Addressing Constraint Coupling and Autonomous Decision-Making Challenges: An Analysis of Large-Scale UAV Trajectory-Planning Techniques

Abstract

With the increase in UAV scale and mission diversity, trajectory planning systems faces more and more complex constraints, which are often conflicting and strongly coupled, placing higher demands on the real-time and response capabilities of the system. At the same time, conflicts and strong coupling pose challenges the autonomous decision-making capability of the system, affecting the accuracy and efficiency of the planning system in complex environments. However, recent research advances addressing these issues have not been fully summarized. An in-depth exploration of constraint handling techniques and autonomous decision-making issues will be of great significance to the development of large-scale UAV systems. Therefore, this paper aims to provide a comprehensive overview of this topic. Firstly, the functions and application scenarios of large-scale UAV trajectory planning are introduced and classified in detail according to the planning method, realization function and the presence or absence of constraints. Then, the constraint handling techniques are described in detail, focusing on the priority ranking of constraints and the principles of their fusion and transformation methods. Then, the importance of autonomous decision-making in large-scale UAV trajectory planning is described in depth, and related dynamic adjustment algorithms are introduced. Finally, the future research directions and challenges of large-scale UAV trajectory planning are outlooked, providing directions and references for future research in the fields of UAV clustering and UAV cooperative flight.

1. Introduction

With the rapid development of unmanned aerial vehicle (UAV) technology, the application of UAVs in logistics, agriculture, mapping, and other fields is becoming increasingly widespread [1,2,3]. UAV trajectory planning (UAV-TP) is one of the core technologies for UAV autonomous flight and mission execution, aiming to enable UAVs to efficiently and safely accomplish their missions in a variety of complex mission environments [4]. The UAV-TP system involves a number of key technologies, including obstacle avoidance, trajectory generation, and dynamic adjustment. Complex mission requirements and constraints make it necessary to comprehensively consider flight time, energy consumption, flight altitude, and changes in the external environment in the process of UAV-TP, and an effective flight trajectory not only improves the efficiency and accuracy of the UAV in performing the mission, but also ensures the safety of the UAV flight, reduces the consumption of resources, and reduces the risk of mission failure [5].

Different from UAV-TP, large-scale UAV trajectory planning (UAV-LSTP) systems focus on the coordinated control of multiple UAVs. UAV-LSTP should not only consider the differences in the performance of each UAV but should also improve the interaction and autonomous decision-making ability among them [6,7]. Therefore, the planning process must account for multiple factors, including real-time environmental awareness, constraint handling techniques, multi-objective optimization, dynamic trajectory adjustment, and autonomous decision-making. By considering these aspects, UAV-LSTP can significantly enhance the overall mission performance of UAVs operating in groups or formations. However, UAV-LSTP is also faced with many challenges. For example, the number of UAVs sharply increases, which not only increases the complexity of the decision space, but also causes the constraints of heterogeneous UAVs to be conflicting or coupled [8]. If constraint handling technology is not effectively used, the disruption of the flight path planning scheme will increase, and the collision risk between UAVs will increase.

Currently, to address these challenges, some researchers and scholars have adopted heuristic algorithms to integrate with UAV-LSTP, aiming to reduce the impact of constraint coupling on UAV mission execution. Heuristic algorithms such as particle swarm optimization and genetic algorithms can effectively perform global search under multi-dimensional constraints, and deal with constraint conflicts and performance differences among multiple UAVs through iterative optimization and global search in order to improve the overall efficiency of the system and the accuracy of trajectory planning [9,10]. These approaches are effective in reducing computational complexity when dealing with large-scale mission scenarios and provide stable solutions in real-time environments. Another group of researchers and scholars use intelligent algorithms to integrate with UAV-LSTP, aiming to improve autonomous decision-making among UAVs. For example, reinforcement learning is able to gradually optimize the decision-making strategy based on reward mechanisms and feedback signals, thus improving the adaptability and efficiency of the system [11,12,13]. Deep learning techniques, on the other hand, use deep neural networks to process and analyze large amounts of complex data to provide UAVs with deeper perception capabilities and decision support, enabling them to respond quickly and accurately to changes and challenges in various mission scenarios. However, while the integration of these approaches has brought significant technological advances and the ability to cope with complex missions for UAV-LSTP, it also faces further challenges in constraint processing techniques and the optimization requirements for autonomous decision-making strategies. In future UAV-LSTP research, there is a need to explore in depth how to better integrate various types of algorithms in order to improve the system’s level of intelligence and adaptability. Therefore, UAV-LSTP needs to be further discussed in terms of constraint processing techniques and autonomous decision-making.

In this paper, a comprehensive review of constraint handling techniques and autonomous decision-making for UAV-LSTP is presented. With multi-rotor UAV as the research object, the constraint handling techniques for UAV-LSTP are categorized from the perspective of mathematical models, and the UAV dynamic adjustment algorithms in autonomous decision-making are elaborated. To the best of our knowledge, there is no systematic summary of the research on this topic. The main contributions of this paper can be summarized as follows:

• In terms of UAV-LSTP classification: This paper proposes a new multi-dimensional classification method, which combines different planning approaches, realization functions and constraints to systematically classify UAV-LSTP. Incorporating constraints into the planning system analysis framework enhances the comprehensiveness and applicability of the classification method. The classification method is applicable to a wide range of environmental scenarios, which provides a basis for researchers to design more targeted optimization algorithms and planning schemes and enhances the flexibility and adaptability of the planning system.
• In terms of constraint handling techniques: this paper summarizes in detail the existing redundant constraint identification and streamlining algorithms, constraint prioritization techniques, as well as constraint fusion and conversion methods. By classifying and analyzing the performance of these techniques, it can improve the planning efficiency of the planning system and effectively reduce the redundancy and conflict of the trajectory planning scheme during the UAV-LSTP planning process, which provides a comprehensive basis for researchers to select and compare the constraint handling techniques.
• In terms of performance assessment of constraint handling techniques: This paper establishes a set of UAV-LSTP constraint handling technique assessment system, which covers the key indexes of constraint handling capability, computational efficiency, robustness and stability, and flexibility and adaptability. The system provides detailed assessment criteria to ensure the feasibility and performance reliability of constraint handling technology in practical applications. Through this evaluation system, researchers and scholars are able to measure and compare different constraint handling techniques more effectively.
• In terms of autonomous decision-making for UAV-LSTP: This paper explores the importance of autonomous decision-making in the planning process of UAV-LSTP, especially in dynamically changing mission environments. Autonomous decision-making mechanisms combining predictive modelling, environment awareness, adaptive control and machine learning algorithms are proposed to enable UAVs to adjust their planning schemes in real time under complex environments. By analyzing these techniques, this paper points out the importance of autonomous decision-making in enhancing mission adaptability and improving mission execution efficiency.

The framework of this paper is shown in Figure 1: Section 1 describes the basic concepts of UAV-LSTP. Section 2 describes the features and application scenarios of UAV-LSTP and categorizes the constraints. Section 3 describes the constraint handling techniques and performance evaluation metrics of UAV-LSTP. Section 4 explores the UAV-LSTP autonomous decision-making and dynamic adjustment algorithms. Section 5 suggests future research directions and challenges. Chapter 6 summarizes the paper.

2. Related Work

Based on the system engineering idea, this section firstly introduces the core features of UAV-LSTP comprehensively and analyses the requirements in various typical application scenarios. Then, the planning approach of UAV-LSTP is discussed in depth, covering the analysis of system functions from task assignment to trajectory optimization. Finally, the common constraints are classified and discussed at the level of strong and weak constraints, comprehensively sorting out the various types of factors affecting the performance of UAV-LSTP and providing a classification basis for the subsequent constraint handling techniques.

2.1. UAV-LSTP Characteristics and Requirements Analysis

2.1.1. Characteristics of UAV-LSTP

The features of UAV-LSTP can be categorized into several aspects, including multi-UAV coordination and communication, task allocation and scheduling, intelligent decision support, adaptivity and flexibility, and real-time performance and responsiveness. The multi-UAV coordination and communication function ensures that UAVs can efficiently interact with each other in terms of data to accomplish complex tasks [14]. The task allocation and scheduling function is concerned with efficiently assigning tasks and optimizing UAV trajectories and resource utilization [15]. Effective UAV trajectory planning relies on intelligent decision support systems for efficient and safe autonomous flight and mission execution. Adaptive and flexible features enable the system to adjust itself in changing environments in order to ensure successful mission accomplishment. Real-time performance and responsiveness ensures that the system can quickly respond to unexpected situations and instantly adjust the plan to ensure timely mission execution [16]. The features of UAV-LSTP are shown in Figure 2.

Multi-UAV Coordination and Communication: UAV-LSTP requires efficient communication and coordination mechanisms to prevent collisions and interference among large-scale UAVs [17,18]. By using advanced wireless communication technologies and self-organizing network protocols, UAVs are able to share position information, mission status, and environmental data in real time and coordinate flight trajectories and mission assignments. This not only improves the efficiency and accuracy of mission execution but also enhances the overall safety and reliability of the system, ensuring that each UAV can efficiently and safely accomplish its missions in complex environments.

