Trajectory Planning of Unmanned Aerial Vehicles in Complex Environments Based on Intelligent Algorithm

Abstract

In recent years, effective trajectory planning has been developed to promote the extensive application of unmanned aerial vehicles (UAVs) in various domains. However, the actual operation of UAVs in complex environments presents significant challenges to their trajectory planning, particularly in maintaining task reliability and ensuring safety. To overcome these challenges, this review presents a comprehensive summary of various trajectory planning techniques currently applied to UAVs based on the emergence of intelligent algorithms, which enhance the adaptability and learning ability of UAVs and offer innovative solutions for their application in complex environments. Firstly, the characteristics of different UAV types, including fixed-wing, multi-rotor UAV, single-rotor UAV, and tilt-rotor UAV, are introduced. Secondly, the key constraints of trajectory planning in complex environments are summarized. Thirdly, the research trend from 2010 to 2024, together with the implementation, advantages, and existing problems of machine learning, evolutionary algorithms, and swarm intelligence, are compared. Based on these algorithms, the related applications of UAVs in complex environments, including transportation, inspection, and other tasks, are summarized. Ultimately, this review provides practical guidance for developing intelligent trajectory planning methods for UAVs to achieve the minimal amount of time spent on computation, efficient dynamic collision avoidance, and superior task completion ability.

1. Introduction

As an aircraft that carries a certain load and performs specific tasks autonomously, an unmanned aerial vehicle (UAV) is remotely controlled by ground operators or even requires no human supervision [1,2,3]. Compared with manned aircraft, UAVs demonstrate higher operational flexibility, smaller size, longer endurance, and better invisibility. As the implementation of UAVs becomes more intelligent, controllable, and widespread, the importance of trajectory planning of UAVs grows in relevance [4,5].

Trajectory planning intends to obtain one or more feasible trajectories of a single or multiple UAV from the origin to the destination with specific tasks or necessary waypoints [6,7]. These planned trajectories are designed to satisfy corresponding constraints, including UAV dynamics [8], obstacle avoidance [9], distance between swarm members [10], and desired formations [11]. These constraints are usually associated with flight safety, trajectory feasibility, and task requirements. The objectives in trajectory planning can be single or multiple. For example, determining the shortest trajectory between two fixed points is an instance of single-goal trajectory planning. In contrast, multiple-goal trajectory planning involves managing several objectives simultaneously, such as minimizing both flight time and control input. The trajectory planning issues for a single UAV regarding the optimal trajectory [12], specific area search [13], and threat avoidance [6] have been extensively studied. Nowadays, due to limitations including battery life, load capacity, and failure rate, the UAV swarm emerges as crucial to expanding the capabilities of a single UAV through cooperation and completing more difficult tasks, which has become the research emphasis all over the world [14].

In the past several decades, researchers have proposed numerous algorithms for trajectory planning issues of single or multiple UAVs. Classical algorithms include artificial potential field (APF) [15], algorithms based on graph search [16], algorithms based on sampling [3], and algorithms based on mathematical models [17]. The graph search-based trajectory planning algorithm often has better completeness in trajectory planning in low-dimensional spaces [18]. Still, it requires complete modeling of the environment, which often leads to dimensionality disasters in high-dimensional spaces. The sampling-based trajectory planning algorithm replaces completeness with probability completeness, thereby improving search efficiency. However, the trajectory often needs to be post-processed utilizing curve fitting and smoothing, which increases the computational cost [19]. Algorithms based on mathematical models [20] incorporate relevant factors into the trajectory planning problem as inequality or equality constraints to obtain the optimal trajectory. However, these algorithms demand extensive computation to solve constrained multi-objective optimization problems [21]. Consequently, it is difficult to apply the mathematical model-based algorithms in complex environments [22]. It is relatively difficult for these classic algorithms to simultaneously meet the requirements of practicality, safety, and complex environmental adaptability in UAV trajectory planning.

With the continuous evolution of artificial intelligence, intelligent algorithms, including machine learning [23], evolutionary algorithms [24], and swarm intelligence [25], have been integrated into the trajectory planning of UAVs. These methods simplify the environment and UAV modeling process and use powerful search methods instead to converge on the target stably, so these algorithms have great advantages over classical algorithms in unknown environments and dynamic obstacles [26,27]. The fault tolerance and learning abilities of machine learning are beneficial for trajectory planning methods to handle dynamic environments [28]. The evolutionary algorithm-based method has a strong global search capability. The characteristics of swarm intelligence [29,30] make it not require central control, giving trajectory planning methods decentralized computational capability. Attributable to the benefits of intelligent algorithm-based trajectory planning, UAVs are widely used in many domains, including transportation [31,32], inspection [33,34], emergency rescue [35], and others.

Currently, there are several review articles on the intelligent algorithms for UAV trajectory planning. For example, Puente-Castro et al. [36] reviewed articles on UAV trajectory planning based on intelligent algorithms. Yahia [37] and Hooshyar [38] systematically introduced UAV trajectory planning using meta-heuristic algorithms, respectively. Poudel et al. [39] summarized bio-inspired algorithms for trajectory planning, highlighting key characteristics, working principles, advantages, and weaknesses. For multiple UAVs, Sharma et al. [40] summarized the UAV swarm trajectory planning techniques for intercepting multiple targets. Tang et al. [41] reviewed the merits and demerits of various swarm intelligence algorithms. However, the existing reviews mentioned above tend to classify and discuss trajectory planning methods from the perspective of intelligent algorithm types, while the constraints of trajectory planning in complex environments are not considered; thus, specific applications based on these intelligent algorithms are not well summarized when analyzing the development of trajectory planning.

To have a more systematic understanding of the characteristics of various trajectory planning methods in complex environments, it is essential to summarize the current progress. This review analyzes trajectory planning characteristics of several typical UAVs and further discusses the challenges of UAV trajectory planning in complex environments. Based on the excellent performance as well as existing problems of intelligent algorithms in these complex conditions, the implementation of UAV trajectory planning through intelligent algorithms is introduced, as shown in Figure 1. Compared with these existing review articles, the main contributions of this work are as follows:

(1)

The trajectory planning features and constraints of typical types of UAV in complex environments are classified and introduced.

(2)

The growth trends, development processes, and specific applications of different intelligent algorithms in complex environments are reviewed and compared.

(3)

The limitations of current UAV trajectory planning algorithms in complex environments and potential future research directions are proposed and discussed.

This review aims to summarize the UAV trajectory planning methods in complex environments within cutting-edge research and provide practical suggestions for the development of intelligent algorithm applications in these scenarios. Differences between this review and existing reviews are shown in

Table 1. Comparison of reviews on intelligent algorithms for UAV trajectory planning.

Publication	Algorithms	Planning Features	Applications
Puente-Castro et al. [36]	Machine learning, evolutionary algorithms, and swarm intelligence algorithms	\	\
Yahia and Mohammed [37]	Metaheuristic algorithms	Complex environment	\
Hooshyar and Huang [38]	Metaheuristic algorithms	Complex environment	\
Poudel et al. [39]	Bio-inspired algorithms	\	\
Sharma et al. [40]	Swarm intelligence algorithms	\	Multiple target interception
Tang et al. [41]	Swarm intelligence algorithms	\	\
This work	Machine learning, evolutionary algorithms, and swarm intelligence algorithms	Complex environment, UAV Types	Transportation, inspection, show, etc.

.

2. Trajectory Planning Features

2.1. Trajectory Planning Features Across Various UAV Types

According to different types of wing and rotor configurations, UAVs currently in widespread use can be broadly classified into fixed-wing UAVs, multi-rotor UAVs, single-rotor UAVs, and tilt-rotor UAVs. Each type has inherent differences in its fuselage structures and aerodynamic features, resulting in different requirements for trajectory planning methods, application areas, and technical challenges. Therefore, it is crucial to develop trajectory planning strategies that are customized to the specific features of each UAVs platform. Representative illustrations of UAVs with different wing configurations are shown in Figure 2 [42,43,44,45].

In terms of flight capabilities, multi-rotor UAVs, single-rotor UAVs, and tilt-rotor UAVs all can hover, and although fixed-wing UAVs cannot hover in place, they can cruise at high speed. In terms of structure, fixed-wing UAVs and multi-rotor UAVs have relatively simple structures, while single-rotor UAVs and tilt-rotor UAVs involve complex pitch-changing mechanisms and state switching issues. From the perspective of dynamic characteristics, multi-rotor UAVs have fast response characteristics, while fixed-wing UAVs have larger minimum turning radius restrictions. The comparison of characteristics between various types of UAVs is shown in

Table 2. Comparison of characteristics among different UAV types.

