Multi-Objective Path Planning for USVs Considering Environmental Factors

Abstract

This study investigates the multi-objective path planning problem for unmanned surface vehicles (USVs), aiming to optimize both travel distance and energy consumption in maritime environments with obstacles, sea winds, and ocean currents. The proposed method accounts for practical constraints, including collision avoidance, kinematic boundaries, and speed limitations. The problem is formulated as a nonlinear multi-objective optimization model with generalized constraints and is solved using an improved particle swarm optimization algorithm enhanced by a vector-weighted fusion strategy. The algorithm adaptively balances exploration and exploitation to obtain diverse Pareto-optimal solutions. Simulation results under varying environmental conditions, along with real-world sea trials, validate the effectiveness of the proposed approach. The outcomes demonstrate that the method enables USVs to generate energy-efficient, smooth trajectories while maintaining robustness and adaptability, offering practical value for intelligent marine navigation.

1. Introduction

Unmanned surface vehicles (USVs) have gained significant attention in recent years due to advances in control theory, artificial intelligence, and autonomous navigation systems [1]. At the same time, the prolonged use of low-quality fuels in conventional maritime vessels has led to serious environmental issues, including air pollution and global warming, pushing shipping-related emissions to critical levels [2]. In response, path planning technologies for USVs have increasingly prioritized energy-efficient navigation to enhance autonomy and promote environmental sustainability [3].  

However, minimizing energy consumption alone is insufficient to fully characterize the complexity of the path planning problem. Route length is a fundamental determinant of voyage time and mission efficiency, and it should be explicitly considered, particularly in the context of long-range or high-endurance operations [4]. Furthermore, dynamic environmental disturbances such as sea winds and ocean currents can substantially affect USV motion [5,6]. When properly modeled and leveraged, these natural forces offer potential benefits in terms of reducing energy use and improving path efficiency and navigational safety [7]. This highlights the practical and theoretical value of multi-objective path planning that simultaneously accounts for energy consumption, route distance, and environmental effects.

Several studies have explored multi-objective path planning for USVs [8]. For instance, Kandel et al. [9] proposed a Pareto-based framework incorporating ocean currents and refueling stations to balance energy usage and travel time, but their model overlooked the time cost of recharging lithium-powered USVs. Lucas et al. [10] applied the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to multi-target planning for underwater gliders in three-dimensional, time-varying currents but did not account for sea wind effects, which are essential for surface vessels. Although NSGA-II is widely adopted in multi-objective optimization, it often struggles to maintain solution diversity in high-dimensional Pareto fronts. Shu Zongyu [11] enhanced a hybrid particle swarm optimization (PSO) algorithm to improve route smoothness and safety but did not address energy considerations. Overall, these efforts demonstrate the potential of multi-objective planning, though gaps remain in modeling energy usage, wind–current interactions, and practical operational constraints.

Among the existing algorithmic approaches, three major algorithmic paradigms have been widely adopted in USV path planning: heuristic search methods, artificial intelligence-based approaches, and swarm intelligence algorithms. Heuristic methods (e.g., Dijkstra’s algorithm, the A* algorithm, and the D* algorithm) offer deterministic solutions on static maps but often struggle in dynamic environments. Artificial intelligence approaches such as reinforcement learning and deep learning provide learning capabilities but typically require large training datasets and extensive tuning. Swarm intelligence algorithms, including PSO [12], genetic algorithm [13], grey wolf optimizer [14], and ant colony optimization [15,16], are inspired by the collective behavior of animals such as birds and fish. Among them, PSO has shown strong performance in dynamic maritime environments due to its conceptual simplicity, fast convergence, and fewer tunable parameters compared to other methods [17]. These advantages make PSO particularly suitable for solving path planning problems in dynamic maritime environments.  

Despite these advances, three major gaps remain. First, many studies consider either ocean currents or sea winds, but rarely both in a unified environmental model. Second, energy consumption is often simplified or omitted, leading to suboptimal paths for long-duration missions. Third, while multi-objective optimization frameworks exist, few integrate environmental modeling, path smoothness, and real-time performance into a cohesive solution. Accordingly, the scientific problem addressed in this study is how to formulate and solve a multi-objective path planning problem for USVs that integrates wind and current effects into energy consumption modeling while ensuring that the resulting paths are both feasible and efficient in real maritime conditions. Based on this, the research hypothesis is that a hybrid swarm intelligence algorithm can provide a set of Pareto-optimal paths that balance distance and energy objectives, and that these solutions remain valid when tested in both simulated and real-sea environments.

To address this problem, this study introduces a multi-objective path planning framework that jointly minimizes energy consumption and path length by explicitly incorporating wind and current effects through a pod-thruster model. The contribution of this study is reflected in three aspects: (1) the integration of sea wind and ocean current into a unified dynamic environmental model; (2) the establishment of a nonlinear multi-objective formulation that incorporates propulsion dynamics and hydrodynamic resistance; and (3) the design of an adaptive PSO-INFO algorithm that enhances convergence and solution diversity in Pareto-optimal path planning. The simulation and field test results show that the proposed method achieves lower energy consumption and improved route smoothness compared to traditional distance-based strategies, thereby enhancing mission feasibility in realistic maritime environments.  

2. Multi-Objective Modeling for USV Path Planning Under Sea Wind and Ocean Current

2.1. Reference Coordinate System

To facilitate the analysis of USV motion, including variations in position and velocity, a suitable coordinate system is essential. This study investigates the resultant forces acting on a USV under the influence of sea wind and ocean current. Accordingly, a fixed geographic coordinate system is adopted as the reference frame, as illustrated in Figure 1.

In this system, the Y-axis points due north and the X-axis points due east. Let V denote the self-propulsion velocity of the USV in still water (i.e., velocity generated by its own thrusters), and let $V_s$ denote the ground-relative velocity of the USV, which is the actual observable motion. The environmental disturbance includes sea wind velocity $V_w$ and ocean current velocity $V_c$. Their respective magnitudes are denoted as $V=\left|V\right|$, $V_s=\left|V_s\right|$, $V_w=\left|V_w\right|$, and $V_c=\left|V_c\right|$. The directional angles $\lambda$, $\gamma$, $\alpha$, and $\beta$ represent the bearings (measured from due north) of V, $V_s$, $V_w$, and $V_c$, respectively. The components of $V_s$ in the eastward and northward directions are denoted as $V_{sx}$ and $V_{sy}$.