Task allocation and scheduling: In the process of UAV-LSTP, it is crucial to reasonably allocate and schedule tasks. Tasks need to be dynamically assigned based on the priority, urgency, and status of each UAV in order to improve the efficiency and overall effectiveness of task execution [19,20,21]. First, the planning system categorizes and orders all tasks. Then, considering the current status of each UAV, including power, load capacity, and location, the planning system reasonably assigns the tasks to the UAVs. In contrast, the dynamic scheduling mechanism records the progress of the tasks and the status of the UAVs in real time during the task execution process, and it reallocates and adjusts the tasks when necessary to ensure the maximization of resource utilization and the task completion rate.

Intelligent decision support: UAV-LSTP often integrates artificial intelligence and machine learning techniques for smarter trajectory selection and decision support [22,23,24]. These technologies can provide more accurate flight trajectories based on historical data and real-time feedback. By analyzing a large amount of historical flight data and mission execution records, machine learning algorithms are able to identify the optimal trajectory strategy and help UAVs select more efficient flight trajectories during missions. In addition, AI technology can process sensor data and environmental changes in real time, making quick responses and adjustments to unexpected situations in order to ensure smooth mission execution. UAV-LSTP can also combine weather forecasts, geographic information, and traffic data to optimize resource allocation and scheduling in order to avoid potential risks and obstacles.

Adaptability and flexibility: Complex mission environments demand that UAVs be highly adaptive, capable of making real-time adjustments based on environmental changes. Facing varied terrain, weather conditions, and unexpected events, UAVs must quickly recognize and adapt autonomously [25]. Through advanced sensors and environment sensing technologies, UAVs are able to collect data from the surrounding environment in real time. Combined with artificial intelligence and machine learning algorithms, UAVs can autonomously analyze these data and dynamically adjust their flight trajectories to cope with unexpected weather changes, unexpected obstacles, and other unforeseen situations. In addition, adaptive UAV-LSTP is able to flexibly adjust the task allocation according to the mission requirements and UAV status in order to improve the efficiency of mission execution [26].

Real-time performance and responsiveness: Compared with a single UAV, UAV-LSTP requires more consideration of UAV decision-making capabilities and responsiveness [27]. To achieve this goal, planning systems are usually equipped with high-performance processors and advanced sensors. Through UAVs’ fast data processing and analysis, UAV-LSTP is able to make decisions at the millisecond level [28]. In addition, the real-time communication network ensures information synchronization between a UAV and the ground control center, as well as other UAVs, enabling the UAV cluster to respond to unexpected events in a coordinated manner. Real-time performance and response speed are important indicators in UAV-LSTP.

2.1.2. Typical Application Scenarios and Requirements Analysis

UAV-LSTP is currently widely used in a variety of scenarios, including environmental monitoring, agricultural monitoring, logistics and distribution, disaster relief, and infrastructure inspection. These application scenarios are shown in Figure 3.

Environmental monitoring: UAV-LSTP is commonly used for forest fire monitoring, atmospheric pollution monitoring, and marine environment monitoring to provide real-time surveillance and data acquisition over a wide area through large-scale UAV collaboration [29,30,31]. For environmental monitoring missions, UAV-LSTP requirements mainly include efficient coverage of a wide area, real-time data acquisition, and multi-level monitoring capabilities. For example, in forest fire monitoring, UAV clusters can quickly capture the fire spreading dynamics and assist managers to develop emergency rescue plans. The mission requirement for UAV-LSTP in this type of mission lies in the ability to transmit high-resolution images and dynamic data in real time. In atmospheric pollution monitoring, UAVs need to collect air quality data collaboratively at different altitudes and regions to support the precise location and rapid control of pollution sources [32]. Such mission requirements for UAV-LSTP include high flexibility, capability of vertically distributed data acquisition, and sensor diversity. Marine environment monitoring, on the other hand, requires UAVs to collaborate in the continuous tracking of ocean temperature, salinity, and pollutant dispersion to provide timely decision-making basis for ecological protection [33], at which time the demand for UAV-LSTP is long endurance and wide-area coverage.

Agricultural monitoring: UAV-LSTP applications in agriculture include tasks such as farmland inspection, crop monitoring and precision fertilizer application, which require UAV collaboration to significantly improve the efficiency and quality of agricultural production. In farmland inspection, UAV-LSTP is required to efficiently cover a wide range of farmland and quickly identify pests and diseases, soil moisture, and crop health, and timely feedback this information to managers [34]. For crop monitoring, UAVs equipped with multispectral and thermal imaging cameras can monitor the growth stages and health status of crops to help farmers make scientific decisions, which requires UAV-LSTP to have accurate data collection capabilities and intelligent analysis support. For precise fertilizer application, UAVs can spot-drop fertilizer according to the real-time needs of crops, which requires UAV-LSTP to include precise path planning and effective task allocation [35] to ensure efficient use of resources and environmental protection.

Logistics and distribution: in logistics and distribution scenarios, UAV-LSTP is used for efficient and fast material delivery, such as e-commerce delivery and emergency transport of medical materials. Logistics missions require UAV clusters to be able to accurately navigate from a warehouse center to a user-specified location for same-day or even hourly delivery [36], which places the mission requirements on UAV-LSTP in terms of route planning accuracy, mission scheduling flexibility, and the ability to collaborate to efficiently complete multiple tasks. For the transport of emergency medical supplies, UAV clusters need to be able to respond quickly to deliver urgently needed medicines and rescue supplies to their destinations in the event of a public health emergency or disaster, which places a demand on UAV-LSTP for efficient emergency response and dynamic mission requirements [37].

Disaster rescue: after natural disasters such as earthquakes and floods, the demand for UAV-LSTP focuses on rapid deployment, real-time monitoring, search and rescue, and material delivery. Disaster rescue missions require UAV clusters to be able to quickly arrive at the affected area, assess the disaster situation through high-resolution cameras and thermal imaging equipment, and help the rescue command center make timely decisions [38]. In addition, SAR missions in complex terrains and hazardous environments impose high sensitivity sensors and precise positioning requirements on UAV-LSTP to improve SAR efficiency and success rate. In terms of material delivery, UAV clusters need to quickly transport rescue materials to the disaster area to ensure the timely supply of materials [39], and this mission requirement for UAV-LSTP is the ability of dynamic task allocation, path optimization and collaborative execution. In addition, in the post-disaster reconstruction phase, UAV clusters also need to perform detailed geographic information acquisition and 3D modelling, which requires UAV-LSTP to have the ability of high-precision data acquisition and multi-machine coordination.

Infrastructure inspection: the needs of UAV-LSTP in infrastructure inspection are mainly in the form of long endurance, fine inspection capability and flexible multi-UAV collaboration. For power line inspections, UAV clusters are required to perform detailed inspections of long-distance power lines to detect insulator and conductor damages, which puts demands on UAV-LSTP for high-precision navigation and continuous monitoring capabilities [40]. The mission requirement for inspection of structures such as bridges and tunnels, on the other hand, requires UAVs to be able to enter narrow spaces and capture details through high-definition cameras, which puts a demand on the UAV system for high maneuverability and high-resolution image acquisition [41]. In pipeline and oil pipeline inspections, UAVs need to fly along the pipelines to monitor their surface conditions and detect possible leaks and corrosion, which demands UAV-LSTP in terms of path-tracking accuracy and monitoring capabilities. In addition, the mission requirement of UAV-LSTP in network coverage assessment is reflected in signal strength monitoring and optimization of base station layout, which requires UAVs to collaborate and efficiently complete the mission in order to improve the quality of service of the communication company’s network [42].

2.2. Analysis of UAV-LSTP Planning Approach and System Functions

UAV-LSTP can be classified according to the planning approach and system functionality. In terms of planning approach, it is mainly classified into global planning method, local planning method and trajectory tracking [43]. In terms of system functions, it can be classified into offline static trajectory planning, online dynamic real-time trajectory planning, unconstrained and constrained trajectory planning [44,45].

2.2.1. Classification by Planning Method

1.

Global planning method

Global planning refers to the generation of flight trajectories from the starting point to the endpoint within the entire mission area using UAV-LSTP, considering all known environmental information and constraints, such as obstacles, flight altitude restrictions, and mission requirements. The goal of global planning is to identify trajectories that ensure flight safety and efficiency. Commonly used methods include the heuristic-search-based A* algorithm [46], which identifies the optimal trajectory by evaluating trajectory costs. The Dijkstra algorithm [47] identifies the shortest trajectory by gradually expanding the path. Various optimization algorithms, such as the genetic algorithm (GA) [48] and particle swarm optimization (PSO) [49], simulate natural evolution and swarm behavior to optimize trajectory planning. These methods comprehensively consider environmental factors and mission requirements to generate optimal flight trajectories that avoid obstacles while satisfying all altitude restrictions and mission needs. Morshed Alam and Moh et al. [50] explored the joint optimization problem of trajectory control, task offloading and resource allocation in an integrated air-ground network. The article proposed a new global optimization model to improve the efficiency of mission processing and efficiently utilize the network resources, which provides an effective solution for the collaboration between UAVs and ground-based networks. Alam et al. [51] conducted an extensive review of the multi-UAV networks with an extensive review of topology control algorithms, analyzing the performance of different algorithms in maintaining network connectivity, stability, and energy efficiency in dynamic environments, the importance of the global network control approach and its potential application in UAV mission execution.

