Unmanned surface vessel path planning method and system based on enhanced particle swarm optimization

Abstract

The invention belongs to the technical field of path planning, and provides an unmanned surface vessel path planning method and system based on enhanced particle swarm optimization, and the method comprises the steps: obtaining a kinematic equation and a kinetic equation of an unmanned surface vessel in a time-varying ocean current environment; constructing a multi-target fitness function for path planning of the unmanned surface vessel based on the obtained kinematics equation and kinetic equation; and solving the constructed multi-target fitness function by adopting an enhanced particle swarm optimization algorithm to obtain an optimal path of the unmanned surface vessel in the time-varying ocean current environment, and completing path planning of the unmanned surface vessel.

Description

Technical Field

[0001] This invention belongs to the field of path planning technology, specifically relating to a path planning method and system for unmanned surface vessels based on enhanced particle swarm optimization. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Unmanned surface vessels (USVs) are important unmanned platforms for the ocean, widely used in fields such as marine monitoring and resource exploration. When performing missions in complex marine environments, USVs face multiple challenges in path planning, including time-varying ocean current disturbances, obstacle avoidance, and energy consumption optimization.

[0004] Traditional path planning algorithms (such as A*, Dijkstra's algorithm, and fast randomized tree search) can find the shortest path in static obstacle environments, but they struggle to effectively model and utilize dynamic ocean currents, and cannot balance multiple conflicting objectives such as path length, energy consumption, and safety. Swarm intelligence algorithms, represented by particle swarm optimization (PSO), have been introduced into this field due to their powerful global optimization capabilities. However, when dealing with USV path planning—a high-dimensional, nonlinear, strongly constrained optimization problem with complex fitness landscapes—the standard PSO algorithm exhibits shortcomings such as susceptibility to local optima, slow convergence speed, sensitivity to initial solutions, and insufficient utilization of prior environmental knowledge.

[0005] In existing technologies, although some studies have attempted to improve performance by adjusting PSO parameters or combining them with other algorithms, most of them have failed to fundamentally solve the problems of insufficient long-term memory capacity of the algorithms, unintelligent adjustment of search direction, and deep coupling with the dynamic characteristics of the environment. Summary of the Invention

[0006] To address the aforementioned issues, this invention proposes a path planning method and system for unmanned surface vessels based on enhanced particle swarm optimization. It employs an improved particle swarm optimization algorithm that integrates fractional calculus and higher-order iterative learning laws, comprehensively considering multiple optimization objectives such as path length, energy consumption, safety, and convergence speed, in order to improve the path planning efficiency of unmanned surface vessels in time-varying ocean current environments.

[0007] According to some embodiments, the first aspect of the present invention provides a path planning method for unmanned surface vessels based on enhanced particle swarm optimization, employing the following technical solution: A path planning method for unmanned surface vessels based on enhanced particle swarm optimization includes: Obtain the kinematic and dynamic equations of an unmanned surface vessel in a time-varying ocean current environment; Based on the obtained kinematic and dynamic equations, a multi-objective fitness function for unmanned surface vessel path planning is constructed. An enhanced particle swarm optimization algorithm is used to solve the constructed multi-objective fitness function, thereby obtaining the optimal path of the unmanned surface vessel in a time-varying ocean current environment and completing the path planning of the unmanned surface vessel.

[0008] As a further technical limitation, the obtained kinematic equations of the unmanned surface vessel are: ;in, This refers to the ground speed of the unmanned surface vessel. For the propulsion time of the unmanned surface vessel; The propulsion speed of the unmanned surface vessel; The speed of the ocean current, i.e., the position. and time The function.

[0009] As a further technical limitation, the obtained dynamic equations of the unmanned surface vessel are as follows: ;in, The total energy consumption of unmanned surface vessels navigating in the marine environment; The energy consumption of the propulsion system for unmanned surface vessels navigating in the marine environment. m is the mass of the unmanned surface vessel. The drag coefficient, For the first The speed of advancement of the segment path, For the first Travel time for a segment of the route The term represents the change in kinetic energy. The power integral term for overcoming resistance; The impact of ocean currents on the energy consumption of unmanned surface vessels navigating in the marine environment. , It is the dot product of propulsion velocity and ocean current velocity.

[0010] Furthermore, the constructed multi-objective fitness function for unmanned surface vessel path planning is: ;in, It is a sequence of path points. This is the path length weighting coefficient. For path length, , n The total number of path points. For the first i The location coordinates of each path point Denotes the Euclidean norm; The energy consumption cost weighting coefficient is used. For the cost of energy consumption, ; For the safety cost weighting coefficient, For the sake of safety, , path point Distance to the nearest obstacle; The smoothness cost weighting coefficient, For the sake of smoothness, , , , These are vectors of adjacent path segments.

[0011] As a further technical limitation, the enhanced particle swarm optimization algorithm employs fractional-order calculus and a higher-order iterative learning mechanism; wherein, the fractional-order calculus adopts a fractional-order history memory mechanism based on the definition of the fractional derivative of Caputo; the higher-order iterative learning mechanism utilizes a fitness improvement mechanism of multiple historical iterations to dynamically adjust the learning rate decay factor according to the environmental complexity to complete the learning of higher-order terms.