We assume that the USV maintains a constant ground-relative velocity magnitude $V_s$. Given the known magnitudes and directions of sea wind and ocean current velocities, the required propulsion velocity V is obtained by subtracting environmental disturbances from the ground-relative velocity. This vector subtraction naturally combines the directional and magnitude effects of environmental forces, especially in crosswind or cross-current conditions. The resulting propulsion vector directly determines the thrust direction and power requirement for each path segment, thereby incorporating the combined influence of wind and current into the energy model. The magnitude of V is as follows:  

$$V={\left[{\left(V_{sx}-V_{w}sin\alpha -V_{c}sin\beta \right)}^2+{\left(V_{sy}-V_{w}cos\alpha -V_{c}cos\beta \right)}^2\right]}^{1/2}$$

(1)

In this study, propulsion control is modeled as constant-speed tracking, which is consistent with typical USV autopilot objectives and ensures a fair basis for path comparison. Within this framework, propulsion velocity varies according to environmental disturbances while the ground-relative speed remains fixed. This simplified yet effective assumption is appropriate for mission-level planning, although it does not fully represent adaptive speed variation or closed-loop feedback in more complex scenarios. The trajectory of the USV is discretized into a sequence of connected sampling points $(x_i,y_i)$. The heading angle $\gamma$ is calculated from the displacement between adjacent points:

$$tan\gamma ={\displaystyle \frac{y_i-y_{i-1}}{x_i-x_{i-1}}}$$

(2)

To maintain a constant ground-relative velocity ${\mathit{V}}_s$, the USV must continuously adjust the magnitude and direction of its self-propulsion velocity $\mathit{V}$ to compensate for variations in environmental conditions. These adjustments directly influence the thrust output of the propulsion system and, consequently, the overall energy consumption throughout the voyage, even when additional hydrodynamic resistance is not present.    

2.2. Mathematical Model of Pod Thrusters

In marine navigation, USVs rely on onboard propulsion systems to counteract environmental disturbances such as sea winds and ocean currents. Accordingly, the magnitude of thrust generated by the propellers is directly related to energy consumption. To enable accurate modeling of this relationship, we develop a mathematical formulation of pod-type thrusters, which are installed at the stern of the USV. All propellers are assumed to have identical performance characteristics, and the USV’s heading is aligned with its travel direction, ensuring non-negative propeller speed. The effective thrust $F_T$ produced by a pod-type thruster is given by the following [18]:

$$F_T=\left(1-t_p\right)\rho n^2{D}_p^2{K}_p$$

(3)

where $t_p$ is the thrust deduction factor; $\rho$ is the water density; n is the rotational speed of the propeller; $D_p$ is the propeller diameter; and $K_p$ is the dimensionless thrust coefficient, which depends on the advance ratio J. The relationship between $K_p$ and J is expressed as follows:  

$$K_p=f_p\left(J\right)=K_0+K_{1}J+K_2{J}^2$$

(4)

where $J={\displaystyle \frac{V_s(1-w_p)}{n{D}_p}}$ is the advance ratio; $w_p$ is the propeller companion current coefficient; and $K_0$, $K_1$, $K_2$ are empirical constants determined by the propeller’s performance curve. By substituting Equation (4) into Equation (3), the thrust can be expressed in quadratic form:  

$$F_T=A{V}_s^2+B{V}_{s}n+C{n}^2$$

(5)

where the coefficients are defined as follows:

$$A=\left(1-t_p\right){\left(1-w_p\right)}^2\rho D_p^2{K}_2$$

(6)

$$B=(1-t_p)(1-w_p)\rho D_{p}3K_1$$

(7)

$$C=(1-t_p)\rho D_{p}4K_0$$

(8)

These coefficients depend on the USV’s structural and hydrodynamic parameters. For a USV equipped with N identical propellers, the total thrust can be expressed as follows:

$$F_T=\sum _{i=1}^N{D}_{F_i}{F}_{T_i}=\sum _{i=1}^N\left[\begin{array}{c}cos{\alpha }_i\\ cos{\beta }_i\\ cos{\gamma }_i\end{array}\right]F_{T_i}$$

(9)

where $D_{F_i}$ is the positive rotational vector of thrust generated by the ith propeller; $F_{T_i}$ is the corresponding thrust magnitude; and ${\alpha }_i$, ${\beta }_i$, ${\gamma }_i$ are the thrust direction angles of the ith propeller. When all propellers provide thrust along the same direction—e.g., $D_{F_i}={[1,0,0]}^T$—the total thrust simplifies to the following:

$$F_T=\sum _{i=1}^N{F}_{T_i}=\sum _{i=1}^N\left[\begin{array}{c}{F}_{T_i}\\ 0\\ 0\end{array}\right]$$

(10)

Assuming that the USV does not reverse course ($V_s\ge 0$) and the propeller direction is constant, the thrust from the i-th propeller can be written as follows:  

$$F_{T_i}=A{\left(V_s^T{D}_{F_i}\right)}^2+B\left(V_s^T{D}_{F_i}\right)n_i+C{n}_i^2$$

(11)

In the typical case where $D_{F_i}={[1,0,0]}^T$, this further reduces to the following:

$$F_{T_i}=A{V}_s^2+B{V}_s{n}_i+C{n}_i^2$$

(12)

The propeller speed $n_i$ can be estimated from the advance ratio using the following:

$$n_i={\displaystyle \frac{V\left(1-{\omega }_p\right)}{D_p{J}_c}}=V\ast c$$

(13)

where $J_c$ is an empirically determined constant representing the advance ratio under steady-state cruising conditions, which enables a linear approximation between propeller speed and vehicle velocity, and c is a derived constant. Substituting into the previous expression yields the following:

$$F_{T_i}=C{c}^2{V}^2+B{V}_{s}cV+A{V}_s^2\to K_1^{\prime }{V}^2+K_2^{\prime }V+K_3^{\prime }$$

(14)

where $K_1^{\prime }$, $K_2^{\prime }$, and $K_3^{\prime }$ constants are determined by structural and operational parameters. Equation (14) provides a practical formulation for estimating thrust as a function of propulsion speed and environmental velocity. 

2.3. Energy and Distance Modeling

This section formulates a multi-objective path planning model that aims to simultaneously minimize two key metrics: the total energy consumption and the total travel distance of the USV. The energy consumption model is derived from the previously established pod-type thruster model, while the distance is calculated geometrically along the planned path.     