2.

Local planning method

Local planning involves dynamically adjusting and avoiding obstacles based on real-time environmental information during the UAV’s flight. Local planning focuses on short-term trajectory adjustments to ensure that the UAV can safely avoid new obstacles or unexpected situations. Common local planning methods include the artificial potential field (APF) method [52], which guides the UAV to avoid obstacles by simulating attractive and repulsive forces. The dynamic window approach (DWA) [53] calculates the optimal obstacle avoidance trajectory while considering the UAV’s speed and acceleration constraints. The rapidly exploring random tree (RRT) method [54] generates feasible trajectories through random sampling. Local planning emphasizes real-time responsiveness to enhance the safety of UAV-LSTP flight trajectories. Xing et al. [55] proposed an improved MATD3 algorithm based on deep reinforcement learning, focusing on local trajectory planning for multi-UAV adaptive collaborative formation. The algorithm focuses on the local collaboration among multiple UAVs and adjusts their flight paths through real-time decision-making, which reflects the characteristics of local planning method, especially in dynamic environments, showing strong adaptability and flexibility.

3.

Trajectory tracking

In UAV-LSTP, trajectory tracking is also an important technology. Trajectory tracking refers to the UAV’s ability to fly precisely along a predefined path or trajectory during its flight [56]. This technology involves more than simple waypoint navigation; it requires the UAV to adjust its flight attitude and speed based on complex trajectory information and environmental conditions to ensure the accuracy of the flight path. In UAV-LSTP applications, trajectory tracking technology enables multiple UAVs to fly collaboratively in the air, avoiding collisions through high-precision navigation and control systems. This capability is especially crucial for applications requiring ex-tensive monitoring, efficient resource allocation, or complex task coordination. Through advanced algorithms and real-time data processing, UAV-LSTP can execute complex trajectory tracking in various mission scenarios [57]. Emami et al. [58] investigated a mean-field based resource allocation method in a multi-intelligent body UAV system, focusing on minimizing information latency. The study demonstrates how intelligent resource allocation and task planning can effectively reduce the information delay in the UAV network, improve the overall performance of the network, and ensure that the UAVs can effectively track the dynamic paths in mission execution.

2.2.2. Analysis of System Functions

1.

Offline Static Trajectory Planning

Offline static trajectory planning is a method of pre-planning and optimizing UAV-LSTP flight trajectories. In this planning approach, the UAV’s flight path is fully determined before execution. First, based on mission requirements and environmental characteristics, the trajectory planning algorithm generates a detailed flight path that includes key waypoints and trajectory segments. These waypoints can specify parameters such as the UAV’s flight altitude, speed, and turning radius [59]. The advantage of offline static trajectory planning lies in its ability to plan complex tasks and flight paths in advance, improving mission completion efficiency through algorithmic optimization. This method is suitable for situations requiring extensive coverage or where the planning environment is well known, such as land surveying and resource management [60]. Offline static trajectory planning effectively reduces in-flight risks and is conducive to data collection and mission execution.

2.

Online Dynamic Real-Time Trajectory Planning

Online dynamic real-time trajectory planning is a method of adjusting UAV-LSTP flight paths in real time based on immediate environmental and mission needs. Compared with traditional static planning, this method is more flexible and responsive, allowing for dynamic adjustments based on real-time data and environmental changes [61]. In online dynamic real-time trajectory planning, the UAV continuously acquires and analyzes sensor data (such as GPS, vision, and radar data) to assess the surrounding environment in real time. Based on these real-time data, the trajectory planning algorithm can dynamically adjust the UAV’s flight path and attitude to avoid obstacles, respond to wind speed changes, or adjust flight speed [62]. This capability enables UAVs to safely execute missions in complex environments.

3.

Unconstrained and constrained trajectory planning

Unconstrained UAV-LSTP aims to optimize the UAV’s flight trajectory in open spaces, primarily focusing on minimizing trajectory length or flight time without specific constraints such as obstacles or altitude restrictions. This type of planning provides researchers with an ideal experimental platform to evaluate and optimize the fundamental performance and effectiveness of trajectory planning algorithms. It is also suitable for examining the performance of the UAV. By eliminating interference from complex environments, unconstrained UAV-LSTP allows researchers to focus on the development and improvement of planning algorithms, verifying their performance in identifying optimal trajectories. This approach not only aids in the initial validation and adjustment of algorithms, but also provides important references for more complex trajectory planning with added constraints. Constrained UAV-LSTP deals with complex environmental conditions and constraints, such as buildings in urban areas, airspace management restrictions, and mission requirements. This planning approach needs to comprehensively consider various limiting factors in the environment to ensure that the UAV can complete its mission safely and efficiently [63,64,65]. By integrating intelligent optimization algorithms, constrained planning can adjust the UAV’s flight trajectory in real time based on updated environmental information, avoiding collisions and violations of flight regulations. Additionally, constrained planning must consider factors such as the UAV’s energy consumption, flight time, and mission priorities to achieve optimal task execution. This complex planning process not only enhances the autonomy and reliability of UAV systems but also enables them to adapt to various complex and dynamic mission requirements.

2.3. Classification by Constraints

In UAV-LSTP, the interaction of and dynamic changes in various constraints, including geometric, dynamic, mission, environmental, resource, and safety constraints, pose significant challenges to trajectory planning. To ensure that UAVs can complete their missions efficiently and safely, it is crucial to accurately handle and optimize these constraints. This not only enhances the feasibility and reliability of the planned trajectories but also optimizes resource utilization and improves overall mission execution efficiency. We classify the constraints involved in UAV-LSTP into strong constraints and weak constraints.

2.3.1. Strong Constraints

In UAV-LSTP, strong constraints refer to mandatory conditions that must be strictly met, such as obstacle avoidance, flight altitude, and no-fly zones. These constraints directly impact the mission’s success and the UAV’s safety. The principles for handling strong constraints typically involve either embedding the constraints into the planning algorithm to ensure that any generated trajectories comply with the requirements or introducing penalty terms into the objective function to reduce the likelihood of violating solutions, thus guiding the optimization process to meet these constraints. Additionally, handling strong constraints may involve dynamically adjusting the flight trajectory to respond to unexpected situations and environmental changes, further ensuring the UAV’s safety and the successful completion of the mission. These methods combine algorithmic precision and flexibility to ensure that UAVs can execute tasks efficiently and safely in complex environments. The nature of strong constraints is shown in

Table 1. Nature, functions, and references of strong constraints.

Type	Nature	Function	Reference
Strong constraint	Cannot be violated and directly determine mission success	- Ensure flight safety - Ensure flight safety - Satisfy physical performance constraints	[66]
Physical constraint	Vehicle speed, altitude, etc.	Limit the maximum speed, minimum turning radius, altitude, etc. of the UAV in the air	[67]
Safe Obstacle Avoidance	Safe distance between UAV and from obstacles	Avoiding collisions and ensuring the safety of UAV and other flying vehicles	[68]
Communication and control limitation	Ensure that the UAV can receive control commands	Ensure real-time communication with the control center during the mission	[69]

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2.3.2. Weak Constraints

In UAV-LSTP, weak constraints refer to conditions that can be relaxed or optimized to a certain extent, such as trajectory smoothness, energy consumption, and communication quality. These constraints further optimize the trajectory quality while ensuring that the strong constraints are met. The principles for handling weak constraints typically involve incorporating them into the objective function, where optimization algorithms strive to improve these additional conditions while satisfying the strong constraints, thereby achieving a balance among objectives. For example, when planning a trajectory, the algorithm can aim to select the path with the lowest energy consumption or ensure the smoothest trajectory to reduce mechanical wear on the UAV, all while meeting strong constraints such as obstacle avoidance and no-fly zones. Additionally, weak constraints can be addressed through multi-objective optimization algorithms, allowing for different optimization goals to be balanced, thus identifying the optimal trajectory under various conditions. The nature of weak constraints is shown in

Table 2. Nature, functions, and references of weak constraints.

Type	Nature	Function	Reference
Weak constraint	Can be flexibly adjusted and ignored under certain conditions	- Increase flexibility in task scheduling - Balancing mission priorities in conflicts	[70]
Time window	Start time and end time adjustment allowed	Adjustment is allowed within the characteristic time	[71,72]
Mission priority	Some minor missions can be postponed	Adjustment of low priority missions in case of multiple missions to optimize resource use	[73]

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The classification of specific UAV-LSTP strong and weak constraints is shown in Figure 4.

