A Review of Collaborative Trajectory Planning for Multiple Unmanned Aerial Vehicles

Abstract

In recent years, the collaborative operation of multiple unmanned aerial vehicles (UAVs) has been an important advancement in drone technology. The research on multi-UAV collaborative flight path planning has garnered widespread attention in the drone field, demonstrating unique advantages in complex task execution, large-scale monitoring, and disaster response. As one of the core technologies of multi-UAV collaborative operations, the research and technological progress in trajectory planning algorithms directly impact the efficiency and safety of UAV collaborative operations. This paper first reviews the application and research progress of path-planning algorithms based on centralized and distributed control, as well as heuristic algorithms in multi-UAV collaborative trajectory planning. It then summarizes the main technical challenges in multi-UAV path planning and proposes countermeasures for multi-UAV collaborative planning in government, business, and academia. Finally, it looks to future research directions, providing ideas for subsequent studies in multi-UAV collaborative trajectory planning technology.

1. Introduction

In the field of multi-unmanned aerial vehicle (UAV) collaborative trajectory planning, important technological challenges include effective communication between UAVs, intelligent path planning, autonomous obstacle avoidance, real-time data processing, and energy management. The development of these technologies allows UAVs to collaborate efficiently in complex environments while ensuring the safety and accuracy of mission execution. For example, intelligent path planning can help UAVs avoid obstacles and replan routes as needed to adapt to environmental changes. Real-time data processing capabilities ensure that UAVs can quickly respond to external information and make appropriate adjustments.

A significant advantage of multi-UAV collaborative operations is their efficiency in executing large-scale and complex tasks. For instance, in extensive agricultural monitoring or disaster response scenarios, multiple UAVs can quickly cover large areas, collect crucial data, and operate more efficiently than single UAVs. Moreover, in military reconnaissance and surveillance tasks, the collaboration of multiple UAVs can provide more comprehensive and continuous monitoring, enhancing the effectiveness of the mission.

With technological advancements, future research in multi-UAV collaborative trajectory planning will focus more on intelligence and autonomy. Utilizing artificial intelligence and machine learning, UAVs will be able to better understand their environment and make more complex decisions. At the same time, Researchers are also exploring more efficient methods of energy use and advanced communication technologies to support long-duration and wide-range task execution.

The core of multi-UAV collaborative trajectory planning lies in efficiently allocating and planning the flight paths of each UAV while avoiding interference and collisions to ensure successful mission completion. This process involves various considerations, including the complexity of the flight environment, communication and coordination mechanisms between UAVs, energy management, and response capabilities to emergencies [1].

Technically, multi-UAV collaborative trajectory planning often relies on advanced algorithms capable of processing large amounts of real-time data and making quick, accurate decisions. These include deterministic algorithms like A* or Dijkstra’s algorithm [2] for planning the shortest path in known environments and non-deterministic algorithms like ant colony optimization [3] and particle swarm optimization [4] for addressing optimization problems in complex and changing environments. Furthermore, with the development of artificial intelligence, deep learning [5] and reinforcement learning [6] are increasingly applied in this field to enhance the flexibility and adaptability of planning strategies.

2. Centralized Framework Algorithm

The centralized framework is widely used in cluster collaborative control, and it is an example of organizational structure and control methods. Under this framework, decision-making and control instruction delivery throughout the cluster are primarily handled by a central node or central controller [7]. This centralized design gives individuals in the cluster more ordered collaborative work capabilities, enabling synergy and efficiency throughout the system.

The central feature of a centralized framework is the dominance of central nodes. A central node acts as a hub for information integration and decentralized transmission of instructions and is responsible for decision-making throughout the cluster [8]. Through a centralized decision-making process, individuals in a cluster are able to take coordinated actions at the same time, thus effectively completing tasks in synergy.

Table 1. Algorithms using a centralized control framework.

Algorithm Type	Algorithm Name
Path Planning Algorithm	Rapidly-exploring Random Trees (RRT) [9,10,11,12] Probabilistic Roadmap (PRM) [13,14,15] Improved Artificial Potential Field (Improved APF) [16,17,18]
Mission Allocation Algorithm	Hungarian Algorithm [19,20,21,22] Maximum Flow Minimum Cut Algorithm [23,24] Genetic Algorithm (GA) [25,26,27]
Control Algorithm	Model Predictive Control (MPC) [28,29] Nonlinear Model Predictive Control (NMPC) [30,31,32] Generalized Predictive Control (GPC) [33,34] linear quadratic regulator (LQR) [35,36]
Collaborative Decision Algorithm	Reinforcement learning (RL) [37,38,39] Collaborative auction algorithm [40,41]

lists most of the centralized framework algorithms used in UAV collaborative trajectory planning.

2.1. Path Planning Algorithm

Path planning is a critical issue for mobile entities such as UAVs when planning their movement paths reasonably within an environment. The centralized framework in path planning can globally consider environmental information, such as avoiding obstacles and planning the optimal path.

2.1.1. Rapidly-Exploring Random Trees Algorithm

The Rapidly-exploring Random Trees (RRT) algorithm provides an effective path-planning solution for multi-unmanned aerial vehicle (UAV) collaborative trajectory planning. RRT is an ideal choice for complex environments and dynamic obstacles in multi-UAV trajectory planning due to its simplicity, efficiency, and ability to handle high-dimensional spaces and complex constraints [9]. The algorithm flow of the RRT is shown in Figure 1.

Improved versions of the RRT algorithm aim to address some of the limitations of the original RRT, such as path optimization, search efficiency, and the capability to handle high-dimensional space problems. The key improvement in improving the RRT (RRT*) algorithm is to optimize the path, making it closer to the optimal solution. RRT* mainly improves rewiring on the basis of the standard RRT algorithm. The equation for rewiring is as follows:

$$\left\{\begin{array}{c}\forall q\in Neighborhood\left(q_{new},r\right),if Collision Free(q_{new},q),\\ if Cost\left(q_{new}\right)+\left|\right|q_{new}-q\left|\right|<Cost q ,\\ then rewire q to q_{new}\end{array}\right.$$

(1)

The application of improved RRT algorithms in multi-UAV collaborative trajectory planning significantly enhances the efficiency, quality of path planning, and coordination between UAVs [10]. These algorithms optimize the search process, ensuring that UAVs can effectively avoid collisions, rapidly respond to environmental changes, and efficiently complete tasks.

In multi-UAV collaborative systems, RRT* is used to generate the least costly paths, especially effective in missions requiring minimized total flight time or energy consumption [11]. By continually optimizing the path cost, RRT* ensures that each UAV’s trajectory is as efficient as possible, while also considering constraints to avoid interference and collisions, achieving safe collaborative flight.

Bidirectional RRT (Bi-RRT) is particularly useful in multi-UAV path-planning problems in complex or large-scale environments. Building search trees from both the start and end points can significantly accelerate the search process, especially when complex obstacles exist between the start and end points [12]. This approach is suitable for urgent mission execution, such as rapid search and rescue, or missions requiring reaching a destination within a specific time frame.

2.1.2. Probabilistic Roadmap Algorithm

The probabilistic Roadmap (PRM) algorithm is a path-planning method primarily used in static environments, suitable for handling high-dimensional spaces and complex constraints. In multi-unmanned aerial vehicle (UAV) collaborative trajectory planning, PRM can effectively generate safe and efficient paths for each UAV while considering the collaborative needs between UAVs and avoiding mutual interference [13].

Although the PRM algorithm has shown strong capabilities in path planning for multi-UAV systems, there is still room for improvement in handling dynamic environments, enhancing path optimization quality, and computational efficiency. Improved versions of PRM, such as Gaussian PRM and Dynamic PRM, offer significant advancements in computational efficiency compared to the original PRM algorithm.