2.3.1. Energy Consumption Model

The planned navigation route is discretized into a series of sampling points. The interval between adjacent points is assumed to be sufficiently small so that the magnitude and direction of sea wind and ocean currents can be considered constant within each segment. For each segment between two sampling points $N_i$ and $N_{i+1}$, the energy consumption is expressed by the following:  

$$E_{T_i}^{N_i{N}_{i+1}}=F_{T_i}^{N_i{N}_{i+1}}·V_{N_i{N}_{i+1}}·{\displaystyle \frac{\left|N_i{N}_{i+1}\right|}{\left|V_s\right|}}=\left(K_1^{\prime }{V}_{N_i{N}_{i+1}}^3+K_2^{\prime }{V}_{N_i{N}_{i+1}}^2+K_3^{\prime }{V}_{N_i{N}_{i+1}}\right){\displaystyle \frac{\left|N_i{N}_{i+1}\right|}{\left|V_s\right|}}$$

(15)

where $T_{N_i{N}_{i+1}}$ is the traversal time for the segment:         

$$T_{N_i{N}_{i+1}}={\displaystyle \frac{\left|N_i{N}_{i+1}\right|}{\left|V_s\right|}}$$

(16)

Summing across all segments, the total energy consumption under idealized conditions (i.e., without environmental resistance) is as follows:

$$E_{T_i}=\sum _{i=1}^{n-1}\left(K_1^{\prime }{V}_{N_i{N}_{i+1}}^3+K_2^{\prime }{V}_{N_i{N}_{i+1}}^2+K_3^{\prime }{V}_{N_i{N}_{i+1}}\right){\displaystyle \frac{\left|N_i{N}_{i+1}\right|}{\left|V_s\right|}}$$

(17)

To account for environmental resistance, an additional energy term is introduced. The total energy consumption along the entire path is thus given by the following:

$$E=E_{T_i}+\sum _{i=1}^{n-1}{F}_d^{N_i{N}_{i+1}}{l}^{N_i{N}_{i+1}}$$

(18)

where $F_d^{N_i{N}_{i+1}}$ denotes the environmental resistance encountered during travel between $N_i$ and $N_{i+1}$, and $l^{N_i{N}_{i+1}}$ is the corresponding segment length.

Environmental resistance $F_d^i$ at sampling point i is modeled as the sum of air and hydrodynamic drag:            

$$F_d^i={\displaystyle \frac{1}{2}}{\rho }_a{C}_a{S}_a{\left|V\right|}^2+{\displaystyle \frac{1}{2}}\left(C_F+\Delta C_F\right){\rho }_c{C}_c{S}_c{\left|V\right|}^2$$

(19)

The frictional resistance coefficient $C_F$ is as follows:              

$$C_F={\displaystyle \frac{0.075}{{\left(lg{R}_N-2\right)}^2}}$$

(20)

where the Reynolds number $R_N$ is defined as follows:                

$$R_N={\displaystyle \frac{VL}{\nu }}$$

(21)

The wetted surface area $S_c$ of the hull is computed as follows:                

$$S_c={\displaystyle \frac{59L}{64-\frac{B}{T}}}\left(1.8T+C_{B}B\right)$$

(22)

In these equations, ${\rho }_a$ is the air density (taken as 1.226 kg/m³); $C_a$ is the air resistance coefficient, which depends on the hull shape and superstructure; $S_a$ is the projected cross-sectional area above the waterline; $\Delta C_F$ is the roughness of the subsidy coefficient, typically set to 0.0004; ${\rho }_c$ is the density of seawater (taken as $1.04\times {10}^3$ kg/m³); $C_c$ is the shape coefficient of the hull; $\nu$ is the kinematic viscosity of water, taken as $1.18831\times {10}^{-6}$ m²/s at 15 °C; L, B, and T are the length, beam, and draft of the USV, respectively; and $C_B$ is the block coefficient.

This comprehensive model captures the nonlinear coupling between relative propulsion velocity, environmental resistance, and energy consumption in realistic marine environments, forming the foundation for environmentally aware path planning.

2.3.2. Path Distance Model

To evaluate the total travel distance, the navigation environment is discretized into a series of sequential sampling points that define the USV’s trajectory. Since the segment length between adjacent points is much smaller than the overall voyage length, it is reasonable to assume that the environmental conditions remain constant within each segment.

The total path length is computed by summing the Euclidean distances between each pair of consecutive sampling points. The distance model is expressed as follows:

$$l=\sum _{i=1}^{n-1}\sqrt{{(x_{i+1}-x_i)}^2+{(y_{i+1}-y_i)}^2}$$

(23)

where l represents the total path length; $(x_i,y_i)$ and $(x_{i+1},y_{i+1})$ are the planar coordinates of the i-th and $(i+1)$-th sampling points, respectively. This simple geometric formulation provides an intuitive and computationally efficient metric for distance-based path evaluation and optimization.

2.4. Environmental Modeling

2.4.1. Sea Wind Model

The sea wind model used in this study is constructed based on near-surface meteorological data, with particular attention paid to wind conditions at a height of 1 m above the sea surface. The surface pressure field is obtained from meteorological forecast charts, while the vertical wind velocity profile is modeled using the atmospheric boundary layer theory. The wind speed $V_w$ at height Z above the sea surface is expressed as follows:

$$V_w={\displaystyle \frac{U_{\ast }}{k}}\left[ln\left({\displaystyle \frac{Z}{Z_0}}\right)-{\phi }_m\right]$$

(24)

Here, $U_{\ast }$ is the friction velocity; k = 0.35 is the Karman constant; $Z_0$ is the sea surface roughness length; and ${\phi }_m$ is a stability correction function that depends on the dimensionless stability parameter $Z/L$, where L is the Monin–Obukhov length. The Businger–Dyer empirical formulation is adopted for ${\phi }_m$, which varies with atmospheric stability as follows:

In the stable conditions ($Z/L>0$), the stratification suppresses turbulence:   

$${\phi }_m=-\beta {\displaystyle \frac{Z}{L}}$$

(25)

In the unstable conditions ($Z/L<0$), enhanced turbulence is represented by the following:

$${\phi }_m=ln0.5(1+{\epsilon }^2)+2ln0.5(1+\epsilon )-2t{g}^{-1}\epsilon +0.5\pi$$

(26)

where  

$$\epsilon ={\left(1-{\gamma }_m{\displaystyle \frac{Z}{L}}\right)}^{1/4},{\gamma }_m=15$$

(27)

In the neutral conditions ($Z/L=0$), ${\phi }_m=0$.