Characteristic	Multi-Rotor UAV	Single-Rotor UAV	Tilt-Rotor UAV	Fixed-Wing UAV
Propulsion	Multiple fixed motors with propellers	One main rotor and anti-torque mechanism	Tiltable rotors with fixed wings	Propeller or jet engine with fixed wings
Lift Generation	Rotors	Rotors	Rotors/fixed wings	Fixed wings
Thrust-Attitude Coupling	Strong coupling	Strong coupling	Strong in rotor mode, weak in fixed-wing mode	Weak coupling
Endurance	<1 h	About 1–3 h	About 3–8 h	About 5–30 h
Speed	About 0–20 m/s	About 0–50 m/s	About 0–100 m/s	About 15–100 m/s
Maneuverability	High	High	Medium (weak in transition)	Low (large turn radius)

. These differences in fuselage structure and flight characteristics also bring different requirements for trajectory planning.

Fixed-wing UAVs represent a class of unmanned vehicles that generate lift via fixed wings and typically use engines or electric motors for propulsion. They offer superior endurance and are particularly suitable for long-duration, heavy-load, or high-altitude tasks. Due to their reliance on continuous forward motion for lift generation, fixed-wing UAVs cannot hover and must sustain a minimum velocity to remain airborne. Therefore, fixed-wing UAVs face notable challenges in trajectory planning, particularly related to stringent dynamic constraints and high requirements for trajectory smoothness, which need to account for factors such as minimum turning radius, pitch rate limit, and climb/descent angle constraints, while avoiding abrupt directional changes [42]. Accordingly, trajectory planning algorithms such as Dubins curves and B-spline trajectories are commonly employed. Recent advancements have also introduced intelligent algorithm-assisted trajectory planning techniques, which enhance flight safety by enabling real-time path risk assessment and trajectory evaluation. For example, Ma et al. [46] developed a strategy that integrated Dubins curve-based trajectory planning for single-UAV coverage tasks and a parallel-interval formation approach for coordinated coverage using fixed-wing UAV swarms to achieve rapid coverage search in complex boundary sea areas. Freitas et al. [47] developed a differential evolution-based algorithm for 3D trajectory planning, using a kth-order non-uniform rational B-spline curve to generate smooth and differentiable paths under climb/dive angle and curvature constraints.

Multi-rotor UAVs rely on multiple propellers to provide lift and attitude control. The most common types include quadrotors and hexacopters. Characterized by their symmetrical structure, high maneuverability, and excellent hovering capabilities, these UAVs offer convenient vertical take-off and landing (VTOL), making them a focal point in the development of advanced trajectory planning methods [48]. Currently, almost all of the most widely used methods, such as sampling, optimization algorithms, intelligent algorithms, and other trajectory planning methods, can be well applied to multi-rotor UAVs because of their high degree of freedom and strong environmental adaptability [49]. When they are applied in complex environments such as urban areas and forested regions, they need to perform rapid dynamic obstacle avoidance and maintain real-time responsiveness. These operational demands pose significant challenges in localization and mapping, especially under the constraints of high-frequency control. Additionally, their relatively small size makes them susceptible to external disturbances such as wind or interference from nearby UAVs, particularly in swarm operations, further complicating trajectory planning and system stability.

As another type of VTOL aircraft, single-rotor UAVs generate lift through a single large main rotor and typically employ a tail rotor or alternative anti-torque mechanisms to maintain directional stability [44]. The most prevalent type of single-rotor UAV is the helicopter, which, with its unique hovering ability and flexible maneuverability, is suitable for tasks that require vertical take-off and landing, low-speed precision operations, or complex terrain access. Due to its main rotor being involved in achieving attitude and lift control, the propulsion is highly coupled with the fuselage attitude, and the trajectory planning of single-rotor UAV requires consideration of the nonlinear and strongly coupled dynamic characteristics [50]. Moreover, their dynamic behavior is highly sensitive to wind disturbances and sudden environmental changes, which complicates planning a stable trajectory. The risks brought by their unique flight characteristics should also be considered. The vertical speed of the planned trajectory needs to be limited to avoid the aircraft entering a vortex ring state, and the landing trajectory should also be smooth to avoid ground resonance. At present, trajectory planning methods for single-rotor UAVs primarily include sampling-based algorithms that leverage large-scale environmental maps for navigation and obstacle avoidance [51], as well as intelligent algorithm-based strategies designed to enhance robustness in disturbed operational conditions [52].

Research on the trajectory planning of tilt-rotor UAVs remains relatively limited. As a novel class of UAV, it combines the structure of fixed-wing UAVs and rotary-wing UAVs. The rotors can be erected to generate vertical lift during take-off and landing and tilted horizontally to provide forward thrust during cruising flight, thereby enabling VTOL capabilities alongside high-speed cruising performance [45]. However, trajectory planning for such UAVs presents significant challenges due to their highly nonlinear dynamics and the strong coupling problem of mode-switching processes. The trajectory needs to consider the smooth transition between the vertical mode and the horizontal mode, and it is difficult to coordinate the trajectory continuity and controllability. In addressing these challenges, trajectory planning methods for tilt-rotor UAVs often employ hybrid algorithms tailored to manage mode-switching dynamics [53].

2.2. Trajectory Planning Features in Complex Environments

In practical application scenarios of complex environments, UAV trajectory planning is influenced by a variety of factors, including obstacles, terrain features, weather conditions, and air defense systems [54]. In this case, the design of trajectory planning methods for UAVs needs to ensure flight stability, maintain task efficiency, and avoid obstacles while conforming to aerodynamic and motion constraints. In multi-UAV systems, additional requirements such as inter-UAV collision avoidance, coordinated communication, and formation control arise, further increasing the dimensionality and complexity of the trajectory planning process [55]. These include higher-dimensional state space and action space, additional constraints, and multi-objective optimization conflicts. The presence of complex and dynamic obstacle environments significantly exacerbates the challenges associated with efficient and reliable trajectory generation.

Dense obstacles in complex environments significantly increase planning difficulty. Typical high-risk scenarios include mountainous terrain, densely built urban areas, and narrow passages in buildings. Dense obstacles will strictly limit the feasible solution space of the UAV and reduce the trajectory tolerance space, requiring the planning method to find a safe trajectory in a limited space, and a large number of obstacle avoidance constraints will greatly increase the computational complexity of trajectory planning methods. Additionally, the narrow environment will amplify the UAV’s dynamic constraints, such as physical limitations, such as maximum acceleration and minimum turning radius, making it more difficult for the trajectory to meet both feasibility and safety requirements. To meet these challenges, current solutions mostly use global coarse planning combined with local optimization methods, constraint optimization methods based on safe flight corridors, and adaptive strategies that integrate machine learning, etc. For complex mountainous environments, Zhang et al. [56] considered terrain and threat areas in the UAV objective function of trajectory planning, as shown in Figure 3a. For complex urban city environments, Lin et al. [57] proposed a stage-by-stage UAV trajectory planning method to plan a collision-free corridor in the offline stage and plan the minimum time trajectory within the corridor in the online stage, enabling rapid generation of feasible UAV trajectories in complex urban landscapes, as illustrated in Figure 3b. For complex, narrow, and constrained environments, Freitas et al. [47] considered the climb/dive angle limitations and optimal turning radius for fixed-wing UAVs and proposed a planning method based on differential evolution to effectively generate viable trajectories through tight spaces, such as tunnels, as displayed in Figure 3c.

In addition to the detected and known obstacles, the presence of unknown and dynamic obstacles introduces additional challenges to UAV trajectory planning in complex environments. First, unknown and dynamic obstacles render offline trajectory planning methods ineffective, while online planning methods face a conflict between real-time requirements and computational complexity in complex environments. Second, it is more difficult to balance safety and trajectory quality, as emergency obstacle avoidance may lead to severe trajectory oscillations or local optima entrapment. The current mainstream solutions include reducing the amount of calculation to increase the planning frequency, enhancing global search capabilities and optimization strategies, or introducing learning algorithms to optimize the prediction accuracy of dynamic obstacles. For instance, Li et al. [58] constructed an online trajectory planning method for UAVs on the basis of the improved deep deterministic policy gradient algorithm for uncertain environments, which introduced a mixed noise consisting of Gaussian noise and Ornstein-Uhlenbeck noise for escaping from local optimality. When the external environment changes, this method does not require remodeling the environment and planning new effective trajectories, saving computing resources. Another method is to use a density-based spatial clustering of applications with noise to extract the position and velocity of dynamic obstacles and generate the collision-free velocity of the UAV via the gradient velocity obstacle. This method retained the original feasible set while ensuring computational efficiency and showed excellent fault tolerance to environmental perception noise, generating collision-free trajectories in real time when facing unknown obstacles [59].

