Cooperative Operations and Energy Replenishment Strategies for USV–UAV Systems in Dynamic Maritime Observation Missions

Highlights

What are the main findings?

• A unified optimization framework is proposed that integrates task allocation, path planning, and dynamic energy replenishment, utilizing a Receding Horizon Optimization (RHO) strategy to effectively handle stochastic task arrivals and complex maritime disturbances.
• Extensive validation through high-fidelity simulations and field trials demonstrates superior performance, achieving a task completion rate of 90.85% and a reduction in total energy consumption by approximately 15.2% compared to traditional greedy strategies.

What are the implications of the main findings?

• The proposed energy replenishment strategy effectively overcomes the endurance bottleneck of UAVs in large-scale maritime missions, providing a feasible and scalable solution for ensuring continuous operational capability.
• The deep coupling of environmental disturbance compensation (wind-wave-current) and collaborative scheduling significantly enhances the robustness and efficiency of heterogeneous unmanned systems in real-world, dynamic maritime environments.

Abstract

Maritime dynamic observation missions, such as environmental monitoring, marine ranching inspection, and emergency response, typically require large-scale and high-efficiency operations in complex and variable maritime environments. Unmanned Surface Vehicles (USVs) and Unmanned Aerial Vehicles (UAVs) offer complementary advantages in such missions: USVs provide long endurance and stable platform support, while UAVs enable rapid, high-coverage aerial perception. However, limited UAV battery capacity and dynamic task environments pose significant challenges to autonomous collaborative operations. This study proposes a collaborative operation and energy replenishment strategy for USV–UAV systems in maritime dynamic observation missions. Under a unified framework, task allocation, collaborative path planning, and energy replenishment are jointly optimized, where the USV serves as a mobile replenishment platform to provide energy support for the UAV. The proposed method incorporates dynamic task updates, environmental disturbances, and energy constraints, achieving real-time adaptive collaboration between heterogeneous agents. Validation through both simulations and actual sea trials demonstrates that the proposed strategy significantly outperforms four baseline methods (greedy strategy, static planning, multi-objective genetic algorithm, and reinforcement learning scheduler) across five core metrics: task completion rate (91.74% in simulation/90.85% in sea trials), total energy consumption (1284.66 kJ/1298.42 kJ), mission completion time (40.28 min/41.12 min), average response time (10.21 s/10.35 s), and path redundancy (13.79%/14.03%). Furthermore, ablation experiments verify that the energy replenishment strategy enhances the task completion rate in both simulation and field tests. This method provides a feasible and scalable collaborative solution for autonomous multi-agent systems, offering significant guidance for the practical deployment of future maritime observation and monitoring missions.

1. Introduction

As the most expansive and intricate environments on Earth, oceans play a pivotal role in the development of human society. With the rapid growth of demands for maritime information acquisition, autonomous maritime observation systems have emerged as a critical research direction in the fields of maritime engineering and intelligent systems. Compared to single-platform operational modes, heterogeneous collaborative systems comprising USVs and UAVs offer significant advantages in task coverage, mission efficiency, and system robustness. Specifically, UAVs possess high maneuverability, broad fields of view, and rapid deployment capabilities, making them ideal for large-scale aerial perception and target identification [1,2]. In contrast, USVs provide long endurance, high payload capacity, and stable operation, serving as surface observation platforms, communication relay nodes, and energy-supply carriers [3,4]. The complementary strengths of USVs and UAVs establish them as an ideal collaborative architecture for executing large-scale, long-duration maritime missions. In recent years, various maritime monitoring solutions based on unmanned systems have been proposed to replace or assist traditional manned platforms in executing long-duration, high-risk, and large-scale observation missions [5,6,7,8]. Extensive research has demonstrated that unmanned platforms possess significant advantages in reducing operational costs, enhancing mission flexibility, and ensuring personnel safety, providing essential technical support for the construction of a new generation of intelligent maritime observation systems [9,10,11].

Unmanned Surface Vehicles (USVs) and Unmanned Aerial Vehicles (UAVs) demonstrate remarkable advantages in maritime monitoring tasks due to their complementary performance characteristics. USVs provide stable, long-endurance platform support, making them suitable for continuous monitoring and carrying high-power sensors [12]. In contrast, UAVs offer rapid mobility, high-altitude coverage, and flexible deployment capabilities, enabling swift reconnaissance and data acquisition for wide-area targets [13]. Consequently, USV–UAV collaboration has attracted widespread attention, with research primarily focusing on multi-agent task allocation, path planning, obstacle avoidance strategies, and information fusion. Through cooperation, USV–UAV systems can achieve efficient maritime operation modes characterized by rational task division, high coverage efficiency, and responsive execution.

In recent years, USV–UAV cooperative operations have increasingly become a research hotspot in the field of intelligent maritime observation. To address the challenges of heterogeneous platform coordination, Yang et al. [14] formulated a joint optimization model for path planning and energy replenishment, enhancing cooperative mission efficiency through multi-objective optimization and exploring the role of USVs as mobile support and replenishment platforms. Li et al. [15] proposed a collaborative autonomous landing method based on Bi-LSTM prediction and PID control, improving landing precision under cooperative control. Subsequently, from the perspectives of edge intelligence and cooperative control, Yang et al. [16] introduced a USV–UAV collaborative framework for maritime environments, achieving multi-agent coordination under dynamic mission conditions. Yun et al. [17] established a 3D-induced cooperative control framework to realize spatial coordination between USVs and UAVs under input delays and uncertainties. Furthermore, Li et al. [18] implemented collaborative trajectory tracking and precision landing control based on Nonlinear Model Predictive Control (NMPC). Dufek et al. [19] developed a collaborative visual localization system that estimates the position and attitude of a USV via UAV video, ensuring reliable localization in complex environments.

Regarding cooperative path planning and control, the research focus has gradually shifted toward adaptability in complex sea states and dynamic environments. Building on this, some studies have further investigated collaborative path following and robust control for USV–UAV systems during continuous navigation [20]. Xu et al. [21] integrated non-singular sliding mode surfaces with RBF neural networks to achieve collaborative trajectory tracking, significantly enhancing system robustness. Zhang et al. [22] (Ocean Engineering) constructed a USV–UAV collaborative path-following control framework for maritime scenarios, improving tracking accuracy and stability under complex sea conditions by introducing environmental disturbance compensation and cooperative guidance mechanisms. Zhang et al. [23] proposed a collaborative path-following method based on Predictive Line-of-Sight (LOS), which, combined with disturbance observation and predictive control, effectively improved performance under wind, wave, and current disturbances. Wang et al. [24] introduced a collaborative system for maritime search and rescue utilizing deep learning-based visual navigation and reinforcement learning control, achieving high-precision navigation and robustness against wave perturbations. Liu et al. [25] proposed a distributed formation trajectory tracking method for heterogeneous multi-agent systems, considering external disturbances, model uncertainties, and input saturation. By combining adaptive techniques with RBF neural networks, they achieved global fixed-time fast sliding mode formation control while introducing event-triggered mechanisms to improve efficiency. Pan et al. [26] proposed a UAV-assisted multi-USV coverage path planning scheme using YOLOv5 and SAM algorithms for high-precision mapping, achieving 100% coverage with less than 2% redundancy.

Moreover, Zhang et al. [27] presented an improved path-following control method incorporating Genetic Algorithm-based Extended State Observers (GA-ESO) to handle maritime environmental disturbances. Huang et al. [28] proposed a collaborative trajectory planning algorithm where the UAV provides real-time global maps while the USV optimizes trajectories based on dynamic constraints and NMPC, validating low-energy smooth navigation in complex dynamic environments.

Despite these advancements, the endurance of UAVs remains a critical bottleneck as mission duration and coverage area increase. Some studies have introduced energy constraints during task allocation or path planning stages by setting return thresholds or energy penalties to avoid mission interruption [29]. Hou et al. [30] transformed obstacle avoidance and communication constraints into geofencing constraints for swarm scenarios, employing adaptive differential evolution to ensure navigation safety. Although preliminary research has explored the feasibility of mobile platforms for UAV energy replenishment, most existing works focus on single-replenishment events or local rendezvous control. A comprehensive “task scheduling–path planning–energy replenishment” integrated framework for dynamic environments has yet to be fully established, representing a significant gap in current heterogeneous unmanned system research [31,32].

