Dynamic UAV Task Allocation and Path Planning with Energy Management Using Adaptive PSO in Rolling Horizon Framework

Abstract

Unmanned aerial vehicles (UAVs) are increasingly deployed in dynamic environments for applications such as surveillance, delivery, and data collection, where efficient task allocation and path planning are critical to minimizing mission completion time while managing limited energy resources. This paper proposes a novel approach that integrates energy management into a rolling horizon framework for dynamic UAV task allocation and path planning. We introduce an enhanced Particle Swarm Optimization (PSO) algorithm, incorporating adaptive perturbation strategies and a local search mechanism based on simulated annealing, to optimize UAV task assignments and routes. The rolling horizon framework enables the system to adapt to evolving task demands over time. Energy consumption is explicitly modeled, accounting for flight, computation, and recharging at designated stations, ensuring practical applicability. Extensive simulations demonstrate that the proposed method reduces the mission makespan significantly compared to conventional static planning approaches, while effectively balancing energy usage and recharging requirements. These results highlight the potential of our approach for real-world UAV operations in dynamic settings.

1. Introduction

Unmanned aerial vehicles (UAVs) have transitioned from research prototypes to versatile platforms in civilian and industrial applications. Beyond traditional surveillance, environmental monitoring, and disaster response, UAVs enable precision agriculture, infrastructure inspection, and public-safety operations. Emerging roles include serving as airborne wireless base stations, delivering medical supplies, facilitating last-mile logistics, and generating real-time three-dimensional maps. Due to their agility, low operational cost, and ability to operate in GPS-denied or hazardous environments, UAVs show transformative potential [1,2]. Their ability to operate autonomously in complex environments makes them ideal for tasks that require rapid deployment and adaptability. However, the efficient coordination of multiple UAVs to accomplish a set of tasks remains a significant challenge, particularly in dynamic settings where task demands evolve over time [3].

Task allocation and path planning are critical components in multi-UAV systems. Task allocation involves assigning specific tasks to individual UAVs, while path planning determines the optimal routes for UAVs to execute these tasks. Traditional approaches often treat these as static problems, assuming that all tasks and environmental conditions are known in advance [4]. However, in real-world applications, such as search and rescue or dynamic surveillance, tasks may appear or change unpredictably, necessitating a more flexible and adaptive planning framework [5].

Energy management further complicates UAV mission planning. UAVs have limited battery capacity, and energy consumption must be carefully managed to avoid mission failures due to depleted batteries. This requires not only efficient path planning but also strategic decisions about when and where to recharge, especially in missions spanning large areas or extended durations [5]. Existing methods often overlook the interplay between task allocation, path planning, and energy constraints, leading to suboptimal performance in dynamic environments [6].

To address these challenges, this paper introduces a novel approach that integrates dynamic task allocation, path planning, and energy management within a rolling horizon framework. The rolling horizon paradigm allows the system to adapt to changing task demands by replanning at regular intervals, incorporating new information as it becomes available [6]. This is particularly advantageous in scenarios where tasks are revealed incrementally or where the environment is subject to change.

At the core of our approach is an enhanced Particle Swarm Optimization (PSO) algorithm, tailored to handle the complexities of UAV coordination. PSO is a population-based metaheuristic known for its efficiency in solving large-scale optimization problems [7]. However, standard PSO may struggle with the dynamic nature of UAV missions and the need for rapid adaptation. To overcome this, we incorporate adaptive perturbation strategies and a local search mechanism based on simulated annealing. These enhancements enable the algorithm to escape local optima and explore the solution space more effectively, leading to better-quality solutions in fewer iterations [8,9]. The contributions of this paper are threefold:

• We propose a rolling horizon framework for dynamic UAV task allocation and path planning, allowing the system to adapt to evolving task demands and environmental conditions.
• We develop an improved PSO algorithm with adaptive perturbation and simulated annealing-based local search, specifically designed to handle the multi-objective nature of the problem, including energy constraints.
• We present a comprehensive energy management model that accounts for flight, computation, and recharging activities, ensuring that UAVs can complete their missions without energy depletion.

Simulation results demonstrate that our method significantly reduces the mission makespan compared to traditional static planning approaches while effectively managing energy consumption and recharging needs. These findings underscore the potential of our approach for real-world UAV applications in dynamic environments.