The Monin–Obukhov length L, which characterizes atmospheric stability, is calculated as follows:          

$$L={\displaystyle \frac{U_{\ast }^2{T}_a\left[ln(Z/Z_0)-{\phi }_m(Z/L)\right]}{k^{2}g(T_a-T_w)}}$$

(28)

where $T_a$ and $T_w$ are the air and sea surface temperatures, g is gravitational acceleration, and $Z_0$ is given by the following:          

$$Z_0={\displaystyle \frac{6.8\times {10}^{-5}}{U_{\ast }}}+4.28\times {10}^{-3}{U}_{\ast }^2-4.43\times {10}^{-4}$$

(29)

To incorporate the effects of the Ekman layer, which includes surface stress, pressure gradient, and Koch forces, the model introduces a boundary layer wind damping correction. The relationship between the geostrophic wind speed G and Rossby number R is expressed as follows:   

$$lnR=A-ln\left({\displaystyle \frac{U_{\ast }}{G}}\right)+{\left({\displaystyle \frac{k^2{G}^2}{U_{\ast }^2}}\right)}^{1/2}$$

(30)

$$sina=-{\displaystyle \frac{B/k}{U_{\ast }/G}}$$

(31)

where a is the angle between surface stress and geostrophic wind, and $A=1.7$ and $B=4.7$ are empirical constants. The Rossby number is defined as $R=G/f{Z}_0$, with f denoting the Koch parameter. By iteratively solving Equations (28)–(31), the wind velocity and direction at Z = 1 m can be determined. The resulting two-dimensional wind field is illustrated in Figure 2.     

2.4.2. Ocean Current Model

The ocean current model in this study is constructed using a time-dependent stream function that characterizes an east–west dominant flow with a north–south meandering structure [19]. The stream function $j(x,y,t)$, which evolves over time t, is defined as follows:                     

$$j(x,y,t)=1-tanh\left({\displaystyle \frac{y-B\left(t\right)cos\left[U(x-ct)\right]}{\sqrt{1+U^{2}B{\left(t\right)}^2{sin}^2\left[U(x-ct)\right]}}}\right)$$

(32)

The meander amplitude is modulated by $B\left(t\right)=B_0+e\times cos(kt+\theta )$, and the parameter values are set as follows: $B_0=1.2$, $U=0.84$, $k=0.4$, $e=0.3$, $\theta ={\displaystyle \frac{\pi }{2}}$, and $c=0.12$. This formulation generates a dynamically varying flow field consistent with mesoscale eddy structures observed in oceanic currents.

The eastward and northward components of the two-dimensional horizontal velocity field are derived as follows:                   

$$\left\{\begin{array}{c}{V}_{cx}(x,y,t)=-{\displaystyle \frac{\partial j}{\partial y}}\hfill \\ V_{cy}(x,y,t)=\phantom{-}{\displaystyle \frac{\partial j}{\partial x}}\hfill \end{array}\right.$$

(33)

Here, $V_{cx}(x,y,t)$ and $V_{cy}(x,y,t)$ represent the velocity components along the X and Y directions, respectively, at position $(x,y)$ and time t. This stream function-based model captures the time-varying nature of ocean currents and enables the generation of synthetic, yet physically plausible, two-dimensional current fields for simulation and analysis. The resulting current field is shown in Figure 3. 

3. Multi-Objective Path Planning Algorithm

3.1. Problem Formulation

In multi-objective optimization problems, multiple objectives are often in conflict, making it infeasible to identify a single solution that simultaneously optimizes all objectives. Instead, the focus is on finding a set of trade-off solutions known as the Pareto optimal set [20]. In this set, improving one objective typically results in the deterioration of at least one other, reflecting the inherent compromises of multi-objective decision-making.

A common approach to solving such problems is to convert them into a single-objective form using weighted summation. While conceptually simple, this method demands prior knowledge of the relative importance of each objective and may perform poorly when objectives are highly conflicting or the Pareto front is non-convex. An alternative and more flexible approach lies in evolutionary computation, which is well-suited for multi-objective optimization due to its population-based nature. By maintaining a diverse set of solutions across generations, these algorithms support simultaneous convergence to the Pareto front and preservation of diversity among solutions. Such characteristics are essential for capturing a representative spread of trade-offs in the objective space. A general multi-objective optimization problem can be mathematically formulated as follows:                    

$$miny=f\left(x\right)=\left(f_1\left(x\right),f_2\left(x\right),\dots ,f_n\left(x\right)\right),s·t·g_i\left(x\right)\le 0$$

(34)

In this formulation, the decision vector $x\in {\mathbb{R}}^m$ belongs to an m-dimensional decision space, and the objective vector $y\in {\mathbb{R}}^n$ consists of n objective functions $f_i\left(x\right)$$(i=1,2,\dots ,n)$ to be minimized. The inequality constraints $g_i\left(x\right)\le 0$$(i=1,2,\dots ,p)$ define the feasible region of the solution space, where p denotes the number of constraints.

Definition 1.

A solution ${\mathbf{x}}^{\ast }$ is Pareto optimal (or non-inferior) if there exists no other solution $\mathbf{x}$ such that $f_i\left(\mathbf{x}\right)<f_i\left({\mathbf{x}}^{\ast }\right)$ for all i.

Definition 2.

The set of all Pareto optimal solutions is called the Pareto optimal set or effective solution set. The corresponding set of objective vectors in the objective space forms the Pareto front.

These foundational concepts provide the theoretical basis for evaluating trade-offs in multi-objective optimization. However, in practice, it remains challenging to obtain a well-distributed and convergent approximation of the Pareto front, particularly when standard algorithms fail to maintain an appropriate balance between exploration and exploitation. To address this, the following section introduces a hybrid optimization strategy that integrates adaptive PSO mechanisms with vector-based recombination to improve solution quality and diversity.      

3.2. Hybrid Particle Swarm and Vector Weighting Algorithm

Given the challenges in applying standard PSO directly to multi-objective optimization, such as premature convergence and limited solution diversity, this study proposes a hybrid particle swarm-vector weighting algorithm (PSO-INFO) to identify non-inferior optimal solutions more effectively.