In complex obstacle environments, UAVs are often required to frequently perform maneuvers such as acceleration and deceleration, turning, and attitude adjustment to avoid densely distributed obstacles. Compared with smooth, straight-line flight, such high-frequency attitude changes and detours make the flight trajectory longer and lead to increased energy consumption of the power system, thereby shortening the UAV’s endurance. In addition, frequent maneuvers make energy consumption more uncertain, and the energy budget and duration of the flight task are difficult to accurately predict. To address this limitation, a common approach is to use trajectory smoothing methods to reduce the energy loss caused by drastic velocity changes and attitude changes. Another approach is to incorporate energy consumption into the trajectory optimization objective function and design energy-optimal trajectories. In addition, various auxiliary measures have also been adopted to improve the endurance of UAVs, thereby extending their application scope. For example, Shao et al. [12] developed a support system comprising battery swap and service stations. To optimize the UAVs’ operation, they proposed a trajectory planning method based on an improved Ant Colony Optimization (ACO) algorithm, aiming to optimize the total flight distance and frequency of landings. Additionally, with the development of solar cell technology, solar-powered UAVs have become an effective solution to improve the endurance and reliability of the electric UAVs for extended tasks [60]. Fuel-powered UAVs can be refueled in the air to replenish energy. Chen et al. [61] established a collaborative trajectory planning method for UAV swarms and tankers and realized the refueling of UAVs by tankers in complex environments, as shown in Figure 4.

In general, dense obstacles in complex environments significantly compress the feasible solution space, increase the computational complexity, and amplify the impact of dynamic constraints on trajectory feasibility. In the face of unknown or dynamic obstacles, traditional offline planning methods are difficult to apply, and online planning methods must balance real-time and safety within a limited time. At the same time, frequent maneuvers significantly increase energy consumption and reduce endurance, making energy management more difficult. The above analysis demonstrates that trajectory planning in complex environments must achieve a multi-objective trade-off between computational efficiency, safety, dynamic feasibility, and energy consumption.

3. Intelligent Algorithms for UAV Trajectory Planning

Considering the difficulties faced by UAV trajectory planning in complex environments, traditional trajectory planning methods of UAVs have shown obvious limitations. In recent decades, intelligent algorithms have shown unique advantages in solving high-dimensional nonlinear programming problems due to their good global search capabilities and adaptability and have represented a significant research direction in UAV trajectory planning. Therefore, trajectory planning methods based on intelligent algorithms are summarized and analyzed.

To analyze the development status, the Web of Science search engine was used to search research articles on intelligent algorithm-based UAV trajectory planning from 2010 to 2024, and they were classified according to the types of intelligent algorithms. The methods are divided into three algorithms: machine learning (ML), evolutionary algorithms (EA), and also swarm intelligence (SI) algorithms. The specific classification is shown in Figure 5, where the dotted arrow indicates that deep reinforcement learning is achieved by combining deep learning and reinforcement learning.

In addition, the number of retrieved research articles on intelligent algorithm-based UAV trajectory planning was counted to analyze the development trend. As shown in Figure 6, the number of related studies has gradually increased in the past 15 years. Especially after 2018, the growth trend has accelerated significantly, indicating that UAV trajectory planning methods based on intelligent algorithms have received widespread attention. In this section, ML, EA, and SI and their applications in UAV trajectory planning are introduced.

3.1. Machine Learning

ML involves algorithms to analyze data, learn from patterns, and enable machines to automatically make decisions and predictions about events. As computer technology continues to develop, deep learning (DL), reinforcement learning (RL), and deep reinforcement learning (DRL) have emerged as significant research directions in ML, which are widely used in trajectory planning of UAVs.

3.1.1. Deep Learning

DL originates from the study of neural networks (NN) and primarily employs deep neural networks (DNN) for learning and prediction. As an imitation of the nervous system of organisms, NN is a large-scale structure formed by layers of connected nodes [36]. DNN can be broadly understood as an NN architecture that incorporates multiple hidden layers [62], which extracts features from data through multi-layer nonlinear transformations, suitable for massive data sets and complex tasks [63]. Subsequently, DNN has evolved into many different network topologies, including convolutional neural network (CNN) [64] and recurrent neural network (RNN).

Following an introduction of an NN model with nonlinear analog neurons for trajectory planning by Glasius in 1995 [23], the development of NN in UAV trajectory planning has been revealed. To improve the feasibility of trajectory planning, Liu et al. [65] considered the tracking characteristics of UAVs and introduced the trajectory planning method based on CNN and model predictive control. Due to the limitation of traditional CNNs in using historical data, this method developed a time-series CNN to adapt to time-series prediction problems by adding time-series properties to it. In contrast, the design of RNNs made them naturally capable of processing and memorizing long-term sequence data. Shaffer et al. [66] explored a method for training RNNs to solve multi-agent trajectory planning problems. In addition, this method included a decentralized version, which enhanced the scalability of the swarm. With the development of NN, numerous derived forms have emerged in recent years [67,68]. Li et al. [69] used a graph neural network (GNN) integrated with a mechanism that allows message-dependent attention and a message-aware graph attention network in UAV trajectory planning for multiple agents, which supported the trajectory planning method to maintain high effectiveness in scalable and unseen environments. Another form of NN in UAV is applied in vision-based navigation, especially obstacle avoidance [70,71,72]. Although NN-based trajectory planning methods typically exhibit strong fault tolerance and learning abilities, the opacity of trained neural networks often restricts their practical applications.

In recent years, end-to-end learning methods have been extensively explored for navigation [73,74,75]. Unlike conventional modular frameworks that process perception, trajectory planning, and control as separate tasks, end-to-end methods aim to directly map raw sensor inputs to control outputs, thereby simplifying the overall system architecture and minimizing the accumulation of intermediate errors [76]. The Transformer architecture has emerged as a powerful tool for achieving end-to-end learning due to its strong representation capabilities and parallel computing characteristics, which have two main components: the encoder and the decoder, as shown in Figure 7 [77]. The encoder is composed of several identical layers stacked together; each layer includes a multi-head self-attention layer (MHSA), a feed-forward network, layer normalization, and a residual connection. The basic structure of the decoder is similar to that of the encoder. Still, MHSA is replaced by a multi-head partial self-attention layer (MHPSA), and each layer has an additional masked multi-head attention layer (Mask-MHA) than the encoder. The encoder extracts the characteristics of the input, and the decoder gradually generates the output based on the encoding result and through Mask-MHA. Based on the self-attention mechanism, Transformer has demonstrated exceptional performance in handling sequential data and capturing long-range dependencies and has proven suitable for various sequence modeling tasks in dynamic environments [78]. Wang et al. [79] demonstrated that the proposed decentralized deep reinforcement learning framework for the UAV swarm trajectory planning, integrating a Transformer architecture with an adaptive reward mechanism to enable spatial cooperation and exploration, outperformed all baselines. Similarly, an innovative end-to-end Transformer-based architecture was designed for sequential data processing, enabling mobile robots to autonomously navigate in various unknown environments and surpassing the performance of existing methods [75].

3.1.2. Reinforcement Learning

RL involves algorithms that enable a UAV to develop its optimal strategy to solve problems in interacting with the environment (Figure 8) [80]. Unlike DL, RL operates without the need for pre-collected data. It focuses on decision-making and action selection in the environment for trajectory planning in unknown environments.

Reinforcement learning methods include basic elements such as an agent that executes decision-making, an environment with which the agent interacts, state representations that encapsulate environmental information, actions that the agent can perform, rewards that quantify immediate performance, policy functions that map states to actions, and value functions that estimate long-term return expectations. The policy defines the mapping relationship from state to action, which is the core of reinforcement learning. According to different learning methods, reinforcement learning methods can be divided into three categories: value-based methods indirectly obtain policy by learning state-action value functions, which are suitable for discrete action spaces; policy-based methods directly optimize policy functions, which can handle continuous action spaces, but there are problems such as large variance and slow convergence; and actor-critic methods combine the advantages of both, using a critic to evaluate value functions and guide an actor to optimize policy, which achieves more stable and efficient learning.