The remainder of this paper is organized as follows: Section 2 reviews related work on UAV task allocation, path planning, and energy management. Section 3 formally defines the problem. Section 4 details the proposed methodology, including the rolling horizon framework and the enhanced PSO algorithm. Section 5 presents the experimental setup and results, followed by a discussion. Finally, Section 6 concludes the paper and outlines future research directions.

2. Literature Review

The coordination of unmanned aerial vehicles (UAVs) for task allocation and path planning has garnered significant attention due to its critical role in autonomous systems. Early studies predominantly focused on static environments, where tasks and environmental conditions are fully known in advance. For instance, ref. [4] introduced a stochastic vehicle routing model with fixed task locations and deterministic travel times, foundational for UAV routing problems. Similarly, ref. [1] explored near-optimal coverage trajectories for UAVs over irregular fields, emphasizing static path optimization. Ref. [10] provided a comprehensive survey of coverage path planning techniques, applicable to static UAV missions, while ref. [11] extended this work with advancements in robotic path planning, including UAV contexts. These static approaches, though influential, fail to address real-world scenarios where tasks and conditions change unpredictably.

To overcome these limitations, research has shifted toward dynamic task allocation and path planning. Ref. [3] investigated cooperative decision making for multi-UAV systems, proposing heuristic methods for dynamic task assignments. Ref. [12] developed decentralized cooperation strategies for UAVs in exploration tasks, focusing on real-time adaptability. Ref. [13] addressed dynamic task allocation in uncertain environments, introducing adaptive algorithms. Ref. [14] tackled cooperative task allocation under communication constraints, ensuring coordination with limited connectivity. Ref. [15] proposed a decentralized algorithm for dynamic task allocation in UAV swarms, integrating real-time communication. The need for continuous adaptation has popularized rolling horizon planning. Ref. [6] applied this approach to dynamic pickup-and-delivery problems, demonstrating its effectiveness in responding to new tasks. For UAVs, ref. [16] combined rolling horizon planning with reinforcement learning for adaptive mission management, though energy constraints were underexplored. Ref. [17] proposed a multi-objective genetic algorithm for dynamic UAV task allocation, yet it lacked full integration of energy and path planning. Ref. [18] derived the downlink coverage as a function of the UAV’s altitude and antenna gain, then applied circle packing theory to design an efficient deployment strategy that maximizes coverage while preventing overlap among UAV coverage areas.

Energy management is critical in UAV mission planning due to limited battery capacities. Ref. [5] analyzed energy consumption in UAV wireless communications, proposing energy-efficient trajectories for single-UAV scenarios. Ref. [19] modeled energy use in drone delivery systems, considering payload and distance. Ref. [20] optimized energy-aware trajectories, accounting for flight dynamics. Ref. [21] introduced energy-efficient path planning with adaptive speed control. Ref. [22] developed cooperative energy-aware coverage planning for UAVs. In multi-UAV contexts, ref. [23] used a genetic algorithm to optimize routes and charging schedules, though it assumed static tasks. Ref. [24] proposed a multi-objective framework balancing energy and mission time, but it overlooked dynamic task arrivals. Ref. [25] proposed to use NSGAII for simultaneously balancing the simultaneous pickup and delivery of medical supplies. Ref. [26] presented a mixed-integer linear programming model along with a heuristic algorithm to optimize the movement and recharging of UAVs deployed as flying base stations in 5G networks. Ref. [27] developed a mixed-integer linear programming model to plan UAV operations—including flight paths, energy management, and task execution—for detecting illegally parked electric scooters in urban areas.

Optimization techniques underpin solutions to these challenges. Particle Swarm Optimization (PSO), introduced by [7], is widely used for its efficiency in large-scale problems. Ref. [28] analyzed PSO’s stability and convergence, enhancing parameter tuning. Ref. [8] improved PSO with a comprehensive learning strategy for multimodal optimization. Ref. [29] proposed a hierarchical PSO with time-varying coefficients for better exploration. Ref. [9] developed an adaptive PSO for dynamic environments. Recent works like [30] combined PSO with simulated annealing for UAV path planning, improving solution quality, while [31] introduced a multi-swarm PSO for scalable task allocation. Other metaheuristics include Differential Evolution (DE) by [32] for trajectory optimization, Artificial Bee Colony (ABC) by [33] for task allocation, Ant Colony Optimization (ACO) by [34] for dynamic path planning, and Genetic Algorithms (GA) by [35] for real-time task allocation.