First, the inertia weight and acceleration factors of the particle swarm are adaptively adjusted using trigonometric functions to better balance global and local search capabilities across different optimization stages. This improves the swarm’s exploration in early stages and convergence in later stages. Second, to mitigate PSO’s tendency to fall into local optima, the algorithm incorporates a vector weighting mechanism that integrates all objective functions to guide particles jointly in the decision space. This cooperative mechanism helps direct particles toward the Pareto front.    

$$w\left(k\right)={\displaystyle \frac{w_{max}-w_{min}}{2}}cos\left(\pi {\displaystyle \frac{k}{k_{max}}}\right)+{\displaystyle \frac{w_{max}+w_{min}}{2}}$$

(35)

where $w_{max}=0.95$; $w_{min}=0.4$; $k_{max}$ is the maximum number of iterations, and k is the current iteration. The change curve of the inertia weight factor at different iteration times is plotted, as shown in Figure 4. 

The acceleration coefficients $c_1$ and $c_2$, controlling individual and social learning, respectively, are defined as follows:      

$$c_1\left(k\right)=c_{a}sin\left({\displaystyle \frac{\pi }{2}}{\displaystyle \frac{\frac{k_{max}}{2}-k}{\frac{k_{max}}{2}}}\right)+c_b$$

(36)

$$c_2\left(k\right)=c_{\alpha }sin\left({\displaystyle \frac{\pi }{2}}{\displaystyle \frac{k-\frac{k_{max}}{2}}{\frac{k_{max}}{2}}}\right)+c_{\beta }$$

(37)

where $c_a$, $c_b$, and $c_{\beta }$ are parameters to be determined, with $c_1,c_2\in [0.5,2.5]$. In this study, the parameters are set as $c_a=1$, $c_b=1.5$, and $c_{\beta }=1.5$. The resulting curves are shown in Figure 5 and Figure 6.

These curves indicate a coordinated transition: when the inertia weight w is large (early stages), $c_1$ is high and $c_2$ is low, encouraging individual exploration. As w decreases (later stages), $c_1$ declines and $c_2$ increases, enhancing swarm convergence. This design balances exploration and exploitation effectively. 

By incorporating the adaptive parameters into the canonical PSO equations, the velocity and position updates become the following:

$$V_{ij}\left(t+1\right)=w\left(k\right)·V_{ij}\left(t\right)+c_1\left(k\right)r_1[P_{ij}\left(t\right)-X_{ij}\left(t\right)]+c_2\left(k\right)r_2[P_{\mathrm{g}j}\left(t\right)-X_{ij}\left(t\right)]$$

(38)

$$X_{ij}(t+1)=X_{ij}\left(t\right)+V_{ij}(t+1)$$

(39)

where $r_i,r_a\in [0,1]$ are random numbers, $P_{ij}$ is the best position of particle i, and $P_{gj}$ is the global best.

Monitoring the swarm’s convergence behavior is essential to assess whether particles have prematurely stagnated in suboptimal regions [21]. A typical indicator is the absence of fitness improvement over successive iterations. This phenomenon is detected by evaluating the following condition:                

$$f\left(x_{k+1}\right)>f\left(x_k\right)$$

(40)

Here, $f\left(x_{k+1}\right)$ and $f\left(x_k\right)$ denote the fitness values at the $(k+1)$-th and k-th iterations, respectively. If this inequality is satisfied for three consecutive iterations, it suggests that the swarm has lost exploration capability and requires diversification to reintroduce solution variability. To counter this challenge and strengthen global search performance, the INFO algorithm is incorporated as a complementary mechanism. INFO is a population-based strategy that enhances diversity and exploration through a three-stage process: rule updating, vector merging, and local search [22].

In the rule updating stage, INFO applies a mean-based strategy known as the MeanRule. This mechanism determines the search direction by combining two weighted mean vectors, each constructed using fitness-based weighting functions. These weights are designed to reflect the relative quality of the solutions, thereby guiding the search process toward more promising regions. A convergence acceleration (CA) factor is also incorporated to adjust the step size dynamically and promote global exploration. During the vector merging stage, two candidate vectors are generated by applying the update rules to the current population. These candidate vectors are then combined with the original solution vector under a probabilistic condition to form a new solution. The merging strategy introduces variability and promotes broader exploration of the search space. The final stage is local search, which aims to refine solutions and avoid stagnation in local optima. If a certain probabilistic threshold is met, a new vector is generated in the vicinity of the global best solution, guided by the MeanRule and other population members. This local exploitation step enhances the convergence accuracy and robustness of the algorithm.

Through the coordinated execution of these three stages, the INFO component effectively complements PSO, contributing to improved optimization performance by balancing exploration and exploitation in high-dimensional search spaces. This adaptive strategy introduces stochastic perturbations to prevent stagnation and maintain solution diversity throughout the optimization process. The procedural flow of the PSO-INFO hybrid algorithm is outlined below:  

Step 1:

Initialize the particle swarm and set relevant parameters.   

Step 2:

Divide the particles into $P_{\mathrm{num}}$ groups with $N/P_{\mathrm{num}}$ particles in each group.       

Step 3:

Evaluate the fitness of each particle and record the optimal particle P in each group. 

Step 4:

Perform standard PSO updates using the adaptive equations for velocity and position.      

Step 5:

Update the global optimal point of each group.   

Step 6:

Collect all group-level optimal points to form the initial population for the INFO algorithm and sort them based on fitness values.

Step 7:

Execute one iteration of the INFO algorithm, including rule updating, vector merging, and local search. 

Step 8:

If the termination condition is satisfied, output the optimal point; otherwise, return to Step 4.      

To validate the performance of the PSO-INFO algorithm, four benchmark test functions are selected. Their expressions, dimensions, search ranges, and optimal values are shown in

Table 1. Test functions.

Function Expression	Dimension	Search Scope	Optimum Value
$f_1\left(x\right)={\sum }_{i=1}^n{\left({\sum }_{j=1}^i{x}_j\right)}^2$	30	[−100, 100]	0
$f_2\left(x\right)=max\left\{|x_i|,1\le i\le n\right\}$	30	[−100, 100]	0
$f_3\left(x\right)={\sum }_{i=1}^n\left[x_i^2-10cos\left(2\pi x_i\right)+10\right]$	30	[−5.12, 5.12]	0
$f_4\left(x\right)=-20exp\left(-0.2\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{x}_i^2}\right)$$-exp\left({\displaystyle \frac{1}{n}}{\sum }_{i=1}^{n}cos\left(2\pi x_i\right)\right)+20+e$	30	[−32, 32]	0.4

.   