[0012] As a further technical constraint, a nonlinear adaptive inertial weight update mechanism is adopted to modulate the complexity of ocean currents. Combined with particle momentum, it escapes the local optimal state caused by eddies and countercurrents, and optimizes the path of the unmanned surface vessel in the time-varying ocean current environment.

[0013] According to some embodiments, a second aspect of the present invention provides an unmanned surface vessel path planning system based on enhanced particle swarm optimization, employing the following technical solution: An unmanned surface vessel path planning system based on enhanced particle swarm optimization includes: The acquisition module is configured to acquire the kinematic and dynamic equations of an unmanned surface vessel in a time-varying ocean current environment. The module is configured to construct a multi-objective fitness function for path planning of unmanned surface vessels based on the acquired kinematic and dynamic equations. The planning module is configured to use an enhanced particle swarm optimization algorithm to solve the constructed multi-objective fitness function, obtain the optimal path of the unmanned surface vessel in a time-varying ocean current environment, and complete the path planning of the unmanned surface vessel.

[0014] According to some embodiments, a third aspect of the present invention provides a computer-readable storage medium, employing the following technical solution: A computer-readable storage medium having a program stored thereon that, when executed by a processor, implements the steps in the unmanned surface vessel path planning method based on enhanced particle swarm optimization as described in the first aspect of the present invention.

[0015] According to some embodiments, the fourth aspect of the present invention provides an electronic device, which adopts the following technical solution: An electronic device includes a memory, a processor, and a program stored in the memory and running on the processor, wherein the processor executes the program to implement the steps in the unmanned surface vessel path planning method based on enhanced particle swarm optimization as described in the first aspect of the present invention.

[0016] According to some embodiments, the fifth aspect of the present invention provides a computer program product, which adopts the following technical solution: A computer program product includes software code, wherein the program in the software code performs the steps of the unmanned surface vessel path planning method based on enhanced particle swarm optimization as described in the first aspect of the present invention.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention is based on the fractional-order historical memory mechanism defined by Caputo, which enhances global search capabilities by utilizing historical evolution information and effectively avoids local optima. It designs a high-order iterative learning law to dynamically adjust the search direction according to the performance improvement trend, thereby accelerating the convergence process. It adopts a nonlinear decreasing inertial weight and dynamic balancing learning factor strategy to adaptively adjust the balance between exploration and development. It introduces an intelligent restart mechanism and a diversity preservation strategy to enhance the robustness of the algorithm. Attached Figure Description

[0018] The accompanying drawings, which form part of this embodiment, are used to provide a further understanding of this embodiment. The illustrative embodiments and their descriptions are used to explain this embodiment and do not constitute an improper limitation of this embodiment.

[0019] Figure 1 This is a flowchart of the unmanned surface vessel path planning method based on enhanced particle swarm optimization in Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the kinematic equations of the unmanned surface vessel in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of the dynamic equations of the unmanned surface vessel in Embodiment 1 of the present invention; Figure 4 This is a schematic diagram of the kinematic model of the unmanned surface vessel in Embodiment 1 of the present invention; Figure 5 This is a schematic diagram of time-varying flow field modeling for an unmanned surface vessel in Embodiment 1 of the present invention; Figure 6 This is a schematic diagram of the headwind current environment in Embodiment 1 of the present invention; Figure 7 This is a schematic diagram of the time-varying ocean current environment in Embodiment 1 of the present invention; Figure 8 This is a schematic diagram of the path planning results in Embodiment 1 of the present invention; Figure 9This is a schematic diagram of the downstream ocean current path planning in Embodiment 1 of the present invention; Figure 10 This is a schematic diagram of the evolution process of the downwind ocean current in Embodiment 1 of the present invention; Figure 11 This is a schematic diagram of three-dimensional statistical comparison of energy consumption with the wind and ocean current in Embodiment 1 of the present invention; Figure 12 This is a schematic diagram of energy consumption analysis in the downstream ocean current path segment of Embodiment 1 of the present invention; Figure 13 This is a schematic diagram of the headwind and tailwind ocean current path planning in Embodiment 1 of the present invention; Figure 14 This is a three-dimensional statistical comparison diagram of energy consumption against ocean currents in Embodiment 1 of the present invention; Figure 15 This is a schematic diagram of energy consumption analysis of the counter-wind ocean current path segment in Embodiment 1 of the present invention; Figure 16 This is a schematic diagram of the evolution process of the counter-wind ocean current in Embodiment 1 of the present invention; Figure 17 This is a schematic diagram comparing the convergence curves of different algorithms for counter-current ocean currents in Embodiment 1 of the present invention; Figure 18 This is a schematic diagram of the alternating ocean current and downwind ocean current path planning in Embodiment 1 of the present invention; Figure 19 This is a schematic diagram comparing the convergence curves of different algorithms for alternating ocean currents in Embodiment 1 of the present invention; Figure 20 This is a schematic diagram of the evolution process of alternating ocean currents in Embodiment 1 of the present invention; Figure 21 This is a schematic diagram of energy consumption analysis of the alternating ocean current path segment in Embodiment 1 of the present invention; Figure 22 This is a structural block diagram of the unmanned surface vessel path planning system based on enhanced particle swarm optimization in Embodiment 2 of the present invention. Detailed Implementation

[0020] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0022] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0023] In this invention, terms such as "upper," "lower," "left," "right," "front," "back," "vertical," "horizontal," "side," and "bottom" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used only to facilitate the description of the structural relationships of the various components or elements of this invention and do not specifically refer to any component or element in this invention. They should not be construed as limiting the invention.