Additional challenges like communication constraints and collision avoidance are also significant. Ref. [36] studied task allocation under communication limits, while ref. [37] proposed decentralized methods for communication-delayed UAVs. Ref. [38] developed collision avoidance algorithms, and Ref. [39] applied reinforcement learning for real-time avoidance. Real-time data processing, vital for dynamic planning, was addressed by [40,41], focusing on efficient algorithms and edge computing.

Despite these advances, critical gaps remain. Few studies integrate task allocation, path planning, and energy management holistically in dynamic settings [17,42]. Rolling horizon applications with energy constraints are limited [16]. PSO methods often lack adaptive perturbation and local search for multi-objective dynamic problems [30,31]. Many assume idealized conditions like instantaneous recharging [24], impractical in reality. This paper addresses these gaps with a unified framework integrating dynamic task allocation, path planning, and energy management, using an enhanced PSO with adaptive perturbation and simulated annealing within a rolling horizon structure, ensuring adaptability and energy efficiency. Furthermore, although machine learning methods can model the environment in a data-driven manner and have attracted attention from some scholars, they heavily rely on task-specific data and exhibit limited generalization capability, making performance tuning across different settings challenging. Moreover, these algorithms require extensive training data and complex environment setups, resulting in high training and deployment costs.

3. Problem Formulation

In this section, we formally define the dynamic task allocation and path planning problem for multiple unmanned aerial vehicles (UAVs) with energy management considerations. The objective is to minimize the mission makespan while ensuring that all tasks are completed and that UAV energy constraints are satisfied in an environment where new tasks emerge over time.

3.1. System Model

Consider a set of $N_U$ UAVs, denoted by $\mathcal{U}=\{U_1,U_2,\dots ,U_{N_U}\}$, operating in a two-dimensional Euclidean space. These UAVs are deployed to service a dynamically evolving set of tasks over a planning horizon divided into H discrete stages, indexed by $h\in \{1,2,\dots ,H\}$. At each stage h, the set of tasks is represented by ${\mathcal{D}}_h=\{D_1,D_2,\dots ,D_{N_{D_h}}\}$, where $N_{D_h}$ denotes the number of tasks available at stage h. Each task $D_j\in {\mathcal{D}}_h$ is located at coordinates $(x_j,y_j)$ and has an associated workload $L_j^h$, which quantifies the amount of service required.

Additionally, there are $N_S$ stationary charging stations, denoted by $\mathcal{S}=\{S_1,S_2,\dots ,S_{N_S}\}$, located at fixed positions $(x_{S_k},y_{S_k})$ for $k=1,2,\dots ,N_S$. Each charging station has a charging rate $r_{\mathrm{charge}}$ and a capacity limit $C_{max}$, which restricts the number of UAVs that can charge simultaneously. UAVs are initially stationed at designated charging stations and must return to a station for recharging when their energy levels are insufficient to continue their tasks.

The distance between any two points $p_m=(x_m,y_m)$ and $p_n=(x_n,y_n)$ (where $p_m,p_n$ may represent tasks or stations) is given by the Euclidean distance:

$$d_{m,n}=\sqrt{{(x_m-x_n)}^2+{(y_m-y_n)}^2}.$$

(1)

3.2. UAV Characteristics

Each UAV $U_i\in \mathcal{U}$ is characterized by the following parameters:

• A constant flight velocity v, which determines the time required to travel between points.
• A maximum energy capacity $E_{max}$, with energy consumption rates $P_{\mathrm{fly}}$ during flight and $P_{\mathrm{comp}}$ during task processing.
• A service rate $S_{\mathrm{rate}}$, which defines the speed at which the UAV processes the workload of a task.

The flight time between two points $p_m$ and $p_n$ is given by

$$t_{m,n}={\displaystyle \frac{d_{m,n}}{v}},$$

(2)

and the corresponding energy consumption during flight is

$$e_{m,n}=P_{\mathrm{fly}}·t_{m,n}.$$

(3)

When processing a workload $L_j^h$ at task $D_j$, the energy consumed by UAV $U_i$ is

$$e_{j,\mathrm{proc}}=P_{\mathrm{comp}}·\left({\displaystyle \frac{L_j^h}{S_{\mathrm{rate}}}}\right).$$

(4)

Note that in this study, the UAV flight speed is modeled as constant. This assumption is justified on two grounds: first, with appropriate training, operators can maintain a stable cruise velocity during typical flight operations; second, it substantially reduces the complexity of the underlying model, thereby enhancing the tractability of the rolling-horizon optimization framework.