Figure 7, Figure 8, Figure 9 and Figure 10 present the convergence results of the PSO-INFO algorithm compared with the PSO-ACO, PSO, and INFO methods. For each function, the maximum number of iterations is set to $T_{max}=100$ and the population size is $n=30$. 

Functions $f_1$ and $f_2$ are single-peak functions used to test the local search ability of the algorithms. The results in Figure 7 and Figure 8 show that PSO-INFO achieves faster convergence and higher solution accuracy.

Functions $f_3$ and $f_4$ are multi-peak functions used to test the global search ability of the algorithms. As shown in Figure 9 and Figure 10, PSO-INFO consistently outperforms the baseline algorithms in terms of global optimization performance. Overall, the PSO-INFO algorithm demonstrates superior robustness, convergence speed, and optimization accuracy, confirming its practical effectiveness for complex optimization problems.

3.3. Algorithmic Framework

The PSO-INFO fusion algorithm guides particle behavior based on both the personal best ($pBest$) and global best ($gBest$) positions. To mitigate premature convergence and enhance population diversity, the algorithm initializes particles in the decision variable space and uses all objective functions jointly to direct their movement. Owing to the varying influence of objectives, particles explore different solution regions, thereby dispersing the swarm across the Pareto front and avoiding convergence toward a single-objective optimum.

Unlike traditional PSO, this approach evaluates global optima by considering the trade-offs among multiple objectives, improving the swarm’s capacity to approximate the non-dominated solution set. It ensures balanced convergence without privileging any single objective.      

Specifically, for a multi-objective problem with n objective functions and a swarm of N particles, each particle j maintains a personal best position $\mathit{pBest}[i,j]$ with respect to each objective function $f_i\left(x\right)$, where $i=1,2,\dots ,n$ and $j=1,2,\dots ,N$. The global best positions $\mathit{gBest}\left[i\right]$ for each objective are updated similarly. During iteration, the algorithm calculates an averaged $\mathit{gBest}$ to guide swarm convergence, while each particle’s $\mathit{pBest}$ is dynamically selected based on its dispersion from corresponding $\mathit{gBest}\left[i\right]$.

In this paper, two objective functions are used for optimization: path energy consumption $f_1\left(x\right)$ and path distance $f_2\left(x\right)$. The flow of the improved multi-objective optimization algorithm is as follows (see Algorithms 1–6):

Step 1:

Initialize the particle swarm. Set the swarm size N, and randomly generate the position $X_i$ and velocity $V_i$ for each particle. Replace the inertia weight factor $\omega$ and acceleration coefficients $c_1$, $c_2$ with the improved nonlinear versions introduced in Section 3.2.        

Step 2:

Divide the particles into $P_{\mathrm{num}}$ groups, each containing $N/P_{\mathrm{num}}$ particles.

Step 3:

Evaluate the fitness of each particle and record the optimal particle P in each group.

Step 4:

Calculate the fitness values for each particle using two objective functions:  

Algorithm 1 Calculate Fitness Values of Particles

1: Input: Particle positions $X[1..N]$ 2: Output: Fitness values ${\mathrm{Fitness}}_1[1..N]$, ${\mathrm{Fitness}}_2[1..N]$ 3: for $i=1$ to N do 4:    ${\mathrm{Fitness}}_1\left[i\right]=f_1\left(X\left[i\right]\right)$ 5:    ${\mathrm{Fitness}}_2\left[i\right]=f_2\left(X\left[i\right]\right)$ 6: end for

Step 5:

Identify the personal best for each particle with respect to both objectives:

Algorithm 2 Identify Personal Best for Each Particle

1: Input: Particle positions $X[1..N]$ 2: Output: Personal best values $pBest[1..2,1..N]$ 3: for $i=1$ to N do 4:    $pBest[1,i]=f_1\left(X\left[i\right]\right)$ 5:    $pBest[2,i]=f_2\left(X\left[i\right]\right)$ 6: end for

Step 6:

Determine the global best for each objective:

Algorithm 3 Determine Global Best for Each Objective

1: Input: Particle fitness values ${\mathrm{Fitness}}_1[1..N]$, ${\mathrm{Fitness}}_2[1..N]$ 2: Output: Global best values $gBest[1..2]$ 3: $gBest\left[1\right]=max\left({\mathrm{Fitness}}_1[1..N]\right)$ 4: $gBest\left[2\right]=max\left({\mathrm{Fitness}}_2[1..N]\right)$

Step 7:

Copy the personal and global bests of each group to form the initial population for the vector weighting algorithm. Sort the population based on fitness values.

Step 8:

Execute a vector-weighted update iteration to generate a new set of optimal candidates.

Step 9:

Calculate the averaged and Euclidean distance between global bests:  

Algorithm 4 Compute Averaged and Euclidean Distance of Global Bests

1: Input: Global best values $gBest\left[1\right]$, $gBest\left[2\right]$ 2: Output: Averaged global best $gBest$, distance $dgBest$ 3: $gBest=\mathrm{Average}\left(gBest\right[1],gBest[2\left]\right)$ 4: $dgBest=\mathrm{Distance}\left(gBest\right[1],gBest[2\left]\right)$

Step 10:

Compute distances between each particle’s personal best vectors:

Algorithm 5 Compute Distances Between Each Particle’s Personal Best Vectors

1: Input: Personal best vectors $pBest[1..2,1..N]$ 2: Output: Distances $dpBest[1..N]$ 3: for $i=1$ to N do 4:    $dpBest\left[i\right]=\mathrm{Distance}\left(pBest\right[1,i],pBest[2,i\left]\right)$ 5: end for

Step 11:

Determine the individual reference vector for velocity and position updates:

Algorithm 6 Determine Individual Reference Vector for Velocity and Position Updates

1: Input: Personal best distances $dpBest[1..N]$, global distance $dgBest$, personal best vectors $pBest[1..2,1..N]$ 2: Output: Updated personal best vectors $pBest[1..N]$ 3: for $i=1$ to N do 4:    if $dpBest\left[i\right]<dgBest$ then 5:      $pBest\left[i\right]=\mathrm{RandSelect}\left(pBest\right[1,i],pBest[2,i\left]\right)$ {Random selection} 6:    else 7:      $pBest\left[i\right]=\mathrm{Average}\left(pBest\right[1,i],pBest[2,i\left]\right)$ {Evaluated selection} 8:    end if 9: end for

Finally, each particle updates its velocity $V_i$ and position $X_i$ based on the selected $gBest$ and $pBest\left[i\right]$. The process iterates until the convergence criterion is met. The Average() function may represent arithmetic mean or weighted averaging based on the predefined strategy. This framework ensures that particles collectively converge toward a well-distributed set of Pareto-optimal solutions, guided by a dynamic and balanced multi-objective mechanism.