3. Constraint Handling Technique

This section first introduces several common constraint handling techniques. Then, it discusses UAV-LSTP constraint handling from three aspects: identifying and simplifying redundant constraints, prioritizing constraints, and integrating and transforming constraints. Finally, it covers the performance metrics used to evaluate constraint handling techniques.

3.1. Real-Time Constraint Handling Techniques in UAV-LSTP

The real-time constraint handling techniques in UAV-LSTP encompass a variety of methods, and they can be primarily categorized into explicit and implicit constraint handling techniques. Explicit constraint handling includes constraint satisfaction problems (CSPs) [74] and mixed-integer linear programming (MILP) [75]. Implicit constraint handling includes the penalty function method [76] and the Lagrange multiplier method [77]. Optimization-based constraint handling techniques can be divided into heuristic algorithms and metaheuristic algorithms [78]. Heuristic algorithms include the A* algorithm [79] and heuristic search algorithms [80]. Metaheuristic algorithms include genetic algorithms (GAs) [81] and particle swarm optimization (PSO) [82]. Model-based constraint handling techniques can be divided into dynamic programming (DP) and Markov decision processes (MDPs) [83]. Dynamic programming methods include the Bellman equation [84]. Markov decision processes include value iteration and policy iteration. Machine-learning-based constraint handling techniques [85] can be divided into supervised learning and reinforcement learning. Supervised learning includes neural networks [86], and reinforcement learning includes Q-learning [87] and deep reinforcement learning [88]. The combination of these techniques can significantly enhance the efficiency and accuracy of constraint handling in UAV-LSTP, as shown in Figure 5.

3.1.1. Redundant Constraint Identification and Simplification

This section analyzes three constraint handling techniques from a mathematical model perspective: redundant constraint identification and simplification, constraint prioritization, and constraint integration and transformation.

1.

Redundant constraint identification

In the process of UAV-LSTP, the number of constraints can sharply increase with task complexity, some of which may be redundant, meaning that they do not affect the solution, but add computational complexity. Therefore, identifying and handling these redundant constraints is a crucial step in optimizing the trajectory planning process. By effectively identifying and removing redundant constraints, the computational load can be significantly reduced, enhancing the efficiency and performance of the algorithm, thereby enabling UAVs to generate optimal trajectories more quickly [89]. Additionally, reducing redundant constraints helps to avoid unnecessary computational overhead, optimize resource utilization, and further improve the responsiveness and stability of UAV-LSTP.

The constraint identification methods in UAV-LSTP include a linear dependency analysis between the constraints, a geometric feasibility domain analysis of constraint sets, and optimization relaxation methods. The linear dependency analysis method involves constructing a constraint matrix and calculating its rank to identify redundant constraints using techniques such as Gaussian elimination or QR decomposition. The geometric feasibility domain analysis approach involves constructing a geometric representation of the constraints, computing their convex hull, and detecting internal constraints to identify redundancies from a geometric perspective. The optimization relaxation method involves relaxing each constraint one by one, constructing a relaxed optimization problem, and solving it for the relaxed variables. Constraints for which the relaxed variables are greater than zero are assessed to determine whether they are redundant. When used in combination, these methods can effectively simplify the constraint set, reduce computational complexity, and improve the optimization performance of trajectory planning [90]. Specific methods for identifying redundant constraints are summarized in

Table 3. Methods for identifying redundancy constraints.

Linear correlation analysis between constraints	Calculate the rank of the constraint matrix A: $\lambda =rank(\mathrm{A})=r$. If the number of constraints m exceeds the rank r of the matrix, there is a redundancy constraint. Specific redundancy constraints can be found using methods such as Gaussian elimination or QR decomposition. QR decomposition decomposes matrix A into orthogonal matrix Q and upper triangular matrix R:$\mathrm{A}=\mathrm{QR}$.        $\mathrm{R}=\left[\begin{array}{cccc}{r}_{11}& r_{13}& \dots & r_{1n}\\ 0& r_{22}& \dots & ⋮\\ ⋮& ⋮& \ddots & ⋮\\ 0& 0& \dots & r_{nn}\end{array}\right]$ If $r_{ii}=0$ exists, the corresponding constraints are redundant.
Geometric feasible domain analysis of constraint sets	Construct geometric representations: combine the geometric representations of all constraints to form a polyhedron or convex polygon. For linear constraints, these geometric representations are typically half-space. Solve the convex hull for the constraint set $\{{\mathrm{A}}_1,{\mathrm{A}}_2,\dots ,{\mathrm{A}}_m\}$, and calculate its convex hull H: $H=\mathrm{conv}({\mathrm{U}}_{i=1}^m\{\left.x\right|{\mathrm{A}}_i\mathrm{x}\le {\mathrm{b}}_i\})$. Geometrically determine which constraints are inside a convex hull, and if all solutions for a constraint are inside a convex hull, the constraint is redundant.
Optimized relaxation method	For each constraint ${\mathrm{A}}_i\mathrm{x}\le {\mathrm{b}}_i$, construct the relaxation optimization problem:          $\begin{array}{l}\min {\epsilon }_i\\ {\mathrm{subject} \mathrm{to} \mathrm{A}}_j\mathrm{x}\le {\mathrm{b}}_j,\forall j\ne i\\ {\mathrm{A}}_i\mathrm{x}\le {\mathrm{b}}_i+{\epsilon }_i\end{array}$ Solve the above optimization problem to obtain the optimal relaxation variable ${\epsilon }_i^{*}$. Determine whether there is redundancy: If ${\epsilon }_i^{*}>0$, then ${\mathrm{A}}_i\mathrm{x}\le {\mathrm{b}}_i$ indicates redundancy.

Note: ${\mathrm{A}}_i$ is the coefficient matrix of $1\times n$, x is the decision variable vector of $n\times 1$, and ${\mathrm{b}}_i$ is the constant vector. $\mathrm{A}$ is the coefficient matrix of $m\times n$, and $\mathrm{b}$ is the constant vector of $m\times 1$. $r$ is the number of linear independent rows. ${\epsilon }_i$ is the relaxation value, and ${\epsilon }_i^{*}$ is the optimal relaxation value.

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2.

Constraint set simplification

In UAV trajectory planning, the goal of simplifying the constraint set is to reduce the computational complexity by identifying and removing redundant or unnecessary constraints, thereby enhancing optimization efficiency and algorithm performance. This approach not only increases solution speed, but also reduces memory usage, improves overall system reliability, and increases response speed, ultimately enabling UAVs to complete tasks more efficiently and adapt to dynamically changing environments.

Heuristic-based large-scale UAV trajectory planning simplification methods utilize heuristic rules and experience to identify and eliminate redundant constraints. These heuristic methods typically exhibit high computational efficiency and strong practical applicability. They can be categorized as follows: distance-based heuristic methods—these methods identify redundant constraints by calculating the distances between constraints [91]; importance-based heuristic methods—these methods identify redundant constraints by evaluating the importance of each constraint to the optimization problem; clustering-based heuristic methods—these methods perform a clustering analysis on constraints to identify similar or redundant constraints [92]. These methods can effectively reduce computational complexity, improving the performance and efficiency of optimization algorithms. Specific methods for constraint simplification are summarized in

Table 4. Streamlining methods based on heuristics.

Distance-based heuristics	● Represent all linear constraints in matrix form: $\mathrm{Ax}\le \mathrm{b}$ ● Calculate the distances ${\mathrm{A}}_i\mathrm{x}\le {\mathrm{b}}_i$ and ${\mathrm{A}}_j\mathrm{x}\le {\mathrm{b}}_j$ between constraints, which can be carried out using the following formula: $d_{ij}=‖{\mathrm{A}}_i-{\mathrm{A}}_j‖$ ● The Euclidean norm is defined as follows: $‖{\mathrm{A}}_i-{\mathrm{A}}_j‖=\sqrt{{{\displaystyle {\sum }_{k=1}^n(a_{ik}-a_{jk})}}^2}$ ● Set a distance threshold Set a distance threshold ε. When the distance between two constraints is less than the threshold, the constraint can be refined. ● Remove redundant constraints Traverse all constraints to $(i,j)$ and remove one of the redundant constraints if $d_{ij}<ϵ$.
Importance-based heuristics	● Measure the importance of a constraint by calculating the Lagrange multiplier for each constraint: $L(\mathrm{x},\lambda )=c^T\mathrm{x}+{\lambda }^T(\mathrm{Ax}-\mathrm{b})$   $\lambda ={[{\lambda }_1,{\lambda }_2,\dots ,{\lambda }_m]}^T$ is the Lagrangian multiplier vector. ● Obtain the Lagrange multiplier ${\lambda }_i$ for each constraint, which reflects the importance of the constraint. Set the importance threshold τ and iterate through all constraints. If the importance of a constraint is less than the threshold τ, the constraint is deleted.
Cluster-based heuristics	● Set the number of clusters K to divide the constraint into K clusters. ● Initialize K clusters: ${\mu }_1,{\mu }_2,\dots {\mu }_k$ ● $\mathrm{For} \mathrm{each} \mathrm{constraint} {\mathrm{A}}_i$, calculate its distance to each cluster center and assign it to the nearest cluster center. ● Update the center of each cluster to the mean of all constraints in the cluster: ${\mu }_k={\displaystyle \frac{1}{\left|C_k\right|}}{\displaystyle {\sum }_{{\mathrm{A}}_i\in C_k}{\mathrm{A}}_i}$ ● For each cluster, select a representative constraint (usually the one closest to the center of the cluster); the rest are considered redundant constraints and can be removed.