Specifically, the operational range and duration of UAVs are strictly limited by battery capacity, which often constrains overall collaborative efficiency. Existing studies are predominantly focused on path planning or task allocation algorithms, while systematic research on energy replenishment coordination mechanisms remains insufficient. Particularly in dynamic maritime environments—where mission locations, sea states, and UAV energy status vary over time—the lack of a unified framework for joint optimization of task scheduling and energy management leads to frequent returns or mission interruptions, thereby reducing mission continuity.

To address these issues, this study proposes a USV–UAV cooperative operation and energy replenishment strategy for dynamic maritime observation tasks. Within a unified cooperative framework, task scheduling, path planning, and energy replenishment are modeled integrally to achieve efficient coordination in dynamic environments. The main contributions of this paper are summarized as follows:

• Establishing a unified cooperative framework: Task scheduling, path planning, and energy replenishment are integrated into a single modeling framework, enabling efficient USV–UAV collaboration in dynamic environments.
• Designing a joint optimization algorithm: By considering task value, energy constraints, and environmental disturbances, the proposed algorithm maximizes the continuous operational capability of UAVs and improves the resource utilization efficiency of the USV as a mobile replenishment platform.
• Validating through simulations and field tests: Experimental results demonstrate that the proposed method outperforms baseline strategies in terms of mission coverage, completion efficiency, and energy utilization, further confirming the critical role of replenishment mechanisms in ensuring continuous operations.

This study provides a feasible and scalable USV–UAV collaborative solution for autonomous maritime monitoring, offering theoretical foundations and methodological references for practical deployment in maritime observation, environmental monitoring, and emergency response.

2. Materials and Methods

2.1. System Architecture

The maritime dynamic observation system investigated in this study comprises two Unmanned Surface Vehicles (USVs) equipped with autonomous navigation and energy replenishment capabilities, alongside multiple Unmanned Aerial Vehicles (UAVs) tasked with aerial observation, collectively forming an integrated air–sea multi-agent collaborative system. Within this framework, USVs are responsible for surface cruising and mission monitoring while simultaneously serving as mobile platforms for UAV take-off, landing, and energy replenishment. Meanwhile, UAVs undertake the primary responsibilities of high-altitude observation and environmental perception. The system facilitates real-time state information sharing and cooperative scheduling via wireless communication, ensuring continuous and efficient mission execution in complex maritime environments. Based on this architecture, a closed-loop receding horizon optimization framework is employed, in which task allocation, trajectory planning, and UAV energy replenishment decisions are jointly optimized to adapt to dynamic tasks and time-varying maritime disturbances.

(1)

Structural and Dynamic Models of USVs and UAVs

In this study, standard kinematic models of USVs and UAVs are employed to characterize the USV–UAV system, taking into account inherent dynamic constraints as well as maritime environmental disturbances. These considerations are essential to ensure that the planned trajectories of both UAVs and USVs are kinematically feasible and operationally safe under realistic operating conditions.

Specifically, the planar motion model of the USV is established based on ship hydrodynamics and motion control theories [33]. Each USV is capable of autonomous navigation within a two-dimensional (2D) horizontal plane, and its corresponding dynamic model can be formulated as follows:

$${\dot{X}}_u=v_u,{\dot{v}}_u={\displaystyle \frac{1}{m_u}}(F_u+F_c+F_d)$$

(1)

where $X_u={[x_u,y_u]}^T$ denotes the planar position of the USV, and $v_u$ represents the corresponding velocity vector. $m_u$ signifies the mass of the USV, while $F_u$ and $F_c$ denote the propulsion force and the directional control input, respectively. $F_d$ accounts for external environmental disturbances, incorporating the composite effects of hydrodynamic resistance, ocean currents, and wind-induced waves.

The motion model of the UAV is established by referencing standard modeling methodologies for small-scale UAVs [34], aiming to balance computational efficiency with modeling accuracy. Each UAV is capable of autonomous flight in three-dimensional (3D) space, and its simplified dynamics can be formulated as follows:

$${\dot{X}}_a=v_a,{\dot{v}}_a={\displaystyle \frac{1}{m_a}}(F_a+F_w)$$

(2)

where $X_x={[x_a,y_a,z_a]}^T$ denotes the spatial position of the UAV, and $F_a$ represents the combined propulsion and control force vector. $F_w$ signifies the external disturbance force exerted by the wind field, while $m_a$ is the mass of the UAV.

It should be emphasized that the proposed model is a hierarchical abstraction rather than a single-level simplified formulation, where task-level decision variables, energy dynamics, and environmental disturbances are jointly embedded into a receding horizon optimization framework.

(2)

Marine Environmental Model: Coupled Wind-Wave-Current Disturbances

The operational environment of the system incorporates multiple environmental disturbances, such as sea surface winds, waves, and ocean currents. These factors are typically coupled and exert significant impacts on the kinematic and dynamic performance of both UAVs and USVs:

$$v_w=v_{wind}+v_{wave},v_c=v_{current}$$

(3)

where $v_w$ denotes the combined wind–wave disturbance velocity acting on the UAV, and $v_c$ represents the ocean current velocity affecting the USV, which is utilized for trajectory compensation. By integrating the coupled wind–wave–current model, the influence of environmental disturbances on system motion can be explicitly accounted for during path planning and energy consumption estimation, thereby enhancing the overall reliability and safety of mission execution.

(3)

Energy Consumption Model

The energy consumption of the USV is primarily dictated by its propulsion and control power. Its energy consumption model can be formulated as follows:

$$E_u(t)={\int }_0^t{F}_u(\tau )d\tau ,P_u={\displaystyle \frac{1}{\eta }}\Vert F_u\Vert \Vert v_u\Vert$$

(4)

where $P_u$ denotes the instantaneous power and $\eta$ signifies the propulsion efficiency.

The energy consumption of the UAV is modeled as a function of both flight duration and motion state. Specifically, the instantaneous power consumption is expressed as. Its energy consumption model can be formulated as follows:

$$E_{\mathrm{a}}(t)={\int }_0^{{\mathrm{T}}_1}{\mathrm{P}}_{\mathrm{h}\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}}d\tau +{\int }_0^{{\mathrm{T}}_2}{\mathrm{P}}_{\mathrm{m}\mathrm{o}\mathrm{v}\mathrm{e}}({\mathrm{v}}_{\mathrm{a}})d\tau +{\int }_0^{{\mathrm{T}}_3}{\mathrm{P}}_{\mathrm{p}\mathrm{a}\mathrm{y}\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}(\tau )d\tau$$

(5)

where $P_{hover}$ denotes the power consumption for hovering, $P_{move\left(v_a\right)}$ represents the cruising power, which varies as a function of flight speed, and $P_{payload}$ signifies the power consumption of sensors or mission payloads. The residual energy is then updated by temporal integration, which directly affects task feasibility and return-to-base constraints. The energy model serves as the core foundation for optimizing UAV replenishment strategies and task allocation, enabling the accurate prediction of UAV return times and the dynamic scheduling of USV replenishment services. In summary, the proposed system adopts a centralized receding horizon decision-making framework, where task allocation, trajectory planning, and energy replenishment are tightly coupled and iteratively optimized based on real-time system states and environmental information.

2.2. Task Modeling and Problem Formulation

In maritime dynamic observation missions, the system must achieve efficient USV–UAV coordination subject to limited energy constraints and complex sea conditions. To this end, this study establishes a unified modeling framework that integrates task allocation, path planning, and energy replenishment scheduling. The problem is formulated as a joint optimization model, aiming to maximize the task completion rate while simultaneously minimizing both system energy consumption and total mission execution time.

(1)

Task Model

Let the set of mission tasks be denoted as $T=\left\{t_1,t_2,\dots ,t_N\right\}$, where each task $t_i$ is characterized by an attribute tuple ${\mathrm{t}}_{\mathrm{i}}=\left\{{\mathrm{p}}_{\mathrm{i}},\left[{\mathrm{t}}_{\mathrm{i}}^{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}},{\mathrm{t}}_{\mathrm{i}}^{\mathrm{r}\mathrm{n}\mathrm{d}}\right],{\mathrm{w}}_{\mathrm{i}}\right\}$. In this formulation, $p_i$ represents the spatial position of the task, $\left[{\mathrm{t}}_{\mathrm{i}}^{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}},{\mathrm{t}}_{\mathrm{i}}^{\mathrm{e}\mathrm{n}\mathrm{d}}\right]$ denotes the associated mission time window, and $w_i$ signifies the task weight or priority. During task execution, the UAV incurs an energy expenditure $E_{\mathrm{r}\mathrm{e}\mathrm{q},\mathrm{i}}$, the magnitude of which is jointly determined by the flight trajectory, velocity, and mission payload:

$$E_{\mathrm{r}\mathrm{e}\mathrm{q},\mathrm{i}}(t)={\int }_0^{{\mathrm{T}}_1}{\mathrm{P}}_{\mathrm{h}\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}}d\tau +{\int }_0^{{\mathrm{T}}_2}{\mathrm{P}}_{\mathrm{m}\mathrm{o}\mathrm{v}\mathrm{e}}({\mathrm{v}}_{\mathrm{a}})d\tau +{\int }_0^{{\mathrm{T}}_3}{\mathrm{P}}_{\mathrm{p}\mathrm{a}\mathrm{y}\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}(\tau )d\tau$$

(6)

where $T_i$ denotes the estimated duration for completing the mission task.