4. Simulation and Experimental Validation

4.1. Environmental Field Simulations

To evaluate the effectiveness of the proposed multi-objective optimization algorithm in realistic maritime scenarios, simulation experiments are conducted using two optimization objectives: path distance and path energy consumption. Each simulation constrains the total path length to less than 900 m and assumes a constant ground-relative velocity of 1 m/s for the USV. In addition to environmental disturbances, static obstacles are incorporated into the simulation environment to reflect complex navigational constraints and ensure collision avoidance. Three distinct environmental conditions are considered: sea wind field, ocean current field, and a combined sea wind and ocean current field. For each condition, the algorithm’s ability to balance the trade-off between path length and energy consumption is analyzed based on the resulting Pareto front.         

4.1.1. Sea Wind Simulation

The first scenario evaluates the algorithm under sea wind conditions. This simulates a realistic marine environment where wind is the primary environmental factor affecting USV motion. The resulting path planning diagram is shown in Figure 11.

The algorithm successfully generates eight feasible trajectories satisfying the optimization constraints. The distance and energy consumption corresponding to each path are detailed in

Table 2. Path distances and energy consumption values under sea wind conditions.

Path	Trailhead	Destination	Distance (m)	Energy Consumption (J)
1	(5,5)	(60,20)	884.76	2,091,542
2			853.53	1,832,790
3			725.24	1,139,070
4			647.06	1,007,540
5			590.28	1,050,270
6			591.08	1,048,860
7			687.49	1,048,020
8			670.19	1,023,480

.  

From the data, it can be observed that longer paths generally result in higher energy consumption due to prolonged exposure to headwinds. However, some shorter trajectories still yield relatively high energy usage depending on their orientation against the wind vector.

Figure 12 presents the derived Pareto front, revealing the trade-off between the two competing objectives: minimizing path length and reducing energy consumption. Each point on the curve corresponds to a non-dominated solution, reflecting an optimal balance under the given wind field.

4.1.2. Ocean Current Simulation

Building on the previous wind-only scenario, this case evaluates algorithm performance under ocean current influence alone. As illustrated in Figure 13, the planned trajectories diverge from the shortest geometric path, adapting to flow patterns to reduce energy consumption.

Eight valid trajectories are obtained, with distance and energy consumption summarized in

Table 3. Path distances and energy consumption values under sea wind conditions.

Path	Trailhead	Destination	Distance (m)	Energy Consumption (J)
1	(5,5)	(60,20)	884.76	2,594,100
2			853.53	2,409,090
3			725.24	1,903,670
4			647.06	1,796,480
5			590.28	1,793,400
6			591.08	1,813,160
7			687.49	1,832,930
8			670.19	1,812,350

.

Compared with the wind-only scenario, ocean currents impose greater energy penalties even for similar path lengths. This is due to the spatial non-uniformity and vector direction of the current field, which significantly affect the relative propulsion velocity and resistance.

The resulting Pareto front is plotted in Figure 14. The curve once again demonstrates a clear inverse relationship between path length and energy consumption, validating the algorithm’s ability to explore a diverse set of non-inferior solutions under current-driven environments.

4.1.3. Combined Wind–Current Field Simulation

To evaluate the algorithm’s adaptability in more realistic conditions, this scenario introduces both wind and ocean current influences. As shown in Figure 15, the generated trajectories reflect the algorithm’s capacity to navigate complex flow environments while balancing energy consumption and travel distance. 

The algorithm identifies eight feasible paths that satisfy the multi-objective constraints. Their distance and energy metrics are presented in

Table 4. Path distances and energy consumption under combined environmental conditions.

Path	Trailhead	Destination	Distance (m)	Energy Consumption (J)
1	(5,5)	(60,20)	884.76	3,281,542
2			853.53	3,337,530
3			725.24	2,642,466
4			647.06	2,908,010
5			590.28	2,812,620
6			591.08	2,781,271
7			687.49	2,813,960
8			670.19	2,803,440

. Notably, although several paths are relatively short, the combined effects of wind and current result in greater energy consumption compared to the single-factor cases. This underscores the compounded impact of environmental forces on USV energy efficiency.

The resulting Pareto front in Figure 16 reveals that achieving optimal trade-offs under combined wind–current fields becomes more challenging. Compared with previous cases, a more pronounced divergence appears between short-distance and low-energy paths, reflecting the algorithm’s nuanced handling of dynamic environmental coupling.

The simulation results across the three environmental scenarios demonstrate that, under the influence of environmental resistance, the shortest path does not necessarily yield the lowest energy consumption, and vice versa. This confirms that path distance and energy cost are not strictly positively correlated in dynamic marine conditions. Moreover, the multi-objective algorithm successfully generates multiple feasible trajectories that vary with environmental complexity and constraint configurations. These findings validate the algorithm’s ability to jointly optimize distance and energy consumption in diverse environments, laying a solid foundation for the subsequent real-world experimental validation.

4.2. Live USV Testing and Data Analysis

To verify the real-world performance of the proposed multi-objective path planning algorithm, live sea trials were conducted in the coastal waters near Xiamen Park. The area is sheltered by breakwaters, providing relatively stable wind and current conditions. An overview of the test environment is shown in Figure 17.

The test procedure is as follows: The system was initialized by powering on the USV and confirming that all onboard modules were functioning correctly. Next, commands such as rostopic echo/odom and Desktop/Run_camera_airmar were executed in Ubuntu under the Robot Operating System (ROS) to activate the LiDAR, the DX900+ seabed detection radar, the anemometer, the inertial measurement unit (IMU), and the magnetic compass.

Initial localization of the USV was established by fusing LiDAR and differential GPS measurements through a SLAM package to construct a three-dimensional environmental map. The IMU and compass provided continuous attitude and heading estimates, which were cross-validated with GPS-derived headings to enhance robustness. Prior to deployment, the IMU underwent factory calibration, the compass was corrected for soft- and hard-iron effects, and LiDAR–GPS alignment was verified during SLAM initialization. These calibration steps ensured consistency across heterogeneous sensors. Redundancy was achieved by combining GPS and compass heading data, allowing the system to remain stable during short-term fluctuations of individual sensors. Although no explicit fault-isolation module was implemented, the fusion framework effectively mitigated noise and drift, ensuring reliable navigation throughout the sheltered-water trials.

