, a collision-free three-dimensional path is planned from the starting point to the end point for the unmanned system in the unified three-dimensional environment model. The hybrid intelligent optimization algorithm takes the particle swarm optimization algorithm (PSO) as the main framework and selects to execute the exploration operator of the Cuckoo Search algorithm (CS) or the development operator of the Whale Optimization algorithm (WOA) according to the adaptive probability strategy during the iteration process. Output the planned 3D path.

[0021] Furthermore, the process of constructing a unified 3D environment model includes: The land terrain undulations of the task area were simulated based on the superposition of Gaussian peak functions. By setting an ocean depth threshold, the three-dimensional environment model is divided into an underwater domain and an above-water domain. The threat areas of radar and anti-aircraft artillery are modeled as hemispherical or cylindrical spaces, and terrain obstacles are modeled as impassable areas.

[0022] Specifically, the implementation process of this embodiment includes: To evaluate the algorithm's performance, such as Figures 1-4 The embodiment shown depicts four 3D testing environments. Figure 1 For the smooth and sparse environment of Env-A, Figure 2 For a moderately complex environment like Env-B, Figure 3 For Env-C peak sparse environment, Figure 4 The Env-D multi-peak dense environment, with increasing terrain and threat complexity, aims to comprehensively test the algorithm's planning capabilities in different scenarios.

[0023] To construct a near-realistic cross-domain task scenario, this embodiment establishes a unified three-dimensional environment model: ; in, X Display three-dimensional geographic space, T static and T dynamic These are static and dynamic threat sets, respectively. The terrain and threat complexity of the four test environments increase sequentially. Specific terrain parameters are shown in Table 1, and core environment parameters are shown in Table 2.

[0024] Table 1

[0025] Table 2

[0026] This unified environment model constructs a near-realistic test benchmark; specific parameters are shown in Table 2. The task starts from the beginning. S (1,1,1) to the finish line E(100,100,80) needs to traverse the water-air medium and pass through multi-height threat areas to verify the algorithm's ability to handle complex cross-domain constraints.

[0027] (1) Three-dimensional geospatial G The space consists of land, ocean, and atmospheric regions. The topographic relief is simulated by superimposing multiple Gaussian peak functions, and the height function is expressed as: ; in, N For the number of mountain peaks, ( x i , y i () represents the coordinates of the mountain peak's center. h i For peak height, σ x,i σ y,i control X , Y The range of directional fluctuations. Defining ocean depth. H ocean ,satisfy Z ( X , Y )≤ H ocean The area is underwater, and the rest is airspace, clearly defining two navigation environments.

[0028] (2) Static Threat Set T static This includes the following two types of fixed threats: Terrain obstacles: if the waypoint P height P Z satisfy P Z <f( P x , P y If the path intrudes into the mountain or underground, it is considered a collision with the terrain, thus preventing the path from encroaching on the mountain or underground. No-fly / no-fly zones include the threat range of defensive facilities such as radar and anti-aircraft guns; in this embodiment, they are modeled as cylindrical or spherical spaces. For example, radar threats... T rader =( x r , y r , R r The threat area is defined as ( x r , y r , H ocean + Rr (The center of the ball) R r The threat space of a hemisphere with radius is represented as: .

[0029] Furthermore, when planning paths based on a hybrid intelligent optimization algorithm, the quality of the path is evaluated using a fitness function, which is a piecewise function, and its construction process includes: Detect whether the path collides with a threat area or terrain; If a collision occurs, a penalty coefficient is applied to the path length to calculate the fitness value; If no collision occurs, the fitness value is calculated based on the physical length of the underwater and above-water portions of the path, combined with the corresponding energy consumption coefficient.

[0030] Specifically, the implementation process of this embodiment includes: Cross-domain path planning aims to find a path from the starting point in a three-dimensional environment model for unmanned systems. S To the finish line E The optimal or suboptimal collision-free path π This belongs to the constrained optimization problem.

[0031] Constraint handling: A feasible path π The following constraints must be met: (1) Boundary constraints: All path points must be located in free space; ; (2) Security constraints: The path must not intersect with any static or dynamic threats; ; (3) Dynamic constraints: The curvature of the path must meet the maximum curvature limit of the platform; .

[0032] Path cost function design: To comprehensively evaluate path quality, a fitness function is designed that takes into account path length, safety, and cross-domain energy loss. F ( π Its construction is based on the difference between collision penalty and energy consumption: (1) Collision penalty mechanism If path π A penalty coefficient is applied upon collision with a threat area or terrain obstacle. η (This embodiment takes) η =1000). Penalty coefficient ηThe path length is much greater than the normal path length, making the fitness value of any collision path significantly worse than that of a feasible path, thus guiding the population to evolve towards collision-free regions. Boundary constraints and dynamic constraints are satisfied through initialization constraints and post-processing methods.