Gaussian PRM is widely used in multi-UAV collaborative exploration tasks in complex or confined spaces. By increasing the sampling density in key areas, this algorithm can more effectively plan paths through difficult-to-reach areas, such as avoiding skyscrapers in urban environments or trees in forests, thereby enhancing the efficiency and safety of UAV exploration [14].

In dynamic environments, such as urban air traffic management or disaster area rescue operations, dynamic PRM can update the UAVs’ path planning in real-time according to environmental changes. This algorithm allows UAVs to adapt to emergencies, move obstacles, or change mission requirements, ensuring the safe and effective completion of tasks while maintaining coordination and communication between UAVs [15].

2.1.3. Improved Artificial Potential Field

The application of the improved Artificial Potential Field (APF) method in multi-unmanned aerial vehicle (UAV) collaborative trajectory planning optimizes the shortcomings of the original APF algorithm in handling issues like local minima, unreachable goals, and mutual interference among multiple UAVs. The formulas for improved APF are as follows:

$$\mathrm{Attraction}: {\mathrm{F}}_{\mathrm{a}\mathrm{t}\mathrm{t}}={\mathrm{k}}_{\mathrm{a}\mathrm{t}\mathrm{t}}(\mathrm{q}-{\mathrm{q}}_{\mathrm{g}\mathrm{o}\mathrm{a}\mathrm{l}})$$

(2)

$$\mathrm{Repulsive} \mathrm{force}: {\mathrm{F}}_{\mathrm{r}\mathrm{e}\mathrm{p}}={\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{k}}_{\mathrm{r}\mathrm{e}\mathrm{p}}(\frac{1}{{\mathrm{d}}_{\mathrm{i}}}-\frac{1}{{\mathrm{d}}_0})\frac{1}{{\mathrm{d}}_{\mathrm{i}}^2}(\frac{\mathrm{q}-{\mathrm{q}}_{{\mathrm{o}\mathrm{b}\mathrm{s}}_{\mathrm{i}}}}{{\mathrm{d}}_{\mathrm{i}}})$$

(3)

$$\mathrm{Resultant} \mathrm{force}: {\mathrm{F}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}={\mathrm{F}}_{\mathrm{a}\mathrm{t}\mathrm{t}}+{\mathrm{F}}_{\mathrm{r}\mathrm{e}\mathrm{p}}$$

(4)

$$\mathrm{Update} \mathrm{location}: q_{new}=q_{current}+\alpha {\mathit{F}}_{total}$$

(5)

By integrating the APF algorithm with other path-planning algorithms (such as RRT and A*), the limitations of the single APF algorithm can be overcome. For instance, the APF algorithm can be used to generate general directions and obstacle avoidance paths, while algorithms like RRT can refine the paths and address local minima issues [16,17]. This hybrid strategy is suitable for multi-UAV systems that need to perform tasks collaboratively in complex environments.

In complex dynamic environments, the improved APF algorithm introduces intelligent obstacle avoidance strategies, such as considering the UAVs’ dynamic capabilities and predicting the movement trends of obstacles. This allows UAVs to navigate around obstacles more flexibly while maintaining a safe distance from other UAVs [18].

2.2. Task Allocation Algorithms

In scenarios where multiple unmanned aerial vehicles (UAVs) collaborate to execute tasks, a centralized framework uses algorithms to determine the tasks that each individual will perform, aiming to maximize the overall benefit.

2.2.1. Hungarian Algorithm

The Hungarian algorithm is primarily used for task allocation in multi-unmanned aerial vehicle (UAV) collaborative trajectory planning, especially when there is a need to distribute a series of tasks efficiently and fairly among multiple UAVs. The algorithm optimizes task distribution by minimizing the total cost or maximizing the total benefit, ensuring that each UAV is assigned the most suitable task, thereby enhancing the efficiency and effectiveness of the entire UAV system [19,20].

In large-scale search and rescue operations, the Hungarian algorithm can be used to assign different search areas to different UAVs, ensuring that each UAV is responsible for a specific area to minimize overlapping searches and guarantee full coverage [21].

In scenarios where multiple UAVs collaborate to track multiple moving targets, the Hungarian algorithm can be used for real-time allocation of UAVs to track different targets, optimizing the allocation based on the distance from the UAVs to the targets and the importance of the targets.

For monitoring complex environments, the Hungarian algorithm can efficiently allocate monitoring tasks to UAVs based on the monitoring efficiency of the UAVs and the importance of the monitoring areas, aiming to minimize the total monitoring time or cost [22].

2.2.2. Max-Flow Min-Cut Algorithm

The Max-Flow Min-Cut theorem is a fundamental theorem in graph theory that finds the maximum flow from a source to a sink in a network flow problem and determines the corresponding minimum cut. This theorem is applied in multi-unmanned aerial vehicle (UAV) collaborative trajectory planning, primarily in task allocation, resource distribution, and path-planning optimization, especially when considering the interactions and resource sharing among multiple UAVs [23].

The effective collaborative operation of a multi-UAV system often relies on a stable and reliable communication network. The Max-Flow Min-Cut algorithm can be applied to the design and optimization of UAV communication networks. By establishing a network model and optimizing the allocation of communication links between UAVs, it ensures the maximum throughput of the communication network throughout the task execution process, thereby enhancing network stability and interference resistance [24].

2.2.3. Genetic Algorithm

The genetic algorithm is a heuristic search algorithm that simulates the principles of natural selection and genetics. It searches the solution space through operations like selection, crossover (hybridization), and mutation to find the best or near-optimal solution to a problem. In multi-unmanned aerial vehicle collaborative trajectory planning, the genetic algorithm can effectively solve issues related to path planning, task allocation, and resource optimization, especially suited for complex, high-dimensional optimization problems. The algorithm flowchart of the genetic algorithm is shown in Figure 2.

In scenarios requiring multiple UAVs to collaboratively complete multiple tasks, the genetic algorithm can be used to optimize task allocation, ensuring that tasks are assigned and executed in the most efficient manner [25]. By representing the task allocation problem as chromosomes (where genes represent the tasks executed by specific UAVs), the algorithm can find the optimal task allocation scheme to maximize overall efficiency or minimize the total time to complete the tasks.

The genetic algorithm can also be used to optimize formation control and obstacle avoidance strategies in formation flying. By optimizing the relative positions and flight paths of the UAVs, efficient formation flying can be achieved while ensuring safety [26,27]. Through iterative improvements in UAV formation configurations, the genetic algorithm helps find the optimal path to avoid collisions in complex environments.

2.3. Control Algorithms

In a centralized framework, the central controller coordinates the actions of multiple entities through real-time monitoring and adjustments. It is responsible for controlling and guiding the specific actions of unmanned aerial vehicles (UAVs), ensuring that they fly according to predetermined flight paths and complete their tasks.

2.3.1. Model Predictive Control

Model Predictive Control (MPC) is an advanced process control method widely used in the industrial and aviation sectors. In the application of multi-UAV collaborative trajectory planning, MPC takes full advantage of its capability to handle multi-constraint, multi-objective problems, providing an effective real-time path planning and control method for UAV groups.

In multi-UAV environments, avoiding collisions between UAVs is crucial. MPC achieves real-time dynamic obstacle avoidance by predicting the future positions of UAVs and adjusting their trajectories within the control loop [28].

For UAV groups carrying specific payloads, such as in logistics delivery or agricultural spraying, MPC can optimize the release process of the payload, ensuring the precision and effectiveness of task execution [29].

MPC has the advantages of optimizing future behavior, superior predictive performance, and the ability to directly consider time and state constraints. However, it also faces challenges such as high computational requirements, the need for real-time optimization problem-solving, and a significant dependence on model accuracy, where inaccuracies can lead to performance degradation.