3.3. Objective

According to the system model and UAVs’ characteristics, this paper formulates the optimization objective as follows. The primary objective is to minimize the mission makespan, defined as the maximum completion time across all UAVs at each stage h. The completion time $T_i^h$ for UAV $U_i$ is the total time spent traveling and processing tasks along its route $R_i^h$. Thus, the makespan at stage h is

$$T_{max}^h=\underset{U_i\in \mathcal{U}}{max}{T}_i^h,$$

(5)

where $T_i^h$ is the total time UAV i spends traveling and processing tasks in stage h.

To ensure energy efficiency, we also consider the total energy consumption as a secondary objective. The energy consumed by UAV $U_i$ during stage h is

$$E_i^h=\sum _{(p_m,p_n)\in R_i^h}{e}_{m,n}+\sum _{D_j\in R_i^h}{e}_{j,\mathrm{proc}}.$$

(6)

The combined objective function at each stage h is formulated as

$$J^h=T_{max}^h+\alpha \sum _{i=1}^{N_U}{E}_i^h,$$

(7)

where $\alpha >0$ is a weighting coefficient that balances the trade-off between makespan and energy consumption.

3.4. Decision Variables

At each stage h, the following decision variables are determined:

• Task allocation: A matrix $W^h\in {\mathbb{R}}^{N_U\times N_{D_h}}$, where $W_{i,j}^h$ represents the portion of the workload $L_j^h$ assigned to UAV $U_i$ for task $D_j$ at stage h; $N_U$ is the number of the UAVs. The allocation must satisfy the following:

  $$\sum _{i=1}^{N_U}{W}_{i,j}^h=L_j^h,\forall D_j\in {\mathcal{D}}_h,$$

  (8)

  with $W_{i,j}^h\ge 0$ for all $i,j$.
• Path planning: A set of routes ${\mathcal{R}}^h=\{R_1^h,R_2^h,\dots ,R_{N_U}^h\}$, where $R_i^h$ is an ordered sequence of nodes (tasks and stations) visited by UAV $U_i$ during stage h. Each route $R_i^h$ starts at a station $S_{{\mathrm{start}}_i}\in \mathcal{S}$ and may include intermediate visits to charging stations for recharging.

3.5. Constraints

The solution must adhere to the following constraints at each stage h:

• Task completion: The entire workload of each task must be allocated to the UAVs:

  $$\sum _{i=1}^{N_U}{W}_{i,j}^h=L_j^h,\forall D_j\in {\mathcal{D}}_h.$$

  (9)
• Energy limit: The cumulative energy consumption of UAV $U_i$ along its route $R_i^h$ must not exceed its maximum energy capacity $E_{max}$, unless the UAV recharges at a station. If recharging is required, the UAV must visit the nearest available station $S_k$ when its energy level drops below a predefined threshold. Upon recharging, the energy is restored to $E_{max}$ in a time period of ${\displaystyle \frac{E_{max}-E_{\mathrm{current}}}{r_{\mathrm{charge}}}}$, where $E_{\mathrm{current}}$ is the remaining energy before recharging. Here, $E_{\mathrm{current}}$ is the remaining battery level of the UAV immediately before recharging.
• Station capacity: The number of UAVs simultaneously charging at any station $S_k$ must not exceed its capacity $C_{max}$.
• Dynamic task updates: Between stages, new tasks may be introduced (up to a maximum of $N_{D_{max}}$ tasks), or the workloads of existing tasks may increase by a rate $\delta$, reflecting the dynamic nature of the environment. Here, $\delta$ is the maximum increment in the workload for existing tasks between stages, while $N_{D_{max}}$ is the maximum allowable number of tasks in the system.

In summary, with the predefined objective function (7), the decision variables, and the constraints, given the sets $\mathcal{U}$ and $\mathcal{S}$, and the dynamically evolving set ${\mathcal{D}}_h$ at each stage h, the problem is to determine the task allocation $W^h$ and the routes ${\mathcal{R}}^h$ that minimize the objective function $J^h$ at each stage, subject to the constraints outlined above. The dynamic arrival of new tasks and the evolving workloads necessitate a replanning strategy, motivating the use of a rolling horizon framework integrated with an adaptive optimization algorithm to ensure timely and efficient mission execution.

4. Methodology of APSO-LS

This section presents the proposed methodology for dynamic UAV task allocation and path planning with energy management. The approach integrates a rolling horizon framework with an Adaptive Perturbation Particle Swarm Optimization algorithm with Local Search (APSO-LS). The rolling horizon framework enables the system to adapt to dynamically evolving task demands, while the APSO-LS algorithm efficiently optimizes task allocation and path planning at each stage, considering both mission makespan and energy consumption.