[0033] (2) Cost of cross-domain energy loss The path is blocked by sea level (height) H ocean It is divided into two parts: underwater and above water, with physical lengths of: ; ; To simplify the model and focus on algorithm performance verification, an energy consumption coefficient is set. ρ water = ρ air =1, which means that energy loss is equivalent to path length.

[0034] (3) Final fitness function Considering the above factors, the piecewise function is defined as follows: ; This function guides the algorithm to find the shortest and least energy-intensive feasible path while ensuring safety.

[0035] Furthermore, in each iteration, the hybrid intelligent optimization algorithm performs the following process for each individual in the population: Generate random numbers; If the random number is less than the first adaptive probability, then the update operator of the Whale Optimization Algorithm (WOA) is executed; If the random number is not less than the first adaptive probability and is less than the sum of the first adaptive probability and the second adaptive probability, then the update operator of the Cuckoo Search Algorithm CS is executed. Otherwise, execute the velocity and position update operators of the Particle Swarm Optimization (PSO) algorithm.

[0036] Specifically, the implementation process of this embodiment includes: Overall algorithm framework: Cross-domain path planning across land, sea, and air is an NP-hard problem, characterized by high dimensionality, multimodality, and strong constraints. This makes it difficult for traditional methods and single algorithms such as PSO, CS, and WOA to balance exploration and development, easily leading to premature convergence or insufficient accuracy. Therefore, this embodiment does not simply stack operators, but proposes a hybrid algorithm, PWCS, based on the complementary characteristics of the three, with PSO as the main framework. Its core lies in driving the collaborative search of the three operators through an adaptive probability strategy (Algorithm 1).

[0037] In this embodiment, each particle represents a candidate path, consisting of a fixed number of path points (including a start point and an end point). The coordinates of the path points are randomly initialized within the three-dimensional spatial boundary, with the start point fixed as the task's starting point. S The endpoint is fixed as the mission endpoint. E Intermediate path points are generated randomly. During initialization, it must be ensured that all path points are within the free space boundary.

[0038] like Figure 5 As shown, the framework dynamically schedules the CS (exploration) and WOA (development) operators with an adaptive probability strategy and uses PSO to guarantee basic convergence, thereby effectively balancing the "exploration-development" contradiction in the search process.

[0039] The specific implementation of the adaptive probability strategy is as follows: Let the first adaptive probability be... P 1( t The second adaptive probability is P 2( t ),in t This represents the current iteration number. T This represents the maximum number of iterations. Its dynamic adjustment strategy follows a linear variation law: ; ; And satisfy P 1( t )+ P 2( t )≤1. Where P 1min , P 1max , P 2min , P 2max This is a preset constant that can be set through experimental calibration or experience based on specific task scenarios.

[0040] PSO update operator: The PSO operator serves as the main framework of the algorithm, employing a linearly decreasing inertia weight to balance the search behavior during the iterative process. Its update formula is as follows: ; This operator is the default option in PWCS and is automatically activated when WOA or CS operations are not performed, ensuring basic convergence capability.

[0041] WOA Development Operators: The WOA operator simulates the encirclement and predation behavior of whales and bubble net attacks, and has strong local development capabilities.

[0042] Surround the prey (when | A |<1 hour): ; in, This is the current globally optimal position. , , Decreasing linearly from 2 to 0, It is a random vector.

[0043] Bubble web attack (when) p <0.5 and | A |<1 hour): ; in, , b It is a constant. l It is a random number between [-1, 1].

[0044] CS exploration operator: The CS operator utilizes the Lévy flight mechanism for large-step random exploration to enhance population diversity and avoid premature convergence. Its position update follows the model of equation (3), and the specific calculation and update process is described in Algorithm 4.

[0045] Furthermore, the first adaptive probability and the second adaptive probability are dynamically adjusted according to the iteration process, and the adjustment strategy is as follows: In the early stages of the iteration, a higher second adaptive probability is set; As the iteration proceeds, the second adaptive probability is linearly decreased, while the first adaptive probability is increased.

