Research, Analysis, and Improvement of Unmanned Aerial Vehicle Path Planning Algorithms in Urban Ultra-Low Altitude Airspace

Abstract

Urban ultra-low altitude airspace (ULAA) presents unique challenges for unmanned aerial vehicle (UAV) path planning due to high building density and regulatory constraints. This study analyzes and improves classical path planning algorithms for UAVs in ULAA. Experiments were conducted using A*, RRT, RRT*, and artificial potential field (APF) methods in a simulated environment based on building data from Chengdu City, China. Results show that traditional algorithms struggle in dense obstacle environments, particularly APF due to local minima issues. Enhancements were proposed: a density-aware heuristic for A*, random perturbation for APF, and a hybrid optimization strategy for RRT*. These modifications improved computation time, path length, and obstacle avoidance. The study provides insights into the limitations of classical algorithms and suggests enhancements for more effective UAV path planning in urban environments.

1. Introduction

The planning of flight paths for UAVs is of great importance to the management of air traffic by UAVs [1]. The development of safe and efficient path planning algorithms can assist UAV operators in reducing operational risks, improving operational efficiency, and increasing revenue [2]. Furthermore, these algorithms can facilitate the supervision of UAVs by relevant regulatory units, while simultaneously ensuring the safety and privacy of individuals within the operational environment [3,4]. In 2024, the Interim Regulations on the Administration of Unmanned Aircraft Flights were implemented in China, which proposed that airspace outside the scope of controlled airspace shall be the airspace suitable for micro, light, and small UAVs [5]. Furthermore, the regulations stipulated that the airspace with a true height of less than 120 m (excluding air exclusion zones, ultra-low), the altitude flight airspace for military aviation, air restriction zones and surrounding airspace, and other areas requiring classification as controlled airspace shall be designated as controlled airspace. The flyable airspace for micro, light, and small UAVs is the key premise of this paper’s research and therefore falls under the category of controlled airspace [6,7,8,9]. In this paper, the aforementioned area is defined as urban ULAA. In normal circumstances, the maximum altitude of urban ULAA for micro, light, and small UAVs is 120 m, which results in the presence of numerous high-rise buildings in this airspace. This not only increases the complexity of urban ULAA, but also makes it more challenging for UAV flight path planning.

The majority of traditional UAV path planning algorithms can be classified into four main categories: geometric algorithms, artificial potential field methods, grid-based search algorithms, and sampling-based algorithms [10]. Geometric algorithms include visible graphs and cell decomposition methods, among others, but they are primarily suited to low-dimensional path planning problems [11,12]. APF assumes the existence of a virtual force, including the repulsive force of obstacles and the attractive force of the target area, and the system moves according to the direction of this combined force. However, APF is prone to the local minimum problem [13]. Grid-based search methods assume that each state corresponds to a grid point. The A* algorithm is a well-known example of this approach. However, the computation time and memory requirements grow exponentially with increasing dimensionality [14]. In high-dimensional state spaces, sampling-based algorithms offer superior performance and probabilistic completeness. This means that, if a feasible path exists, the probability that the algorithm will fail to find it tends to zero as the number of samples increases [15]. However, this class of algorithms also provides only weak global guarantees. Therefore, in terms of the characteristics of the algorithms themselves, sampling-based algorithms are more suitable for path planning in urban ULAA.

2. Related Research

A preliminary examination of the existing literature indicates that the path planning problem in urban ultra-low altitude airspace can be effectively addressed through the use of sampling-based algorithms. The most widely used and influential sampling-based path planning algorithms are Probabilistic Roadmap (PRM) and Rapid Exploration Random Tree (RRT). The PRM algorithm is suitable for problems with environmental prior knowledge, which are difficult to deploy in terminals for UAVs flying in the complex environment of the urban ultra-low altitude airspace [16,17,18]. Conversely, RRT algorithms are favored by researchers for higher efficiency in practical applications [19]. Moreover, due to the differing problems to be solved, researchers sought to enhance the RRT algorithm. The most fundamental improvement is the RRT* algorithm, which is a motion planning algorithm based on incremental sampling and guarantees asymptotic optimality, i.e., it can converge to the optimal solution almost deterministically [20,21]. Subsequently, in order to increase the speed of convergence and at the same time improve the exploration ability of the RRT* algorithm in highly cluttered environments, Zaid Tahir et al. introduced a new concept of potentially guided bidirectional trees in our proposed Potentially Guided Intelligent Bi-directional RRT* (PIB-RRT*) and Potentially Guided Bi-directional RRT* (PB-RRT*). The proposed algorithms greatly improve the convergence rate and have a more efficient memory utilization [22].