4.1. Overview of the Proposed Approach

The proposed methodology addresses the dynamic nature of the problem by dividing the planning horizon into discrete stages. At each stage h, the current set of tasks is optimized using the APSO-LS algorithm, which determines the optimal task allocation and routes for the UAVs. As new tasks emerge or existing task workloads change, the system replans at the subsequent stage, incorporating the updated information. This rolling horizon approach ensures that the UAVs can adapt to changes in real time while maintaining efficient operation.

The APSO-LS algorithm is specifically designed to handle the complexities of the problem, including the need for rapid adaptation and the integration of energy constraints. It combines the global search capabilities of PSO with adaptive perturbation strategies to maintain diversity and a simulated annealing-based local search to refine solutions and escape local optima.

4.2. Rolling Horizon Framework

The rolling horizon framework divides the mission into H stages, each corresponding to a specific time interval. At the beginning of each stage h, the system observes the current set of tasks ${\mathcal{D}}_h$, their workloads $L_j^h$, and the positions and energy levels of the UAVs. The APSO-LS algorithm is then employed to solve the optimization problem for stage h, determining the task allocation $W^h$ and routes ${\mathcal{R}}^h$ that minimize the objective function $J^h$.

Between stages, new tasks may be added to the system (up to a maximum of $N_{D_{max}}$ tasks), or the workloads of existing tasks may increase by a predefined rate $\delta$. This dynamic update is incorporated into the next stage’s optimization, ensuring that the UAVs continuously adapt to the evolving environment.

The key advantage of the rolling horizon framework is its ability to handle uncertainty and dynamism by replanning at regular intervals, thus avoiding the computational intractability of solving the entire dynamic problem at once.

4.3. Adaptive Perturbation PSO with Local Search (APSO-LS)

To solve the optimization problem at each stage, we propose the APSO-LS algorithm, which enhances the standard PSO with adaptive perturbation and local search mechanisms. In this algorithm, each particle in the APSO-LS algorithm represents a candidate solution, consisting of the following:

• Task allocation: A matrix $W\in {\mathbb{R}}^{N_U\times N_{D_h}}$, where $W_{i,j}$ denotes the workload assigned to UAV $U_i$ for task $D_j$.
• Routes: A set of routes $\mathcal{R}=\{R_1,R_2,\dots ,R_{N_U}\}$, where each $R_i$ is an ordered sequence of tasks and charging stations visited by UAV $U_i$.

The particle’s position is encoded as a vector that combines the flattened task allocation matrix and the route sequences for all UAVs. The population of PSO is initialized using a heuristic approach to ensure feasibility and diversity according to the following rules.

• Task allocation: Workloads are initially assigned to UAVs based on their proximity to tasks, ensuring that each task’s workload is fully allocated.
• Routes: Initial routes are constructed by assigning tasks to UAVs in a greedy manner, considering energy constraints and the need for recharging.

This heuristic initialization provides a good starting point for the optimization process, reducing the number of iterations required for convergence.

In APSO-LS, we introduce an adaptive perturbation strategy to dynamically adjust the exploration–exploitation trade-off. The perturbation rate $\rho$ is adjusted based on the improvement in the global best solution. If the global best has not improved for a certain number of iterations, $\rho$ is increased to encourage exploration. Conversely, if improvements are frequent, $\rho$ is decreased to focus on exploitation. The velocity update equation incorporates the perturbation rate given in (10):

$$v_{k+1}=w{v}_k+c_1{r}_1(p_{\mathrm{best}}-x_k)+c_2{r}_2(g_{\mathrm{best}}-x_k)+\rho ·\xi ,$$

(10)

where w is the inertia weight, $c_1$ and $c_2$ are cognitive and social coefficients, $r_1$ and $r_2$ are random numbers, $p_{\mathrm{best}}$ is the personal best position, $g_{\mathrm{best}}$ is the global best position, and $\xi$ is a random perturbation vector. The corresponding position update mechanism is provided in (11):

$$x_{k+1}=x_k+v_{k+1}.$$

(11)

To further refine the solutions and escape local optima, a simulated annealing (SA)-based local search is applied to the best particle in each iteration.