[0046] Specifically, the implementation process of this embodiment includes: Adaptive selection probability: In PWCS, three operators work synergistically: PSO provides rapid directional exploitation and convergence capabilities, WOA enhances fine-grained searching of the optimal solution region, and CS injects diversity into the population through lévy flight, preventing premature convergence. An adaptive probability strategy dynamically schedules these three operators, forming a collaborative "exploitation-fine-grained search-exploration" model. In the early stages of iteration, a higher CS probability is set to encourage global exploration; as iterations progress, the CS probability is linearly reduced while the WOA probability is increased to strengthen local exploitation. PSO, as the fundamental operator, maintains a consistently high execution probability, ensuring the overall convergence of the algorithm. This mechanism allows the algorithm to dynamically adjust its strategy according to the search phase, effectively balancing exploration and exploitation.

[0047] For the aforementioned complex constraints, a penalty function method is used to process them, and the degree of constraint violation Φ( π Added as a penalty term to the fitness function: ; in, η For a larger penalty coefficient, Φ( π ) represents a path π The sum of the degree of violation of various constraints (such as entering the threat zone, exceeding the boundary, etc.). This method transforms the original constrained problem into an unconstrained optimization problem, guiding the search toward the feasible region.

[0048] Furthermore, the process of executing the update operator of the Cuckoo Search Algorithm CS is the Lévy flight mechanism, which includes: Calculate the random step size that follows a Lévy distribution; A new individual position is generated based on the random step size and the current individual position.

[0049] Specifically, the implementation process of this embodiment includes: Cuckoo Search (CS) Algorithm: The CS algorithm is inspired by the parasitic species of the cuckoo, and its core is the Lévy flight mechanism. Lévy flight generates random walks with step sizes following a heavy-tailed distribution, and its position update is calculated as follows: ; The CS algorithm, with its short step size and occasional large jumps, has a strong global exploration capability and can effectively escape local optima; however, due to the lack of directional guidance in its search, it has a slow convergence speed and insufficient local exploration accuracy.

[0050] Furthermore, the process of executing the update operator of the Whale Optimization Algorithm (WOA) includes: Determine the current behavior pattern based on random numbers and parameters; If it is in the prey encirclement mode, the individual will move to the current global optimal position; If it is a bubble net attack mode, the individual will move along a spiral path towards the current global optimal position.

[0051] Specifically, the implementation process of this embodiment includes: WOA simulates the bubble-net hunting behavior of humpback whales. Its core mechanisms are prey encirclement and spiral renewal. The prey encirclement mechanism is calculated as follows: ; This mechanism gives WOA excellent local exploration capabilities, but its global exploration is relatively limited. The algorithm's characteristics are summarized in Table 3.

[0052] Studies have shown that single algorithms such as PSO, CS, and WOA are difficult to effectively balance exploration and development. This embodiment integrates these three algorithms, mainly based on three considerations: complementary mechanisms (PSO provides a convergence framework, CS enhances global exploration, and WOA is responsible for fine-grained development), balanced performance (simple structure and superior performance), and collaborative feasibility (significant differences in the mathematical characteristics of core operators facilitate adaptive collaboration rather than simple stacking). The characteristics and roles of each algorithm are summarized in Table 3.

[0053] Table 3

[0054] Furthermore, before outputting the 3D path, a post-processing procedure is also included: The planned path point sequence is smoothed using cubic spline interpolation to generate a continuous and smooth flight trajectory.

[0055] Specifically, the implementation process of this embodiment includes: Experimental setup: To verify the effectiveness of the PWCS algorithm, simulation experiments were conducted. The test environment consisted of four cross-domain scenarios involving land, sea, and air, with increasing terrain and threat complexity.

[0056] The experiments were conducted on the MATLAB R2021a platform, with an Intel Core i7-10750H CPU, 16GB of memory, and Windows 10 operating system. The comparison algorithms included PSO, CS, WOA, and two ablation variants: PWCS-PSOWOA (CS removal) and PWCS-PSOCS (WOA removal). To ensure fairness in the comparison, all algorithms shared the same parameters: population size of 30, maximum number of iterations of 100, and 100 independent runs in each environment. Specific parameters are shown in Table 4.

[0057] Table 4

[0058] The following seven evaluation metrics are used to comprehensively evaluate the algorithm performance: best fitness value, worst fitness value, average fitness value, standard deviation, convergence algebra, success rate, and average running time.

[0059] The analysis focuses on two types of environments: Env-B (moderate complexity) to test the algorithm's general performance, and Env-D (multimodal dense) to challenge its extreme programming capabilities. Results from Env-A and Env-C have been included in the comprehensive comparison.