[0024] In this invention, terms such as "fixed connection," "connected," and "linked" should be interpreted broadly, indicating a fixed connection, an integral connection, or a detachable connection; a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can determine the specific meaning of these terms in this invention based on the specific circumstances, and they should not be construed as limitations on the invention.

[0025] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0026] Example 1 Embodiment 1 of this invention introduces a path planning method for unmanned surface vessels based on enhanced particle swarm optimization.

[0027] like Figure 1 The method for unmanned surface vessel path planning based on enhanced particle swarm optimization, as shown, includes: Obtain the kinematic and dynamic equations of an unmanned surface vessel in a time-varying ocean current environment; Based on the obtained kinematic and dynamic equations, a multi-objective fitness function for unmanned surface vessel path planning is constructed. An enhanced particle swarm optimization algorithm is used to solve the constructed multi-objective fitness function, thereby obtaining the optimal path of the unmanned surface vessel in a time-varying ocean current environment and completing the path planning of the unmanned surface vessel.

[0028] To achieve path planning for unmanned surface vessels with ocean current sensing capabilities, this embodiment employs an enhanced particle swarm optimization (E-PSO) algorithm, integrating four collaborative innovation mechanisms, specifically: 1) Fractional-order historical memory mechanism, namely a memory system based on the fractional derivative of Caputo, can capture and utilize the long-range time dependence in the evolution of particle velocity, thereby enabling complex learning from historical optimization trajectories.

[0029] 2) High-order iterative learning strategies, namely adaptive learning mechanisms, selectively strengthen the speed components related to fitness improvement in multiple consecutive iterations, thereby accelerating the convergence to a high-quality solution.

[0030] 3) Adaptive inertial weight decay with sinusoidal acceleration factor, that is, the non-linear decreasing inertial weight combined with the sinusoidal modulation of cognitive and social acceleration coefficients, can dynamically balance global exploration and local development throughout the optimization process.

[0031] 4) Ocean sensing particle initialization and adaptation, namely the initialization strategy, which allocates 30% of the population to trajectories consistent with the favorable water flow direction, and combines the ocean water flow adaptation term during operation to guide the particles to move towards areas with higher energy efficiency.

[0032] This embodiment primarily addresses the problem of autonomous path planning for unmanned surface vessels (USVs) in complex marine environments. In the presence of time-varying ocean currents, the USV needs to navigate from its initial position... Move to target location At the same time, it is necessary to avoid static obstacles and adapt to the ocean current field that changes in space and time. Under the premise of comprehensively considering multiple indicators such as path length, energy consumption, smoothness and safety, the total cost function should be minimized to determine an optimal collision-free path.

[0033] The kinematic model of the unmanned surface vessel in this embodiment is as follows: Figure 4 As shown, this includes the dynamic equations and kinematic equations, specifically: In the marine environment, the movement of a USV is influenced by both its own propulsion system and ocean currents. For example... Figure 2 The kinematic equations shown give the USV's actual ground velocity as follows: (1) in, For USV advancement time, The velocity of the USV relative to the ground is (m / s). The propulsion speed of the USV is (m / s). Let p be the ocean current velocity (m / s), which is a function of position p and time t.

[0034] like Figure 3 The dynamic equations of the USV shown indicate that the total energy consumption during navigation in a marine environment consists of two parts: propulsion system energy consumption and energy consumption due to ocean currents. (2) The propulsion system needs to overcome the inertia and hydrodynamic drag of the USV, and its energy consumption is calculated as follows: (3) Where m is the mass of USV. The drag coefficient, For the first The speed of advancement of the segment path (m / s). For the first The travel time (s) of the segment path; in formula (3), the first term The term represents the change in kinetic energy, the second term. The power integral term is used to overcome resistance.

[0035] The effect of ocean currents on USVs can be either assist (with the current) or resistance (against the current), and its impact on energy consumption is as follows: (4) in, This is the dot product of propulsion velocity and ocean current velocity. When hour, <0 indicates energy saving; when hour, A value greater than 0 indicates an increase in energy consumption. In a still water environment, ,therefore .

[0036] The time-varying flow field modeling of the unmanned surface vessel in this embodiment is as follows: Figure 5 As shown, specifically: (1) Still water environment (no ocean currents) As a baseline scenario, this environment is free from ocean currents, primarily validating the algorithm's path planning capabilities in a purely obstacle-based environment. The kinematic model of the USV in a still water environment is simplified as follows: (5) (6) in This represents the actual velocity vector (m / s) of the USV. Let m be the expected velocity vector of the USV relative to the water body. In this scenario, the total energy consumption equals the propulsion energy consumption, and m = 50 kg is the mass of the USV. =0.5 is the drag coefficient. =2.0m / s is the cruising speed, and Δt is the travel time for the path segment.