Note: $‖ \cdot ‖$ denotes the Euclidean norm of the vector. $a_{ik}$ and $a_{jk}$ represent the elements in column $k$ in matrices ${\mathrm{A}}_i$ and ${\mathrm{A}}_j$, respectively. $C_k$ represents k clusters, and $\left|C_k\right|$ represents the number of constraints in k clusters.

.

3.1.2. Constraint Prioritization

In UAV-LSTP, constraint prioritization is an effective method for handling constraint conditions [93]. The basic principle involves assigning different priorities to each constraint condition and gradually satisfying these constraints based on their priorities to ensure that critical constraints are addressed first. This approach effectively manages various constraints, such as obstacle avoidance, flight time limits, and mission waypoint sequencing during complex trajectory planning, thereby avoiding conflicts and contradictions. Moreover, priority settings can be dynamically adjusted according to specific mission requirements in order to flexibly adapt to different planning scenarios. In practical applications, constraint prioritization methods can be combined with heuristic and meta-heuristic algorithms to further enhance trajectory planning efficiency and effectiveness through optimized solutions. The steps for determining constraint prioritization are as follows:

1.

Determining constraint types and classification

Firstly, categorize all constraint conditions into different categories. Common classifications include the following:

• Geometric constraints: obstacle avoidance constraints, trajectory smoothing constraints, etc.
• Dynamic constraints: maximum speed, acceleration, turning radius, etc.
• Mission constraints: mission waypoint sequencing, flight time limits, etc.
• Environmental constraints: weather conditions, no-fly zones, etc.

2.

Determining constraint importance

Evaluate the importance of each type of constraint to establish its priority in trajectory planning. The evaluation can be based on several factors:

• Safety: constraints ensuring flight safety (e.g., obstacle avoidance and no-fly zone constraints) typically have the highest priority.
• Mission requirements: constraints directly related to mission completion (e.g., waypoint sequencing and time limits) follow in priority.
• Flight performance: constraints affecting flight performance (e.g., speed and acceleration limits) are given higher priority.
• Environmental adaptation: constraints requiring adaptation to environmental changes (e.g., weather conditions) have slightly lower priority.

3.

Quantitative evaluation and ranking

Quantitatively assess and rank the constraints using various methods:

• Weight method: assign a weight to each constraint, reflecting its importance; the sum of the weights equals 1.
• Analytic hierarchy process (AHP): compare constraints by constructing judgment matrices to compute the relative weights for each constraint.
• Fuzzy comprehensive evaluation method: use fuzzy logic to evaluate constraints fuzzily and calculate comprehensive scores.

4.

Determining priority order

Based on the results of the quantitative evaluation, prioritize the constraints. High-priority constraints are considered first in the trajectory planning process, while lower-priority constraints are optimized after satisfying higher-priority constraints.

5.

Dynamic adjustment and optimization

In the actual trajectory planning process, dynamically adjusting the priority of constraints based on real-time conditions is crucial. For example, during flight, if new obstacles or environmental changes are detected, it may be necessary to adjust the priority of avoidance constraints to ensure that the UAV can safely maneuver around obstacles. Simultaneously, as the mission progresses, constraints such as task point visitation sequence and flight time limits may also need reevaluation and adjustment to accommodate new flight paths and environmental changes. This dynamic adjustment mechanism enhances the flexibility and adaptability of UAV trajectory planning, ensuring that optimal trajectories are consistently identified in complex and changing environments. This ultimately improves the success rate and safety of mission execution.

A diagram of the process of UAV-LSTP based on constraint priority sorting is shown in Figure 6.

3.1.3. Constraint Fusion and Transformation

Unlike constraint prioritization, constraint fusion and transformation are designed to synthesize different types of constraints to ensure that the planned trajectory can meet them [94]. These constraints may include obstacle avoidance constraints, trajectory smoothing constraints, time-of-flight restrictions, mission point access sequences, and maximum velocities and accelerations. By standardizing the representation of these constraints, they can be effectively integrated into the comprehensive objective function. In order to further optimize the solution, it is also possible to introduce relaxation variables and adopt the form of weighted sums, penalty functions, and Lagrangian multiplier methods. Through these means, the effective fusion of constraints can be realized so as to identify the best trajectory for the UAV in a complex environment. This method not only improves the efficiency of trajectory planning, but also enhances the flexibility and reliability of the UAV in performing tasks. The steps to achieve constraint fusion and transformation are as follows:

1.

Uniform constraint representation

Different types of constraints are converted into a unified mathematical form for comprehensive processing. Common methods include the following:

• Standardized representation: converts all constraints into standard linear or nonlinear inequalities or forms of equations.
• Relaxation variable introduction: for strict constraints, introduces relaxation variables and converts them into a more manageable form.

2.

Construct a comprehensive objective function

In trajectory planning, it is not only necessary to meet all constraints, but also to optimize a certain target (e.g., trajectory length, flight time, and energy consumption). Thus, a comprehensive objective function is constructed.

$$\begin{array}{l}\min f(x)\\ \mathrm{subject} \mathrm{to} g_i\left(x\right)\le 0, i=1,2,\dots ,m\\ h_j\left(x\right)=0, j=1,2,\dots ,p\end{array}$$

(1)

Here, $x$ represents the decision variable in the optimization problem, which is usually a vector. $f(x)$ is the objective function. $g_i\left(x\right)$ represents the inequality constraint function, and $i$ represents the $i$th inequality constraint. $h_j\left(x\right)$ represents the equality constraint function, and $j$ represents the first $j$ inequality constraint. $m$ is the number of inequality constraints, and $p$ is the number of equality constraints.

3.

Convergence of constraints

By introducing a penalty function or a Lagrangian multiplier, the constraints are fused into the objective function. Common methods include the following:

• Penalty function method:

$$\min \Phi (x)=f(x)+{\displaystyle {\sum }_{i=1}^m{a}_i\max {(0,g_i(x))}^2+}{\displaystyle {\sum }_{j=1}^p{\beta }_j{h}_j{(x)}^2}$$

(2)

Here, $\Phi (x)$ represents the objective function with a penalty function, and $a_i$ and ${\beta }_j$ represents the penalty parameters. $\max {(0,g_i(x))}^2$ only penalizes the part that violates the constraint, and if $g_i(x)\le 0$, the penalty value is 0.

• Lagrange multiplier method: the Lagrange multiplier is introduced to add constraints directly to the objective function.

$$L(x,\lambda ,\mu )=f(x)+{\displaystyle {\sum }_{i=1}^m{\lambda }_i{g}_i(x)+}{\displaystyle {\sum }_{j=1}^p{\mu }_j{h}_j(x)}$$

(3)

Here, $L(x,\lambda ,\mu )$ denotes the Lagrangian function. ${\lambda }_i$ and ${\mu }_j$ denote the Lagrange multipliers. ${\displaystyle {\sum }_{i=1}^m{\lambda }_i{g}_i(x)}$ denotes the linear combination of the constraint function $g_i(x)$, and ${\displaystyle {\sum }_{j=1}^p{\mu }_j{h}_j(x)}$ denotes the linear combination of the constraint function $h_j\left(x\right)$.

4.

Optimize the solution

Appropriate optimization algorithms are used to solve the comprehensive objective function. Common optimization algorithms include the following:

• Linear programming (LP) and integer linear programming (ILP): for linear constraints and objective functions.
• Nonlinear programming (NLP): applicable to nonlinear constraints and objective functions.
• Mixed-integer nonlinear programming (MINLP): deals with complex constraint problems with both discrete decision variables and continuous variables.
• Heuristics and meta-heuristics: includes the genetic algorithm (GA), particle swarm optimization (PSO), and simulated annealing (SA), which are suitable for complex and multi-objective optimization problems.

A flowchart of UAV-LSTP based on constraint fusion and transformation is shown in Figure 7.