Owing to the strength in learning optimal strategy, RL-based UAV trajectory planning methods have been developed. Q-learning is a basic RL algorithm that learns which action to choose in each state to bring the maximum cumulative reward by iteratively updating the Q value (state-action value function). Zhao et al. [81] combined asynchronous methods with the tabular Q-learning algorithm and proposed an asynchronous RL architecture for trajectory planning in discrete space. This method alleviated the issue where classical RL relies on continuous updates from a single agent to learn policies and easily leads to slow convergence. However, this method is specifically designed for the fully known environment. Q-learning cannot use geometric distance information when only part of the information about the environment is available. Therefore, Zhang et al. [82] proposed a trajectory planning method according to geometric reinforcement learning (GRL), in which the reward matrix is adaptively updated by the geometric distance and risk information from detection sensors and other UAVs. Moreover, by adjusting the parameters in GRL, a balance between safety and cost-effectiveness can be achieved. Cui et al. [83] proposed a trajectory planning algorithm to plan a collision-free trajectory based on multi-layer RL, which included a lower-layer RL that led the UAV to the terminal location and a higher-layer RL that avoided dynamic obstacles. Compared with classical Q-learning, this method collects both global and local information to significantly enhance performance. However, for continuous states and large state spaces, traditional RL algorithms may encounter the curse of dimensionality.

3.1.3. Deep Reinforcement Learning

Traditional RL is generally applicable only when the set of states and actions is a finite discrete basis and the number of states and actions is small. The cases in practical applications may be very complex, and it is challenging to define discrete states. To deal with high-dimensional input data, NN is used in RL to fit the policy function and value function [84]. This method is called deep reinforcement learning (DRL), which is a cutting-edge research direction in ML. DRL combines the perception capabilities of DL with the decision-making capabilities of RL. As an environment-independent algorithm, DRL demonstrates greater effectiveness in managing high-dimensional UAV trajectory planning in complex, unknown, uncertain, and dynamic environments compared to earlier conventional algorithms that rely on prior knowledge.

Differing from conventional methods where neural networks are commonly opaque, He et al. [85] introduced a twin delayed deep deterministic policy gradient (TD3) reinforcement learning method for UAV trajectory planning and a model explanation method based on feature attribution to achieve model explainability, which generated some easy-to-interpret text and visual explanations. Yan et al. [86] developed a DRL method using an improved dueling double deep Q-networks (D3QN) algorithm for Q-value prediction and an action selection policy for UAVs in dynamic environments with potential enemy threats. For multi-UAV cooperative trajectory planning in obstacle and narrow environments, Xing et al. [11] introduced a UAV swarm adaptive cooperative trajectory planning method according to improved DRL by innovatively introducing long short-term memory (LSTM) RNN to the multi-agent twin delayed deep deterministic policy gradient (MATD3) network, which improved the optimality of trajectory planning and adaptability to narrow passages. Wang et al. [87] developed a trajectory planning method according to D3QN that operates without the need for any prior knowledge of the environment and other UAVs. However, for DRL-based methods, designing an appropriate reward function that effectively guides the agent toward the desired behavior remains a non-trivial task. If the reward function is not carefully designed, the final result may not align with the original objectives.

3.1.4. Other Machine Learning Methods

DL, RL, and DRL have been extensively applied in UAV trajectory planning. In addition, other types of ML methods have also been tried in this field, including newly proposed methods and traditional machine learning methods. Transfer learning (TL) is a method that transfers the common features or model parameters learned in a source task to a target task to improve the performance of the target task. Bo et al. [88] established the pretrained model, utilizing the TL method to incorporate it into formal training, thereby integrating prior knowledge to enhance training performance and endow UAV with the capability to autonomously avoid obstacles and plan trajectories in unknown environments. For the UAV trajectory planning problem with connectivity outage constraint, Fontanesi et al. [89] proposed a TL method that leverages a teacher policy trained in a source domain to accelerate the learning in a target domain. Moreover, Pérez-Cutiño et al. [90] proposed an algorithm that recursively generates trajectories based on the output of neural networks and random forests (RF) to calculate energy-efficient trajectories for UAVs. Support vector machine (SVM), also a traditional machine learning method, is often used to establish safe flight corridors for UAV in trajectory planning [91,92].

Table 3. Comparison of UAV trajectory planning methods employing various types of machine learning.

Category	Algorithm	Contributions	Reference
DL	CNN	Adding time-series properties to CNN to adapt to time-series prediction problems	[65]
	RNN	Solving multi-agent trajectory planning problems together with a decentralized version	[66]
	GNN	Combining a mechanism that allows message-dependent attention and a message-aware graph attention network	[69]
	Transformer	Powerful representation capabilities and parallel computing characteristics	[77]
RL	Asynchronous RL	Combining asynchronous methods with the tabular Q-learning algorithm alleviates the slow convergence of classical RL.	[81]
	GRL	Adaptively updating the reward matrix based on geometric distance and risk information when only partial information about the map is available	[82]
	multi-layer RL	Collecting both global and local information	[83]
DRL	TD3	Proposing a model explanation method based on feature attribution to achieve model explainability	[85]
	D3QN	Combining the greedy strategy with heuristic search rules to improve the learning efficiency of the D3QN during the training phase	[86]
	MATD3	Introducing LSTM RNN into the environment perception end of the MATD3 network and developing an improved potential field-based dense reward function	[11]
Others	TL	Integrating prior knowledge, improving the effect of formal training	[88]
	RF	Improving accuracy and stability in the case of a few samples	[90]
	SVM	Establishing safe flight corridors for trajectory planning	[91]

provides a summary of the development of various MLs in UAV trajectory planning. Among them, DL can be trained on data, making the UAV trajectory planning method highly adaptable in complex environments. In contrast, insufficient or inappropriate training data may lead to unsatisfactory planned trajectories. RL does not require the collection of training datasets in advance and is better suited for trajectory planning in unknown or dynamic environments. ML-based UAV trajectory planning methods’ fault tolerance and learning abilities demonstrate considerable advantages for dealing with complex and dynamic environments. Additionally, certain challenges persist, including the unpredictability of ML algorithms and the potential for erroneous decisions that may result in safety and reliability issues.

3.2. Evolutionary Algorithms

The core idea of EA is to imitate the evolutionary process of natural populations and continuously optimize the quality of solutions. They are a probabilistic optimization algorithm based on the model of natural evolution [93]. EAs do not require gradient information and therefore do not require the continuity and differentiability of functions, making them suitable for addressing problems that traditional optimization algorithms find difficult to solve in UAV trajectory planning.

A statistical analysis was conducted to quantify the number of research studies utilizing each type of EA for UAV trajectory planning from 2010 to 2024, with the results visualized in Figure 9. The statistical results indicate that the number of research studies based on genetic algorithms (GA) and differential evolution (DE) is significantly higher than other types of EAs; therefore, these two methods are the main discussion content of this section.

3.2.1. Genetic Algorithm

GA involves a random global search algorithm that simulates natural biological evolution and was first proposed by Holland in 1975 [94]. This heuristic algorithm is based on genetics and Darwinian evolution and imposes no limitations on derivation and function continuity.

In UAV trajectory planning, GA provides advantages including adaptability, global optimality, and implicit parallelism [95]. Cao et al. [96] transformed the minimum stay time into the shortest trajectory combinatorial optimization in a complex battlefield environment with multiple bases and used GA to generate reconnaissance trajectories. Ergezer and Leblebicioglu [97] developed new mutation operators tailored to task requirements and constraints to plan a better trajectory for maximizing information collection. For multi-UAV, Sahingoz [98] developed a parallel GA to calculate a feasible trajectory for each UAV in a known environment. Shorakaei et al. [99] implemented trajectory planning for multi-UAV based on probability graphs and parallel GA to optimize the trajectory of each of the UAVs and avoid UAV collisions. However, in complex search spaces, GA also faces challenges of slower convergence speed, longer calculation time, and the risk of prematurely converging to a local optimum. Various improvements have been introduced to enable GA to escape the local optimum, one of which is the vibration genetic algorithm (VGA). VGA is implemented by periodically using vibrational mutation operators on all genes in the entire population to disperse individuals [100]. Pelivanoglu [101] then extended VGA to the multi-frequency vibration genetic algorithm (mVGA), incorporating the fuzzy c-means clustering method and Voronoi diagram to improve the initial population. This method effectively reduced the calculation time in addressing UAV trajectory planning problems. However, the vibration mechanism introduces additional parameters requiring adjustment, and the performance of the VGA may be susceptible to these parameter settings.

3.2.2. Differential Evolution

DE involves a stochastic global search algorithm that was proposed by Storn and Price [102]. The order and method of selection, crossover, and mutation operations in DE differ from those in GA. Compared with traditional GA, DE has lower computational complexity, efficient memory utilization, and faster convergence [103].