[0037] (2) Downwind ocean current environment In this scenario, the ocean current direction is basically consistent with the path travel direction, and the angle between them is θ∈[0°,90°). This scenario best demonstrates the algorithm's ability to utilize favorable ocean currents to reduce energy consumption and shorten travel time. The mathematical model of the ocean current field is as follows: (7) (8) in, Let A be the spatial velocity distribution function, A = 0.2 be the time-varying amplitude, and ω = 2π / 360. o rad / s is the angular frequency (period 1 hour), φ=0 is the initial phase. Let be the unit direction vector from the starting point to the ending point. =0.5 m / s as the base flow velocity, This represents the distance from the current location to the center of the map. This represents the normalized maximum radius.

[0038] (3) Adversary ocean current environment like Figure 6 As shown, in this scenario, the ocean current direction is opposite to the path travel direction, with an angle θ∈(90°,180°] between them. This is the most challenging scenario, examining the algorithm's ability to cope with adverse current conditions and its energy consumption control strategy. The mathematical model of the ocean current field is: (9) The negative sign indicates that the ocean current direction is opposite to the path direction; the other parameters are the same as in the downwind scenario. In the energy consumption calculation for the impact of ocean currents in the upwind scenario, the dot product Vd... Vc < 0, resulting in an increase in energy consumption, Ecurrent > 0.

[0039] (4) Time-varying ocean current environment like Figure 7 The simulation shown depicts a time-varying ocean current environment in a real ocean, featuring a complex current field with two main currents and a double-vortex structure. This scenario best tests the algorithm's intelligent decision-making capabilities in highly complex and spatially non-uniform flow fields. The current field employs a superposition model: (10) (11) (12) in, Main ocean current component ( i =1,2), For vortex components (j=1,2) =2.0、 = 1.5 is the main ocean current intensity coefficient (positive and negative indicate opposite directions). To get to the center , The distance (H and W are the map height and width, respectively). =50、 =40 is the attenuation coefficient. Let be the rotation transformation matrix. =1.0、 = 0.8 represents the vortex intensity (positive or negative indicates clockwise / counterclockwise). To reach the center of the vortex , distance, =15、 =20 is the vortex attenuation coefficient. , This represents the relative coordinate difference.

[0040] In this embodiment, path quality is evaluated by a combination of several conflicting metrics. For example, bypassing obstacles can improve safety but increases path length and energy consumption; utilizing ocean currents can reduce energy consumption but may deviate from the shortest path. This embodiment employs a multi-objective fitness function to comprehensively assess the merits of the path.

[0041] To evaluate path quality, this embodiment employs a multi-objective fitness function that balances competing objectives, namely... (13) in, It is a sequence of path points. This is the path length weighting coefficient. For path length, The energy consumption cost weighting coefficient is used. For the cost of energy consumption, For the safety cost weighting coefficient, For the sake of safety, The smoothness cost weighting coefficient, This is at the cost of smoothness.

[0042] Path length reflects the actual distance traveled by the USV from the starting point to the destination. It is a fundamental indicator for path planning, and its calculation formula is as follows: (14) Where n is the total number of path points, The coordinates (in raster units) of the i-th path point. Represents the Euclidean norm; the actual physical length is δ = 1.0 m / grid is the grid resolution. A shorter path length means higher path planning efficiency.

[0043] The energy cost is directly taken as the total energy consumption, encouraging the algorithm to find paths that can fully utilize the ocean current's assistance, i.e.: (15) Safety cost measures the distance between the path and obstacles, reflecting the safety of the path. (16) in, path point Distance to the nearest obstacle =3 is the safety radius (grid unit). When The safety cost at that point is 0; otherwise, it increases quadratically as the distance decreases. Smaller This indicates a safer path. The degree of turning in the smoothness cost assessment path affects the maneuverability and energy consumption of the USV, i.e. (17) (18) in, , These are vectors of adjacent path segments. Smaller. This indicates a smoother path with fewer turns, which helps reduce control difficulty and mechanical wear.

[0044] The comprehensive settings in this embodiment enable the optimization algorithm to find a path that achieves a balance between optimal travel distance, energy efficiency, trajectory smoothness, and collision safety, while also clearly taking into account the beneficial or detrimental effects of time-varying ocean currents.

[0045] This embodiment employs an Enhanced Particle Swarm Optimization (E-PSO) algorithm based on fractional-order calculus and higher-order iterative learning mechanisms to address the USV path planning challenge in complex time-varying ocean current fields. It mainly integrates four key innovations: Caputo fractional-order history memory, higher-order iterative learning, adaptive inertial weight decay, and ocean-sensing particle initialization.

[0046] The classic particle swarm optimization algorithm uses iterative equations to explore the optimal position of an individual particle. ) and global optimal position ( The gauge velocity and position update equations are used to update the particle's position and velocity to achieve the optimal solution. The equations for updating the gauge velocity and position are expressed as follows: (19) (20) in, It is a particle At any moment speed; It is a particle At any moment Location; , These represent cognitive and social factors, respectively, which control the particle to adjust its speed based on its individual and global optimal positions. , for Random numbers within an interval; The inertial weight controls the degree to which the particle's current velocity affects its new position.

[0047] While effective for simple optimization problems, standard PSO encounters significant limitations when handling USV path planning in complex marine environments: First, the complex time-varying functions of ocean current interactions, favorable / unfavorable currents, and spatially non-uniform flow fields create a multimodal fitness landscape. Second, the high-dimensional constraint space simultaneously satisfies collision avoidance, path smoothing, energy minimization, and ocean current development requirements. Third, prematurely convergent standard PSO lacks sufficient detection capability in complex environments, leading to suboptimal local solutions. To address these challenges, this embodiment proposes an Enhanced Particle Swarm Optimization (E-PSO) algorithm with four collaborative improvement strategies.