3.2. Performance Evaluation of Constraint Handling Technique

To ensure the effectiveness and robustness of constraint handling techniques in UAV-LSTP, it is essential to first consider the diversity and complexity of constraint conditions across different flight environments and mission requirements. Second, algorithms should be evaluated to assess the computational efficiency of constraint handling techniques, ensuring that they can provide optimal UAV-LSTP solutions within a reasonable timeframe. Additionally, robustness in handling uncertainty and unexpected scenarios should be examined to ensure stable operation in complex and dynamic UAV-LSTP environments. A comprehensive evaluation from these perspectives enhances the overall capability of UAV trajectory planning technology. Specific metrics include the following:

• Constraint handling capability: The performance of constraint handling techniques should be evaluated under various coupled constraint conditions through simulations of different mission environments. This involves setting up complex obstacle layouts to test the effectiveness of constraint handling, assessing UAV flight smoothness through trajectory smoothing, and evaluating UAV-LSTP efficiency under time constraints by limiting flight time. Additionally, it is essential to assess the performance of constraint handling techniques in dynamically adjusting constraint priorities, especially their adaptability to environmental changes. These techniques should be able to adjust the priorities of different constraints rapidly based on real-time environmental information to ensure that the UAVs can execute missions safely and efficiently in complex and changing environments. Evaluating the capability of adjusting constraint priorities ensures the overall performance and reliability of UAV-LSTP.
• Computational efficiency: The computational efficiency of constraint handling techniques in UAV-LSTP should be evaluated, especially their performance in handling large numbers of constraints and dynamic adjustments. In simulations of large-scale mission tests, planning systems need to rapidly process complex constraint combinations and perform dynamic adjustments to meet mission requirements and environmental changes. Simultaneously, it is necessary to assess the resources required by constraint handling techniques during the computation process, including the computational power and storage space. Recording resource usage under different task scales and complexities helps to determine their feasibility and cost-effectiveness in UAV-LSTP. Evaluating computational efficiency contributes to optimizing algorithms to maintain high computational performance while minimizing resource consumption.
• Robustness and stability: The robustness of constraint handling techniques in different environments should be evaluated, including their ability to handle uncertainties, noise, and system failures [95]. This requires planning systems to not only obtain optimal trajectory planning solutions under ideal conditions but also to quickly adjust constraint conditions when faced with unexpected situations. Additionally, it is essential to ensure the stability of UAV-LSTP over prolonged operation periods, preventing system crashes due to frequent adjustments in constraint handling techniques.
• Flexibility and adaptability: The adaptability of constraint handling techniques in various mission requirements and flight scenarios should be evaluated, including adjustments in constraint handling techniques, which are crucial for assessing the flexibility of UAV-LSTP solutions. This can be achieved by simulating diverse mission requirements to test the performance of constraint handling techniques when dealing with different types of tasks. Additionally, constraint handling techniques need the capability to dynamically adjust resource allocation based on task priorities in order to respond to real-time changes and unexpected situations. Through these comprehensive tests, the flexibility and adaptability of the technology in practical applications can be fully evaluated, ensuring its efficient and reliable task completion in dynamic environments. These tests provide a comprehensive understanding of the technology’s adaptability and robustness in different environments, ensuring its effective operation in the varied practical applications of UAV-LSTP.

4. Autonomous Decision-Making in UAV-LSTP

This section first introduces the concept of UAV-LSTP control technology and its importance. Then, the development trend of dynamic tuning algorithms is elaborated from three key techniques: first, the predictive modelling aspect focuses on how to predict the future mission environment using historical data and real-time information. Second, adaptive control techniques emphasize the maintenance of flight stability and accuracy by dynamically adjusting control parameters. Third, the application of machine learning technology provides UAV communities with enhanced autonomous decision-making capabilities.

4.1. Control Technology of UAV-LSTP

The UAV-LSTP control technique in complex environments achieves efficient collaboration and flexible response of UAV swarms during mission execution through intelligent optimization algorithms, adaptive regulation and real-time feedback, ensuring mission precision, stability and overall system robustness. This technique not only needs to consider the precise control of a single UAV but also needs to coordinate the collective behaviour and task allocation of multiple UAVs. Abro and Abdallah et al. [96] point out that the combination of digital twin technology and control theory can simulate the actual operating environment of UAVs, improve the safety and control accuracy of the system, and thus achieve more intelligent control. Kovryzhenko et al. [97] proposed a data-driven control method to optimize the control strategy through real-time data, reduce the dependence on traditional models, and enhance the adaptive ability of UAVs in complex environments. Hoshu et al. [98] explored the auto-tuning technique based on relay-embedded integrators, which improves the attitude control and trajectory tracking performance of UAVs through the design of cascade control systems. Abitha and Saleem et al. [99] proposed different modelling approaches and trajectory control algorithms, highlighting the key role of control algorithms in UAV trajectory planning. Therefore, advanced control algorithms and techniques are essential to enhance the autonomy, precision and mission execution efficiency of UAVs. Through intelligent control algorithms, UAVs can autonomously make decisions and adjustments in complex environments, reducing the dependence on human intervention and enhancing mission flexibility and responsiveness. At the same time, precise control technology ensures that UAVs can precisely follow a trajectory during flight, avoiding yaw and error, and especially in large-scale missions can ensure that multiple UAVs work together to achieve efficient task allocation and execution.

4.2. Dynamic Adjustment Algorithm

In a dynamic environment, many constraints of the UAV-LSTP change, especially environmental constraints and resource constraints. Environmental constraints such as weather conditions (e.g., wind speed, wind direction, rainfall) and no-fly zones may change at any time, which has a direct impact on the flight trajectory of the UAV and requires real-time trajectory adjustments to avoid hazardous areas [100,101,102]. In addition, the rate of battery power consumption and the stability of the communication link can be affected by unforeseen events during flight, affecting the UAV range and control capability. These dynamic changes require a high degree of flexibility and adaptability in trajectory planning to ensure that the UAV can reach the designated position within a limited time.

4.2.1. Predictive Modelling and Adaptive Optimal Control

Predictive models analyze historical data and current states to forecast potential future scenarios, providing a basis for decision-making. Adaptive control dynamically adjusts control parameters based on real-time feedback to ensure optimal UAV performance in changing environments. Meanwhile, machine learning techniques continuously learn and optimize, enabling the system to autonomously improve trajectory planning and decision-making capabilities, thereby enhancing overall efficiency and flexibility [103]. In the process of UAV-LSTP, predictive models play a crucial role, especially in dynamic and complex planning environments [104,105]. By utilizing historical data and real-time information, predictive models can forecast potential obstacles, weather changes, and other dynamic factors, thereby adjusting flight trajectories in advance to ensure UAV safety and mission efficiency. Additionally, predictive models enhance the UAV’s autonomous decision-making capabilities, enabling the UAV-LSTP system to react and adjust quickly in response to unforeseen circumstances. Therefore, predictive models not only enhance the accuracy and efficiency of trajectory optimization but also strengthen the UAV’s adaptability and flexibility in dynamic and complex environments.

Figure 8 depicts a schematic diagram of a predictive model applied in UAV-LSTP, which can be divided into four crucial stages: the initial planning stage, prediction model stage, dynamic adjustment stage, and execution and feedback stage.

The initial planning stage is a fundamental component of UAV-LSTP, involving preliminary planning and analyses of task requirements and resource conditions. During this stage, factors such as mission objectives, UAV performance parameters, and environmental constraints are comprehensively considered to develop an initial task plan. The specific steps include a task requirement analysis, a resource assessment, task allocation, and the formulation of planning schemes. The task requirement analysis clarifies specific goals and requirements, while the resource assessment provides insights into UAV performance and available resources. Task allocation involves assigning tasks to different UAVs, as well as establishing flight trajectories and time windows. Finally, optimized algorithms generate preliminary task plans, which undergo initial assessments to ensure feasibility and effectiveness. The initial planning phase provides crucial foundational data and strategies for subsequent stages such as prediction modeling, dynamic adjustment, execution, and feedback.

The prediction model stage is the most crucial component of UAV-LSTP, encompassing real-time environmental perception, data preprocessing, prediction model training, and environmental state forecasting. It predicts future environmental changes based on current and historical data, including weather variations, obstacle movements, wind speed, and direction [106,107]. By preemptively anticipating these changes, the UAV-LSTP system can adjust flight trajectories in advance to avoid potentially hazardous areas and ensure flight safety. For instance, if the prediction model detects approaching strong winds or adverse weather conditions, the UAV can proactively change altitude or flight path to steer clear of these areas. Moreover, if the model forecasts obstacles potentially appearing along the current flight path, the UAV can swiftly adjust its trajectory to mitigate collision risks. This analysis enhances the feasibility of pre-planned trajectories.

The dynamic adjustment stage is a crucial component of UAV-LSTP, involving the real-time optimization and adjustment of mission planning. Initially, during trajectory planning, candidate trajectories are generated based on predictive model data, and these trajectories undergo safety assessments to ensure feasibility and safety under various environmental conditions. Additionally, this phase includes ongoing dynamic adjustments, continuously updating environmental perception data to promptly acquire real-time information. These data and predictive outcomes are used to dynamically adjust trajectories in order to respond to environmental changes and unforeseen circumstances. This continuous adjustment process enables UAVs to operate efficiently and safely in complex and dynamic environments, thereby optimizing the reliability and flexibility of mission execution.

The execution and feedback stage is a critical step in UAV-LSTP, integrating the comprehensive efforts of the original planning stage, predictive modeling stage, and dynamic adjustment stage to generate and execute optimized mission plans. During the original planning stage, initial mission plans are formulated. In the predictive modeling stage, historical and real-time data are used to forecast environmental changes and provide supportive data. The dynamic adjustment stage involves the continuous monitoring and updating of environmental information for real-time trajectory adjustments. The mission execution phase translates the outcomes of these steps into actual operational plans, generating final execution plans based on current real-time data. This phase ensures that UAVs can accurately and efficiently complete missions according to the latest environmental information and task requirements, thereby enhancing mission flexibility and adaptability.