• Neighborhood search: Small perturbations are applied to the task allocation and route sequences to generate neighboring solutions.
• Acceptance criterion: A neighboring solution is accepted if it improves the objective function, with a probability $exp(-\Delta J/T)$, where $\Delta J$ is the change in the objective function and T is the current temperature.
• Cooling schedule: The temperature T is gradually decreased according to a cooling rate $\alpha$, allowing the algorithm to converge to a high-quality solution.

This local search mechanism enhances the exploitation capability of the algorithm, ensuring that the final solution is both optimal and feasible. In addition, energy management is a critical component of the proposed methodology. During the evaluation of each particle, the energy consumption of each UAV is tracked along its route:

• Energy check: Before visiting each task, the UAV’s current energy level is checked. If the energy is insufficient to reach the task and return to the nearest station, the UAV is routed to the nearest available charging station.
• Charging time: The time spent charging is calculated based on the required energy to reach $E_{max}$, using the station’s charging rate $r_{\mathrm{charge}}$.
• Station capacity: The algorithm ensures that the number of UAVs charging at any station does not exceed $C_{max}$ by scheduling charging slots accordingly.

This logic ensures that UAVs can complete their assigned tasks without energy depletion, while also respecting the capacity constraints of the charging stations. The fitness of each particle is evaluated using the objective function $J^h$, which combines the makespan $T_{max}^h$ and the total energy consumption ${\sum }_{i=1}^{N_U}{E}_i^h$, as defined in Section 3. Additionally, penalties are imposed for any constraint violations, such as incomplete task allocation or energy depletion. The pseudo-code of the APSO-LS algorithm proceeds according to Algorithm 1.

The integration of the rolling horizon framework with the APSO-LS algorithm provides a robust solution to the dynamic UAV task allocation and path planning problem, balancing efficiency, adaptability, and energy management.

Algorithm 1 APSO-LS Algorithm

1: Input: problemData 2: Initialize population of particles (route + workload encoding) 3: Initialize velocities, perturbation rate $\rho$, temperature T 4: Evaluate fitness of each particle using $J^h$ 5: Set personal best $p_{\mathrm{best}}$ and global best $g_{\mathrm{best}}$ 6: while stopping criterion not met do 7:    for each particle p do 8:      Update velocity using (10) 9:      Update position using (11) 10:      Decode solutions into routes and allocations 11:      Repair infeasible routes (energy and station capacity constraints) 12:      Evaluate fitness using $J^h$ 13:      if fitness improves then 14:         Update $p_{\mathrm{best}}$ 15:         Decrease $\rho$ 16:      end if 17:    end for 18:    Update $g_{\mathrm{best}}$ if a better solution is found 19:    Apply simulated annealing local search to $g_{\mathrm{best}}$: 20:       Generate neighbor by 2-opt swap + workload adjustment 21:       Accept if $\Delta J<0$ or $exp(-\Delta J/T)>rand$ 22:       $T\leftarrow \alpha T$ 23:    Adjust perturbation rate $\rho$ if no improvement for 5 iterations 24: end while 25: return $g_{\mathrm{best}}$

5. Experimental Results and Discussions

This section presents the experimental results of the proposed methodology for dynamic UAV task allocation, path planning, and energy management, utilizing the Adaptive Perturbation PSO with Local Search (APSO-LS) algorithm within a rolling horizon framework. The simulations, conducted using the provided MATLAB 2024a implementation, evaluate the algorithm’s performance across multiple stages with dynamically evolving task demands. We analyze the convergence behavior, solution quality, and practical implications based on the generated figures, focusing on makespan minimization and energy efficiency.

5.1. Experimental Setup

The experiments simulate a scenario with $N_U=3$ UAVs, $N_S=3$ charging stations, and an initial set of $N_{D_{\mathrm{initial}}}=5$ demand points, with a maximum of $N_{D_{max}}=7$ demands over a planning horizon of $H=3$ stages. The UAV parameters include a maximum energy capacity $E_{max}=100$, flight velocity $v=10$, flight power consumption $P_{\mathrm{fly}}=1$, computation power consumption $P_{\mathrm{comp}}=2$, and service rate $S_{\mathrm{rate}}=1$. Charging stations have a charging rate $r_{\mathrm{charge}}=5$ and capacity limit $C_{max}=2$. Demand workloads are randomly initialized between 5 and 15, with new demands added or workloads increased by up to 3 units per stage, as implemented in the “runOnce” function.