Measures to address these challenges include the following:

• using more efficient numerical optimization algorithms and hardware to accelerate computation
• improving model accuracy through system identification and online learning methods
• employing adaptive control techniques to adjust control strategies in response to model uncertainties and external disturbances.

2.3.2. Nonlinear Model Predictive Control

Nonlinear model predictive control (NMPC) is a variant of model predictive control (MPC) that is suited for handling the dynamics of nonlinear systems. Compared to traditional MPC, NMPC can more accurately simulate and control systems whose behavior changes nonlinearly with state and control inputs.

Nonlinear controllers are widely used in high-precision trajectory tracking, capable of accurately following paths in complex environments [30].

NMPC is also extensively used in the landing of multi-UAV systems, particularly in tasks requiring precise landings, such as on irregular terrains or moving platforms. By considering the nonlinear dynamics of the UAVs and environmental constraints, NMPC can implement precise and safe landing strategies [31,32].

Compared to linear MPC, solving nonlinear optimization problems usually requires more computational resources and has higher computational complexity. Additionally, the solution speed for nonlinear optimization problems can be slower, making real-time control more challenging.

However, with advancements in computational technology and optimization of algorithms, NMPC is expected to play a larger role in the application of multi-UAV systems in the future.

2.3.3. Generalized Predictive Control (GPC)

Generalized Predictive Control (GPC) is a model-based predictive control strategy whose application in multi-unmanned aerial vehicle (UAV) collaborative trajectory planning demonstrates its capability in optimizing predictive control strategies.

During formation flying missions, GPC can coordinate the relative positions and speeds of multiple UAVs to maintain a stable formation. By predicting the future states of each UAV and considering the dynamic constraints between them, GPC optimizes the control inputs for the entire formation to adapt to environmental changes and mission requirements, while ensuring safe distances within the formation to prevent collisions [33].

GPC is also widely used in managing UAV payloads, especially for tasks requiring precise payload delivery, such as emergency rescue or supply drops. GPC optimizes the timing and location of payload release by predicting environmental factors like wind direction and speed that affect the payload’s descent trajectory [34]. This GPS calculation ensures the optimal release point and method are used, guaranteeing the payload reaches its intended destination accurately.

2.3.4. Linear Quadratic Regulator (LQR)

The Linear Quadratic Regulator (LQR) significantly enhances the flight performance and safety of unmanned aerial vehicles (UAVs) in multi-UAV systems. LQR optimizes the system’s response and stability by minimizing a cost function, balancing state deviations and control effort usage. The cost function minimized is as follows:

$$J={\int }_0^{\infty }(x^{T}Qx+u^{T}Ru)dt$$

(6)

In this context, $Q$ and $R$ are weight matrices used to quantify the cost of state deviations and control inputs, respectively. $Q$ is typically set as a positive semi-definite matrix to ensure the penalization of state deviations, while $R$ is set as a positive definite matrix to ensure the cost of control efforts.

Maintaining stable altitude and speed is crucial for UAVs during flight missions. LQR can optimize control strategies, allowing UAVs to maintain target altitude and speed in the face of vertical wind shear or changes in forward resistance, thus enhancing the reliability and efficiency of flight [35]. In tasks requiring precise altitude control, LQR can adjust lift to maintain or reach the target altitude. By considering the cost of altitude deviation and lift adjustment, LQR can optimize the altitude control strategy [36].

LQR excels in enhancing flight stability, but it still faces challenges in practical applications, such as model accuracy and the selection of weight matrices. Improving the accuracy of the system model through model identification techniques, adjusting weight matrices to balance control performance and energy consumption, and complementing with other control strategies (like nonlinear control, model predictive control, etc.) can further enhance the effectiveness of LQR in stabilizing UAV flight.

2.4. Collaborative Decision Algorithm

Collaborative decision-making algorithms enable UAVs to effectively collaborate toward a common goal by sharing information and resources. These algorithms facilitate network communication, allowing each agent to independently assess situations, plan actions, and interact with other agents for negotiation. This process optimizes the efficiency and effectiveness of the overall mission execution. Through such collaboration, UAVs can synchronize their efforts, adapt to dynamic environments, and make collective decisions that improve the success rate of the mission, showcasing the strength of distributed intelligence and shared decision-making in complex operations.

2.4.1. Reinforcement Learning

In scenarios requiring the collaboration of multiple agents, a centralized framework through collaborative decision-making algorithms achieves global optimal trajectory planning. In multi-unmanned aerial vehicle collaborative trajectory planning, reinforcement learning (RL) algorithms can optimize the decision-making process of UAV groups based on environmental feedback, enabling efficient and safe task execution.

The Bellman equation is one of the most fundamental equations in reinforcement learning, which describes the relationship between the state value function and the action value function. It is the foundation of value function iteration algorithms and continuously approximates the optimal value by iteratively calculating the state value function or action value function. The Bellman equation is as follows:

$$\mathrm{V}\left(\mathrm{s}\right)=\mathrm{E}[\mathrm{R}+\mathsf{\gamma }\mathrm{V}(\mathrm{s}\prime \left)\right|\mathrm{s},\mathrm{a}]$$

(7)

where $\mathrm{R}$ represents the reward obtained in state $\mathrm{s}$ after executing action $\mathrm{a}$; $\mathsf{\gamma }$ represents the discount factor, which determines the importance of future rewards, usually ranging from 0 to 1; $\mathrm{s}\prime$ represents the next state that action a may reach after execution; E represents the expected value, representing the expected value function of the next state s’ after executing action a; and $\mathrm{a}$ represents the action selected in state s.

Reinforcement learning algorithms train UAVs to identify and avoid obstacles in unknown or dynamically changing environments. Through interactive learning with the environment, UAVs can discover the optimal flight paths, effectively dealing with complex terrain or sudden obstacles. Moreover, reinforcement learning enables UAVs to predict the behavior of other UAVs, thereby avoiding collisions between them [37].

In tasks requiring intensive communication, RL algorithms can optimize the communication strategies and data-sharing mechanisms among UAVs. The UAV group learns how to adjust communication frequency and protocols based on communication quality, mission requirements, and environmental conditions, improving communication efficiency and collaborative operation performance [38].

For tasks that require close cooperation among multiple UAVs, such as joint search, area surveillance, or construction tasks, RL can help UAV groups learn the most effective collaboration strategies. UAVs can learn how to allocate observation areas, synchronize actions, and share observation data to achieve efficient coverage of the target area [39] RL can also optimize the role allocation and task-switching strategies among UAVs, making collaborative operations more flexible and adaptable.

2.4.2. Collaborative Auction Algorithm

The collaborative auction algorithm is a distributed decision-making process algorithm commonly used in multi-UAV systems for task allocation and resource optimization. In this algorithm, tasks or resources are considered auctionable items, with UAVs or agents acting as bidders to dynamically allocate tasks or resources through the auction process. This method is extensively used in scenarios that demand rapid response and high levels of collaboration.

In large-scale surveillance and reconnaissance missions, the collaborative auction algorithm provides a dynamic and efficient method to allocate observation areas or specific targets to a multi-UAV system [40]. The algorithm allows each UAV to bid for different tasks or areas based on its current location, capabilities, and the cost of executing the tasks, thus ensuring efficient task allocation.

Communication is a key element in coordinating and allocating tasks among UAVs using the collaborative auction algorithm. Every step, from task announcement and bid submission to the final task allocation decision, depends on effective communication within the UAV system. However, this process might require frequent exchanges of information, particularly with a large number of UAVs involved, leading to significant communication overhead that could affect the system’s efficiency and response speed. To address these issues, more efficient communication protocols can be designed to reduce the volume of data exchanged in each communication while maintaining the necessity and accuracy of the information [41].