Predictive models play a crucial role in UAV-LSTP trajectory planning, significantly enhancing the safety and efficiency of UAV missions by anticipating environmental changes in advance, optimizing trajectory planning, enhancing real-time adjustment capabilities, improving mission success rates, and supporting collaborative planning. In dynamic and complex environments, utilizing predictive models for trajectory planning is essential to ensuring the smooth completion of UAV missions.

4.2.2. Environment Awareness and Multi-Level Adaptive Control

In UAV trajectory planning, environment awareness and multi-level adaptive control play a key role. Through real-time awareness of environmental changes and dynamic adjustment of flight parameters and trajectory planning strategies, UAVs can flexibly respond to uncertainties such as unexpected obstacles, poor weather conditions, or changes in mission requirements [108,109,110]. For example, when encountering complex flight environments, the multilevel adaptive control system can rapidly adjust the speed, heading, and altitude of the UAV to ensure that it can efficiently complete the mission while ensuring safety. In addition, multilevel adaptive control can optimize energy consumption, extend endurance, and improve mission success. Through the real-time feedback mechanism, the multilevel adaptive control system significantly enhances the UAV’s ability to cope with complex dynamic environments and autonomy, making its performance more robust and reliable in various application scenarios. Figure 9 demonstrates the working principle of environment sensing and multi-level adaptive control in the UAV-LSTP system.

Environmental awareness and obstacle avoidance adaptivity: by acquiring the flight parameters of the UAV and the surrounding environmental parameters, the multilevel adaptive control system is able to dynamically adjust the flight parameters (e.g., speed and altitude) of the UAV according to the real-time measured environmental data (e.g., wind speed and direction) in order to optimize the energy consumption and flight stability [111]. For example, when the wind speed suddenly increases or the wind direction changes, the multilevel adaptive control system will respond quickly to adjust the flight trajectory and flight attitude to avoid unnecessary energy consumption or the risk of loss of control. This combination of real-time environment sensing and multi-level adaptive control not only improves the flight efficiency and safety of the UAV-LSTP in complex and changing environments, but also enhances its ability to perform missions. The system can effectively avoid obstacles and optimize path planning, thus ensuring that the UAV can safely and stably complete its mission in challenging environments.

Position control adaptivity: by monitoring the UAV’s position, obstacle information, and target position in real time, the position control system uses a planning algorithm to generate a desired trajectory. Based on these inputs, the position control loop dynamically adjusts the UAV’s position and flight parameters to ensure that the UAV flies along the desired trajectory. When the UAV deviates from the intended trajectory or detects an obstacle, the position control loop is able to quickly compute and issue an adjustment command to correct the flight path, avoid the obstacle, and return to the desired trajectory [112]. This adaptive adjustment process ensures that the UAV is able to perform the intended task with high accuracy and optimizes the accuracy and safety of trajectory tracking, thus improving the overall task performance and system reliability.

Adaptive attitude control: attitude control is a key component in the UAV-LSTP (UAV localization and attitude control) system, which ensures stable flight of the UAV in complex environments by combining position control commands with attitude control commands. The attitude control system relies on adaptive control based on a radial basis function neural network (RBFNN) to adjust the attitude of the vehicle through real-time attitude feedback to make it close to the desired attitude. Specifically, the position control commands provide target position and trajectory information, while the attitude control commands are responsible for attitude adjustment to achieve these positional goals. The RBFNN attitude controller can dynamically correct the flight deviation to ensure that the UAV maintains a stable and precise attitude under various flight conditions, thus enhancing flight safety and mission execution accuracy. In addition, Raissi et al. [113] proposed physical-information-based neural networks (PINNs) to solve differential equations of dynamical systems and used them for control task optimization. For example, when optimizing flight trajectories, PINNs can ensure that the control model agrees with the actual physical behavior by minimizing the deviation between the observed data and the laws of physics. This physics-driven learning approach reduces the need for large-scale datasets while ensuring that the model follows realistic physical constraints.

Adaptive control of speed and acceleration: adaptive control of speed and acceleration aims to adjust the speed and acceleration parameters of the UAV in real time according to the needs of the mission and changes in the external environment. This control system is able to optimize the distribution of speed and acceleration based on real-time environmental sensing data (e.g., wind speed, wind direction, etc.) to reduce energy consumption and ensure stable UAV flight [114]. For example, when the UAV is in a complex airflow or encounters sudden wind changes, the adaptive speed control system is able to respond quickly by adjusting the flight speed and acceleration to maintain flight smoothness and avoid unnecessary energy consumption and risk of loss of control. This process enhances the UAV’s adaptability in changing environments and improves the efficiency of mission execution.

In UAV-LSTP planning, environment awareness and multi-level adaptive control significantly improve the efficiency and flexibility of the system by optimizing the task assignment and trajectory planning of multiple UAVs. The adaptive control dynamically adjusts the flight trajectory and behavior of each UAV according to its real-time status and mission requirements to ensure the optimal execution effect of the mission. This capability is especially critical in complex mission execution and large-scale UAV cooperative operations. It can not only flexibly respond to unexpected situations and environmental changes, but also reduce task conflicts and resource wastage by optimizing resource scheduling, thus significantly improving the overall task execution efficiency and success rate [115].

4.2.3. Machine Learning and Autonomous Decision Making

In the process of UAV-LSTP, machine learning plays a crucial role. Through this method, UAVs can learn and extract patterns from vast amounts of historical data, thereby enhancing the accuracy and efficiency of trajectory planning [116]. For example, by utilizing deep learning models to analyze accumulated flight data, UAVs can predict potential future obstacles and environmental changes, allowing for preventive adjustments during the initial planning stages. Additionally, machine learning can adaptively optimize the trajectory planning process, continuously improving decision-making based on real-time feedback, thereby equipping UAVs with stronger capabilities and autonomy to handle dynamic and complex environments. Machine learning can also be integrated with other technologies, such as deep learning and reinforcement learning, to accomplish more complex tasks, such as multi-UAV collaborative planning and task allocation [117]. In addition, transformer-based reinforcement learning methods have shown great potential in recent years for long sequence data processing such as UAV trajectory control. The transformer model can effectively deal with the long-time dependence on UAV trajectories because its multi-attention mechanism can simultaneously focus on inputs at different time steps, thus improving the computational efficiency while maintaining the model performance [118,119]. Overall, machine learning significantly enhances the autonomous decision-making capabilities of UAV trajectory planning, improving the safety and reliability of task execution. Figure 10 illustrates the basic principles of UAV-LSTP based on machine learning.

Real-time data analysis: Machine learning can utilize real-time sensor data—such as visual, radar, and GPS data—to quickly and accurately analyze the current state of the environment. This includes information on wind speed, temperature, and air pressure as well as the positions and dynamics of surrounding obstacles or other aircraft [120,121,122]. The collected data are then preprocessed, which includes filtering, normalization, and feature extraction, to remove noise and extract key information. The preprocessed data are input into the machine learning model, which calculates and analyzes the data to map the complex environmental information into command data that the UAV can read and understand. These command data help the UAV adjust its flight strategy in real time, ensuring the safety and optimized performance of its trajectory, allowing it to maintain efficient and reliable autonomous flight in complex and changing environments.

Trajectory planning optimization: Based on the preprocessed data, planning and environmental prediction are conducted to update and adjust the UAV’s trajectory in real time. Machine learning-based UAV-LSTP allows UAVs to adapt to complex and changing environments, enhancing the reliability and efficiency of autonomous flight. For instance, machine learning can optimize trajectory selection, flight altitude, speed, and turning radius to accommodate unexpected situations and environmental changes. Combined with deep learning technology, machine learning also enhances the UAV’s obstacle avoidance capabilities, enabling it to recognize and avoid obstacles while adhering to dynamically changing flight restrictions. This capability not only improves the UAV’s task execution efficiency but also enhances its safety and flexibility in various environments.

Autonomous decision-making: Machine learning algorithms can enable information sharing and coordination among UAVs, allowing each drone to make optimal decisions based on global information. For instance, in multi-UAV collaborative flights, tasks can be allocated, flight paths can be adjusted, and unexpected situations can be managed. These decisions, based on the machine learning models’ analysis of current and predicted environments, can optimize task execution efficiency and ensure safety [123,124,125]. Through machine learning, UAVs can exchange and process data in real time, enhancing the flexibility and responsiveness of the overall system. This not only improves the collaborative capabilities of multi-UAV systems, but also allows for quick responses and adjustments in complex environments, ensuring efficient task completion and flight safety.

5. Future Directions and Challenges

This section first introduces the challenges currently faced by UAV-LSTP in terms of computational load and the complexity of communication technology, followed by the future technological trends in UAV-LSTP.