[0048] Traditional particle swarm optimization algorithms only utilize information from the current iteration and lack long-term memory capabilities. To enhance temporal memory and achieve complex trajectory learning, this embodiment incorporates a fractional-order historical memory mechanism based on the definition of the fractional derivative of Caputo.

[0049] The formula for Caputo fractional memory components is: (twenty one) in, ∈(0,1) is the fractional-order parameter, m is the memory depth, k is the historical backtracking index coefficient, k=1 corresponds to the "previous time", and k=m corresponds to the "farthest time". It is a particle At any moment speed, It is a particle At any moment speed, The formula for calculating the Caputo weighting coefficient is: (twenty two) in, ∈(0,1) is a fractional parameter that controls the rate of memory decay; m is the memory depth (historical algebra); k is the historical backtracking index (k=1 for the previous generation, k=m for the furthest history). For particles In the The speed of the generation; h=1 is the time step; Γ( () is the Gamma function; this fractional mechanism has significant advantages: firstly, by adjusting... The memory length can be continuously adjusted when... When the algorithm retains long-term memory, it retains long-term memory when the memory is small. When the current value is large, the algorithm prioritizes short-term memory, providing flexible memory control. Secondly, the Caputo weights allow the importance of historical information to decrease naturally over time, preserving key motion patterns while avoiding information saturation. Furthermore, the fractional derivative maintains long-term dependency characteristics, enabling the algorithm to effectively capture and utilize the temporal evolution patterns within the ocean current environment.

[0050] In this embodiment, fractional-order parameters Determined adaptively based on environmental complexity: (twenty three) This represents a measure of normalized ocean current complexity, i.e. (twenty four) in, The average ocean current velocity, This is the maximum speed of the USV. ∈[0.4,0.8], the more complex the ocean currents, The larger the ocean current, the more the algorithm focuses on recent history; the calmer the ocean current, the more... The smaller the value, the more the algorithm relies on long-term experience.

[0051] To accelerate convergence and improve solution accuracy, this embodiment introduces a high-order iterative learning mechanism that utilizes the fitness improvement trend of multiple historical iterations. Inspired by iterative learning control theory, it adaptively adjusts the particle search direction based on the performance evolution pattern.

[0052] Higher-order learning terms are defined as: (25) in, ∈(0,1) is the learning rate decay factor. It is a particle At any moment speed, This represents the fitness improvement between successive iterations, where m is the learning and memory depth.

[0053] Learning weights as It decreases exponentially, emphasizing recently successful search directions while gradually reducing the influence of old trajectories. max(0, The operator ensures that only the velocity component related to fitness improvement contributes to the learning term, thus realizing a selective reinforcement mechanism.

[0054] Learning rate decay factor for marine environments Dynamically adjusted according to environmental complexity: (26) Where ∈[0.75, 0.95], = + Combined with obstacle density ( ) and ocean current complexity ( ), is the comprehensive environmental difficulty index.

[0055] The high-order learning strategy provides three key benefits: by weighting the velocity vectors, the algorithm can automatically identify and strengthen effective search directions according to their related fitness improvements; multi-iteration aggregation smooths the random fluctuations of single-iteration performance and enhances the stability of the algorithm; when trapped in local optima (consecutive small values), the reduced learning term allows other PSO components to promote exploration into new regions.

[0056] During the entire optimization process, the inertia weight w critically balances global exploration and local exploitation. Traditional fixed or linearly decreasing inertia weights cannot adapt to different convergence characteristics in the ocean environment. For this reason, this embodiment adopts a non-linear adaptive inertia weight update mechanism, that is (27) (28) Where Φ(t) is a smooth transition function, = 0.9, = 0.4, k is the current iteration, and T is the maximum number of iterations.

[0057] The cosine-squared function Φ(t) realizes a gradual transition from exploration to exploitation. In the early iterations (k << T), Φ(T) ≈ 1, and w ≈ , promoting extensive exploration and identifying promising regions in the search space. In the middle iterations (k ≈ T / 2), Φ(T) decreases steadily, gradually shifting towards exploitation while maintaining sufficient exploration ability. In the late iterations (k → T), Φ(T) → 0, and w ≈ , focusing on local refinement and solution accuracy.

[0058] For the ocean environment, the adaptive weight is further adjusted according to ocean current complexity: [[ID=5s3]](29) This modulation increases the inertia in the complex ocean environment, enhances the particle momentum, and escapes from local optimal states caused by vortices and countercurrents, is the ocean current complexity.

[0059] To achieve a dynamic balance between exploration and development, the cognitive (c1) and social (c2) acceleration coefficients in this embodiment are adjusted using a sine function: (30) (31) in, = 2.5, = 1.0, = 0.5, = 2.5, where k is the current iteration and T is the maximum number of iterations.

[0060] The sinusoidal modulation in this embodiment enables a smooth transition from individual-oriented exploration in the early iterations (high c1, low c2) to group-oriented development in the later iterations (low c1, high c2), promoting comprehensive search space coverage, followed by convergence refinement.