Moreover, UAVs can be encouraged to make local decisions where possible, and reliance on central decision-making can be reduced through information fusion techniques, significantly lowering communication frequency and data volume.

3. Distributed Framework Algorithm

The distributed framework algorithm is a commonly used organizational structure and control method in cluster collaborative control. Unlike centralized framework algorithms, the distributed framework decentralizes decision-making and controls instruction dissemination across each individual within the cluster, with each individual responsible for their own decision-making and execution. This framework design enhances the system’s flexibility and robustness, making it suitable for distributed environments and large-scale systems (

Table 2. A list of most of the distributed framework algorithms used in UAV collaborative trajectory planning.

Algorithm Type	Algorithm Name
Path Planning Algorithm	Greedy Algorithm [42,43,44] Dynamic Programming Algorithm [45,46,47] Monte Carlo Algorithm [48,49]
Mission Allocation Algorithm	Pheromone Model Algorithm [50,51,52] Dynamic Role Assignment Algorithm [53,54,55] Priority-based Task Queue Algorithm [56,57,58]
Control Algorithm	Consensus Learning Algorithms [59,60,61] Multi-Agent Reinforcement Learning [62,63,64,65,66]
Collaborative Decision Algorithm	Distributed Model Predictive Control [67,68,69,70] Distributed Constraint Optimization Problem [68,71,72]

).

3.1. Path Planning Algorithm

In a decentralized framework, individuals achieve local path planning through communication with nearby peers, which means that individuals can make decisions based on information from neighboring entities, enhancing the system’s flexibility.

3.1.1. Greedy Algorithm

The greedy algorithm is an algorithm for solving optimization problems, making the locally optimal choice at each step with the hope that this will lead to a globally optimal solution.

In multi-UAV search and rescue missions, the greedy algorithm can be used to quickly allocate UAVs to different search areas. At each step, the algorithm selects the UAV that is closest to a search area and not yet assigned and allocates it to that area [42]. Although this method is simple, it can rapidly generate a feasible search plan in emergency situations, responding quickly to rescue needs.

Due to its simplicity in implementation and computational efficiency, the greedy algorithm is widely used in collaborative trajectory planning of multi-UAV systems, especially suitable for scenarios requiring high computational speed or having a large solution space [43]. However, it is important to note that the greedy algorithm may not always produce the globally optimal solution, so it should be used with caution or in combination with other algorithms for optimization in scenarios where optimality is a critical requirement [44].

3.1.2. Dynamic Programming Algorithm

The dynamic programming algorithm (DP) is a method used to solve multi-stage decision process optimization problems. It breaks down the original problem into smaller sub-problems, solves these sub-problems first, and then gradually finds the optimal solution to the original problem. Dynamic programming is particularly suited for problems with overlapping sub-problems and optimal substructure properties and can be applied in multi-unmanned aerial vehicle (UAV) systems for path planning, resource allocation, and task scheduling.

In multi-UAV search missions, dynamic programming can optimize search paths and task allocation [45]. The algorithm starts by dividing the search area into multiple sub-areas, then defines the state of each UAV’s search in each sub-area, and gradually optimizes the search path for each UAV through dynamic programming, ultimately constructing an optimal search plan for the entire group.

The application of dynamic programming in multi-UAV systems provides an effective method for achieving efficient collaborative operations in complex environments [46]. However, it is important to note that as the problem size increases, the computational complexity of dynamic programming also rises rapidly. Therefore, in practical applications, it is necessary to use appropriate optimization strategies, such as state space pruning and memoized search, to enhance the algorithm’s efficiency [47].

3.1.3. Monte Carlo Algorithm

The Monte Carlo algorithm is a method based on random sampling to solve problems in mathematics, physics, engineering, and other fields. It estimates the probabilistic distribution characteristics of variables through simulation or random sampling processes, such as numerical integration and optimization problems. In multi-unmanned aerial vehicle collaborative trajectory planning, the Monte Carlo algorithm can be used for path planning, target localization, and decision-making, especially in environments with high uncertainty and task complexity [48].

The main processes of the Monte Carlo algorithm include random sampling, expected value estimation, integral estimation, variance estimation, and confidence interval. The main formula is as follows:

$$\mathrm{Expected} \mathrm{value} \mathrm{estimation}: \mathrm{E}[\mathrm{f}(\mathrm{x})]=\frac{1}{\mathrm{N}}{\sum }_{\mathrm{i}=1}^{\mathrm{N}}\mathrm{f}\left({\mathrm{x}}_{\mathrm{i}}\right)$$

(8)

$$\mathrm{Integral} \mathrm{estimation}: {\int }_{\mathrm{a}}^{\mathrm{b}}\mathrm{f}(\mathrm{x})\mathrm{d}\mathrm{x}\approx \frac{\mathrm{b}-\mathrm{a}}{\mathrm{N}}{\sum }_{\mathrm{i}=1}^{\mathrm{N}}\mathrm{f}\left({\mathrm{x}}_{\mathrm{i}}\right)$$

(9)

$$\mathrm{Variance} \mathrm{estimation}: {\mathsf{\sigma }}^2=\frac{1}{\mathrm{N}-1}{({\sum }_{\mathrm{i}=1}^{\mathrm{N}}\mathrm{f}\left({\mathrm{x}}_{\mathrm{i}}\right)-\mathrm{E}[\mathrm{f}(\mathrm{x})])}^2$$

(10)

$\mathrm{E}\left[\mathrm{f}\right(\mathrm{x}\left)\right]$ is the estimate of the expected value of function f in the input space, and ${\mathrm{x}}_{\mathrm{i}}$ is a random sample on the interval [a, b].

The advantage of the Monte Carlo algorithm lies in its simplicity and wide applicability, as it does not depend on the specific mathematical form of the problem and is particularly suited to solving complex system problems that are difficult to address with traditional analytical methods [49]. However, the accuracy and reliability of the Monte Carlo algorithm depend largely on the number of samples; large-scale sampling can lead to a significant increase in computational cost.

3.2. Task Allocation Algorithms

Distributed task allocation algorithms enable the efficient and fair distribution of a series of tasks among agents (UAVs) in a multi-unmanned aerial vehicle (UAV) system without a central control unit. These algorithms allow each agent to make decisions based on local information through local communication and computation, while also taking into account the optimization objectives of the entire system, such as minimizing the total completion time or maximizing efficiency.

3.2.1. Pheromone Model Algorithm

The pheromone model algorithm is often mentioned in the context of algorithms like ant colony optimization (ACO), where the core concept is derived from the natural behavior of ants finding a food source by releasing and tracking pheromones. However, when discussed independently of ACO, it can be abstractly understood as a communication and decision-making mechanism based on pheromones (a virtual or mathematically defined marker), which can be widely applied in multi-agent systems for path planning, task allocation, and other issues.