5.1. Analysis of Current UAV-LSTP Challenges

5.1.1. UAV-LSTP Computational Load

With the sharp increase in the number of UAVs and task demands, the computational load of UAV-LSTP has risen dramatically. Traditional planning algorithms often rely on global optimization or complex search algorithms, which become highly costly and fail to meet real-time trajectory planning needs when dealing with large UAV numbers. Additionally, traditional planning algorithms tend to fall into local optima in high-dimensional search spaces, unable to fully utilize global information. Therefore, it is necessary to design efficient planning algorithms to reduce the computational complexity of the system. Currently, some researchers and scholars have adopted the mean-field gaming (MFG) approach, which is particularly suitable for multi-UAV systems in ultra-dense environments. MFG reduces computation and complexity by simplifying the impact of each UAV into a mean-field in place of the impact of individual UAVs [126,127]. In addition, deep reinforcement learning has demonstrated significant potential, especially by combining deep learning techniques with traditional trajectory planning algorithms to create smarter and adaptive systems that enable UAV-LSTPs to quickly adapt to changing mission requirements in real-time environments. However, one of the main challenges of deep reinforcement learning is its sensitivity to changes in the environment, which makes it possible for models to require extensive retraining when the environment changes significantly. To address this issue, techniques such as transfer learning and continuous learning are being introduced to alleviate the model’s reliance on extensive retraining and to enable the system to maintain efficient performance through online learning in the face of new environments. This hybrid approach is not only suitable for planning in static environments, but also able to cope with complex dynamic environments. Therefore, designing efficient UAV-LSTP collaborative trajectory planning algorithms that combine deep reinforcement learning and distributed computing will help to reduce computational complexity and improve planning efficiency.

5.1.2. Complexity of UAV-LSTP Communication Technology

The complexity of information synchronization covers numerous elements, such as communication protocols, network topology optimization, response protocol algorithms, cryptography and data integrity, and system reliability [128,129,130]. For the UAV-LSTP system, information synchronization and communication are the basis for achieving multi-UAV cooperative operations, which is directly related to the safety and effectiveness of the whole system. Real-time synchronization of information such as position, speed, and mission status is required between UAVs to ensure efficient collaboration during flight, thus avoiding collisions and mission conflicts. However, in practical applications, communication delay and signal interference are the main problems affecting the accuracy and timeliness of information synchronization. Especially in UAV-intensive airspace or areas with more congested signals, the communication system of UAVs is highly susceptible to the negative impact of these factors. The study by Ladosz et al. [131] shows that urban areas with complex electromagnetic environments and high-density communication networks are prone to problems such as signal interruption, data loss, etc., thus affecting the information transmission and flight safety of UAVs. To solve these problems, researchers have proposed a variety of technological innovations. On the one hand, improving the existing communication protocols and signal processing algorithms can effectively reduce the communication delay and enhance the anti-jamming ability to ensure the stability and real-time information transmission between UAVs. On the other hand, the optimization of infrastructure is also crucial. For example, by increasing relay stations and optimizing network topology, the reliability and speed of information transmission can be greatly improved [132]. In addition, modern cryptography and data integrity protection techniques have been gradually introduced into UAV systems to ensure that information is protected from malicious attacks and data tampering during transmission [133]. In the future, with the expansion of UAV group size and the increase of mission complexity, how to further improve the robustness of the communication system and the efficiency of information synchronization will become an important direction for the development of UAV-LSTP system. This not only involves breakthroughs in communication technology, but also requires innovations in distributed network architecture and response protocol algorithms to further enhance the scalability and security of the system.

5.2. Future Trends in UAV-LSTP Technology

5.2.1. UAV-LSTP Joint Task Allocation and Trajectory Planning for Task Diversification

The UAV-LSTP technology plays a crucial role in enabling efficient task execution through integrated task allocation and trajectory planning [134]. Through intelligent task allocation algorithms, the system is able to dynamically allocate tasks according to task types, priorities and the specific capabilities of each UAV, thus maximizing the efficiency of resource utilization. The speed and accuracy of task allocation is critical to overall system efficiency, especially in large-scale mission scenarios where the system needs to make quick decisions to respond to changing environments and mission requirements. At the same time, accurate trajectory planning not only takes into account the safety and efficiency of the flight path but also enables a flexible response to a variety of complex mission requirements, such as patrolling, monitoring, rescue, and other mission types. This comprehensive system design and optimization strategy enables the UAV-LSTP to perform well in dynamic and changing mission execution scenarios, providing key technical support for the efficient execution of diverse missions, thus promoting the wide application and advancement of UAV technology in practical applications.

5.2.2. UAV-LSTP Integration of 3D Technology for Modelling Complex Environments

One of the significant research directions for UAV-LSTP is the use of heterogeneous UAVs to collaboratively perform real-time 3D modeling, particularly in response to the frequent natural disasters in mountainous regions in recent years [135]. These areas are often affected by landslides, making it difficult for traditional rescue methods to accurately assess road damage. UAVs equipped with advanced sensors and imaging devices, such as LiDAR and high-resolution cameras, can precisely scan and record various ground details from the air. Multiple UAVs can work together, coordinating their flight paths and sharing data in real time according to pre-assigned tasks. Through the generation of high-precision 3D maps in real time, rescue teams can more accurately assess the affected areas, including the location and type of damaged buildings, blocked roads, and other obstacles. This information is crucial for rescue personnel to prioritize and plan their actions effectively. Moreover, the collaborative data collection by UAVs reduces the risk of search-and-rescue personnel entering disaster zones directly, enhancing the safety of rescue operations and providing detailed geographical data for post-disaster reconstruction. These data aid in the replanning of roads and infrastructure after disasters. Therefore, the mature technology of UAV-LSTP will provide robust technical support for emergency response and post-disaster reconstruction scenarios.

5.2.3. UAV-LSTP Combining Satellite and Edge Computing for Global Communication and Response Optimization

Realizing the combination of UAV-LSTP with satellite interconnection and edge computing is the key to enhance the communication capability and response speed of UAV. With the wide-area coverage and stable communication links provided by satellites, UAVs are able to maintain real-time data transmission in any geographic location and complex environments, and this continuous coverage independent of ground infrastructure greatly improves the efficiency of mission execution, especially in remote areas or areas lacking communication facilities [136,137,138]. Satellite communication ensures that decision makers can update mission commands, receive sensor data, and remotely control and adjust UAVs in real-time, guaranteeing the real-time and reliability of mission execution, while expanding the application scenarios of UAV-LSTP. On the other hand, edge computing technology decentralizes computing power to the UAV or edge nodes close to the data source, which significantly improves the efficiency and response speed of the system. Compared to the traditional way of relying on remote server support, edge computing is able to directly process a large amount of data—such as high-definition video, images, and sensor data—and perform real-time calculations for trajectory planning and complex algorithms during flight, thus reducing transmission delays and optimizing resource utilization. Through the combination of satellite communications and edge computing, UAVs can flexibly respond to complex environments and multi-mission execution, which not only improves system performance but also lays a solid foundation for the future development of intelligent and autonomous flight systems. The integration of this technology enhances the reliability and efficiency of mission execution, giving the UAV system greater adaptability in a wide range of application scenarios.

Based on the above technology trends, I have a strong interest in UAV multi-mission optimization, collaborative autonomous planning, and the application of intelligent systems in dynamic environments. Specifically, I would like to address the complex challenges encountered during large-scale UAV collaboration through in-depth research on multilevel control of UAV-LSTP, optimization of mission assignment, and application of intelligent algorithms in multi-UAV systems. In the future, I will focus on exploring how to utilize the combination of deep reinforcement learning, distributed computing, and edge computing to enhance the autonomy, real-time performance, and adaptability of the system, so as to further promote the application and development of UAV technology in complex scenarios.

6. Conclusions

The rapid development of UAV technology has brought a lot of convenience to several fields, such as the efficient distribution of express logistics and the rapid prevention of forest fires. However, with the increase of mission complexity, the corresponding constraints are increasing, and these constraints are often conflicting and coupled, which brings great challenges to the performance of UAV-LSTP. Although the existing constraint optimization algorithms have been applied in a more mature way, they usually treat UAVs as plasmas and ignore the complex constraints at the physical level, which makes it difficult to comprehensively cope with the demands in practical applications. Therefore, this paper provides an in-depth discussion on constraint handling techniques and autonomous decision-making for UAV-LSTP from the perspective of mathematical modelling. Firstly, the paper details the application scenarios of UAV-LSTP and classifies the constraints in terms of both strong and weak constraints. Then, it focuses on constraint handling techniques, including redundant constraint identification and streamlining, priority ranking, and constraint fusion and transformation, and discusses the performance evaluation criteria of these techniques. Then, the focus of the dynamic adjustment algorithms for UAV-LSTP is analyzed in terms of three key technology areas: predictive modelling, adaptive control, and machine learning. Finally, by analyzing the challenges of UAV-LSTP in terms of computational complexity and communication techniques, this paper points out the key issues that still exist in this field. Meanwhile, several future research directions are proposed, aiming to provide references and insights for subsequent research to promote the further development and improvement of UAV-LSTP technology.