The APSO-LS algorithm is configured with $N_{\mathrm{particles}}=20$ particles and a maximum of $N_{\mathrm{iterations}}=50$ iterations per stage, using an initial perturbation rate $\rho =0.3$, inertia weight $w=0.7$, cognitive coefficient $c_1=1.5$, and social coefficient $c_2=1.5$. The objective function balances makespan and energy consumption with a weighting factor $\alpha =0.1$, as defined in (7). In this study, simulation experiments are independently conducted three times to obtain relatively reliable results.

5.2. Results

5.2.1. Convergence Analysis

Figure 1, Figure 2 and Figure 3 (corresponding to the three independent runs, as shown in the convergence curve subfigures on the left) illustrate the evolution of the optimal objective values over 50 iterations for each stage. Several observations can be made.

• Rapid Decline in the Initial Phase

There is a rapid decline in the initial phase followed by stabilization. In most stages, the objective values decrease rapidly within the first 10–20 iterations, indicating that the algorithm can quickly identify relatively good feasible solutions in its early phase. Thereafter, the curves gradually level off, suggesting that the combined effects of global and local search facilitate overall population convergence.

• Variations Among Different Runs

Run 1: In stage 1, the initial value is approximately 25, eventually converging to 16.08; in stage 2, the value decreases from about 30 to 27.57; in stage 3, it declines from around 40 to 21.55.

Run 2: In stage 1, the value drops from approximately 21 to 12.28, indicating a more effective utilization of the initial population and search direction in this run; in stage 2 and stage 3, the values converge to 21.03 and 26.62, respectively.

Run 3: In stage 1, the initial value is higher (around 37), eventually converging to 26.41; stage 2 converges to 26.05; while in stage 3, the initial value is notably high (exceeding 50), ultimately converging to 45.75.

These observations reveal that, under different random initialization and task environments, the convergence curves display certain fluctuations across stages, yet a clear reduction in objective values is achieved overall.

• Overall Statistics

Considering the final optimal values in stage 3 from the three runs (21.55, 26.62, and 45.75), the mean is 31.30 with a standard deviation of 12.77. This suggests that for stages with a larger scale or higher complexity, the algorithm may experience considerable fluctuations due to randomness in initialization and environmental factors. Nevertheless, on average, the algorithm demonstrates robust adaptability to dynamic environments.

5.2.2. UAV Routes and Allocation Visualization

Corresponding to the convergence curves, the right-hand side subfigures of Figure 1, Figure 2 and Figure 3 depict the UAV trajectories and task allocations for each stage in each run (with different colored lines representing distinct UAVs). The following observations can be made from these path visualizations.

• Division of Labor and Path Coverage

In stage 1, there are only five initial task points. The three UAVs are assigned tasks based on their respective distances to the task points and remaining energy levels, resulting in relatively simple paths.

In stages 2 and 3, as the number of task points or workload increases, the paths become more complex. Occasional crossings or sequential visits to charging stations among UAVs occur to satisfy energy constraints.

The stage 1 paths in run 2 are the shortest (with a final makespan of only 12.28), indicating that the algorithm in this run achieved a more efficient task division and route design at the initial stage, thereby enabling the UAVs to complete all requirements with minimal flight and waiting times.

• Charging Station Visits and Energy Management

Some of the UAVs are observed to incorporate visits to charging stations prior to heading toward or executing new tasks. Since the algorithm’s objective function integrates both energy consumption and completion time, mid-flight charging is performed only when necessary—either when endurance is insufficient or when it benefits the overall makespan.

When tasks are more scattered or the workload is heavier (for example, stage 3 in run 3), UAVs may frequently shuttle between task points and charging stations, resulting in a relatively higher final makespan (45.75). This outcome reflects the adaptability of the rolling horizon strategy in complex environments, while also highlighting the influence of environmental or initialization challenges on the results.

5.2.3. Comparison with Standard PSO Algorithm

To better demonstrate the superiority of the proposed algorithm, we present the results obtained using the basic Particle Swarm Optimization (PSO) algorithm. The results of the standard PSO are shown in Figure 4, Figure 5 and Figure 6.

Compared to the results obtained with the standard PSO, it can be observed that the APSO-LS algorithm exhibits superior adaptability and efficiency. The average makespan of APSO-LS and the standard PSO are 31.30 and 39.6757, respectively. This indicates that the standard PSO struggles to handle dynamic demands, leading to higher makespans. The standard PSO may face difficulties with local optima and dynamic updates, whereas APSO-LS’s adaptive perturbation and local search overcome these limitations. The stable convergence and feasible routes further validate these advantages.