The ACO formula is as follows:

$${\mathrm{p}}_{\mathrm{i}\mathrm{j}}^{\mathrm{k}}\left(\mathrm{t}\right)=\left\{\begin{array}{c}\frac{{\left[{\mathsf{\tau }}_{\mathrm{i}\mathrm{j}}\left(\mathrm{t}\right)\right]}^{\mathsf{\alpha }}·{\left[{\mathsf{\eta }}_{\mathrm{i}\mathrm{j}}\left(\mathrm{t}\right)\right]}^{\mathsf{\beta }}}{\sum _{\mathrm{s}\in \mathrm{C}}{\left[{\mathsf{\tau }}_{\mathrm{i}\mathrm{s}}\left(\mathrm{t}\right)\right]}^{\mathsf{\alpha }}·{\left[{\mathsf{\eta }}_{\mathrm{i}\mathrm{s}}\left(\mathrm{t}\right)\right]}^{\mathsf{\beta }}}, \mathrm{j}\in \mathrm{C}\\ 0, \mathrm{j}\notin \mathrm{C}\end{array}\right.$$

(11)

where the mutual distance between node $\mathrm{i}$ and node $\mathrm{j}$ is ${\mathrm{d}}_{\mathrm{i}\mathrm{j}}\left(\mathrm{i},\mathrm{j}=1,2,...,\mathrm{n}\right)$, the pheromone concentration on the path connecting node $\mathrm{i}$ and node $\mathrm{j}$ at time $\mathrm{t}$ is ${\mathsf{\tau }}_{\mathrm{i}\mathrm{j}}\left(\mathrm{t}\right)$, ${\mathsf{\eta }}_{\mathrm{i}\mathrm{j}}\left(\mathrm{t}\right)=\frac{1}{{\mathrm{d}}_{\mathrm{i}\mathrm{j}}}$ is the heuristic function, and ${\mathrm{p}}_{\mathrm{i}\mathrm{j}}^{\mathrm{k}}\left(\mathrm{t}\right)$ denotes the probability of ants from point $\mathrm{i}$ to point $\mathrm{j}$ at time $\mathrm{t}$.

The pheromone model algorithm can be used in the collaborative flight path planning of UAV swarms, commonly in flying path planning for multi-UAVs during search, surveillance, or mapping missions, to avoid obstacles and ensure comprehensive task coverage [50,51,52].

3.2.2. Dynamic Role Assignment Algorithm

The dynamic role assignment algorithm is a strategy in multi-agent systems that allows each agent (such as UAVs) to dynamically change its role and behavior based on the current environmental conditions and task requirements. This algorithm is particularly suited for scenarios with varying types of tasks and changing environments, as it can enhance the adaptability and efficiency of the entire system.

Dynamic role assignment is often used in complex search and rescue missions. UAVs can dynamically switch between “rapid search” and “detailed search” roles based on the characteristics of the search area and changing task requirements [53]. During rapid search, UAVs cover larger areas quickly, and upon detecting potential targets, some UAVs may switch to the detailed search role, slowing down to conduct thorough examinations [54].

By flexibly adjusting the behaviors and responsibilities of agents, the dynamic role assignment algorithm enables multi-agent systems to adapt more effectively to complex and changing task environments, thereby increasing the efficiency and success rate of mission execution [55].

3.2.3. Priority-Based Task Queue Algorithm

The priority-based task queue algorithm is an effective method for managing and allocating tasks in multi-task environments, especially in multi-agent systems like multi-unmanned aerial vehicle (UAV) systems. This algorithm assigns a priority level to each task and sorts and executes the tasks according to their priority levels, ensuring that urgent or important tasks are addressed first. This approach is suitable for scenarios requiring dynamic response and efficient handling of multiple tasks [56].

Multi-UAV systems that employ the priority-based task queue algorithm are commonly used for monitoring urban traffic flow, accidents, and violations. During peak times or special events (such as large sports events or public gatherings), the priority of traffic monitoring tasks increases to ensure a timely response to traffic congestion and accidents. The priority-based task queue algorithm enables UAV systems to dynamically adjust their monitoring focus, giving priority to areas with worse traffic conditions [57,58].

3.3. Control Algorithm

Control algorithms are a series of computational steps used to guide system behavior to achieve predetermined objectives. They function by continuously receiving information about the system’s state, calculating control signals, and adjusting the system’s operations to ensure stable operation along a predetermined path or manner.

3.3.1. Consensus Learning Algorithms

The consensus learning algorithm is designed to allow multiple agents, such as UAVs and robots, to reach a common understanding, decision, or action plan through distributed computation. In multi-agent systems, this algorithm is particularly important as it enables agents to act in a coordinated manner even in the absence of central control. Consensus learning focuses not only on the final uniform outcome but also on the learning process to achieve this result.

The principle of the consensus learning algorithm is that multiple agents adjust their states through local interactions (information sharing, state updating, etc.) to eventually reach a common state or decision. This process is not dependent on a central controller but is achieved through distributed collaboration among agents in the network [59].

In a distributed multi-drone network, network connectivity and communication delay introduce errors, which will seriously affect the convergence time and delay of consensus results. When there is a communication delay t between UAV f and UAV i, the formula is as follows:

$$\dot{x_i}(t+1)=x_i(t)+{\sum }_{j\in {\Omega }_i}{a}_{ij}\left[x_j\right(t-{\tau }_{ij})-x_i(t-{\tau }_{ij}\left)\right]$$

(12)

where $\dot{x_i}$ is the value of UAV i, $a_{ij}$ is the consensus weight coefficient between UAV i, and UAV $j$, $T_{con}$ represents the consensus convergence delay of multiple unmanned aerial vehicle tracking networks. When $t\to T_{con}$, the values of all UAVs will gradually reach consensus, as follows:

$$\underset{\mathrm{t}\to {\mathrm{T}}_{\mathrm{con}}}{\lim }\dot{{\mathrm{x}}_{\mathrm{i}}}\left(\mathrm{t}\right)=\underset{\mathrm{t}\to {\mathrm{T}}_{\mathrm{c}\mathrm{o}\mathrm{n}}}{\mathrm{l}\mathrm{i}\mathrm{m}}\dot{{\mathrm{x}}_{\mathrm{j}}}(\mathrm{t})$$

(13)

In applications where UAVs are required to perform extended monitoring, the consensus learning algorithm can help UAVs dynamically adjust their patrol strategies based on actual observed events, such as illegal activities or environmental changes, ensuring that critical areas receive sufficient attention [60,61].

3.3.2. Multi-Agent Reinforcement Learning

Multi-agent reinforcement learning (MARL) is a machine learning approach that extends the traditional reinforcement learning framework to accommodate the interactive environment of multiple agents in a multi-agent system. In MARL, each agent learns how to act to maximize some cumulative reward based on its interaction with the environment. Compared to single-agent reinforcement learning, MARL has to deal with additional complexities, such as cooperation, competition, and the interdependence of actions among agents [62].

MARL is commonly used for formation flying and aerial control, such as adaptive formation and formation switching. UAVs use MARL to learn how to automatically adjust their formation shape in response to environmental changes (like wind speed variations and the emergence of obstacles), maintaining an optimal flight configuration. UAV swarms can learn to dynamically change their formation structure during different phases of a mission (e.g., transitioning from search to surveillance) to meet task requirements [63,64,65].

Furthermore, multi-agent reinforcement learning is extensively used in aerial cooperative search and rescue for dynamic search area allocation. In search and rescue missions, UAV swarms learn through MARL how to dynamically adjust their search areas based on real-time feedback (such as information from already searched areas) to improve search efficiency and coverage [66].

3.4. Collaborative Decision Algorithm

Collaborative decision-making algorithms are a category of algorithms designed to achieve effective cooperation and decision synchronization among agents in multi-agent systems, such as multi-UAV systems and multi-robot systems. The key to these algorithms is enabling each agent to maintain a degree of independence while collaborating through information sharing, negotiation, and joint decision-making to address common or individual tasks. These algorithms facilitate coordinated action, optimize collective performance, and enhance the ability to respond dynamically to changes in the environment or mission objectives.

3.4.1. Distributed Model Predictive Control

Distributed model predictive control (DMPC) is an advanced control strategy suitable for multi-agent systems, such as multi-UAV systems and multi-robot systems. It extends the concept of model predictive control (MPC) to distributed systems, allowing each agent (UAV, robot, etc.) to make independent decisions and control actions while considering the overall system performance. DMPC combines the foresight and optimization characteristics of MPC with the flexibility and scalability of distributed systems, making it well-suited for solving complex problems requiring multi-agent collaboration.