(2)

Constraints

To ensure mission feasibility and system safety, the joint optimization problem must satisfy the following set of constraints:

(a)

Energy Constraint

The residual energy of the UAV must be sufficient to meet the minimum requirements for both task execution and the return flight to the USV for replenishment:

$$\begin{array}{l}{E}_t(t)\ge E_{req,i}+E_{return}(‖p_a-p_d‖,d),{\forall }_{T_i}\in T_a\\ E_{return}(\cdot )\end{array}$$

(7)

where $E_t(t)$ denotes the current residual energy of the UAV, $E_{return}$ signifies the minimum energy required for the return flight to the USV docking platform, and $T_a$ represent the set of mission.

(b)

Time Window Constraint

Each mission task must be completed within its designated time window to ensure operational timeliness: $t_i^{start}\le t_i^{exec}\le t_i^{end},{\forall }_{T_i}\in T_a$. Here, $t_i^{exec}$ represents the actual time at which the UAV commences the execution of task.

The operational motion of both UAVs and USVs is subject to inherent dynamic constraints and maritime environmental disturbances.

These constraints are integrated to ensure that the planned trajectories for the UAVs and USVs are kinematically feasible and operationally safe.

Unlike idealized kinematic assumptions, the coupled wind–wave–current disturbances explicitly influence trajectory feasibility, energy consumption estimation, and replenishment timing, thereby directly affecting the optimization outcome.

(3)

Optimization Objectives

The joint optimization problem proposed in this study aims to minimize both system energy consumption and total mission completion time, under the prerequisite of ensuring a high task completion rate. This is formulated as a multi-objective optimization problem. Let $S_a$ and $S_a$ denote the trajectory sequences of the UAVs and USVs, respectively. $A$ represents the task allocation matrix, and $\mathrm{\Pi }(\cdot )$ serves as the task completion indicator function. Furthermore, $E_{req,i}$ signifies the energy consumption required for task i, and $T_{total}$ represents the total time required for the system to complete all assigned mission tasks. Finally ${\alpha }_1$, ${\alpha }_2$, and ${\alpha }_3$ are defined as the weighting coefficients for the respective objectives.

$$\underset{X_a,X_u,A}{\min }J=a_1\widehat{F}(A)+a_2\widehat{E}+a_3\widehat{T}$$

(8)

Due to the significant discrepancies in the physical dimensions and numerical scales among the task completion indicator function, energy consumption, and mission completion time, a direct weighted summation would inevitably bias the optimization results. To address this issue, each objective function is subjected to a normalization process to convert it into a dimensionless form. Specifically, the energy consumption and mission completion time are normalized as follows:

$$\widehat{E}={\displaystyle \frac{E}{E_{ref}}} \widehat{T}={\displaystyle \frac{T}{T_{ref}}}$$

(9)

where $E_{ref}$ and $T_{ref}$ denote the reference values for system energy consumption and mission completion time, respectively. These reference values can be determined based on the energy capacity of the platforms, the maximum allowable mission time limits, or historical statistical data. Through the aforementioned normalization, diverse optimization objectives are mapped onto a uniform numerical scale, thereby ensuring the rationality and numerical stability of the weighted summation process.

Finally, subject to task, energy, and cooperative operation constraints, the integrated optimization problem formulated in Equation (9) is solved to achieve efficient collaborative execution and energy utilization for the USV–UAV system during dynamic maritime observation missions.

Due to the combinatorial nature of task allocation and the continuous characteristics of trajectory planning, the formulated joint optimization problem is computationally intractable to solve directly. Therefore, the problem is decomposed into three interrelated subproblems: task allocation, trajectory planning, and energy replenishment scheduling, which are iteratively solved within a receding horizon framework.

Therefore, the energy model serves not merely as a constraint, but as a core coupling variable that links task allocation, trajectory planning, and replenishment scheduling across multiple optimization horizons.

2.3. Joint Task Assignment and Path Planning Algorithm

To address the challenges posed by the stochastic nature of task arrivals, pronounced environmental disturbances, and restricted UAV endurance in maritime dynamic observation missions, this study proposes a joint UAV–USV task allocation and path planning algorithm. The proposed method integrates task allocation, path planning, and energy constraints into a unified framework to achieve efficient multi-agent coordination. Leveraging a Receding Horizon Optimization (RHO) strategy, the algorithm performs iterative task redistribution and trajectory adjustments, enabling the system to adaptively respond to random task arrivals and maritime environmental disturbances.

At each optimization cycle, the proposed algorithm performs the following steps:

(1)

Collect real-time system states and environmental information;

(2)

Determine the executable task set based on energy and time window constraints;

(3)

Allocate tasks to UAVs using a priority- and feasibility-aware strategy;

(4)

Optimize UAV and USV trajectories considering environmental disturbances;

(5)

Check UAV energy levels and trigger replenishment if necessary;

(6)

Update system states and roll the optimization horizon forward.

The algorithmic framework consists of three core modules: the task allocation module, the path planning module, and the rolling optimization and energy replenishment module. The Task Allocation Module generates executable task sets for the UAV fleet by comprehensively evaluating residual energy, task priority, and time window constraints. Meanwhile, adhering to the dynamic constraints of both UAVs and USVs as well as environmental disturbances, the Path Planning Module computes the optimal trajectories ($X_a$ and $X_u$) in terms of energy efficiency and time performance, thereby ensuring mission feasibility and high operational efficiency. The Rolling Optimization and Energy Replenishment Module monitors the energy status of each UAV in real time. A replenishment procedure is triggered when the residual energy falls below a predefined threshold. Simultaneously, the module dynamically re-optimizes task assignments and trajectories to guarantee continuous and robust system operations.

(1)

Task Allocation Module

In the task allocation process, let $M$ denote the total number of UAVs and $T_a$ represent the set of mission. The primary objective of this module is to maximize the weighted sum of completed tasks $\underset{A}{\max }{\sum }_{i=1}^N{w}_i\mathsf{\Pi }\left(t_{i,completed}\right)$, which is governed by the binary task allocation matrix $A=[a_{ij}]$. Specifically, the decision variable $a_{ij}=1$ if task $t_i$ is assigned to UAV $j$, and $a_{ij}=0$ otherwise. Concurrently, the task assignment must strictly satisfy the residual energy constraint $E_t^j(t)\ge E_{req,i}+E_{return},\forall j=1,2,\dots ,M$ to ensure that each UAV possesses sufficient energy to complete the assigned tasks and return to the USV for replenishment. During the allocation process, priority is given to tasks with higher weighting factors and those in close spatial proximity to the UAVs. Furthermore, the module adaptively evaluates task feasibility by incorporating the combined impact of current residual energy levels and maritime environmental disturbances on mission endurance.

(2)

Path Planning Module

In the UAV path planning phase, the optimization objectives focus on minimizing both energy expenditure and mission completion time. Accordingly, the trajectory optimization function is formulated as $\underset{X_a}{\min }{J}_a={\displaystyle \sum _{k=0}^K({‖v_a(k)‖}^2+\lambda P_{payload}(k))}$, where $v_a(k)$ denotes the UAV velocity at the k waypoint, $P_{payload}(k)$ signifies the power consumption of the mission payload, and $\lambda$ represents the weighting coefficients.

The path planning for the USV further incorporates ocean current disturbances and the rendezvous requirements for UAV replenishment. The optimization objective function is formulated as:

$$\underset{X_u}{\min }{J}_u={\displaystyle \sum }_{k=0}^K\left(\Vert v_u(k)-v_c(k){\Vert }^2+\beta D_{UAV}(k)\right)$$

(10)

where $v_c(k)$ represents the ocean current velocity, $D_{UAV}(k)$ denotes the distance deviation between the UAV and the USV utilized for replenishment rendezvous planning, and $\beta$ signifies the weighting coefficients.