[0060] In the moderately complex environment Env-B, the 3D path comparisons of various algorithms are as follows: Figure 6 As shown, the two-dimensional path comparisons of each algorithm in the Env-B environment are as follows: Figure 7 As shown in Table 5, the performance statistics are as follows.

[0061] Table 5

[0062] In the moderately complex Env-B environment, the performance of each algorithm is as follows: PSO has a tortuous path close to the threat zone, making it prone to getting trapped in local optima. It has the highest fitness (182.24) and requires 84 generations to converge. CS has a jagged path with relatively good fitness (177.02), but converges slowly (60 generations). WOA has an invalid rise at the end of the path, resulting in poor fitness (185.17) and a success rate of only 91%. In contrast, PWCS plans the smoothest path, has the lowest fitness (173.97), converges the fastest (57 generations), and maintains a 100% success rate. Although its average time is slightly higher (0.27s), it achieves the best balance in path quality, convergence speed, and reliability, verifying its effectiveness and practicality in moderately complex environments.

[0063] Extremely Complex Environment (Env-D) Analysis: In the Env-D environment with multi-peak dense threats, the path planning results and convergence curves of each algorithm are shown below. Figure 8 , Figure 9 Quantitative statistics are shown in Table 6.

[0064] Table 6

[0065] In the extremely complex environment of Env-D, the shortcomings of a single algorithm are amplified: PSO converges prematurely and gets stuck in local optima early on; CS suffers from severe oscillations in the convergence curve due to Lévy flight, resulting in poor stability; WOA converges quickly but stops at suboptimal solutions early and lacks development capabilities. Figure 9 The marked failure solutions visually reveal the limitations of the comparative algorithms in planning complex environments. PWCS achieved the lowest fitness value (173.80), a 100% success rate, smooth paths, and comprehensive threat avoidance. Figure 8 Its convergence curve ( Figure 9 It combines rapid descent with continuous optimization, effectively balancing exploration and development, and its planning results are stable and significantly better than all the comparison algorithms.

[0066] Quantitative analysis of overall performance: For a comprehensive evaluation, Table 7 summarizes the overall performance of each algorithm in four test environments (Env-A to Env-D).

[0067] Table 7

[0068] Table 7 summarizes the performance data of each algorithm under four environments. Analysis shows that: (1) Path quality: PWCS has the lowest fitness in all environments, and its advantage increases with the complexity of the environment. Its standard deviation is "small" in all environments, and its stability is significantly better than WOA and CS.

[0069] (2) Convergence characteristics: WOA converges the fastest but is premature; CS converges slowly and oscillates violently; PWCS shows continuous optimization ability in complex environments (such as Env-C still obtaining the optimal solution after 97 iterations).

[0070] (3) Planning reliability: PWCS and PSO maintained a 100% success rate in all environments; the success rates of WOA and CS decreased as the environment deteriorated (95% and 96% respectively in Env-D). PWCS had the best average fitness in most environments.

[0071] (4) Computational efficiency: CS runs the fastest (0.03–0.05s) but the solution quality is poor; WOA is relatively fast (0.10–0.16s) but the success rate and quality are not ideal; PSO takes a moderate amount of time. PWCS takes a slightly longer time (0.27–0.45s), but it achieves a high-quality path and 100% success rate at a moderate time cost.

[0072] It should be noted that WOA and CS exhibit significantly higher worst fitness and standard deviation due to infeasible paths generated during some operations, reflecting the instability of their search strategies. In summary, PWCS demonstrates a balanced performance in path quality, convergence, reliability, and computational efficiency, effectively solving the explore-explore dilemma and possessing significant engineering application value.

[0073] To verify the contributions of each component, ablation experiments were conducted. PWCS-PSOWOA (CS removal), PWCS-PSOCS (WOA removal), and the standard PSO were compared. The paths and convergence curves of each algorithm variant are shown below. Figure 10 , Figure 11 Each algorithm was run 100 times, and the performance is shown in Table 8.

[0074] Table 8

[0075] The results show that removing the CS weakens exploration but increases fitness. The spiral development mechanism of the WOA is indispensable for improving local search accuracy. Removing the WOA impairs the algorithm's development capability, worsening the average fitness to 194.30. The lack of efficient WOA development leads to extremely difficult convergence, resulting in a lengthy and ineffective search, and the runtime surges to 3.46 seconds. The complete PWCS outperforms all variants in both path quality and efficiency. Ablation experiments verify the necessity of PWCS component collaboration.

[0076] Example 2 In this embodiment, a computer terminal device is provided, including: One or more processors; A memory, coupled to the processor, for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the steps of the three-dimensional path planning method for the above-described land, sea and air cross-domain unmanned system.