[0061] Standard random initialization cannot utilize prior knowledge of favorable ocean current patterns. Therefore, this embodiment introduces an ocean-aware initialization strategy, which guides the initial population by initializing 30% along the direction of ocean currents to improve the quality of the initial solution and the convergence speed.

[0062] Randomly select an initial location on the map ( Then read the ocean current information at that location. ( According to ocean current strength Different generation strategies are employed: (1) Strong ocean current areas ( >0.1m / s When the ocean current is strong, particles move along the direction of the current to generate the next waypoint: (32) (33) in, The starting position is randomly selected; This is the ocean current velocity vector at that location; The magnitude of the ocean current speed, The basic step size unit is λ, which is the step size magnification factor. The stronger the ocean current, the larger the step size magnification factor λ, so that particles can make fuller use of the strong ocean current region.

[0063] (2) Weak ocean current areas ( ≤0.1m / s When ocean currents are weak, small-scale random perturbations can be performed to maintain exploration diversity. (34) Here, rand(-7.5, 7.5) represents a random perturbation within the range [-7.5, 7.5]. In this case, the algorithm degenerates into random initialization to avoid unnecessary bias in weak flow regions.

[0064] To balance the quality of the initial solution and the diversity of the population, the algorithm employs a hybrid initialization strategy: 30% of the particles are initialized using ocean-guided initialization (utilizing ocean current information), while 70% of the particles are initialized using standard random initialization (maintaining diversity). This strategy provides high-quality initial solutions while preventing the population from converging prematurely to local regions.

[0065] To prevent premature convergence and avoid stagnation, during continuous iteration... When the improvement in fitness stagnates, this embodiment triggers a smart restart mechanism: (35) Among them, the favorable flow = 0.6, vortex flow = 0.8, countercurrent = 1.3, This is a comprehensive environmental difficulty index.

[0066] After restarting and reactivation, the following steps are executed: First, the elite preservation strategy retains the top 25% of particles in terms of fitness, ensuring that high-quality solutions discovered are not discarded. Second, the ocean-guided reinitialization strategy reinitializes the remaining 50% of particles using the ocean-sensing strategy (Formulas 28-30), refocusing the population on favorable ocean current regions. Then, the random perturbation mechanism randomly distributes the remaining 25% near the global optimum with a noise amplitude of 35 grid units, increasing the diversity of local exploration. Finally, the memory reset operation clears historical velocities and fitness records to facilitate new explorations and avoid interference from outdated information.

[0067] Integrating all enhancement components, the complete E-PSO speed update equation is: (36) (37) (38) in: It is a particle At any moment speed, , These represent cognitive and social factors, respectively, which control the particle to adjust its speed based on its individual and global optimal positions. The nonlinear adaptive inertia weights at the t-th iteration. , for Random numbers in an interval For fractional memory terms, For higher-order iterative learning terms, = 0.35sin( () represents the fractional memory weights. = 0.25 For higher-order learning weights, For ocean current adaptation, = 0.4 For ocean adaptation weights, = 0.1 To maintain weights for diversity, For ocean current adaptation, D(t) is the stochastic diversity term. = 0.5 is the adaptive strength coefficient. The current position of particle i The ocean current velocity vector at that location, = 0.05, Let k be a uniform random vector, and T be the number of previous iterations and T be the maximum number of iterations.

[0068] The computational complexity of each iteration of E-PSO is: (39) in, d is the total size, d is the dimension, and m is the memory depth. For the number of obstacles, The number of grid cells used for ocean current assessment.

[0069] With a complexity of O(PSO) = O( Compared to the standard PSO, E-PSO introduces approximately ( + The cost factor, in typical values ​​m≈7-10, d≈12-16 and A value of ≈10-20 is still acceptable.

[0070] Case Analysis In this embodiment, the experimental scenario is a 150×150 grid map containing multiple irregular static obstacles. The starting point is set to... = [10, 120], endpoint set to = [140, 40], grid resolution is 1.0 m / grid. USV safety radius is set to 2 grids, and maximum steering angle is 30°.

[0071] The experiment was designed with four environmental scenarios: (1) Still water environment ( = 0); (2) Downwind current environment (current direction is consistent with the desired course); (3) Upwind current environment (current direction is opposite to the desired course); (4) Complex vortex current environment (containing 2 main currents and 2 vortices). The mathematical models of the ocean current field are shown in formulas (5), (6), (7), (8), (9), (10), (11) and (12).

[0072] The USV physical and ocean current parameters are set as shown in Table I. All comparison algorithms used the same population size (1200) and number of iterations (300) to ensure fairness. Ten independent experiments were conducted for each scenario, and the average performance was statistically analyzed. The experiments were run on a computer configured with an Intel i7-12700H CPU and an NVIDIA RTX 3060 GPU, and the algorithm was implemented based on MATLAB R2023a.

[0073] Table 1. Physical parameters and ocean current parameters of the USV

[0074] To comprehensively evaluate algorithm performance, this embodiment establishes a multi-dimensional evaluation index system: (1) Path length Path length reflects the sailing distance and is a basic indicator for path planning, which is calculated based on formula (12).