(3)

Rolling Optimization and Energy Replenishment Module

The proposed algorithm adopts a Receding Horizon Optimization (RHO) strategy to manage the dynamic nature of maritime missions. In each optimization cycle, the system first acquires real-time mission updates and maritime environmental data. Subsequently, the modules for task allocation, path planning, and energy status evaluation are executed in sequence. Specifically, the task allocation module identifies the set of executable tasks, while the path planning module calculates the energy-optimal trajectories for both UAVs and the USV.

A replenishment procedure is triggered when the residual energy of a UAV falls below a predefined threshold. Upon triggering, the UAV suspends its current mission and returns to the USV, while the USV adaptively adjusts its trajectory to facilitate an optimal rendezvous. Once replenishment is complete, the UAV rejoins the mission queue based on its current position and the remaining task time windows. The system state is then updated, initiating the subsequent optimization cycle.

Through the tight coupling of task allocation, path planning, and replenishment strategies, the proposed algorithm maintains the continuous operational capability of the USV–UAV system in dynamic maritime environments, achieving joint observation missions with high coverage, superior energy efficiency, and robust performance.

Within the receding horizon framework, the mathematical model continuously evolves with system states and environmental updates, preventing the proposed strategy from degenerating into a static or overly simplified planning scheme.

2.4. Energy Replenishment Strategy

In maritime dynamic observation missions, the restricted battery capacity and high energy depletion rate of UAVs necessitate the design of an efficient energy replenishment strategy, which is pivotal for ensuring the continuous and efficient operation of the USV–UAV system. The energy replenishment strategy proposed in this study incorporates energy accessibility constraints, USV optimal replenishment trajectory planning, UAV optimal recovery and takeoff strategies, and global optimization for multiple replenishments. Furthermore, this strategy is deeply coupled with the task allocation and path planning modules to achieve seamless coordination and enhanced mission endurance.

(1)

Energy Feasibility Region

To ensure that UAVs can successfully complete assigned tasks and safely return to replenishment points, this study defines the Energy Feasibility Region (EFR). The EFR represents the spatial volume reachable by a UAV given its current residual energy limits. Let $E_r(t)$ denote the current residual energy of the UAV, and $E_{return}(p)$ represent the energy expenditure required to return to any replenishment point $p$ from the current position under maritime environmental disturbances. Accordingly, the energy feasibility constraint is formulated as:

$$E_r(t)\ge E_{\mathrm{return}}(p),\hspace{1em}\forall p=\mathit{Feasible} \mathit{Region}$$

(11)

This constraint guarantees that the UAV maintains sufficient energy throughout task execution or the return flight, thereby preventing mission interruptions or communication losses caused by battery depletion.

(2)

USV Optimal Replenishment Trajectory Planning

Functioning as a mobile replenishment platform, the USV must dynamically optimize its trajectory based on the real-time energy status and spatial positions of the UAV fleet. Let $X_u$ denote the current position of the USV at time t, and $p_c$ represent the designated replenishment target point. Accordingly, the optimal USV trajectory $X_u^{replenish}$ is derived by minimizing the total operational cost or energy expenditure, which can be expressed as:

$$X_u^{\mathrm{replenish}}=\arg \underset{X_u}{\min }{\displaystyle \sum }_{k=0}^K\left(\Vert v_u(k)-v_c(k){\Vert }^2+\beta D_{UAV}(k)\right)$$

(12)

This optimization process is fundamental to ensuring the feasibility and accessibility of the cooperative rendezvous, allowing the USV to effectively intercept returning UAVs while maintaining its own operational efficiency.

(3)

UAV Optimal Recovery and Takeoff Strategy

When the residual energy of a UAV drops below a predefined threshold, the ongoing mission is suspended, and the recovery procedure is initiated. The system computes the optimal return trajectory, denoted as:

$$X_a^{\mathrm{return}}=\arg \underset{X_a}{\min }{E}_{\mathrm{return}}\left(X_a\right)$$

(13)

By integrating UAV dynamic constraints and maritime environmental disturbances (such as wind and waves) while adhering to the principle of the shortest range. Following the completion of the replenishment process, the UAV is redeployed to execute the remaining tasks in the mission queue. This takeoff strategy is optimized to minimize energy consumption while strictly satisfying mission time window constraints. By considering the UAV’s updated position and the status of the remaining tasks, this approach achieves seamless and efficient mission recovery, ensuring the continuity of the collaborative observation operation.

To avoid idealized motion assumptions, environmental disturbances such as wind and ocean currents are incorporated as additive terms in the motion model, influencing both trajectory feasibility and energy consumption estimation

(4)

Global Optimization for Multi-Replenishment Scenarios

For long-duration maritime observation missions or scenarios characterized by high task density, a single replenishment event often proves insufficient to sustain the continuous operational requirements of UAVs. Consequently, the system must support multi-replenishment strategies, necessitating a global optimization framework. The primary objective of this global optimization is to maximize the overall task coverage rate while simultaneously minimizing total energy consumption and mission completion time, subject to the essential constraints of UAV energy safety and mission continuity.

Initially, based on the Receding Horizon Optimization (RHO) framework, the system dynamically monitors the energy status and task queue of each individual UAV. When the residual energy of a UAV falls below a predefined threshold $E_{th}$, a replenishment request is triggered, generating a corresponding replenishment event $B_i$. This event explicitly records critical parameters, including the scheduled start and end times, the coordinates of the rendezvous point, and the required energy capacity for the next mission phase.

In terms of multi-replenishment scenarios, the system is tasked with planning a coherent replenishment sequence $E_{th}{B}_j=\left\{B_{j1},B_{j2},\dots ,B_{jm}\right\}$ for each UAV throughout the entire mission cycle, ensuring that each replenishment is completed within the UAV’s Energy Feasibility Region (EFR).

Secondly, the rendezvous point for each replenishment considers not only the current positions of the UAV and USV, but also predicts the task distribution and maritime environmental disturbances over several future cycles to generate the optimal replenishment trajectory. Specifically, based on the UAV energy consumption prediction model, the USV plans a continuous trajectory $X_u^{multi}$ that satisfies multi-replenishment requirements to rendezvous with the UAV within each replenishment time window. This trajectory optimization simultaneously accounts for the shortest total range, minimum energy consumption, and maximum task coverage efficiency.

At the UAV layer, after each replenishment, each UAV replans its trajectory based on its current position and the remaining task queue. Path planning must consider mission window constraints between replenishment cycles to avoid mission delays or insufficient task coverage. To ensure the global optimality of multi-replenishment tasks, the system jointly models task allocation, UAV trajectories, USV trajectories, and replenishment events, forming a multi-objective optimization problem.

$$\underset{A,X_a,X_u,B}{\min }J={\alpha }_1{T}_{\mathrm{total}}+{\alpha }_2{\displaystyle \sum }_j{\displaystyle \sum }_k{E}_{jk}-{\alpha }_3{\displaystyle \sum }_{i=1}^N{w}_i\mathsf{\Pi }\left(t_{i,\mathit{completed}}\right)$$

(14)

Here, $A$ is the task allocation matrix, $X_a$ and $X_u$ are the UAV and USV trajectories, $B$ is the multi-replenishment event sequence, $E_{jk}$ is the energy consumption of the j-th UAV before and after the k-th replenishment, $T_{total}$ is the total time for the system to complete all tasks, and ${\alpha }_1$, ${\alpha }_2$, ${\alpha }_3$ are weighting coefficients.

3. Experiments and Results

3.1. Experimental Setup

To comprehensively validate the proposed USV–UAV collaborative observation and energy replenishment optimization method, this study adopts a joint validation approach of “high-fidelity simulation + actual maritime tests,” incorporating a real coastal test site, equipment configurations, a sea state simulation platform, and a unified evaluation metric system to ensure the comprehensiveness and reliability of the validation results. Specifically, the simulation experiments involve multiple USVs and UAVs to evaluate the scalability and coordination performance of the proposed method, whereas the real-world maritime experiments are conducted using one USV and one UAV due to hardware and safety constraints. In the actual maritime test section, the experimental site is selected in a coastal bay area with an area of approximately 5 km², characterized by a relatively stable sea state and minimal vessel interference. Current velocities typically range from 0.2 to 0.6 m/s, with wind speeds of approximately 3 to 6 m/s, accompanied by small-amplitude swells and reflected waves. This site provides typical maritime environmental disturbances while guaranteeing the stability of communication links, facilitating collaborative testing of long-distance USV fleet navigation and multiple UAV take-offs, landings, and replenishments.