In order to adapt RRT* to dynamic environments, scholars proposed Extended RRT* (ERRT*) and Dynamic RRT* (DRRT*) [23,24]. Based on these proposals, Quick-RRT* (Q-RRT*), PQ-RRT*, and EB-RRT algorithms and Neural RRT* algorithms were developed. Q-RRT* expands the possible parent vertex collections by considering the vertex collections in the hyper-sphere as well as their ancestors up to a user-defined parameter depth. This expansion of the set of possible parent vertices improves the quality of the initial solution and the convergence rate. The number of potential parent vertices is increased, thereby enhancing the quality of the initial solution and the convergence rate [25]. The PQ-RRT* algorithm, based on the P-RRT* and Q-RRT* algorithms, employs the attractiveness of the target region as a sampling strategy, extends the search scope of the Choose Parent process, and improves the reconnection PQ-RRT* process, which further improves the convergence speed [26]. The elastic bands-based Expeditious Exploration Random Tree (EB-RRT) algorithm constructs a hierarchical framework comprising two planners. The global planner generates feasible heuristic trajectories in dynamic environments using time-based RRT algorithms [27]. The dynamic replanner updates the heuristic trajectories in dynamic environments through internal contraction forces and obstacles’ repulsive forces, thereby updating the nodes on the time-based heuristic trajectory. The optimal path planning algorithm based on convolutional neural network Neural RRT* generates the training dataset, which includes map information and optimal paths, using the A* algorithm. The convolutional neural network is then trained to predict the probability distribution of the optimal paths on the map. This process guides the sampling process [28,29]. The NRRT* achieves a better performance in comparison with existing optimal path planning algorithms. Based on the references above, this paper summarizes the various existing path planning algorithms in tabular form (see

Table 1. Comparison of UAV Path Planning Algorithms.

Algorithm	Category	Key Features	Advantages	Disadvantages
A*	Grid-based Search	Uses heuristic to find shortest path	Guaranteed to find the shortest path in the grid	High computational cost in large or complex grids
RRT	Sampling-based	Randomly explores the search space	Efficient in high-dimensional spaces	May produce suboptimal or inefficient paths
RRT*	Sampling-based	Improves RRT with asymptotic optimality	Guarantees optimal path with enough samples	Requires more computation than RRT
APF	Potential Field	Uses attractive and repulsive forces	Simple and fast in obstacle-free environments	Prone to local minima, may fail in dense areas
PRM	Sampling-based	Constructs a roadmap with random samples	Effective when prior knowledge of the environment is available	Not suitable for dynamic or unknown environments
Q-RRT*	Sampling-based	Expands parent vertex collections to improve	Faster convergence compared to standard RRT*	More complex implementation
PQ-RRT*	Sampling-based	Combines P-RRT* and Q-RRT* for better performance	Improved path quality and convergence speed	Increases computational overhead
Neural RRT*	Sampling-based	Uses neural networks to guide sampling	Learns from data to optimize path planning	Requires extensive training data and computational resources

).

3. Research and Analysis

In order to ascertain the applicability of previous viewpoints on path planning algorithms to the path planning of UAVs in urban ultra-low altitude airspace, we designed experiments to that end. In the experiment, the complete building information of selected areas in Chengdu City, China was extracted from the OpenStreetMap website to serve as the obstacle environment for UAV path planning. Takeoff and landing points were established at locations with varying building densities, and distances between takeoff and landing points were adjusted to encompass short, medium, and long distances. Subsequent experiments were conducted using four algorithms: A*, RRT, RRT*, and the artificial potential field method. These experiments were performed for the same takeoff and landing points at each distance in order to assess the performance of each algorithm.

3.1. Research and Analysis of Builidings in ULAA

As previously stated, the urban ultra-low altitude airspace is characterized by a high density of buildings, which presents a significant challenge for the planning of UAV flight paths. In the environment model presented in this paper, we intercepted the building planar model at different altitude layers, and the results indicate that the density of buildings decreases with the increase in altitude, from 0 m to 120 m, within each altitude layer. However, despite this decrease, the buildings remain densely populated. Please see

Table 2. Information on buildings in ULAA.