In the application process, UAV trajectory planning is usually modeled as an optimization problem and solved using DE. Brintaki and Nikolos [104] designed an offline trajectory planner based on DE for known static environments, demonstrating that DE can effectively find feasible trajectories for UAV under constraints within an acceptable period. However, traditional strategy configuration and parameter tuning methods are cumbersome, so researchers have introduced adaptive mechanisms to improve performance. Adhikari et al. [105] proposed a fuzzy adaptive DE (FA-DE) for the 3D UAV trajectory planning problem, which automatically adjusts parameters through a fuzzy logic controller. This method can better explore and exploit the search space and reduce the possibility of premature convergence. Yu et al. [106] designed an adaptive selection mutation operator for constraint differential evolution (CDE), which determines the probability of an individual entering the mutation phase according to the individual’s fitness value and constraint violation, thereby improving the exploitation and maintaining the exploration. It is worth noting that when UAVs operate in a complex environment, the number of constraints increases, increasing the requirements for trajectory planning methods. In recent years, the ensemble strategy method has been used to design high-efficiency DE algorithms [107,108,109]. Chai et al. [110] developed the Multi-Strategy Fusion Differential Evolution (MSFDE) algorithm, which integrates the multi-population strategy, teaching-learning-based optimization (TLBO)-based adaptive strategy, and interactive mutation strategy to improve the performance of UAV trajectory planning with multi-objective constraints in complex environments.

3.2.3. Other Evolutionary Algorithms

In addition to GA and DE, other types of EAs have been tried to plan UAV trajectories. One type is the genetic programming (GP) proposed by Koza [111], in which the potential solutions are coded in the form of trees instead of the linear chromosomes widely used in GA. Yang et al. [112] used GP for UAV trajectory planning and proposed several specially designed functions and a redesigned decoding system. They pointed out that GP showed better modeling and optimizing ability in trajectory planning. Another method is the evolution strategy (ES), which has a different selection operation compared to GA. Hohmann et al. [113] proposed the hybrid evolutionary strategy (HES) that combines ES with the exact Dijkstra algorithm for multi-objective trajectory planning of UAV. In addition, for the multi-objective trajectory planning problem for UAVs in 3D large-scale urban environments, the same research team used traditional ES and multi-objective covariance matrix adaptation evolution strategy (MO-CMA-ES) as optimizers to solve the established optimization problem, thereby planning trajectories for UAVs [114].

Table 4. Comparison of UAV trajectory planning methods employing various types of EAs.

Category	Algorithm	Contributions	Reference
GA	GA	Solving complex combinatorial optimization problems	[96]
	GA	Proposing new mutation operators for specific problems	[97]
	parallel GA	Developing a parallel implementation of GA to find a solution faster.	[98]
	parallel GA	Trajectory planning based on probability graph and parallel GA	[99]
	mVGA	Using the vibrational mutation operators to solve the premature convergence of GA	[101]
DE	DE	Designing an offline UAV trajectory planner based on DE	[104]
	FA-DE	Introducing a fuzzy logic controller to automatically adjust parameters	[105]
	CDE	Designing an adaptive selection mutation operator	[106]
	MSFDE	Integrating multi-population strategy, adaptive strategy, and interactive mutation strategy	[110]
Others	GP	Designing special function and symbol operators for GP	[112]
	ES	Combining ES with the exact Dijkstra algorithm	[113]
	MO-CMA-ES	Proposing an energy model and a noise model for a UAV	[114]

provides an overview of the development of various EAs in UAV trajectory planning. The implicit parallelism of EA makes it more efficient when dealing with large-scale problems. Meanwhile, operations such as crossover and mutation can explore multiple possible solutions in the solution space, endowing EAs with strong global search capabilities. The problem of classical EAs prematurely converging to local optima in some cases has also been alleviated by introducing certain mechanisms. However, it is worth noting that the performance of EAs is sensitive to parameters including population and crossover and mutation probabilities. Improper parameter selection may adversely affect the effectiveness of trajectory planning.

3.3. Swarm Intelligence

Swarm intelligence (SI) originated in nature as a bionic intelligence algorithm. In the biological world, individuals within a group often exhibit coordinated and orderly behaviors during their activities [115]. In this way, simple tasks completed by individuals can be superimposed to accomplish complex tasks. SI provides another solution for UAV trajectory planning to deploy relatively basic agents for intricate and goal-based behaviors by emulating the natural group dynamic systems [116].

The number of research studies on UAV trajectory planning according to each SI algorithm is analyzed from 2010 to 2024 (Figure 10). It shows that the research on particle swarm optimization (PSO) and ant colony optimization (ACO) has the fastest-growing trend and the largest cumulative number, which are mainly summarized.

3.3.1. Particle Swarm Optimization

PSO originated from the study of the predatory behavior of bird flocks. It assumes that individuals navigate the search space as ideal particles and utilize information sharing among group members to transition the entire group from a disordered state to an ordered state to obtain the optimal solution [117]. The search space is defined as the set of all probabilistic solutions to the problem. Multiple particles are initialized with random velocities and positions in the search space. At each time step, each particle needs to calculate its fitness value and adjust its velocity and position based on the global optimal solution and individual optimal value. In PSO, the $i$-th particle updates its velocity and position at the $T$-th step according to the following equation [40]:

$$\begin{array}{l}{V}_i^{T+1}=W{V}_i^T+r_1{C}_1(P_{best}-X_i^T)+r_2{C}_2(G_{best}-X_i^T)\\ X_i^{T+1}=X_i^T+V_i^T\end{array}$$

(1)

where $X_i^T$ and $V_i^T$ denote the position and velocity vectors of the $i$-th particle at $T$-th step, $W$ represents the inertia weight that maintains a balance of global and local search capabilities, $C_1$ and $C_2$ denote the acceleration constants preset by users, $r_1$ and $r_2$ denote the random numbers that are generated in the range of $\left[0,1\right]$, $P_{best}$ denotes the optimal position of the $i$-th particle at $T$-th step, $G_{best}$ denotes the global optimal position, respectively.

The advantages of PSO lie in its minimal parameter settings and ease of implementation [25]. However, the optimization trajectory is limited by the individual and group particle experience, and over-reliance on individual particles is possible, making the algorithm become trapped in local optima. Numerous enhanced algorithms based on PSO have been proposed to address this challenge of UAV. To plan a trajectory with a balance of the flying distance, altitude, and cost, Liu et al. [118] addressed the issues of local optima and premature convergence by integrating a new adaptive sensitivity decision operator with PSO, achieving global search and fast convergence capabilities. Meanwhile, computation time was reduced by locating the potential position of the particle that was determined with high probability while eliminating other candidate particles. In addition, Phung et al. [119] proposed a new spherical vector-based particle swarm optimization (SPSO) algorithm for UAV trajectory planning in multi-threat complex environments via the correspondence of particle position and UAV velocity, turning angle, and diving angle. SPSO was used to efficiently search the UAV configuration space to determine the optimal trajectory by minimizing the cost function.

3.3.2. Ant Colony Optimization

ACO originated from a heuristic algorithm that simulates the activities of ants [120]. Ants release pheromones and travel in directions with high pheromone concentrations. This cooperative mechanism allows the ant colony to accumulate pheromones faster on shorter trajectories, ultimately finding the shortest trajectory. As an imitation of natural behavior, ACO first models the UAV flight area using nodes and initializes the number and origin location of agents [121]. Then, the agents construct trajectories and deposit pheromones accordingly. The probability distribution of $k$-th agent choosing the next node to visit is as follows:

$$P_{ij}^k(t)=\left\{\begin{array}{ll}{\displaystyle \frac{{\left[{\tau }_{ij}(t)\right]}^{\alpha }{\left[{\eta }_{ij}(t)\right]}^{\beta }}{{\displaystyle \sum _{s\in allo{w}_k}{\left[{\tau }_{is}(t)\right]}^{\alpha }{\left[{\eta }_{is}(t)\right]}^{\beta }}}}\hfill & s\in allo{w}_k\hfill \\ 0\hfill & \mathrm{otherwise}\hfill \end{array}\right.$$

(2)

where $P_{ij}^k(t)$ denotes the probability of agent $k$ moving from node $i$ to node $j$ at time $t$, $\alpha$ represents the importance coefficient of pheromone concentration, $\beta$ represents the importance coefficient of heuristic information, ${\tau }_{ij}$ represents the pheromone concentration accumulated on the link $\left(i,j\right)$, ${\eta }_{ij}$ represents the heuristic information, $allo{w}_k$ represents the nodes to be visited by agent $k$. Regulating $\alpha$ and $\beta$ can controlling the tendency to choose trajectories. When all agents complete an action, the pheromone concentration on each link trajectory is updated based on the following equation:

$${\tau }_{ij}(t+1)=(1-\rho ){\tau }_{ij}(t)+\rho {\displaystyle \sum _{k=1}^m\Delta }{\tau }_{ij}^k$$

(3)

where $\rho$ is the pheromone evaporation coefficient, $m$ is the number of agents, and $\Delta {\tau }_{ij}^k$ is the pheromone concentration released by the $k$-th agent on the trajectory link node $i$ to node $j$. The agent tends to move in the direction where the pheromone concentration is higher, leading to the global optimal trajectory with the highest pheromone intensity.