[0077] In this embodiment, a computer-readable storage medium is also provided, on which a computer program is stored. When the computer program is executed by a processor, it implements the steps of the three-dimensional path planning method for the above-described land, sea and air cross-domain unmanned system.

[0078] This invention provides a three-dimensional path planning method for cross-domain unmanned systems operating across land, sea, and air, effectively overcoming the technical shortcomings of existing methods in this area. Through the constructed unified environment model, it can more realistically simulate complex cross-domain geographical and multi-dimensional threat scenarios, providing a precise input basis for path planning. The proposed hybrid intelligent optimization algorithm organically integrates the core advantages of different algorithms through an adaptive strategy, significantly improving the balance between global exploration and local development capabilities, thereby effectively avoiding premature convergence. This method can plan safe and collision-free paths in test environments of varying complexity, fundamentally guaranteeing its success rate. The planned paths demonstrate superiority in length, smoothness, and comprehensive threat avoidance capabilities. Ultimately, this invention significantly improves the overall efficiency and path planning reliability of cross-domain unmanned systems in complex adversarial environments.

[0079] The above are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A three-dimensional path planning method for a land-sea-air cross-domain unmanned system, characterized in that, include: Obtain geographic information and threat source information for the task area; Based on the aforementioned geographic information and threat source information, a unified three-dimensional environment model is constructed; Based on the hybrid intelligent optimization algorithm, a collision-free three-dimensional path is planned from the starting point to the end point for the unmanned system in the unified three-dimensional environment model. The hybrid intelligent optimization algorithm takes the particle swarm optimization algorithm (PSO) as the main framework and selects to execute the exploration operator of the Cuckoo Search algorithm (CS) or the development operator of the Whale Optimization algorithm (WOA) according to the adaptive probability strategy during the iteration process. Output the planned 3D path.

2. The method according to claim 1, characterized in that, The process of constructing a unified 3D environment model includes: The land terrain undulations of the task area were simulated based on the superposition of Gaussian peak functions. By setting an ocean depth threshold, the three-dimensional environment model is divided into an underwater domain and an above-water domain. The threat areas of radar and anti-aircraft artillery are modeled as hemispherical or cylindrical spaces, and terrain obstacles are modeled as impassable areas.

3. The method according to claim 1, characterized in that, When planning paths based on a hybrid intelligent optimization algorithm, the quality of the path is evaluated using a fitness function, which is a piecewise function. The construction process of this fitness function includes: Detect whether the path collides with a threat area or terrain; If a collision occurs, a penalty coefficient is applied to the path length to calculate the fitness value; If no collision occurs, the fitness value is calculated based on the physical length of the underwater and above-water portions of the path, combined with the corresponding energy consumption coefficient.

4. The method according to claim 1, characterized in that, In each iteration, the hybrid intelligent optimization algorithm performs the following process for each individual in the population: Generate random numbers; If the random number is less than the first adaptive probability, then the update operator of the Whale Optimization Algorithm (WOA) is executed; If the random number is not less than the first adaptive probability and is less than the sum of the first adaptive probability and the second adaptive probability, then the update operator of the Cuckoo Search Algorithm CS is executed. Otherwise, execute the velocity and position update operators of the Particle Swarm Optimization (PSO) algorithm.

5. The method according to claim 4, characterized in that, The first adaptive probability and the second adaptive probability are dynamically adjusted according to the iteration process, and the adjustment strategy is as follows: In the early stages of the iteration, a higher second adaptive probability is set; As the iteration proceeds, the second adaptive probability is linearly decreased, while the first adaptive probability is increased.

6. The method according to claim 4, characterized in that, The process of executing the update operator of the Cuckoo Search Algorithm (CS) is the Lévy flight mechanism, which includes: Calculate the random step size that follows a Lévy distribution; A new individual position is generated based on the random step size and the current individual position.

7. The method according to claim 4, characterized in that, The process of executing the update operator of the Whale Optimization Algorithm (WOA) includes: Determine the current behavior pattern based on random numbers and parameters; If it is in the prey encirclement mode, the individual will move to the current global optimal position; If it is a bubble net attack mode, the individual will move along a spiral path towards the current global optimal position.

8. The method according to claim 1, characterized in that, Before outputting the 3D path, a path post-processing procedure is also included: The planned path point sequence is smoothed using cubic spline interpolation to generate a continuous and smooth flight trajectory.

9. A computer terminal device, characterized in that, include: One or more processors; A memory, coupled to the processor, for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors perform the steps of the method as described in any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-8.

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