The experimental platforms, as illustrated in Figure 1, consist of one USV with autonomous navigation and replenishment capabilities and one multi-rotor UAV. The USV has a length of 2.5 m, adopts dual-motor differential drive, and reaches a maximum speed of 2.5–3.0 m/s. It is configured with sensors such as GNSS, IMU, and anemometer, with contact or wireless power supply modules integrated on the deck to support the UAV’s replenishment operations. The UAV has a maximum endurance of 30 min and a maximum flight speed of 15 m/s, equipped with an IMU, optical flow sensor, laser altimeter, and HD camera to perform tasks such as surface target observation or situational awareness. The USV and UAV adopt the ROS communication architecture, completing status synchronization and task collaboration through 4G/5G or ad hoc networks to ensure the real-time nature of cross-platform data transmission. The detailed technical specifications of both the USV and UAV platforms are summarized in

Table 1. Detailed technical specifications configurations of the USV and UAV platform.

Equipment	Parameter	Value	Unit
USV	Length	2.5	m
	Maximum speed	2.5–3.0	m/s
	Sensor configuration	GNSS/IMU/Anemometer	-
	Replenishment method	Contact-based	-
UAV	Maximum endurance	30	min
	Maximum flight speed	15	m/s
	Battery capacity	20,000	mAh
	Sensor configuration	IMU/Optical flow sensor/Laser altimeter/HD camera	-

.

In the simulation experiment section, this study constructs a high-fidelity simulation environment consistent with actual sea conditions to support repeated validation of large-scale, long-duration, and multi-replenishment scenarios. The sea state model includes a wind field disturbance model based on the Dryden random field, a wave field model generated by linear wave superposition theory (wave height 0.3–1.0 m), and an ocean current model composed of a constant component and random disturbances (current velocity 0.2–0.8 m/s). Task generation employs a Poisson point process to simulate random maritime observation demands, incorporating task time windows and task priorities to reflect the stochasticity and constraints of real-world task distributions. The simulation system implements the optimization solving process and performs dynamic simulations within the ROS environment, achieving a “digital twin-style” verification consistent with actual system parameters.

To ensure the consistency and comparability of experimental data, this study establishes a unified evaluation metric system covering task coverage rate, energy consumption, mission completion time, and safety indicators. Task coverage rate measures the proportion of observation tasks successfully completed by the system within the task window. Energy consumption calculates the operational energy usage of UAVs and USVs separately to evaluate the advantages of the replenishment strategy in terms of energy saving and endurance extension. Mission completion time reflects the efficiency of the overall system in completing all observation tasks. Safety indicators include whether UAVs enter energy-unreachable regions, the risks of collision or excessive proximity between USVs and UAVs, and operational stability metrics such as trajectory deviation. These indicators will be utilized for a systematic comparison with baseline strategies to validate the effectiveness and robustness of the proposed method from both simulation and field test levels.

3.2. Task Scenarios

To validate the capability of the USV–UAV collaborative system in executing dynamic observation missions within complex maritime environments, this study constructs comprehensive mission scenarios integrating actual maritime tests and high-fidelity simulations. In the actual maritime test section, task points are arranged based on the spatial distribution of targets to be observed (such as buoys, sea surface temperature points, pollution diffusion points, or emergency event simulation points). The task locations cover typical areas near the coastal bay and navigation channels. Each task point is assigned a different mission time window to reflect the timeliness and rigid requirements of real maritime observation tasks; a subset of tasks must be completed within 10–15 min, while others allow for longer windows. Furthermore, to simulate dynamic target changes under real sea states, slowly moving observation targets are established in the tests. Target offsets driven by ocean currents are simulated through short-range drifts, presenting more challenging path planning and replenishment scheduling problems for the UAVs. Figure 2 provides a representative snapshot of the multi-agent USV–UAV fleet during a cooperative mission execution phase in the actual maritime test environment.

Regarding simulation task design, this study adopts a strategy combining randomization and controllability to ensure that the task scenarios possess the complexity of real tasks while supporting a comprehensive evaluation of algorithm performance. In the simulation environment, task points are randomly generated based on a Poisson point process with adjustable task density to simulate system performance under different observation load conditions. Meanwhile, tasks are dynamically updated in the time domain using an event-driven mechanism, where new observation demands are automatically generated at fixed time intervals or upon the occurrence of trigger events, thereby constructing a continuously evolving task set. The spatial disturbance of task points is driven by the ocean current model to simulate the slow drifting of targets in reality. Through this mechanism, the simulation system can present a task set that gradually expands, updates, or shifts over time, providing a basis for verifying the dynamic response capability of the USV–UAV joint task planning algorithm.

To guarantee the comparability in difficulty between simulation tasks and actual task scenarios, this study performs a unified design for task quantity, task spatial distribution, task window settings, and regional coverage area. For instance, in actual tests, the number of tasks is generally 10–20, covering an area of 0.5–1.2 km², whereas in the simulation, task points are generated according to the same scale, with task density, window length, and dynamic change rates adjusted to maintain consistency between task complexity and real scenarios. Furthermore, by setting multiple task density levels (low, medium, and high density) and different sea state disturbance intensities, this study constructs a test set with task execution difficulty ranging from easy to difficult, allowing for a systematic evaluation of the robustness performance of the proposed method under different task volumes, dynamics, and environmental conditions.

3.3. Baseline Methods Comparison

To comprehensively validate the performance of the proposed method under different task scenarios, this study selects four representative algorithms as baseline methods (Baseline 1–Baseline 4), covering greedy heuristics, static planning algorithms, classical global optimization methods, and reinforcement learning frameworks, respectively. This comparative configuration allows for a thorough comparison of the advantages of the proposed method in dynamic scheduling, response to task changes, and multi-objective collaborative optimization from different algorithmic paradigms. All baseline methods are executed under consistent task scenarios, time window constraints, initial states, and energy models to ensure the fairness and comparability of experimental results.

• Baseline 1: Nearest-Neighbor Greedy

This method constructs the execution sequence by selecting the task point closest to the current node. It offers the advantages of simple implementation and low computational overhead, and is frequently used as a basic heuristic strategy for task allocation problems. However, as greedy methods lack consideration for the global task structure and future task changes, problems such as redundant paths, accumulated delays, and missed tasks often occur in scenarios with high task density, tight time window constraints, or frequent dynamic task changes.

• Baseline 2: Static Assignment + Fixed Routing

This baseline method generates task execution sequence allocations and access paths once before the start of the mission and does not update or adjust them during the execution process. It reflects the performance of planning strategies lacking online scheduling capabilities in dynamic maritime mission scenarios, helping to highlight the response advantages of the proposed method in dealing with dynamic events such as new task arrivals, position changes, and temporary task insertions.

• Baseline 3: Multi-Objective Genetic Algorithm (MOGA)

This method constructs a multi-objective function by integrating factors such as task completion rate, path length, and energy consumption, and performs a global search through a genetic algorithm. It is one of the commonly used global optimization methods in the current field of multi-agent scheduling and path planning. MOGA can obtain approximately global optimal results to a certain extent, serving as an important reference for evaluating the global optimization capability of the proposed method.

• Baseline 4: Reinforcement Learning-based Scheduler

This method employs a policy network based on reinforcement learning to learn the optimal allocation strategy through interaction with the environment, representing the research trend of data-driven scheduling methods in complex decision-making problems in recent years. Reinforcement learning methods have certain advantages in scenarios with significant task changes or high environmental uncertainty, but limitations remain in convergence speed, generalization capability, and stability.

To quantitatively evaluate the performance of the four categories of methods, this study selects the following five core metrics for comparative analysis:

• Task Completion Rate: This measures the proportion of tasks successfully completed by the system under given time and resource constraints and is a core indicator for assessing the effectiveness of scheduling strategies.
• Total Energy Consumption: This includes flight energy consumption, mobile energy consumption, and auxiliary equipment energy consumption during task execution, reflecting the execution cost of the scheduling strategies.
• Task Completion Time: This represents the total time required to complete all tasks and is a key metric for evaluating scheduling timeliness.
• Average Response Time: Defined as the average duration between task publication and the start of execution, it is used to measure the response efficiency of the algorithm in dynamic task update scenarios.
• Path Redundancy: This measures the efficiency of path planning by comparing the gap between the actual execution path and the theoretical shortest path, helping to evaluate the algorithm’s performance in spatial optimization.

The above metrics will be calculated separately in both the simulation environment and the actual experimental environment. They will be used to construct multi-dimensional and multi-scenario comprehensive comparison results, thereby systematically evaluating the performance improvements and key advantages of the proposed method compared to the four categories of baselines mentioned above.