DMPC relies on the concepts of local model prediction and global coordination. Each agent uses its local model to predict future behaviors and makes optimized decisions based on these predictions. At the same time, agents share information through some form of communication to ensure the coordinated consistency of the entire system [67].

In UAV formation flying, precise position control and path planning are required to maintain specific formations and relative positions. Applications of DMPC in this area include dynamic formation shape adjustment, formation maintenance, and position transitions within the formation to adapt to mission requirements or respond to environmental changes [68,69].

Safety is one of the most critical considerations in multi-UAV systems. DMPC must plan paths that avoid fixed and moving obstacles while ensuring that UAVs maintain safe distances from each other to prevent collisions. This includes rapid path replanning in emergency situations [70].

3.4.2. Distributed Constraint Optimization

Distributed constraint optimization (DCO) is a specific type of optimization algorithm that seeks optimal solutions in multi-agent systems (such as multi-UAV systems and multi-robot systems) while meeting a set of distributed constraints. DCOP is applied in various fields, including but not limited to collaborative control, resource allocation, and scheduling problems. The essence of these problems is how to achieve a global or near-global optimal solution through cooperation among agents while maintaining their autonomy.

In path planning and obstacle avoidance, DCO provides an efficient solution framework for multi-UAV systems, enabling UAVs to autonomously and collaboratively complete tasks in complex environments. For example, in a monitoring mission covering a large geographic area, each UAV needs to plan its flight path to cover specific monitoring points while avoiding static obstacles like buildings and trees, as well as dynamic obstacles posed by other UAVs [70].

When UAVs detect potential path conflicts or new obstacles, they enter a negotiation and adjustment phase. During this phase, agents may need to replan their flight paths, adjust their flying altitudes, or change the order of monitoring points they visit to resolve conflicts and meet constraints. This feedback-based iterative process continues until the flight plans of all UAVs no longer have conflicts and meet all mission requirements and constraints [68,71,72].

After completing this process, each UAV will execute the mission following the finalized flight path. During execution, UAVs still need to maintain communication to respond to contingencies, such as dynamically avoiding newly emerging obstacles or adjusting paths to deal with emergencies from other UAVs.

4. Main Technical Challenges in Multi-UAV Path Planning

4.1. Collaborative Control

Collaborative control refers to individuals in a swarm achieving common mission objectives by sharing information, making joint decisions, and executing actions collaboratively. In collaborative control, the cooperation between individuals is based on mutual understanding and support, allowing the entire swarm to complete tasks in a more intelligent and efficient manner. Collaborative control emphasizes collective behavior and outcomes rather than just individual control [73].

4.1.1. Information Sharing

Information sharing is the core mechanism of swarm collaborative control, facilitating a comprehensive understanding of the environment throughout the system by real-time sharing of information on environmental perception, task status, and individual locations. Shared environmental data enables individuals to have a more comprehensive understanding of the current environment, providing a real-time and accurate environmental map [74]. Sharing state information allows individuals within the swarm to be aware of each other’s locations and motion statuses, laying the foundation for collaborative decision-making and enabling coordinated actions and conflict avoidance. Information sharing establishes a real-time and efficient communication network, making the entire swarm operate as an integrated entity, enhancing collective cognition and collaborative work, and increasing the swarm’s flexibility and efficiency in complex tasks and environments [75]. Thus, information sharing is not only a technical means but also a key factor for the successful implementation of collaborative control in swarm intelligence systems [76].

4.1.2. Task Allocation

In a swarm, task allocation is crucial for ensuring efficient and collaborative completion of tasks by each individual. The collaborative control system must consider multiple factors, such as individual capabilities, the urgency of tasks, and execution efficiency, to achieve optimal task completion [77]. Capability assessment, which includes sensor performance and flight capabilities, allows the system to allocate tasks more accurately and improve execution efficiency. The urgency of tasks becomes a primary factor, with the system allocating tasks to individuals based on the urgency of different tasks, ensuring that mission objectives are completed within a limited time. Considering execution efficiency, the system performs a comprehensive evaluation of each individual’s performance to allocate tasks reasonably, promoting efficient collaborative work within the swarm [78].

Intelligent algorithms and mathematical models can be used to optimize task allocation, enhancing collaborative efficiency. Task allocation is a strategic decision, and scientifically reasonable allocation facilitates better coordination within the swarm, ultimately leading to optimal mission completion [79,80].

4.1.3. Synchronization and Coordination

Synchronization and coordination are fundamental to ensuring collaborative work within a swarm. Within the swarm, individuals maintain synchronized actions and coordinated paths through mutual communication and collaboration, enhancing the efficiency and flexibility of the entire group [81]. Synchronization control requires individuals within the swarm to act in unison during task execution, achievable through centralized control or distributed algorithms. Coordination control involves the sensible planning of paths to ensure individuals avoid collisions and successfully complete tasks. The system needs to continuously monitor the location and movement status of individuals, dynamically adjusting path planning [81].

Synchronization and coordination must also account for communication delays and uncertainties. Advanced synchronization mechanisms and real-time adjustment strategies can compensate for these delays, maintaining the overall synchrony and coordination of the swarm. This is vital for the swarm’s collaborative efficiency and execution effectiveness. Scientific and effective strategies enable the swarm to better adapt to complex task environments and achieve a higher level of collaborative control [82,83].

4.1.4. Fault Tolerance

In swarm operations, the system must address issues like communication failures and sensor errors to ensure overall stability and reliability. A fault-tolerant design enables the swarm to continue performing tasks effectively even when certain components fail, maintaining the expected performance level. To resolve communication failures, redundant communication links or message retransmission mechanisms can be implemented to ensure the reliability of information transmission [84]. For sensor inaccuracies, the system should monitor and correct data in real-time to improve overall robustness. Mutual backup and complementary designs allow individuals within the swarm to substitute for one another, enhancing the system’s availability and reliability. In terms of decision-making mechanisms, the collaborative control system needs to flexibly adjust in case of individual failures, such as reallocating responsibilities or replanning routes, to ensure the entire system continues to operate efficiently under abnormal conditions. The implementation of fault tolerance ensures the resilience and reliability of the swarm in facing various challenges, safeguarding the efficient completion of tasks [85].

4.1.5. Dynamic Adaptability

In a swarm, dynamic adaptability is crucial for ensuring that individuals can adjust their behavior in real-time to suit the environment and tasks. The collaborative control system needs the capability to perceive environmental changes, capturing information such as obstacle movement and wind speed fluctuations, allowing the entire swarm to flexibly respond to changes in external conditions. The system should dynamically adjust individual behavior based on environmental perception and task requirements, such as changing flight altitude, adjusting speed, and replanning routes, to ensure efficient task completion in various scenarios. Achieving dynamic adaptability requires individuals to have intelligent decision-making and execution capabilities [86].

4.2. Obstacle Avoidance

UAV obstacle avoidance is a key technology for ensuring flight safety in UAV operations. The reliability and efficiency of the UAV obstacle avoidance system largely depend on the accurate acquisition of sensor data. Sensors serve as the UAV’s eyes and ears, providing critical information for the obstacle avoidance system through real-time environmental perception [75].

UAV obstacle avoidance systems typically incorporate various types of sensors to meet the perception needs of different environmental factors. LIDAR (Light Detection and Ranging) is a commonly used sensor that provides precise distance measurements, identifying the location and shape of obstacles. Cameras are another common type of sensor, which, through image processing techniques, capture visual information of the environment, including the appearance and relative position of obstacles. Additionally, ultrasonic sensors are often used to measure the distance between the UAV and the ground, which is very effective for obstacle avoidance during low-altitude flights [87].