ACO has been used to address the requirements of minimizing threat exposure and minimizing the trajectory length required to cover a given area in UAV trajectory planning [122]. For example, Akshya et al. [123] used ACO to find the optimal trajectory covering a given area and compared it with the minimum spanning tree approximation algorithm. The result showed that ACO was better than the latter. In addition, ACO is a distributed algorithm based on individual collaboration and has strong scalability and adaptability. Therefore, it has unique advantages in dealing with the trajectory planning of UAV swarms. Rosalie et al. [124] combined the optimal chaotic migration model with ACO and introduced the chaotic ant colony optimization for coverage (CACOC) algorithm to solve the area coverage problem of UAV swarms. Subsequently, Dentler et al. [7] extended CACOC by a collision avoidance mechanism to compute UAV target waypoints, which effectively completed the coverage task and reduced the average tracking error of UAVs, while increasing the average minimum distance of UAVs.

3.3.3. Other Swarm Intelligence Algorithms

In addition to PSO and ACO, numerous swarm intelligence algorithms are developed, including the firefly algorithm (FA) that imitates the information exchange between fireflies [125,126], bat algorithm (BA) that imitates the echolocation behavior [127], artificial bee colony optimization (ABC) that imitates the intelligent foraging behavior [128], pigeon-inspired optimization (PIO) algorithm that imitates geomagnetic navigation and landmark navigation [129], whale optimization algorithm (WOA) that imitates the hunting characteristics hierarchy of whales [130], grey wolf optimization (GWO) algorithm which imitates the predatory behavior of gray wolves [131,132], dragonfly optimization algorithm (DOA) that imitates the foraging behavior of dragonflies [133]. SI algorithms exhibit substantial large-scale search capabilities and strong scalability, which supports the resolution of complex UAV trajectory planning challenges.

However, SI algorithms also have their limitations, including significant computational complexity, slow convergence, and a tendency to get trapped in local optima. To overcome these shortcomings, hybrid algorithms have been proposed to combine the advantages of individual algorithms to address specific challenges and improve overall performance. To speed up the convergence of bat positions updating in BA, Lin et al. [26] proposed an improved APF method and introduced a chaotic strategy to avoid falling into local optima. Wu et al. [27] introduced an adaptive chaos-Gaussian switching-solving strategy and coordinated decision-making mechanism into the basic WOA, overcoming the shortcoming that WOA is prone to falling into local minima. The combination of methods enhances the global search capability, accelerates the convergence speed, and avoids falling into local optima, which can have better optimization performance and adaptability in trajectory planning.

A summary of the development of various SI algorithms in UAV trajectory planning is shown in

Table 5. Comparison of UAV trajectory planning methods employing various types of SI algorithms.

Category	Algorithm	Contributions	Reference
PSO	PSO	Proposing an adaptive sensitivity decision operator to address the limitations of local optimal and premature	[118]
	SPSO	SPSO searches for solutions within the configuration space rather than the Cartesian space to improve the chances of identifying quality solutions.	[119]
ACO	ACO	Using ACO to provide an approximate solution	[123]
	CACOC	Using chaotic dynamics to replace the random part of ACO to improve performance on the coverage problem	[124]
	CACOC	Extending CACOC by a collision avoidance mechanism	[7]
Others	BA	Using the artificial potential field method to speed up the convergence of bat position updates	[26]
	WOA	Introducing an adaptive chaos-Gaussian switching method coupled with a coordinated decision-making framework to overcome the defect of local minima	[27]

. The SI algorithm can achieve optimization through local interactions between individuals without central control. Therefore, SI-based UAV trajectory planning methods inherently have parallel processing capabilities, enabling them to improve the computational efficiency of trajectory planning. Additionally, the SI algorithm exhibits robustness against individual failures and environmental changes, maintaining effective performance in dynamic and uncertain environments.

4. Trajectory Planning Applications in Complex Environments

According to the systematic analysis of the impact of UAV types and complex environments on UAV trajectory planning and the theoretical progress of intelligent algorithms in trajectory planning, the following content further explores the application of trajectory planning methods according to intelligent algorithms in actual complex task environments. Existing studies have shown that trajectory planning methods based on machine learning, evolutionary algorithms, or swarm intelligence algorithms have demonstrated successful application in typical scenarios such as transportation and inspection. Starting from the characteristics of various tasks, the technical implementation pathways of trajectory planning methods based on intelligent algorithms are summarized across different application scenarios. The adaptability and advantages of these methods in addressing complex factors, such as obstacles, limited communication, and environmental uncertainty, are further analyzed, thus revealing the practicality and development potential of trajectory planning methods based on intelligent algorithms in complex environments.

4.1. Transportation

4.1.1. Slung-Load Transportation

A UAV can transport cargo by rigidly attaching it to the body or by suspending it with cables. The rigid connection method is relatively simple and suitable for delicate operations, while the increased inertia may diminish the attitude response rate of the UAV. The cable suspension method is a common cargo-carrying method for rotary-wing UAVs. This method reduces the impact of the payload on the rotational inertia and avoids the issue of mismatch between the payload and the fuselage shape of the UAV but introduces new constraints to trajectory planning, such as payload swing and cable tension [134]. The swing of the payload increases the instability of the UAV, while excessive cable tension can potentially cause the cable to break. The additional constraints make it more challenging to plan the UAV transportation trajectory in a complex environment.

For the UAV slung-load system, Li et al. [135] proposed a technique for generating the minimum swing trajectory of the UAV suspended load according to Deep Q-Networks (DQN) to control the swing of the suspended load within a certain range during the entire transportation process. Hua et al. [136] proposed a time-optimal trajectory planning strategy based on convex optimization and DRL, which fully considered physical constraints such as velocity, acceleration, and cable tension to ensure the cable tension was within the acceptable range. For time-sensitive cargo delivery tasks in environments with static obstacles, Faust et al. [137] developed a trajectory planning method that combined a sampling-based method and RL to deliver the payload to their destinations promptly without collisions while maintaining bounded load displacement, as shown in Figure 11. The method developed a swing-free strategy constrained to an action subspace, and the RL policy was modified to handle diverse tasks through the use of task-specific action spaces. To optimize the trajectory length, task duration, and energy consumed during the task for a UAV slung-load system, Ergezer [138] developed a multi-objective GA to solve the trajectory planning problem and developed problem-dependent mutation-like operators to avoid obstacles.

For larger or heavier cargo, a single UAV may be insufficient. The collaboration of multiple UAVs is a practical solution to increase payload-carrying capacity. This modular approach offers greater flexibility, with the number of UAVs adjustable based on the task requirements. Different from the trajectory planning of a single UAV, effectively addressing spatial, time, and task coordination among different UAV trajectories is crucial for solving the coordinative trajectory planning problem. The constraints introduced under such tasks mainly include collision avoidance [139], cooperation requirements [140], and formation shape change [141]. The cable suspension method introduces passive degrees of freedom to the UAV, resulting in swing during flight. To solve the problem, Li et al. [142] introduced a trajectory planning method according to the RL algorithm of an approximate value function. In this method, the parameter vector of the approximate value function was acquired via training, and the greedy strategy was used to generate the flight trajectory, aiming to ensure uniform tension on the suspension cables and efficiently transport the load to the target location.

In summary, existing research has fully demonstrated the wide application and significant advantages of trajectory planning methods based on intelligent algorithms in UAV transportation tasks. Such methods generally adopt reinforcement learning or evolutionary algorithms and achieve efficient trajectory planning under multiple constraints such as cable tension, load swing, obstacle avoidance, and time optimization, and they have good generalization and adaptability. With the increase in task complexity, research has gradually expanded to multi-UAV coordinative transportation tasks, solving problems such as time synchronization, spatial coordination, and load distribution. However, these methods still face some challenges, including unstable convergence, insufficient adaptability to dynamic environments, and high complexity of multi-UAV coordinative strategies. Therefore, although trajectory planning methods of intelligent algorithms show practical value and development potential for transportation tasks, further in-depth research is still needed in terms of algorithm efficiency, safety assurance mechanisms, and system coordinative strategies.