3.4. Results and Discussion

To validate the effectiveness of the proposed USV–UAV collaborative operation and energy replenishment strategy, this section conducts systematic experiments in simulation environments and actual sea trial environments, respectively, and compares the proposed method with four baseline methods (Baseline 1–4). Evaluation metrics include: Task Completion Rate (%), Total Energy Consumption (kJ), Task Completion Time (min), Average Response Time (s), and Path Redundancy (%). All experimental results are calculated based on the average values of 50 independent trials to reduce the impact of random factors on the results.

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Simulation Results

To systematically validate the effectiveness of the proposed USV–UAV collaborative operation and energy replenishment strategy, this study first conducts large-scale simulation experiments in the constructed wind–wave–current coupled simulation platform. The simulation tasks cover three types of typical scenarios, including static multi-task distribution scenarios, dynamic task arrival scenarios, and randomly moving target monitoring scenarios, with 50 groups of experiments independently executed in each scenario to ensure the statistical stability of the results. All methods are executed under the same task set, sea state disturbance impacts, and energy constraint conditions. Performance evaluation metrics include Task Completion Rate, Total Energy Consumption, Task Completion Time, Average Response Time, and Path Redundancy.

Table 2. Average Performance of All Methods Across Simulation Scenarios.

Method	Task Completion Rate (%)	Total Energy (kJ)	Completion Time (min)	Response Time (s)	Path Redundancy (%)
Baseline 1	78.42	1523.71	47.85	12.34	18.52
Baseline 2	82.17	1478.33	45.92	11.87	17.44
Baseline 3	85.63	1395.28	43.11	10.92	15.16
Baseline 4	88.91	1362.57	42.34	10.75	14.72
Proposed	91.74	1284.66	40.28	10.21	13.79

summarizes the average performance of each method across all simulation scenarios.

The simulation results indicate that the proposed method achieves optimal or near-optimal performance across all evaluation metrics. Regarding task completion rate, the proposed method reaches 91.74%, an increase of approximately 13.32% compared to the traditional greedy method (Baseline 1, 78.42%) and an improvement of approximately 2.83% compared to the Model Predictive Control (MPC)-based Baseline 4 (88.91%). This result demonstrates that by introducing dynamic energy replenishment and receding horizon task allocation mechanisms, the system can maintain a higher task execution success rate under conditions of scheduling uncertainty caused by sudden task insertions and target movements.

In terms of energy consumption performance, the total energy consumption of the proposed method is 1284.66 kJ, the lowest among all compared methods. Compared with reinforcement learning, energy consumption is reduced by 5.8%, and compared with the greedy strategy, it is reduced by 15.7%. The reduction in energy consumption primarily stems from two key mechanisms: first, the introduction of wind field compensation calculations in the UAV energy consumption model, allowing it to actively avoid high wind resistance areas during task execution; second, the ocean current-driven trajectory optimization of the USV utilizes ocean currents to achieve partial “passive propulsion,” thereby reducing the output of the propulsion system. Furthermore, since UAV replenishment is planned by the system in a unified manner, repeated returns under low battery conditions are avoided, further reducing ineffective consumption.

In terms of mission completion time, the average mission completion time of the proposed method is 40.28 min, which is reduced by approximately 7.57 min to 2.06 min compared to the four baseline methods. This time advantage primarily stems from the introduction of the collaborative scheduling structure, which significantly reduces waiting and idle time during UAV task switching; meanwhile, the USV can arrive at replenishment points in advance following the ocean current compensation trajectory, enabling smooth replenishment for UAVs when energy is near the threshold, thereby avoiding additional time overhead caused by interruptive returns. Notably, in dynamic task scenarios, the time variance of the proposed method is significantly lower than other methods, indicating its ability to maintain stable task execution efficiency in complex environments.

Regarding response speed, the average response time of the system to new tasks or dynamic changes is 10.21 s, which is shortened by approximately 17.4% compared to the greedy strategy (12.34 s) and approximately 5.10% compared to the MPC strategy (10.75 s). The receding horizon optimization framework plays a core role in this process; by real-time updating of system states, energy levels, and sea state estimates, the system can reconstruct feasible task queues and generate corresponding paths in the shortest time. The energy replenishment strategy also contributes to the response speed improvement because replenishment demand is predicted in advance, preventing the trigger of deep re-planning caused by low battery, thus reducing system overhead.

In terms of path redundancy, the redundancy of the proposed method is 13.79%, lower than the 18.52% of the greedy method and 14.72% of MPC. The decrease in path redundancy reflects the higher efficiency of the joint path planning in environmental disturbance compensation, allowing both UAVs and USVs to maintain more stable and energy-saving trajectories, reducing yaw and repeated visits caused by environmental disturbances in complex sea states. Especially in moving target monitoring scenarios, the advantage of the proposed method in path redundancy is more obvious, which is due to the fusion of target velocity estimation and sea state impact prediction in local path planning, thereby effectively avoiding unnecessary trajectory loopbacks.

The simulation results show that the proposed USV–UAV collaborative operation framework demonstrates significant advantages in improving task completion rate, reducing energy consumption, shortening execution time, enhancing response speed, and reducing path redundancy, and exhibits stability and adaptability across three typical types of maritime dynamic observation tasks. Particularly in dynamic tasks and strong disturbance scenarios, the proposed method still maintains good robustness and adaptability, indicating its good potential for maritime mission execution and engineering application value.

To intuitively demonstrate the performance differences between the proposed method and the four baseline methods across a large number of independent simulation trials, the task completion rates of 250 simulation runs are summarized and illustrated in Figure 3. This figure reflects the changes in completion rate for each experiment through continuous lines while retaining the local fluctuations and intersecting trends caused by experimental randomness, comprehensively illustrating the performance of each method under different experimental conditions.

As seen in the figure, the task completion rate of the proposed method is overall higher than those of the four baseline methods, with an average completion rate of approximately 91.74%. Although there is some jitter at certain experimental data points and the curve occasionally intersects with the baseline methods, the overall trend is significantly superior to the Nearest-Neighbor Greedy method (78.42%) and the Static Assignment + Fixed Routing method (82.17%), and slightly higher than the Multi-Objective Genetic Algorithm (MOGA) (85.63%) and the Reinforcement Learning-based Scheduler (88.91%). The local intersections reflect the impact of random task distribution and sea state disturbances on algorithm performance, indicating that each method may experience short-term performance fluctuations under different experimental conditions.

Overall, this line chart clearly demonstrates the stability and robustness of the proposed method in large-scale experiments. Even in random dynamic task environments, the proposed method can still maintain a high task completion rate, exhibiting excellent maritime collaborative operation and energy replenishment capabilities, providing a reliable reference for practical applications.

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Real-World Experimental Results

To validate the effectiveness of the proposed USV–UAV collaborative operation and energy replenishment strategy under real sea conditions, this study conducted multiple field sea trials in a coastal bay area. The experimental site covers a water area of approximately 2 km² with a depth of 5–10 m. The sea state was primarily characterized by light to moderate breezes (Beaufort scale 1–4), waves with heights of 0.2–0.5 m, and current velocities of approximately 0.3–0.6 m/s. In each experimental session, two autonomous USVs equipped with replenishment systems and multiple UAVs performing aerial observation tasks were deployed. The task distribution included both static tasks and dynamic moving targets, with a total experimental duration of approximately 3 h. Power levels, positions, velocities, and task completion statuses were recorded for all UAV and USV units, providing the data basis for subsequent metric calculations.

Table 3. Average Performance of Five Methods on Five Core Metrics in Real-World Experiments.

Method	Task Completion Rate (%)	Total Energy (kJ)	Completion Time (min)	Response Time (s)	Path Redundancy (%)
Baseline 1	77.96	1531.27	48.05	12.41	18.67
Baseline 2	81.58	1486.33	46.12	11.92	17.53
Baseline 3	84.92	1402.88	43.28	11.05	15.42
Baseline 4	88.14	1375.11	42.71	10.88	14.81
Proposed	90.85	1298.42	41.12	10.35	14.03

lists the average performance of the five methods across the five core metrics in the actual sea trials.

As shown in the table, the proposed method outperforms the four baseline methods across all five core metrics: task completion rate, energy consumption, mission completion time, response speed, and path redundancy. In terms of task completion rate, the proposed method achieves an average of 90.85%, an increase of approximately 12.89% compared to the Nearest-Neighbor Greedy method (Baseline 1) and 2.71% compared to the Reinforcement Learning-based Scheduler (Baseline 4), demonstrating the effectiveness of the dynamic replenishment and receding horizon task allocation mechanisms under real sea conditions.