These sensors work together to form the perception capabilities of the UAV obstacle avoidance system. When the UAV is in operation, LIDAR scans the surrounding environment with laser beams to obtain precise distance and location information of obstacles. At the same time, cameras capture real-time images, from which environmental features are extracted using computer vision technology. Ultrasonic sensors monitor the distance between the UAV and the ground, ensuring safety during low-altitude flights [88,89].

During the acquisition of sensor data, the timeliness and consistency of the data are crucial. Since UAVs need to respond quickly to environmental changes, delays in sensor data can lead to degraded system performance. Therefore, UAV obstacle avoidance systems often use high-performance sensors and optimize the data transmission and processing workflow to reduce latency [90].

Overall, the acquisition of sensor data is a critical component of the UAV obstacle avoidance system, directly affecting its perception capabilities and obstacle avoidance effectiveness. By selecting appropriate sensor types, optimizing fusion algorithms, and enhancing real-time processing technologies, the reliability and applicability of the UAV obstacle avoidance system can be further improved, ensuring efficient and safe flight in complex and variable environments.

4.3. Collision Detection

In UAV collision detection, the control strategy typically employed is central to ensuring that the system is able to take appropriate actions when a potential collision threat is detected. These include the adoption of planning algorithms such as dynamic obstacle avoidance paths that adjust the UAV’s flight path in real time to avoid potential collision obstacles [91]. The system should also integrate autonomous obstacle avoidance systems, which autonomously respond in real time to avoid potential collisions by sensing obstacles in the environment. Dynamic flight attitude adjustment is a key control strategy that adjusts the flight altitude and attitude to ensure the UAV is able to pass safely when an obstacle is detected [92]. Communication cooperative control plays a key role in multiple UAV systems, ensuring cooperative obstacle avoidance between UAVs through cluster coordination and centralized control decisions [75]. In contrast, predictive control strategies avoid potential collision threats in advance by predicting environmental changes and adopting predictive path planning [93]. The integrated application of these control strategies ensures that UAV systems can intelligently identify and avoid potential collision risks in flight, improving flight safety and reliability.

4.4. Application of SLAM Technology in UAV Obstacle Avoidance and Collision Avoidance

The key role of SLAM (Simultaneous Location and Mapping) technology in UAV obstacle avoidance systems is to combine it with multi-UAV collaborative path planning to form a more intelligent, collaborative flight control system. SLAM technology enables UAVs to achieve autonomous navigation and plan obstacle avoidance paths in unknown environments through sensor fusion and complex algorithms [94]. On this basis, the integration of multi-UAV collaborative path planning further improves the system’s performance, which is embodied in support of cluster location, dynamic path planning, the integration of path planning and obstacle avoidance strategy, etc.

SLAM technology provides support for clustered positioning of multiple UAVs, enabling mutual knowledge of position and motion status between multiple UAVs through collaborative awareness and map building [74]. When SLAM is combined with multiple UAV collaborative planning paths, each UAV in the cluster can collaboratively design paths based on real-time updated map and location information, avoiding collisions and conflicts [95].

For collaborative design aspects of dynamic path planning, SLAM technology provides real-time map and location information, providing the basis for collaborative path planning of UAVs in clusters. Multiple UAV systems can intelligently integrate path planning and obstacle avoidance strategies to ensure that the entire cluster is able to fly safely and efficiently.

In terms of the integration of path planning with obstacle avoidance strategies, SLAM technology provides more comprehensive environmental information, both static and dynamic obstacles [96]. When SLAM is combined with multi-UAV collaborative path planning, the system can integrate path planning and obstacle avoidance strategies more intelligently, ensuring that every UAV in the cluster is able to fly safely and efficiently [97].

In terms of real-time feedback and adjusting the cluster path, real-time environmental feedback of SLAM technology combined with multiple UAV collaborative planning paths enables the entire cluster to sense environmental changes in real-time and adjust flight paths cooperatively [98]. This real-time feedback enables clusters to flexibly and efficiently avoid obstacles in complex environments.

Collectively, the combination of SLAM technology with multiple UAV collaborative path planning makes the entire system more adaptable and intelligent, improving the safety and efficiency of clustered flights [99]. In the future, with the continuous development of SLAM technology, UAV obstacle avoidance systems will be more intelligent, flexible, and adaptable to more complex and varied application scenarios [100].

5. Applications and Countermeasures of Multi-UAV Collaborative Trajectory Planning

The advancement of multi-UAV collaborative trajectory planning technology has impacted various sectors such as government, business, individual, and academic research, introducing new challenges and opportunities.

5.1. Government Applications and Countermeasures

The government plays a crucial role in the application of multi-UAV collaborative trajectory planning technology, acting not only as regulators but also as promoters and practitioners of the technology. Government agencies can use multi-UAV systems to enhance the quality of public services and improve emergency response capabilities. Additionally, they can play a key role in various fields such as environmental protection and urban planning.

5.1.1. Emergency Management and Rescue

Following natural disasters such as earthquakes, floods, and forest fires, governments can deploy multi-UAV systems for rapid disaster area reconnaissance to assess the situation, locate stranded individuals, and provide immediate and accurate information support for rescue decisions. A swarm of UAVs can work collaboratively to cover extensive search areas, significantly enhancing search efficiency and rescue speed [101,102,103,104].

5.1.2. Environmental Monitoring and Protection

Government environmental agencies can utilize multi-UAV systems for environmental quality monitoring, including air quality, water pollution, and ecological monitoring of wildlife protection areas. Through collaborative trajectory planning, multi-UAVs can achieve intensive monitoring of specific areas, allowing for the timely detection and addressing of environmental issues [105,106].

5.1.3. Traffic Management

For urban traffic management, governments can employ multi-UAV systems to monitor traffic flow and record violations. A swarm of UAVs can provide real-time surveillance of key road sections during peak periods, offering data support for traffic congestion warnings and rapid accident response, thereby optimizing urban traffic conditions [107,108,109].

5.1.4. Urban Planning and Infrastructure Inspection

In urban planning and infrastructure development, multi-UAV systems can be utilized for topographical mapping, monitoring construction progress, and regular inspection of existing infrastructure [110,111]. Through efficient collaborative operations, UAV swarms can provide high-precision maps and real-time construction scenes, assisting governments in timely monitoring of project progress and ensuring the quality of the work [112,113].

5.1.5. Public Safety Monitoring

Governments can deploy multi-UAV systems for tasks such as safety monitoring of large-scale events and patrolling key areas, effectively preventing and combating criminal activities. Through coordinated flight, UAV swarms can achieve extensive real-time video surveillance, enhancing public safety and security [114,115].

5.1.6. Implementation Strategies

To fully leverage the potential of multi-UAV technology in the aforementioned areas, governments need to implement the following countermeasures:

• Establish specific laws and regulations that define the safety standards and privacy protection requirements for UAV operations.
• Create a support system for the research and development and application of multi-UAV technology, including financial aid, tax incentives, and other measures.
• Strengthen cooperation with research institutions and businesses to jointly promote the innovation and application of multi-UAV technology.
• Conduct public education campaigns to enhance public awareness and acceptance of multi-UAV technology.

Through these measures, governments can not only ensure the safe and compliant use of multi-UAV technology but also effectively harness this technology for the public good, improving the efficiency and quality of public services.

5.2. Corporate Applications and Countermeasures

At the corporate level, the application of multi-UAV collaborative trajectory planning technology mainly focuses on improving operational efficiency, reducing operating costs, enhancing service capabilities, and developing new business models. With technological advancements, enterprises can manage and deploy UAV swarms more effectively, creating significant value across various industries.