[0075] (2) Sailing time The sailing time represents the total time required for the USV to complete the entire route, taking into account both the route length and the influence of ocean currents. (40) in, Let be the physical length (m) of the i-th path segment. Let be the actual ground velocity vector (m / s) of the USV in the i-th segment. For the desired propulsion velocity vector, Let be the ocean current velocity vector at the midpoint of this segment. In still water conditions, ,but ,in =2.0 m / s is the cruising speed. The short sailing time demonstrates the algorithm's effective use of ocean currents.

[0076] (3) Energy consumption indicators Total energy consumption is the core indicator for evaluating the economic efficiency of route planning. A complete mathematical model of energy consumption is established based on the law of conservation of energy, and the calculation is based on formulas (3) and (4).

[0077] (4) Ocean current utilization rate index (only applicable to scenarios with ocean currents) Ocean current utilization rate quantifies the degree to which the algorithm utilizes favorable ocean currents, reflecting the consistency between the path and the direction of the ocean current. (41) (42) in, Let be the angle between the direction of the i-th path segment and the direction of the ocean current at the midpoint of that segment. The unit direction vector of the path segment. The unit direction vector of the ocean current. ∈[ [100%, 100%], the larger the value, the more the path tends to sail with the current, and the more fully the algorithm makes use of the ocean current.

[0078] (5) Security Costs The safety cost reflects the proximity of the path to the obstacle and is obtained based on formula (14).

[0079] (6) Smoothing cost The smoothness cost reflects the severity of the path change, based on formulas (15) and (16).

[0080] Still water environment experiment results In a still water environment without the influence of ocean currents, the path planning results of the four algorithms are shown in Table 2 and... Figure 8 As shown, the enhanced PSO (green curve) plan has the shortest and smoothest path, effectively avoiding all obstacle areas; the basic PSO (pink curve) and GA (red curve) plans have similar paths with moderate lengths; while the SSA (blue curve) plan has a significantly longer path with considerable detours.

[0081] Table 2 Path Planning Results

[0082] The results of the downstream ocean current environment experiment are as follows: Figure 9 , Figure 10 , Figure 11 , Figure 12 As shown in Table 3; the experimental results of the reverse ocean current environment are as follows: Figure 13 , Figure 14 , Figure 15 , Figure 16 , Figure 17 As shown in Table 4; the experimental results of alternating ocean current environment are as follows: Figure 18 , Figure 19 , Figure 20 , Figure 21 As shown in Table 5.

[0083] Table 3 Results of Downwind Currents

[0084] Table 4 Results of the counter-wind current

[0085] Table 5 Results of alternating ocean currents

[0086] This embodiment introduces an ocean current-aware initialization strategy, encouraging the population to explore favorable ocean current areas and improving the quality of initial solutions. It proposes a fractional-order historical memory mechanism based on Caputo's definition, utilizing historical evolutionary information to enhance global search capabilities and effectively avoid local optima. A high-order iterative learning law is designed to dynamically adjust the search direction based on performance improvement trends, accelerating the convergence process. A nonlinear decreasing inertia weight and dynamic balancing learning factor strategy are employed to adaptively adjust the balance between exploration and development. An intelligent restart mechanism and a diversity preservation strategy are introduced to enhance the algorithm's robustness. Extensive simulation experiments in four typical ocean environments (still water, downwind current, upwind current, and complex vortex current) demonstrate that the improved PSO algorithm significantly outperforms the standard PSO, Genetic Algorithm (GA), and Sparrow Search Algorithm (SSA) in path planning, energy consumption optimization, and operational stability. Specifically, in a downwind current environment, the improved PSO algorithm achieves energy consumption reductions of 61.4% and 77.4% compared to the standard PSO and SSA, respectively, with a current utilization rate of 94.3%. In terms of path length, the improved PSO algorithm shortens the path by 14.5% and 32.7% compared to the standard PSO and SSA in still water environments, respectively. Furthermore, the improved PSO algorithm converges 39.2% faster than the standard PSO and has a 57.2% lower standard deviation, demonstrating superior stability.

[0087] Example 2 Embodiment 2 of the present invention introduces an unmanned surface vessel path planning system based on enhanced particle swarm optimization.

[0088] like Figure 22 The illustrated unmanned surface vessel path planning system based on enhanced particle swarm optimization includes: The acquisition module is configured to acquire the kinematic and dynamic equations of an unmanned surface vessel in a time-varying ocean current environment. The module is configured to construct a multi-objective fitness function for path planning of unmanned surface vessels based on the acquired kinematic and dynamic equations. The planning module is configured to use an enhanced particle swarm optimization algorithm to solve the constructed multi-objective fitness function, obtain the optimal path of the unmanned surface vessel in a time-varying ocean current environment, and complete the path planning of the unmanned surface vessel.

[0089] The detailed steps are the same as those of the unmanned surface vessel path planning method based on enhanced particle swarm optimization provided in Example 1, and will not be repeated here.

[0090] Example 3 Embodiment 3 of the present invention provides a computer-readable storage medium.

[0091] A computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps in the unmanned surface vessel path planning method based on enhanced particle swarm optimization as described in Embodiment 1 of the present invention.

[0092] The detailed steps are the same as those of the unmanned surface vessel path planning method based on enhanced particle swarm optimization provided in Example 1, and will not be repeated here.

[0093] Example 4 Embodiment 4 of the present invention provides an electronic device.