Building Height 1	Number of Buildings	Building Density 3
>0 m	3323	8.86%
≥20 m	1323	3.46%
≥40 m	696 2	1.68%
≥60 m	696	1.68%
≥80 m	627	1.52%
≥100 m	391 2	0.94%
≥120 m	391	0.94%

¹ These data are derived from the open street map or calculated based on information on the number of floors in a building, which is assumed in the text to be 3 m high on a single floor. ² There are no buildings in the statistics with heights in the middle of 40–60 m and between 100 and 120 m, so there are two rows with the same data. ³ Building density is calculated as the ratio of the sum of the projected area of the building’s architectural form to the area of the study area.

and Figure 1 and Figure 2 for detailed statistics.

Figure 1 depicts a two-dimensional representation of the urban ULAA, wherein the height of the buildings is represented by colour. Buildings of greater height are represented by yellow, while those of lesser height are represented by purple. Table 2 illustrates the variation in the number of buildings with height in the urban area under investigation, as well as the planar area of the airspace occupied by the 2D projections of the buildings. Figure 2 then demonstrates the density of buildings on specific height layers, with the buildings coloured in a manner consistent with that employed in Figure 1.

3.2. Research and Analysis on the Use of Classical Path Planning Algorithms in ULAA

In this study, the experiments were conducted using Python version 3.10 on the Windows 11 operating system with an Intel Core i5-12600KF processor and 32 GB of RAM. In the experiment, take-off and landing points were established in areas with varying degrees of building density, with distances between them adjusted to simulate a range of scenarios. In this paper, a 6 km by 6 km 36 square kilometer area in a real city is transformed into a two-dimensional discrete grid of 500 by 500 pieces. In this grid, obstacles are represented by elements with a value greater than 0, while passable free space is represented by elements with a value of 0. In terms of colour, the brighter the location, the higher the buildings are, and the darker the location, the lower the buildings are.

The experimental results demonstrate that the classical path planning algorithms cannot be directly adapted to the model of urban ULAA. Furthermore, the results of the experiment corroborate the conclusions previously drawn in the literature and provide more detailed insights.

As illustrated in Figure 3a, take-off and landing points were established in areas of greater urban density, with the distance between them being of medium length. The results of the path planning demonstrate that the artificial potential field method is unable to reach the target due to the “local minima” problem. As illustrated in the figure, the algorithm is unable to identify a viable path when the repulsive field around the obstacle traps the path. Although the RRT* algorithm generates a relatively smooth path that avoids the majority of major obstacles, the path exhibits some detours in proximity to the target point. This may be attributed to the additional distance traveled to circumvent the obstacles. This may indicate that the RRT* algorithm requires more iterations to identify a superior path in regions with a high density of obstacles. In comparison to the RRT* algorithm, the RRT algorithm generates more direct paths. However, these paths also exhibit some meandering, particularly in the middle portion, which is more tortuous. This may be attributed to the randomness of the algorithm in finding feasible paths. Furthermore, the paths are situated in closer proximity to obstacles, which may increase the risk of collisions. The paths generated by the A* algorithm are the most direct, demonstrating the algorithm’s capacity to identify the shortest paths within the mesh. However, the proximity to obstacles is particularly pronounced in certain areas, which may not be optimal in practical applications, particularly in instances where the boundaries of obstacles are uncertain or in a dynamic environment.

In Figure 3b, the building density around the takeoff and landing points is sparse, yet the distances are consistent with those depicted in Figure 3a, which is also a medium distance. It is evident from this figure that all four algorithms are capable of accurately generating the paths between the take-off and landing points. Notably, the RRT and RRT* algorithms do not include the additional walking distance introduced in Figure 3a to circumvent obstacles. The paths generated by the artificial potential field algorithm are consistently successful in reaching the landing point, whereas the paths generated by the A* algorithm are locally optimal in this instance, resulting in excessively lengthy generated paths. The length of the generated path is excessive.

As illustrated in Figure 4a and Figure 4b, the takeoff and landing points were positioned in regions with higher and lower densities of buildings, respectively, in a manner analogous to the experiment depicted in Figure 3. However, the distance between these points differed from that observed in the aforementioned experiment, which exhibited a longer distance. It can be observed that as the distance between the takeoff and landing points increases, the RRT, RRT*, and A* algorithms are still capable of generating a path between the takeoff and landing points. However, the artificial potential field method, which was previously planned to the region with dense buildings, is consistent with the experimental results in Figure 3 and falls into a local minimum.

Subsequently, the data from all experiments were tabulated and evaluated according to several metrics presented in

Table 3. Statistics of performance evaluation metrics for each algorithm.