Furthermore, our measurements indicate that the average execution time per run is approximately 0.6192 s, which, when compared to the 0.5871 s recorded for the standard PSO, does not represent a significant reduction in runtime.

5.2.4. Discussions

From the above results and analysis, the following findings can be drawn.

Convergence behavior: The convergence curve drops rapidly in the early iterations, indicating a strong global search capability of the particle swarm. This is attributed to the global search ability of the PSO algorithm combined with the local search operator designed in this study. In the middle and later stages, the curve flattens while still achieving improved solutions, reflecting the effectiveness of the adaptive perturbation strategy. This strategy helps the algorithm to escape local optima and continuously refine solutions without introducing excessive disturbance that could harm convergence.

Adaptability to dynamic task updates: Since task numbers and loads are updated at each stage, static planning would struggle to accommodate sudden or incremental demands. By reapplying PSO optimization at each stage, the algorithm can dynamically adjust path planning and task assignments based on new task requirements or UAV energy states, reducing ineffective scheduling.

Energy-aware scheduling: By incorporating energy consumption weights in the objective function and inserting necessary charging operations when detecting low UAV energy levels, the algorithm minimizes the impact of charging delays and excessive flight distances on the makespan while ensuring task completion. In multiple experiments, UAVs successfully returned to charging stations for replenishment before energy depletion.

Robustness of the algorithm: Although there is significant variation in stage 3 across three independent runs (21.55 vs. 45.75), the overall results consistently converge to feasible solutions within a limited number of iterations. The algorithm demonstrates good scheduling efficiency at an average makespan of 31.30. Given the high-dimensional, strongly nonlinear, and stochastic nature of UAV scheduling problems, these results validate the algorithm’s robustness in general cases.

Trade-off between makespan and energy consumption: In this study, makespan and energy consumption are merged into a single objective function, with a weighting coefficient $\alpha$ to balance the trade-off. If a particular application prioritizes endurance and energy efficiency, a larger $\alpha$ can be used; conversely, if minimizing completion time is critical, reducing $\alpha$ will emphasize time-based objectives.

Impact of random initialization and dynamic configurations: The results from three independent runs suggest that random initialization and varying dynamic task configurations significantly influence the final outcome. To mitigate this dependency, parallelized or multi-population strategies could be introduced. Additionally, reinforcement learning or other adaptive methods could be incorporated to quickly determine superior initial solutions at each stage, further improving convergence speed and solution quality.

In summary, the results from three independent runs fully demonstrate the effectiveness and robustness of the improved PSO (APSO-LS) when applied to multi-UAV dynamic scheduling within a rolling time-domain framework. Whether observed from the rapid decline and stable convergence of the convergence curve or from the UAVs’ flexible access to task points and charging stations in the visualized paths, the algorithm exhibits a comprehensive advantage in balancing task completion time and energy consumption. Although randomness and dynamic changes introduce some fluctuations, the overall performance still showcases excellent scalability and adaptability. This lays a solid foundation for future applications in larger-scale, multi-task UAV scenarios.

6. Conclusions and Future Work

This paper introduced a novel methodology for dynamic UAV task allocation, path planning, and energy management, using the Adaptive Perturbation PSO with Local Search (APSO-LS) algorithm within a rolling horizon framework. The experimental results demonstrate that the approach effectively minimizes makespan and manages energy in dynamic environments. The rolling horizon framework ensures adaptability, and the weighted objective function balances makespan and energy. Key contributions include a unified dynamic framework, enhanced PSO with local search, and validated energy-aware planning for real-world UAV applications.

Nevertheless, we recognize that the current formulation remains an idealized abstraction and must be refined before field deployment. First, although we assume a constant cruise speed for tractability, real-world UAVs encounter wind gusts, payload shifts, and aerodynamic drag that cause speed fluctuations. Future work will therefore develop a closed-loop flight control module—leveraging model predictive control (MPC) and disturbance observers—to actively compensate for external disturbances and enforce near-constant airspeed while minimizing additional energy consumption. Second, to scale APSO-LS to larger fleets and more complex environments, we will implement a parallelized architecture using GPU-accelerated particle evaluations and asynchronous global-best updates. This will enable real-time replanning for dozens of UAVs across hundreds of tasks. Third, our energy model assumes homogeneous UAVs and fixed power rates. We plan to extend it to heterogeneous platforms by integrating manufacturer flight logs to derive phase-dependent power profiles and battery degradation curves.