4.1.2. Multi-Destination Transport

In addition to the single-destination case, UAVs can also provide supplies to multiple units per delivery to further reduce the delivery cost in the transport scenario. For this more complex task scenario, the constraints on UAV energy consumption, flight time, and obstacle avoidance in the modeling of single-destination transportation are simple, and the constructed model cannot meet the actual delivery needs. In such cases, factors such as pickup and delivery order, maximum load, and endurance need to be considered to plan the trajectories for the UAV, which is a large-scale planning problem.

Regarding the energy consumption variation of UAVs, mixed time windows of the customers, and simultaneous delivery and pickup, Du et al. [143] used the large neighborhood search algorithm to accelerate the convergence rate and introduced an improved GA-based cooperative trajectory planning algorithm to optimize the trajectory, service UAV allocation jointly, and minimize the total energy cost of the UAV swarm during delivery. The proposed algorithm was verified on the Solomon standard data, indicating that the solution obtained by the proposed algorithm has a lower transportation cost relative to classic GA and PSO.

The flexibility of the UAV enhances the efficiency of material transportation, but it is worth noting that some UAVs, especially multi-rotor UAVs, also have disadvantages such as small payload and short range, which reduces the scope of application of pure UAV transportation solutions. The increase in vehicle load and endurance can reduce the delivery cost to a certain extent [143]. Traditional vehicles have the characteristics of large capacity and high reliability. Therefore, integrating UAVs with traditional delivery vehicles is a promising solution to maximize the benefits of both methods and optimize logistics efficiency. Petr and Kutěj [144] developed a model for cooperating ground vehicles and UAVs to supply units on the battlefield. They proposed a metaheuristic algorithm based on ACO as the solution, which improved the probabilistic strategies for UAV deployment, customer assignment, and local search refinement. The attempt shows that the savings achieved by the cooperation of ground vehicles and UAVs are significant, optimizing the delivery process to achieve minimal total completion time while minimizing the total cost of transportation.

These studies demonstrate that trajectory planning methods based on intelligent algorithms exhibit strong multi-objective optimization capabilities, can globally optimize transportation trajectories and service allocation while considering constraints such as payload limits, endurance, and time windows, and show high adaptability in ground-air coordinative delivery scenarios. Evolutionary algorithms and swarm intelligence algorithms are commonly used in such tasks, and the convergence speed of the algorithm and the quality of the solution are improved by combining strategies proposed according to the characteristics of specific problems. However, the complexity of modeling and solving such multi-objective, multi-constraint problems is considerable. Intelligent algorithms often entail significant computational overhead and stability challenges, particularly in dynamic environments, where optimality is difficult to guarantee.

4.2. Inspection

4.2.1. Predetermined Checkpoints

A typical case of an inspection task involves surveying several locations of interest, which requires a UAV with detection capabilities to plan a trajectory through these locations.

The checkpoint-based trajectory planning is an important component for inspection. In this problem, a UAV trajectory needs to be generated to visit all checkpoints while minimizing a specific objective function under several constraints. In practical applications, where reconnaissance often involves multiple targets, it is crucial to study autonomous strategies for planning a collision-free, shortest, or most economical trajectory. Checkpoint-based trajectory planning is non-deterministic polynomial complete (NP-complete), which has no optimal solution in polynomial time. Many studies have simplified this problem to generating an optimal sequence of checkpoints. The trajectory is identified by connecting these checkpoints with straight-line segments.

However, the generated trajectory may be unflyable because the UAV is not able to follow a non-smooth trajectory [145,146]. To plan the smooth trajectory of the target coverage task with predetermined checkpoints, Pehlivanoglu et al. [147] used a splines parameterization trajectory and proposed a GA-based UAV trajectory planning method. This method used the Voronoi diagram, ACO, and clustering methods to enhance the initial population of GA, thereby accelerating the convergence process and significantly shortening the planning time for feasible trajectories. The example phenotypes of individuals from the initial population before and after the enhancement are shown in Figure 12. Compared with conventional GA, the enhancement of the initial population provides random and controlled diversity, significantly reducing the computational time.

In the reconnaissance task of predetermined checkpoints, the UAV trajectory planning method based on intelligent algorithms usually models the task as a combinatorial optimization problem and obtains the trajectory by optimizing the visit sequence of target points and combining smoothing methods. With the assistance of evolutionary algorithms and swarm intelligence algorithms, such methods demonstrate strong global search abilities and multi-objective optimization capabilities, which can improve solution efficiency and handle complex constraints. However, these methods have problems such as sensitive parameter settings and being prone to getting trapped in local optima when handling large-scale checkpoint scenarios or complex environmental constraints, and their application in dynamic environments is still limited.

4.2.2. Minimum Time Search

In tactical inspection tasks, such as frontier search and target discovery, UAVs need to find one or more unknown targets as quickly as possible. The uncertain flight endpoint and the search time requirements make the trajectory planning of UAVs more complicated. Due to the limitations of endurance and flight speed, it is challenging for a single UAV to achieve such minimum time search (MTS) tasks.

Multiple UAV cooperations can improve reconnaissance efficiency by dividing the task into different parts that can be executed simultaneously. Intending to find lost targets in the minimum possible time, Perez-Carabaza et al. [13] developed the ACO-based trajectory planning method for a UAV swarm, which included a heuristic function designed specifically for MTS, enabling ACO to generate high-quality initial solutions and accelerate algorithm convergence. The method achieved better solutions in considerably less computational time compared to several heuristics or optimization algorithms previously tested in the MTS problem. However, policies for UAVs and the problem complexity often require continuous monitoring of the UAV states, which requires communications to be maintained at all times. To enhance the practicality of the trajectory planning method, this research team refined their previous method by incorporating constraints related to communication and collision avoidance, which reduced the time required to locate unknown targets, ensuring continuous multi-hop communication with the ground control station and collision avoidance among UAVs [120].

These studies have demonstrated the effectiveness of intelligent algorithm-based trajectory planning methods in minimum-time search tasks. The implementation path usually includes task area division, search strategy design, initial trajectory generation, and trajectory optimization. The methods exhibit good extensibility to multi-UAV systems, significantly enhancing parallel search efficiency. However, they lack sufficient real-time and robustness in situations where the environment changes rapidly, which limits their application in some practical scenarios.

4.2.3. Sweep Coverage

Another type of inspection task focuses on maximizing information acquisition from target regions. In such tasks, UAVs traverse the entire area to collect relevant sensor information, which can be classified as sweep coverage tasks [148]. To perform these tasks autonomously, coverage trajectory planning is a fundamental problem. Cakici et al. [149] introduced a GA-based trajectory planning method for a UAV swarm with the initial population generated from seed trajectories by the pattern search method and the solution of the multiple traveling salesman problem (mTSP). Similarly, Xie and Chen [150] proposed a GA-based method for trajectory planning to cover multiple disjoint regions with the new sets-based chromosome representation and crossover and mutation operators. However, these methods are implemented in a centralized manner, which hampers system autonomy and makes them susceptible to communication interference. Wang et al. [151] proposed an accurate coverage exploration distributed PSO trajectory planning algorithm based on distributed PSO and an online lawn mower algorithm for achieving complete area coverage and reliable reconnaissance of targets, which used geofencing to handle forbidden zones, boundaries, and collision avoidance and also designed the jump-out mechanism and a revisit mechanism to save invalid search work, as shown in Figure 13. In addition, with the development of end-to-end algorithms, Zhu et al. [76] exploited the state-of-the-art Transformer together with the weighted A* to develop a machine learning algorithm aimed at minimizing the total age of information of data gathered by a UAV from a ground IoT network, demonstrating that this trained model can generate solutions without the need to retrain the model.

Some inspection tasks aim for the UAV swarm to collect maximum information while minimizing the time required. Valente et al. [54] proposed a population-based metaheuristic algorithm called harmony search (HS) for the complete coverage trajectory planning task, which reduced the task time by minimizing the number of turns and was applied to the regular or irregularly shaped region. For tasks where UAVs need to fly close to the 3D terrain surface to thoroughly cover all areas for reconnaissance, Mou et al. [152] developed a geometric method to project a 3D irregular terrain surface into multiple weighted patches and proposed a DRL multi-UAV trajectory planning method based on a leader-follower architecture. The high-level leader UAV (LUAV) used the swarm deep Q-learning (SDQN) RL algorithm to select patches, and the low-level follower UAV (FUAV) planned the coverage trajectory using the spiral-zigzag searching pattern. To mitigate the communication constraints of the LUAV, SDQN incorporates an observation history module that leverages a CNN combined with a mean embedding technique. This method enables efficient and complete patch coverage with minimal overlap and outperforms reinforcement learning approaches such as the vibrating particles model and multi-agent spanning tree coverage in terms of total coverage time. In addition, factors such as unpredictable obstacles and emergencies may lead to UAV malfunctions or disruptions in communication links. To address such complex scenarios, Hu et al. [153] proposed a distributed online collaborative deep Q-learning algorithm trajectory planning method for multi-UAV systems, which introduced an efficient environmental information fusion technique to facilitate UAV collaboration and enable global situational awareness and allowed the algorithms to generate real-time coverage paths that minimize task duration while avoiding overlap, omissions, and collisions.