5.2.1. Precision Agriculture

UAV swarms in agriculture can be used for soil analysis, crop growth monitoring, pest and disease detection, and precise spraying of pesticides or nutrients. Through collaborative operations, UAVs can cover large areas of farmland, collecting high-resolution images and data that can aid farmers in making more accurate decisions. For example, data collected by UAVs can be used to determine which areas need more water or nutrients to enhance crop yield and quality while reducing resource waste [116,117,118,119].

5.2.2. Logistics and Delivery

In the logistics industry, multi-UAV collaborative operations can achieve rapid and efficient sorting and delivery of goods, especially suitable for dense urban areas and remote regions. UAV swarms can plan optimal routes based on real-time traffic and environmental data, collaboratively completing large-scale delivery tasks, reducing the impact of traffic congestion on delivery efficiency, and enhancing the overall efficiency of the logistics system [120,121,122].

5.2.3. Implementation Strategies

To ensure effective utilization and risk minimization when leveraging multi-UAV collaborative trajectory planning technology, businesses should adopt the following strategies:

• Continuously invest in R&D for UAV technology, especially in areas like collaborative planning, automation control, communication systems, and obstacle avoidance algorithms.
• Understand and comply with relevant laws and regulations, including legal restrictions on UAV flight, airspace management, and data protection laws. Regularly assess compliance in business activities to ensure all operations are within legal boundaries.
• Assess risks associated with UAV operations, including technical failures, data security, and privacy breaches, and develop corresponding risk management plans.
• Train employees in UAV operation skills to ensure they are familiar with the latest UAV technology and safety standards, and establish a professional UAV operation team, including pilots, data analysts, and maintenance technicians.
• Conduct market research to understand customer needs and industry trends to guide the application and development of UAV technology and services.
• Establish data protection policies and strengthen technical security measures for UAV systems to prevent hacking attacks and data breaches.

By implementing these strategies, businesses can not only effectively utilize multi-UAV collaborative trajectory planning technology to enhance operational efficiency but also maximize the commercial value and social impact of the technology while ensuring operational safety and compliance.

5.3. Academic, Research, and Industry Applications

In the academic, research, and industrial sectors, the application of multi-UAV collaborative trajectory planning technology is reflected in deepening research, promoting innovation, and enhancing education and training. This technology not only provides research institutions with a wealth of topics but also offers innovative solutions and business opportunities for enterprises, while opening new areas in higher education and vocational training.

5.3.1. Research Institutions

Research institutions primarily focus on the fundamental theories and technology development in multi-UAV collaborative trajectory planning. Existing research delves into the basic principles of UAV swarm collaborative control, such as distributed decision-making, collaborative navigation, real-time data processing, and communication protocols. Through simulation and experimental verification, they can identify and address key issues in technology implementation, providing theoretical and technical support for the safety, efficiency, and reliability of UAV collaborative operations.

5.3.2. Higher Education Institutions

Higher education institutions demonstrate their application in this field through education and talent cultivation. By offering related courses, such as UAV design, avionics, artificial intelligence, and robotics technology, universities provide students with systematic learning and practical opportunities. Moreover, colleges can collaborate with businesses and research institutions on actual research projects or case studies, enhancing students’ practical skills and innovative capabilities [123,124,125].

5.3.3. Enterprises

Enterprises primarily manifest their application of multi-UAV collaborative trajectory planning technology in product development and commercial services. UAV manufacturers and service providers utilize the latest research findings to develop more powerful, intelligent, and collaborative-capable UAV systems. These products and services are widely used in agriculture, forestry, construction, logistics, and security monitoring, helping enterprises to improve operational efficiency, reduce costs, and create new value [126,127,128].

5.3.4. Vocational Training

Vocational training institutions use multi-UAV collaborative trajectory planning technology to train professional UAV operators, maintenance technicians, and data analysts for society and enterprises. Through specialized courses and practical operation training, participants can acquire the necessary skills and qualifications to meet the industry’s demand for professional talent [129,130].

6. Conclusions and Future Direction

This paper reviews the current commonly used centralized control and distributed control path-planning algorithms, as well as heuristic algorithms, in the application and research progress of multi-UAV cooperative trajectory planning. This paper summarizes the advantages and disadvantages of various algorithms in multi-UAV trajectory planning applications.

Centralized control path-planning algorithms have global advantages. They provide optimal path-planning solutions, but they face high computational complexity when handling complex tasks, making it difficult to maintain real-time performance in large-scale applications.

Distributed control path-planning algorithms enhance system robustness and scalability by distributing computation and decision-making, better addressing single-node failures and adapting to large-scale applications. However, since each UAV makes decisions based only on local information, these algorithms struggle to guarantee a globally optimal solution.

Heuristic algorithms perform well in multi-UAV cooperative path planning by designing appropriate heuristic functions to effectively reduce computational complexity and improve planning efficiency, gradually approaching the optimal solution. However, their performance depends on the design of heuristic functions and parameter adjustments, requiring optimization for different scenarios.

Multi-UAV cooperative trajectory planning technology is widely applied in government, enterprises, and academia, presenting new challenges and opportunities. Governments enhance public service quality and emergency response capabilities by deploying multi-UAV systems; enterprises improve efficiency and reduce costs in precision agriculture, logistics delivery, and infrastructure inspection; academia and industry collaborate to deepen basic research, drive technological innovation, and train a large number of professionals through education and training. To promote the healthy development of this technology, relevant laws and regulations need to be formulated, policy support strengthened, technology research and application promoted, public education conducted, and international cooperation enhanced.

The collaborative trajectory planning technology of multiple unmanned aerial vehicles has broad development prospects in the future. To further enhance its intelligence, automation, and efficiency, future research should focus on the following directions.

• Develop more intelligent path-planning algorithms by combining reinforcement learning with existing optimization algorithms. Reinforcement learning can continuously improve strategies through continuous environmental interaction and feedback, enabling drones to achieve optimal path planning in dynamic environments, which will greatly enhance the flexibility and adaptability of the system. In addition, combining cutting-edge technologies such as artificial intelligence, machine learning, and computer vision with multi-drone trajectory planning can enhance the autonomous decision-making ability of drones. The use of computer vision technology for environmental perception and obstacle recognition, combined with machine learning algorithms for data analysis and path optimization, will significantly improve the autonomous decision-making level of drones in complex environments.
• Research a path-planning algorithm based on energy optimization, which optimizes flight paths and task allocation strategies to maximize the utilization of limited energy resources and extend the endurance of drone mission execution. Develop an energy management system to monitor and regulate the energy consumption of unmanned aerial vehicles in real-time, especially in long-term and large-scale tasks. Ensure the smooth completion of tasks through energy optimization algorithms. In addition, developing low-latency and high-reliability communication protocols and distributed collaborative decision-making mechanisms can enhance the rapid response and coordination capabilities of multiple unmanned aerial vehicle systems in complex tasks. Studying self-organizing networks among multiple drones to improve communication stability and efficiency will ensure efficient collaboration of the system in emergency rescue and disaster response.
• Strengthen the application and validation of multi-drone collaborative trajectory planning algorithms in practical scenarios, continuously optimize and improve the algorithms through on-site testing and data feedback. Large-scale and multi-scenario application testing will help collect actual operational data, analyze algorithm performance and shortcomings, and make targeted improvements and optimizations. In the fields of urban traffic management and large-scale monitoring, through repeated practice and improvement, the practical application effect and reliability of multi-drone systems can be improved.

In conclusion, multi-UAV cooperative trajectory planning technology has broad development prospects in the future. By combining theoretical research and practical application, it will continue to advance the intelligence, automation, and efficiency of multi-UAV cooperative operations, further expanding its applications in various fields.