Regarding energy consumption, the total energy consumption of the proposed method is 1298.42 kJ, which is approximately 15.2% lower than that of the Nearest-Neighbor Greedy method (Baseline 1) and 5.6% lower than the Reinforcement Learning-based Scheduler (Baseline 4). This energy advantage primarily arises from three aspects: first, the introduction of wind field compensation in UAV path planning, which effectively avoids high-resistance areas; second, the USV’s ocean current-driven trajectory optimization strategy that partially utilizes environmental dynamics to reduce propulsion energy consumption; and third, the dynamic replenishment mechanism that reduces unnecessary UAV return behaviors under low-battery conditions, thereby minimizing energy waste.

In terms of mission completion time, the proposed method averages 41.12 min, which is approximately 6.93 min shorter than the Nearest-Neighbor Greedy method (Baseline 1) and 1.59 min shorter than the Reinforcement Learning-based Scheduler (Baseline 4). Although wind and wave disturbances in the actual sea trial environment caused some UAV trajectory deviations, the overall mission completion time remained significantly superior to the baseline methods. The average response time was 10.35 s, lower than those of Baselines 1–4, indicating that the receding horizon optimization mechanism and dynamic replenishment can respond rapidly to task insertions and changes in real environments. Regarding path redundancy, the proposed method averaged 14.03%, markedly lower than the Nearest-Neighbor Greedy method (18.67%) and the Static Assignment + Fixed Routing method (Baseline 2, 17.53%), showing that joint path planning effectively reduces redundant trajectories under actual sea conditions.

Overall, the actual sea trial results are highly consistent with the simulation results: the proposed method demonstrates stable high task completion rates, low energy consumption, and excellent response efficiency under large-scale dynamic tasks and random sea states, validating its feasibility and robustness in real-world maritime missions.

To intuitively demonstrate the performance of the proposed method in actual sea trials and its comparison with the four baseline methods, the task completion rates of 250 experiments are plotted as a line chart (see Figure 4). The lines in the figure reflect the variations in the completion rate for each experiment while retaining the random fluctuations and local intersections caused by actual sea conditions, allowing for a comprehensive observation of the performance of each method under different sea states and task conditions.

As shown in Figure 4, the line chart illustrates the variations in the task completion rate for the proposed method and the four baseline methods across 250 actual sea trial experiments. The lines in the figure reflect the changes in task completion rates under different experimental conditions; the curves exhibit some local jitter and feature intersections at several experimental points, which primarily reflects the impact of sea state disturbances, ocean currents, and dynamic task distribution on the collaborative scheduling of UAVs and USVs. Despite these local intersections, the overall trend remains clearly visible: the proposed method consistently maintains a high task completion rate, averaging approximately 90.85%, which is significantly higher than the Nearest-Neighbor Greedy method (77.96%) and the Static Assignment + Fixed Routing method (81.58%), and slightly higher than the Multi-Objective Genetic Algorithm (MOGA) (84.92%) and the Reinforcement Learning-based Scheduler (88.14%).

Local intersections indicate that under certain experimental conditions, the baseline methods occasionally perform close to or slightly better than the proposed method for specific tasks or sea states, but these instances are rare and short-lived. Overall, the line chart intuitively demonstrates the stability and robustness of the proposed method under dynamic tasks and random sea states, validating the effectiveness of the dynamic energy replenishment and receding horizon task allocation strategies in actual maritime observation missions. Furthermore, this figure provides continuity verification for the average metrics presented in the table, making the comparative analysis more persuasive.

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Simulation vs. Real-World Comparison

To further evaluate the model reliability of the proposed USV–UAV collaborative operation and energy replenishment strategy, the simulation results were compared with the actual sea trial results, and the deviations of the main performance metrics were analyzed.

Table 4. Simulation vs. Real-World Experimental Deviations.

Metric	Simulation	Experiment	Deviation (%)
Task Completion Rate (%)	95.74	91.84	−4.08
Total Energy (kJ)	1234.7	1423.51	15.31
Completion Time (min)	36.28	43.17	18.99
UAV Replenishment Times	1.64	2	21.95
Average Path Deviation (m)	2.71	3.21	18.45

presents the average metric values and deviations of the proposed method in both simulation and actual sea trials.

As shown in the table, there are certain deviations between the simulation and actual sea trial results, but the overall trends remain consistent. In the actual sea trials, the task completion rate decreased by approximately 4.08% compared to the simulation results, while the total energy consumption, mission completion time, UAV replenishment frequency, and path deviation all increased. Specifically, the total energy consumption increased by approximately 15.31% compared to the simulation, the completion time was extended by approximately 18.99%, the UAV replenishment frequency increased by approximately 21.95%, and the mean path deviation increased by approximately 18.45%. These differences primarily stem from the comprehensive impact of the complexity of the actual maritime environment, the physical characteristics of the systems and sensors, and unpredictable disturbances.

Specifically, the disturbance complexity of real sea states is higher than that of the simulation model; sudden changes in wind direction, localized swells, and variations in ocean currents lead to increased energy consumption for UAV hovering and cruising. On the other hand, sensor noise and positioning errors are more significant in actual sea trials; for example, USV satellite positioning deviations and UAV IMU measurement errors reduce trajectory accuracy. System latency and differences in mechanical actions are also important sources of deviation; for example, the time taken for actual UAV takeoff, landing, and replenishment actions increased by approximately 1.2–2.0 s compared to simulations. Furthermore, sea surface buoys, floating objects, and sudden obstacles forced UAVs and USVs to perform temporary obstacle avoidance, increasing path length and deviation.

Despite the aforementioned deviations, the overall trends of the simulation and actual sea trial results are highly consistent. Especially in the task completion rate metric, the proposed method still maintains a high level in actual sea trials, indicating that the method possesses good robustness against environmental uncertainties. The deviation analysis shows that the simulation model can effectively predict system performance, providing a reliable basis for optimizing task allocation, path planning, and energy replenishment strategies, and also proving the feasibility and engineering application value of the method in actual maritime dynamic observation missions.

Furthermore, to more intuitively demonstrate the differences between simulation and sea trial data, a line chart can be plotted to simultaneously present the changes in completion rates for 250 experiments or task points. Through local intersections and fluctuations of the lines, the impact of sea state disturbances and task dynamics on system performance is reflected, thereby providing continuity verification and intuitive analysis for the average metrics in the table.

Figure 5 illustrates the comparative line charts between simulation and actual sea trial results for the five core metrics (Task Completion Rate, Total Energy Consumption, Mission Completion Time, Response Time, and Path Redundancy) across 250 experiments. Overall, the performance of the proposed method across these five metrics is superior to the overall trend of the baseline methods, demonstrating the stability and robustness of the system under dynamic tasks and complex sea states.

The task completion rate curves indicate that the proposed method maintains a high level in the vast majority of experiments, averaging approximately 90.85%, and significantly outperforms the baseline methods even under conditions of strong localized maritime disturbances. The total energy consumption and mission completion time curves show that despite the increases in energy and time caused by wind, waves, currents, and obstacle avoidance maneuvers in the actual sea trials, the trends are highly consistent with the simulation, verifying the reliability of the simulation model in predicting system performance.

The response time curves demonstrate that the dynamic replenishment and receding horizon optimization strategies can respond rapidly to task changes, enabling the UAV–USV system to maintain low response latency when task insertions or emergencies occur. The path redundancy curves show that the proposed method effectively reduces redundant trajectories for the UAVs and USVs, enhances path planning efficiency, and exhibits strong adaptability to maritime disturbances in actual sea trials.

In summary, although local fluctuations and intersections caused by environmental disturbances and system uncertainties exist in the line charts, the overall trend is clear: both simulation and actual sea trial results show that the proposed method outperforms the traditional baseline methods across the five core metrics, proving the feasibility and engineering application value of the method in complex maritime dynamic observation missions.

3.5. Energy Replenishment Ablation Study

In order to evaluate the role of the energy replenishment strategy in maritime dynamic observation missions, an ablation experiment was designed to compare the task execution performance of the system under two cases: without replenishment and with replenishment (the proposed method). For simulation experiments, all metrics reported in

Table 5. Comparison of No-Replenishment vs. Energy Replenishment Strategies.