These studies mainly focus on the two goals of maximizing information collection and minimizing task time. They generally adopt environmental discretization modeling combined with machine learning, evolutionary algorithms, or swarm intelligence algorithms, and deal with practical constraints through technologies such as geographic fencing and jump-out mechanisms. This type of method shows significant improvement in coverage efficiency, adaptability, and scalability and can flexibly adapt to diverse terrains, no-fly zones, and dynamic changes in tasks. However, there are still challenges such as real-time bottlenecks and a lack of robustness, especially in environments with dense obstacles. The computational complexity problem is particularly prominent.

4.3. Others

A UAV can also be equipped with a variety of weapons for combat tasks. It is necessary to consider threat sources, including terrain obstacles, enemy radars, and defense forces, alongside the target and task requirements in this situation. One approach is to follow a trajectory that avoids the air defense threat area. For example, Aslan [154] considered the cost of enemy threats in the task field and the fuel cost to evaluate the trajectory determined for the UAV based on a modified immune plasma algorithm (IPA), called centrifuge IPA (centIPA). Duan et al. [155] proposed an NN trained by the imperialist competitive algorithm (ICA) and used this hybrid method to solve the problem of global trajectory planning for UAVs avoiding threat areas. In addition, low-altitude flight is also commonly used. Due to the terrain-mask effects, UAVs flying at low altitudes are less likely to be detected by enemy radars and much safer than flying at high altitudes. Duan et al. [156] proposed a UAV 3D trajectory planning method that mixed ACO and DE algorithms to plan a trajectory that both avoided the threat area and minimized fuel consumption. In the process of ant pheromone updating, DE was used to optimize the pheromone trail of the ACO model, which maintained the strong robustness of ACO while accelerating the global convergence speed. Niu et al. [157] proposed an adaptive neighborhood-based search enhanced artificial ecosystem optimizer to plan the minimum flight altitude trajectory for a UAV. It introduced quadratic interpolation to solve the premature convergence problem, thereby improving the capability to find the global optimum in conjunction with the adaptive neighborhood search strategy.

Formation applications of UAVs are also important in swarm shows or carrying out specific tasks. This requires the UAV to maintain a relative distance within a certain range during flight. Due to its non-deterministic polynomial hard (NP-hard) characteristics, collision avoidance constraints, and close formation requirement, UAV formation flight trajectory planning is challenging. For the arrival time coordination requirements of multiple UAVs, Chen et al. [158] used the Dubins trajectory to reduce the dimension of complicated trajectory planning problems and proposed a multi-UAV trajectory planning method based on PSO so that the UAVs in the swarm arrived at the expected location on time. Huang et al. [159] used the Voronoi diagram to model the environment consisting of multiple threat sources and proposed an improved ant colony optimization algorithm (IACO) that redefined the heuristic information function and pheromone update method. This multi-UAV trajectory planning method generated the initial trajectory by IACO and induced the k-degree smoothing method to ensure the smoothness of the trajectories and multi-UAV arrival at the targets simultaneously or with an acceptable time interval. When encountering complex obstacles and narrow passages in unknown environments, the difficulty is greatly increased because it involves formation maintenance and formation changes. This is because the UAV swarm needs to maintain formation, but also needs to change formations when encountering obstacles to pass through narrow passages. To solve this problem, Xing et al. [11] developed a multi-UAV adaptive trajectory planning method by introducing LSTM RNN into the environment perception end of the MATD3 network. The adaptive formation maintaining model and transformation strategy were proposed for the formation cooperation issue and navigating narrow passages, respectively.

In combat tasks, trajectory planning methods usually combine task requirements with threat modeling to build multi-objective optimization models such as target constraints, threat avoidance, and fuel consumption, and mainly generate safe flight trajectories that can avoid enemy defense areas through hybrid intelligent algorithms. Formation flight task research focuses on spatiotemporal coordination issues, solving the problems of coordinated arrival of multiple UAVs, maintaining relative spacing, synchronous formation flight, and obstacle avoidance. These studies have shown that trajectory planning methods based on intelligent algorithms can effectively cope with high-dimensional constraints, multi-source threats, and dynamic environmental changes. However, there are still problems such as strong dependence on perception accuracy and communication stability, and limited scalability of large-scale multi-UAV systems.

5. Trends and Challenges

Trajectory planning is a core scientific problem in the application of UAVs in complex fields. Using intelligent algorithms to plan trajectories for UAVs has been widely studied and has been partially applied. However, UAV trajectory planning in complex environments continues to present several challenges and constraints that require further investigation and refinement.

• In many cases, the environmental information used for trajectory planning is incomplete or uncertain, containing many unpredictable dynamic factors that evolve. One common approach is to plan the trajectory for UAVs online, which has become a current research trend. The update rate is one of the important requirements for online trajectory planning, which will affect the quality of the planned trajectory and even flight safety. To address this challenge, finding more efficient intelligent algorithms or representing the trajectory with fewer parameters is necessary, thereby reducing the computational time required for planning the trajectory.
• Intelligent algorithms are one of the novel solutions to plan trajectories for UAVs, and they have unique advantages in complex environments. However, significant challenges persist and cannot be overlooked. EAs and SI algorithms have the advantages of strong adaptability, good robustness, and strong parallelism, but they may face the challenge of falling into local optima, which may mislead the trajectory planning of the UAV. Despite numerous attempts to address this issue, further research is required to ensure global convergence throughout the optimization process. The characteristics of DL make it highly adaptable in complex environments, while its unpredictability and the potential for erroneous decisions may result in safety and reliability issues. Furthermore, when applying RL- or DRL-based trajectory planning methods in practical scenarios, the environment rarely provides useful reward feedback, typically indicating either partial or full task completion. The sparse reward problem may significantly slow the convergence of the algorithm or even fail to find a feasible trajectory within an acceptable time.
• To cope with complex environments, UAV trajectory planning methods based on intelligent algorithms are often expected to balance coordination, accuracy, collision avoidance, and efficiency. Current research usually focuses on developing UAV trajectory planning methods tailored to specific scenarios or requirements. In transportation applications, factors such as terrain and obstacles are generally considered. Coordinated delivery between UAVs and ground vehicles and multi-UAV cable-suspended load transportation are gradually becoming a research trend. Still, the current related research based on intelligent algorithms usually models the load as a point mass, which lacks general applicability. The main research objectives of UAV trajectory planning in inspection applications include minimizing search time and maximizing information collection. Consequently, developing real-time trajectory planning methods capable of processing large volumes of information is a direction that warrants further research. Existing UAV trajectory planning methods based on intelligent algorithms each demonstrate unique advantages. However, approaches that achieve a balance across multiple scenarios may be more practical for real-world applications.

6. Conclusions

Pursuing efficient, real-time, and scalable trajectory planning methods for complex environments is a prominent issue in UAV research. Recent articles on intelligent algorithm-based UAV trajectory planning were reviewed. The increasing trend in the number of related research proves that intelligent algorithms have become one of the popular research directions in UAV trajectory planning. Current approaches are generally sufficiently practical in avoiding falling into local optima, circumventing obstacles, and minimizing computational costs. The characteristics of ML learning action strategies are well-suited for online trajectory planning. In particular, DRL makes up for the capacity to handle large state-action spaces, is ideal for complex environments, and has been widely used in this area. The mechanism of EA and SI algorithms determines that they are adaptive and easy to parallelize. They are suitable for solving complex, large-scale, nonlinear, and non-differentiable optimization problems in UAV trajectory planning and can search the solution space in parallel in multiple directions. The UAV trajectory planning method based on intelligent algorithms has fully considered factors such as terrain, obstacles, and meteorology in its application. Online trajectory planning leveraging intelligent algorithms adaptable to diverse scenarios represents a critical direction in the development of UAVs. Key contents include addressing the unpredictability of ML and mitigating the problem of EAs and SI algorithms falling into local optima. In applications, multi-agent coordination and the interactions between UAVs and the environment are also research focuses. These advancements will provide effective solutions for the applications of transportation, inspection, and other domains.