Algorithm	Average Time (s)	Average Path Length	Average Distance to Obstacles
RRT*	56.78	373.16	142.64
RRT	57.14	393.00	136.67
A*	0.54	347.00	159.33
APF	2933.33	——	191.79

, which assess the suitability of the four algorithms for operation in urban ULAA. The A* algorithm is presumed to exhibit the optimal performance based on the statistical results. However, as illustrated in the preceding plotting of Figure 3 and Figure 4, the A* algorithm tends to select routes that are excessively proximate to buildings in densely developed areas with the objective of generating paths of minimal length. This approach may prove dangerous, as it is susceptible to falling into a local optimum when the distances between certain take-off and landing points are too great. This ultimately results in suboptimal overall paths. While the RRT and RRT* algorithms are similar, RRT* exhibits slight superiority over R and RT, both of which traverse considerable distances to circumvent potential collisions with buildings. APF, on the other hand, can only generate a complete path between the takeoff and landing points in the absence of excessive density of obstacles. However, this process is considerably more time-consuming than that of the other algorithms. Indicators specific to each type of example are shown in Figure 5.

4. Improvement of Classical Path Planning Algorithms in ULAA

In response to the issues identified in the preceding simulation experiments, this paper proposes targeted enhancements to the four algorithms. In order to address the issue of paths planned by the A* algorithm being situated in close proximity to buildings, this paper employs the standard A* search framework and modifies the heuristic function h to take into account the basic Euclidean distance from the node to the target and the environmental density. This approach can enhance the practical viability of path planning by circumventing complex or hazardous regions while maintaining the efficacy of the algorithm. The pseudo-code is illustrated in

Table 4. Classical and Enhanced A* with Density-Aware Heuristic.

Classical A* Algorithm	Improvement of the A* Algorithm
Input: S (start), G (goal), O (obstacle grid)	Input: S (start), G (goal), O (obstacle grid)

.

To address the APF algorithm’s susceptibility to local minima, a random perturbation (noise) is introduced into the calculation of the total force. This enables the path planning algorithm to “jump out” and continue searching for the globally optimal path in the vicinity of the potential local minima. This approach increases the randomness and exploratory nature of the algorithm, which helps to find better paths in complex environments and improve obstacle avoidance. The initial value of the step parameter in the experiment is 0.5, and it will be adjusted according to the distance between the current point and the target point. When the distance is less than 5, the step is reduced to 0.2; when the distance is between 5 and 10, the step is 0.3. In the event that the distance exceeds 10, the step is 0.5. The gravitational potential function’s attraction force is directly proportional to the Euclidean distance between the current point and the target point, while the repulsive force function’s repulsive force is inversely proportional to the distance between the current point and the obstacle. The pseudo-code is shown in

Table 5. Classical and Enhanced AFP algorithm.

Classical APF Algorithm	Stochastic Potential Field
Input: S (start), G (goal), O (obstacle grid)	Input: S (start), G (goal), O (obstacle grid)

.

In order to address the issues of slow convergence of the RRT* algorithm and the tendency to take longer detours in order to avoid buildings, this paper proposes a hybrid optimization strategy comprising dynamic search radius, path smoothing, reconnection, and goal bias. Dynamic search radius: As the number of nodes in the tree increases, the search radius is decreased in a manner that is proportional to the number of nodes. This enables the algorithm to explore the space in greater depth during the initial stages, while directing its attention to local optimization in subsequent stages. Path smoothing entails the optimization of the initial path by eliminating superfluous nodes and creating shortcuts. This can result in a notable reduction in the length and complexity of the paths. Reconnection: Following the addition of new nodes to the tree, efforts are made to reconnect nearby nodes with the objective of reducing their path cost. This facilitates the identification of superior paths. A goal bias is introduced when randomly sampling nodes, whereby a probability is added to bias the search towards the goal node, thus accelerating the exploration of the target region. The probability of biasing towards the goal node is defined by a goal bias parameter, which determines whether a return to the goal node is made or not, based on this parameter, when generating random nodes. This method determines whether the sampling point is biased towards the goal position by a random number generator. If the generated random number is less than the set value of the goal_bias parameter, the target point is directly returned as the sampling node. The incorporation of a dynamic search radius and goal bias enables the algorithm to approach the target region in a more expeditious manner, thereby reducing the overall number of iterations. The application of path smoothing and reconnection techniques was demonstrated to markedly enhance the quality of the paths generated, resulting in more streamlined and condensed routes while circumventing superfluous lengthy detours. The aforementioned optimization strategies enable the algorithm to adapt more effectively to scenarios involving increased obstacles or complex distributions, thereby improving the efficiency of pathfinding and enhancing the algorithm’s resilience. The pseudo-code is presented in

Table 6. Classical and Improved RRT Star Algorithm with hybrid optimization method.