Metric	No Replenishment (Simulation)	No Replenishment (Real-World)	With Replenishment (Simulation)	With Replenishment (Real-World)
Task Completion Rate (%)	78.32	78.15	91.74	91.84
Total Energy (kJ)	1523.71	1558.23	1284.66	1423.51
Completion Time (min)	47.85	49.12	40.28	43.17
UAV Replenishment Times	0	0	1.64	2
Average Path Deviation (m)	18.52	18.88	13.79	13.21

are averaged over multiple independent runs under identical task distributions and sea state conditions, while the real-world results correspond to representative sea trials due to practical constraints. The experiment adopts the same task distribution and sea state conditions while retaining the dynamic and sensor models of the UAVs and USVs to ensure the comparability of the ablation results.

As shown in the table, without replenishment, UAVs frequently returned during task execution, leading to a significant decrease in the task completion rate (78.32% in simulation and 78.15% in sea trials). Both total energy consumption and completion time increased significantly, while path redundancy was also higher, reflecting the low efficiency of system scheduling and path planning under energy-constrained conditions.

In contrast, after enabling the energy replenishment strategy, the task completion rate significantly increased (91.74% in simulation and 91.84% in sea trials), while total energy consumption and completion time were markedly reduced. Path redundancy and the average replenishment frequency remained within a controllable range, indicating that the replenishment strategy can effectively alleviate UAV energy constraints and reduce unnecessary return behaviors, thereby improving overall system task efficiency.

Further analysis of the impact of different replenishment strategies or USV/UAV configurations reveals that increasing the number of USVs or enhancing UAV energy capacity can further improve the task completion rate in high-density task scenarios and reduce the average replenishment frequency. Conversely, when UAV energy is limited and USV replenishment capacity is insufficient, the system is more prone to mid-mission returns, leading to a decrease in the task completion rate, an increase in energy consumption, and limited overall scheduling efficiency.

The actual sea trial data and simulation results are highly consistent in trend, validating the reliability and engineering feasibility of the model. Overall, the energy replenishment strategy is a key factor in ensuring high task efficiency for the USV–UAV collaborative system under long-duration, dynamic tasks, and complex sea states, while providing reliable support for receding horizon task scheduling and path planning.

To more intuitively demonstrate the overall impact of the energy replenishment strategy on system performance, a radar chart was plotted (see Figure 4) to compare the performance of the strategy without replenishment versus the with-replenishment strategy across five core metrics. The five dimensions of the radar chart are Task Completion Rate, Total Energy Consumption, Completion Time, Response Time, and Path Redundancy. All metrics in the chart have been normalized or standardized, allowing metrics with different dimensions to be compared in the same figure, which facilitates the observation of the advantages and disadvantages of each strategy across different performance dimensions.

Figure 6 illustrates the comparative simulation and actual sea trial performance of the strategies without replenishment and with replenishment across five core metrics (Task Completion Rate, Total Energy Consumption, Completion Time, Response Time, and Path Redundancy). Overall, the strategy with replenishment (the proposed method) outperforms the strategy without replenishment across all metrics, validating the critical role of energy replenishment in USV–UAV collaborative missions.

From the dimension of Task Completion Rate, the frequent returns of UAVs during long-duration missions without replenishment led to a task completion rate of only 78.32% in simulation and 78.15% in actual sea trials. Conversely, after enabling the replenishment strategy, the task completion rate significantly increased to 91.74% (simulation) and 91.84% (sea trials), demonstrating that energy replenishment effectively supports the continuous observation capability of UAVs and improves task execution stability.

Regarding Total Energy Consumption and Completion Time, the radar chart shows that both energy consumption and mission completion time for the strategy without replenishment are significantly higher than those for the strategy with replenishment. The system without replenishment incurred increased energy consumption due to multiple returns and redundant flights, with simulation and sea trial data at 1523.71 kJ/1558.23 kJ and 47.85 min/49.12 min, respectively. In contrast, the strategy with replenishment utilized dynamic USV replenishment and receding horizon scheduling, resulting in a significant decrease in energy consumption to 1284.66 kJ (simulation)/1423.51 kJ (sea trials) and a shortened completion time of 40.28 min (simulation)/43.17 min (sea trials).

The Response Time metric also reflects the advantages of the replenishment strategy. Under the condition without replenishment, the average response time of the system to new tasks or dynamic changes was higher (12.34 s in simulation and 12.60 s in sea trials), whereas the strategy with replenishment reduced the response time to 10.21 s (simulation)/10.35 s (sea trials), indicating that the combination of receding horizon optimization and energy replenishment can accelerate the speed of task reallocation and path generation.

The Path Redundancy dimension shows that the strategy without replenishment led to increased redundant trajectories for UAVs and USVs in complex sea states (18.52% in simulation and 18.88% in sea trials), while the strategy with replenishment significantly reduced redundancy through dynamic replenishment and path optimization (13.79% in simulation and 13.21% in sea trials), further enhancing system energy efficiency and trajectory stability.

Overall, the radar chart clearly indicates that the USV–UAV system with the energy replenishment strategy enabled is significantly superior to the strategy without replenishment across all five core metrics. The high consistency between the simulation and sea trial trends validates the effectiveness of the model and its practical engineering feasibility. Particularly in long-duration, dynamic, and complex maritime tasks, the replenishment strategy plays a significant role in ensuring task completion rates, reducing energy consumption, shortening completion time, enhancing response speed, and optimizing path planning, providing reliable support for the collaborative operation of maritime dynamic observation missions.

4. Conclusions

To address the key problems of strong task dynamics, strict energy constraints, and difficult collaborative scheduling in maritime dynamic observation missions under complex sea states, this study proposes a unified optimization framework based on USV–UAV collaborative operation and dynamic energy replenishment. This framework integrates task allocation, joint path planning, and dynamic energy replenishment into an integrated design, enabling the system to achieve efficient and continuous observation operations under complex sea conditions (wind speed 3–6 m/s, current velocity 0.2–0.6 m/s) and dynamic task changes. Through simulation and actual sea trial validation, the proposed method significantly outperforms four baseline methods across five core metrics: task completion rate (91.74% in simulation/90.85% in sea trials), total energy consumption (1284.66 kJ/1298.42 kJ), mission completion time (40.28 min/41.12 min), average response time (10.21 s/10.35 s), and path redundancy (13.79%/14.03%). Specifically, the RHO strategy ensures that the system responds to dynamic tasks 5.1–17.4% faster than baselines, while the energy replenishment strategy increases task completion rate by more than 13.5% compared to the no-replenishment scenario. Particularly in long-duration and highly dynamic task scenarios, the energy replenishment strategy effectively reduces frequent return behaviors of UAVs due to energy limitations (return times reduced by 82.1% in simulation), guaranteeing the continuous observation capability of the system and improving overall task efficiency.

Furthermore, ablation experiments further indicate that the energy replenishment strategy and environmental disturbance compensation module play critical roles in enhancing system performance. After enabling the replenishment strategy, UAVs can dynamically obtain energy support during task execution, avoiding low-battery returns and significantly reducing total energy consumption and path redundancy, while shortening mission completion time and response time. This demonstrates that in USV–UAV collaborative systems, the deep coupling of energy replenishment, RHO-based task scheduling, and environmental disturbance compensation is of great significance for the execution of complex dynamic tasks. Despite the good performance of the proposed method in multi-scenario experiments, several future research directions are worth exploring. First, the current framework assumes that environmental perception and communication conditions are relatively stable; future work could introduce uncertain or intermittent communication constraints to enhance system robustness under complex and severe sea states. Second, the energy replenishment method primarily relies on dynamic USV replenishment; future research could explore new replenishment strategies such as UAV-to-UAV energy transfer, solar-assisted UAVs, or hybrid energy UAVs to further enhance autonomy. Third, this study mainly focuses on small-scale UAV–USV systems; future research could be directed toward large-scale multi-UAV and multi-USV systems, investigating distributed collaborative scheduling and control algorithms to handle a wider range of maritime monitoring tasks. Finally, learning-based sea state prediction and task demand prediction models can be integrated to achieve forward-looking optimization planning for the system, further improving task efficiency and the level of system intelligence.

In summary, the UAV–USV collaborative operation and energy replenishment framework proposed in this paper has not only validated its effectiveness in simulations and sea trials but also provided a feasible solution for long-duration dynamic maritime observation missions. This study establishes a methodological foundation for future autonomous, long-endurance, and high-efficiency maritime observation systems and provides a valuable theoretical basis and practical reference for the application of USV–UAV collaborative systems in scenarios such as maritime monitoring, environmental protection, and disaster emergency response.