[0094] An electronic device includes a memory, a processor, and a program stored in the memory and running on the processor. When the processor executes the program, it implements the steps in the unmanned surface vessel path planning method based on enhanced particle swarm optimization as described in Embodiment 1 of the present invention.

[0095] The detailed steps are the same as those of the unmanned surface vessel path planning method based on enhanced particle swarm optimization provided in Example 1, and will not be repeated here.

[0096] Example 5 Embodiment 5 of the present invention provides a computer program product.

[0097] A computer program product includes software code, wherein the program in the software code performs the steps of the unmanned surface vessel path planning method based on enhanced particle swarm optimization as described in Embodiment 1 of the present invention.

[0098] The detailed steps are the same as those of the unmanned surface vessel path planning method based on enhanced particle swarm optimization provided in Example 1, and will not be repeated here.

[0099] The above description is merely a preferred embodiment of this practice and is not intended to limit the scope of this practice. Various modifications and variations can be made to this practice by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of this practice should be included within the protection scope of this practice.

Claims

1. An unmanned surface vehicle path planning method based on enhanced particle swarm optimization, characterized in that, The method comprises the following steps: acquiring kinematic equation and dynamic equation of an unmanned surface vehicle in a time-varying ocean current environment; constructing a multi-objective fitness function for path planning of the unmanned surface vehicle based on the acquired kinematic equation and dynamic equation; solving the constructed multi-objective fitness function by using an enhanced particle swarm optimization algorithm to obtain an optimal path of the unmanned surface vehicle in the time-varying ocean current environment, and completing path planning of the unmanned surface vehicle.

2. An unmanned surface vehicle path planning method based on enhanced particle swarm optimization according to claim 1, characterized in that, The obtained kinematic equation of the unmanned surface vehicle is ; wherein, is the ground speed of the unmanned surface vehicle; is the propulsion time of the unmanned surface vehicle; is the propulsion speed of the unmanned surface vehicle; is the sea current speed, i.e. the function of the position and the time .

3. An unmanned surface vehicle path planning method based on enhanced particle swarm optimization according to claim 1, characterized in that, The obtained dynamics equation of the unmanned surface vehicle is ; wherein, is the total energy consumption of the unmanned surface vehicle sailing in the marine environment; is the energy consumption of the propulsion system of the unmanned surface vehicle sailing in the marine environment, m is the mass of the unmanned surface vehicle, is the resistance coefficient, is the propulsion speed of the first section path, is the sailing time of the first section path, is the kinetic energy change term, is the power integral term for overcoming resistance; is the energy consumption of the ocean current influence of the unmanned surface vehicle sailing in the marine environment, , is the dot product of the propulsion speed and the ocean current speed.

4. An unmanned surface vehicle path planning method based on enhanced particle swarm optimization according to claim 3, characterized in that, The constructed multi-objective fitness function for unmanned surface vessel path planning is as follows: ;in, It is a sequence of path points. This is the path length weighting coefficient. For path length, , n The total number of path points. For the first i The location coordinates of each path point Denotes the Euclidean norm; Energy consumption cost weighting coefficient For the cost of energy consumption, ; For the safety cost weighting coefficient, For the sake of safety, , path point Distance to the nearest obstacle; The smoothness cost weighting coefficient, For the sake of smoothness, , , , These are vectors of adjacent path segments.

5. An unmanned surface vehicle path planning method based on enhanced particle swarm optimization according to claim 1, characterized in that, The enhanced particle swarm optimization algorithm adopts a fractional order calculation and a high-order iterative learning mechanism; the fractional order calculation adopts a fractional order history memory mechanism based on a Caputo fractional order derivative definition; the high-order iterative learning mechanism utilizes a fitness improvement mechanism of multiple historical iterations, dynamically adjusts a learning rate decay factor according to complexity of an environment, and completes high-order item learning.

6. An unmanned surface vehicle path planning method based on enhanced particle swarm optimization as claimed in claim 1 characterized by, A nonlinear adaptive inertia weight updating mechanism is used to modulate complexity of the ocean current, and in combination with particle momentum, the mechanism escapes from a local optimal state caused by a vortex and a counter current, and optimizes the obtained path of the unmanned surface vehicle in the time-varying ocean current environment.

7. An unmanned surface vehicle path planning system based on enhanced particle swarm optimization, characterized in that, The method comprises the following steps: an acquiring module configured to acquire kinematic equation and dynamic equation of an unmanned surface vehicle in a time-varying ocean current environment; a constructing module configured to construct a multi-objective fitness function for path planning of the unmanned surface vehicle based on the acquired kinematic equation and dynamic equation; a planning module configured to solve the constructed multi-objective fitness function by using an enhanced particle swarm optimization algorithm to obtain an optimal path of the unmanned surface vehicle in the time-varying ocean current environment, and complete path planning of the unmanned surface vehicle.

8. A computer readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to implement the steps of the unmanned surface vehicle path planning method based on the enhanced particle swarm optimization according to any one of claims 1-6.

9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and running on the processor, characterized in that, The processor executes the program to implement the steps of the unmanned surface vehicle path planning method based on the enhanced particle swarm optimization according to any one of claims 1-6.

10. A computer program product comprising software code, characterized in that, The program in the software code implements the steps of the unmanned surface vehicle path planning method based on the enhanced particle swarm optimization according to any one of claims 1-6.

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