Classical RRT Star Algorithm	Improved RRT Star Algorithm
Input: Input: S (start), G (goal), O (obstacle grid), B (bounds), Params	Input: Input: S (start), G (goal), O (obstacle grid), B (bounds), Params

.

5. Result and Discussion

The RRT*, A*, and APF algorithms demonstrated notable improvements across all evaluation metrics. The most significant changes included substantial reductions in computation time, particularly for the APF algorithm, as well as enhancements in path length and safety for the RRT* and A* algorithms. These outcomes illustrate the efficacy of the implemented optimizations in enhancing the efficiency and reliability of these path planning algorithms in real-world applications, as illustrated in

Table 7. Enhanced Potential Field with Random Perturbation.

Algorithm	Average Time (s)	Average Path Length	Average Distance to Obstacles
RRT*	56.78, (9.45) 1 ↓83.40% 2	373.16, (252.97) ↓32.20%	142.64, (164.37) ↑15.23%
A*	0.54, (0.27) ↓50.00%	347.00, (259.62) ↓25.18%	159.33, (167.01) ↑4.82%
APF	2933.33, (1.06) ↓99.97%	(349.57) ——	191.79, (165.97) ↓13.46%

¹ Data in parentheses are optimized test data, data before commas are from Table 3. ² Percentages indicate the proportion of the changed data to the original data (Table 3).

.

As illustrated in Figure 6a, Figure 6b and Figure 6c, the paths generated by the enhanced A* algorithm are no longer situated in close proximity to buildings in regions with high building density. In contrast, the paths generated by the improved APF algorithm can already reach the take-off and landing points. In any case, the points are situated at an acceptable distance from the buildings and along paths of an appropriate length. Furthermore, the improved RRT* algorithm demonstrates a reduction in the number of nodes, a decrease in path length, and the avoidance of lengthy detours to circumvent obstacles when compared to the RRT algorithm.

Consequently, the proposed enhancements addressed these issues effectively. The density-aware heuristic for the A* algorithm resulted in safer paths by avoiding areas with high building density. Introducing random perturbation in the APF method helped it escape local minima, improving its performance in dense obstacle environments. The hybrid optimization strategy for RRT*, which included dynamic search radius adjustment, path smoothing, reconnection, and goal bias, significantly reduced computation time and path length while enhancing obstacle avoidance. These improvements are consistent with findings from previous studies, such as the work on enhanced RRT* algorithms, which emphasized the need for adaptive strategies in complex environments.

6. Conclusions

In this study, we undertook a comprehensive analysis and improvement of several classical path planning algorithms, including A*, RRT, RRT*, and Artificial Potential Field (APF), with the objective of enhancing their efficacy in addressing the challenges posed by urban Ultra-Low Altitude Airspace (ULAA) for Unmanned Aerial Vehicles (UAVs). The distinctive features of ULAA, including high building density and regulatory constraints, present considerable challenges for UAV operations. The enhancements, which included a density-aware heuristic for A*, random perturbations in APF, and a hybrid optimization strategy in RRT*, demonstrated notable improvements in computational efficiency, path safety, and obstacle avoidance.

The results demonstrate that these enhanced algorithms offer substantial advantages over traditional methods, particularly in complex urban environments with densely packed obstacles. The modified A* algorithm, with its density-aware heuristic, effectively avoided regions with a high risk of collision while maintaining efficient path planning. The incorporation of random perturbations into the APF algorithm effectively addressed the issue of local minima, thereby enhancing its reliability in dense environments. The RRT* algorithm, enhanced with dynamic search radius, path smoothing, reconnection, and goal bias strategies, not only reduced computation time but also produced more optimized paths with fewer detours.

In future work, we intend to further investigate the integration of Unmanned Aerial Vehicle (UAV) flight dynamics into our path planning algorithms. This will entail a comprehensive examination of the impact of factors such as speed, acceleration, and maneuverability on the efficacy of these algorithms, along with an investigation into potential modifications to enhance performance for diverse UAV types. Furthermore, we seek to integrate real-time adaptive techniques, potentially through the application of machine learning, to augment the resilience and adaptability of these algorithms. We also intend to investigate their deployment in dynamic environments where obstacles may be in motion or subject to change.