Environmental data acquisition then proceeded: Wind speed and direction were recorded by the anemometer, with wind speeds fluctuating around 1.5 m/s and predominantly blowing toward the west–northwest (measured clockwise from the north). Concurrently, the DX900+ radar (Airmar Technology Corporation, Milford, NH, USA) measured ocean currents, which averaged around 1.7 m/s and flowed generally northeast.

Upon setting the destination, the algorithm calculated a multi-objective optimal path based on energy consumption and a minimum path length constraint. The computational efficiency of PSO-INFO was profiled on a desktop with an Intel i7 CPU and 16 GB RAM (Santa Clara, CA, USA). The typical runtime for benchmark functions (100 particles, 200 iterations) was under 2 s. For USV path-planning cases, convergence was achieved in under 10 s. Memory usage peaked at a few hundred megabytes, which is well within the capacity of modern on-board systems. To clarify the operational context, simulations and sea trials were conducted under open-loop execution with constant-speed tracking, reflecting the scope of the present study. This framework is suitable for demonstrating the feasibility of the proposed planner, though it does not explicitly address adaptive control in highly dynamic environments.

The planned path was visualized in RViz, and the USV was navigated from Start(0, 0) to End(360, 330) in autopilot mode at a constant ground-relative speed of 2.4 m/s. Figure 18 shows the shortest actual sailing trajectory obtained during the experiment. The USV successfully completed the multi-constrained path in approximately 189 s. The evolution of the heading angle throughout the voyage is shown in Figure 19, demonstrating active course adjustments in response to environmental disturbances.

To evaluate power performance, Figure 20, Figure 21, Figure 22 and Figure 23 depict the current and voltage trends of battery packs No. 1 and No. 2. The experiment assumed a constant ground-relative speed $V_s$, and the USV adjusted its thrust accordingly. During the early phase of navigation, the USV encountered increasing environmental resistance as the current gradually intensified before stabilizing. This process reflected adaptive energy consumption in response to the combined effects of wind and current.

Following the analysis of the shortest-distance trajectory, the experiment also examined the route with the lowest actual energy consumption, which was selected from among the multiple multi-objective, multi-constraint paths generated by the algorithm. As illustrated in Figure 24, the USV followed this optimal energy-saving trajectory and completed the voyage in approximately 203 s. The corresponding heading angle variation during navigation is shown in Figure 25, which is divided into three segments: from the starting point to point A (0–110 s), from point A to point B (110–157 s), and from point B to the endpoint (157–203 s).

Battery data recorded during the voyage are presented in Figure 26, Figure 27, Figure 28 and Figure 29. Notably, a substantial increase in current is observed between points A and B, which indicates higher power demands in this segment. This phenomenon is likely caused by intensified resistance from environmental disturbances.

To maintain constant sailing speed in dynamic marine conditions, the USV continually adjusts its propeller output. Consequently, its actual energy consumption must be computed based on battery voltage and current data over time. The total energy consumption of the USV is calculated using Equation (41):

$$E_{\mathrm{sum}}=\sum _{t=0}^n\left(U_t^1\times I_t^1+U_t^2\times I_t^2\right)\times \Delta t$$

(41)

where $U_t^1$ and $I_t^1$ denote the voltage and current of battery pack No. 1 at time t, respectively; $U_t^2$ and $I_t^2$ correspond to battery pack No. 2; and $\Delta t$ is the sampling interval (1 s in this case). Using this method, the actual energy consumption and path lengths for all eight planned routes were computed and are summarized in

Table 5. Path distances and energy consumption in real-sea trials.

Path	Distance (m)	Energy Consumption (J)
1	468	980,490
2	458.4	1,180,240
3	453.6	1,302,600
4	516	1,879,800
5	501.6	1,219,800
6	487.2	907,180
7	463.2	1,052,800
8	468	980,490

.

Finally, a Pareto front is plotted in Figure 30 to visualize the trade-off between path length and energy consumption under real-world conditions. The curve reflects the algorithm’s ability to balance distance efficiency and power economy in physical marine environments.

To further verify the reliability and reproducibility of the proposed method, an additional set of sea trials was conducted under different environmental conditions. In this experiment, the maximum path length was set to 480 m and the maximum energy consumption was set to 1,700,000 J. The USV was operated at a constant speed of 2.4 m/s, navigating from (0 m, 0 m) to a target near (400 m, 150 m). The environmental conditions included a wind speed of approximately 1.5 m/s from the east to northeast and a current of about 1.0 m/s from the east to southeast. Six Pareto-optimal trajectories were obtained. The shortest path measured 408 m, while the most energy-efficient path consumed 1,258,430 J, representing a 23.2% saving compared to the highest-energy solution. These results demonstrate that the algorithm consistently produces feasible Pareto-optimal solutions across different conditions, confirming its effectiveness and reproducibility.

In summary, the live sea trials confirm the practical effectiveness of the proposed multi-objective path planning algorithm. The USV successfully navigated both the shortest-distance path and the minimum-energy path, with onboard sensors capturing real-time wind and current conditions. Comparative analysis of voltage and current profiles reveals that different environmental resistances across path segments significantly impact energy consumption. The measured results align closely with the simulation predictions, demonstrating the algorithm’s robustness and adaptability in complex maritime environments, and laying a solid foundation for further deployment in real-world autonomous navigation scenarios.

5. Conclusions

This study addresses the multi-objective path planning problem for USVs navigating in complex marine environments influenced by sea winds and ocean currents. A nonlinear optimization model is developed to minimize path distance and energy consumption under constraints such as collision avoidance, motion limits, and environmental disturbances. An improved particle swarm optimization algorithm (PSO-INFO), featuring adaptive inertia and acceleration adjustment via trigonometric functions, is proposed to enhance convergence and search efficiency. Benchmark tests demonstrate that PSO-INFO outperforms traditional PSO and hybrid methods in terms of global search and optimization accuracy. By leveraging multiple objectives to guide particle evolution, the algorithm achieves a diverse set of Pareto-optimal solutions, enabling efficient trade-offs under varying environmental conditions. Simulations in different marine scenarios and real-world USV experiments confirm the model’s robustness, adaptability, and energy efficiency. These findings suggest that the proposed approach can provide mission-specific path guidance for USVs across a wide range of operational scenarios. Future work will incorporate additional dynamic factors and explore alternative optimization strategies to further improve planning performance.