ESCAPE: an efficient and safe distributed UAV swarm exploration framework with collision avoidance perception

Abstract

Significant progress has been made in distributed unmanned aerial vehicle (UAV) swarm exploration. In complex scenarios, existing methods typically rely on shared trajectory information for collision avoidance, but communication timeliness issues may result in outdated trajectories being referenced when making collision avoidance decisions, preventing timely responses to the motion changes of other UAVs, thus elevating the collision risk. To address this issue, this paper proposes a new distributed UAV swarm exploration framework. First, we introduce an improved global exploration strategy that combines the exploration task requirements with the surrounding obstacle distribution to plan an efficient and safe coverage path. Secondly, we design a collision risk prediction method based on relative distance and relative velocity, which effectively assists UAVs in making timely collision avoidance decisions. Lastly, we propose a multi-objective local trajectory optimization function that considers the positions of UAVs and static obstacles, thereby planning safe flight trajectories. Extensive simulations and real-world experiments demonstrate that this framework enables safe and efficient exploration in complex environments.

Introduction

UAV swarms play a critical role in applications such as 3D reconstruction, environmental monitoring, and forest search-and-rescue [1–3]. Swarms can efficiently explore vast, hazardous, or hard-to-reach environments where a single UAV would struggle to complete the task alone. By collaborating in real time and sharing information, multiple UAVs are well suited to missions that require broad spatial coverage and rapid data acquisition. As environmental complexity increases, however, ensuring safe and efficient flight for all vehicles in the swarm becomes increasingly challenging.

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Figure 1

(a) shows exploration experiments conducted in the indoor environment. (b) shows the complete mapped environment and the UAV swarm’s exploration trajectory

Although significant progress has been made in the field of UAV swarm exploration in terms of path planning and task allocation, existing methods still rely on high-frequency communication and global information. However, in highly dynamic and obstacle-dense environments, this reliance is often impacted by communication bandwidth limitations and obstacles, preventing UAVs from performing efficient global path planning. This results in increased back-and-forth movements, wandering, and redundant travel, leading to unnecessary resource waste. Additionally, existing methods often lack detailed research on collision avoidance. Many strategies rely on optimizing UAV trajectories to minimize conflicts but fail to effectively address the dynamic real-time collision issues. Most methods treat collision avoidance as an additional objective in the optimization process, rather than a core component of the decision-making framework [4, 5]. Therefore, especially in complex environments, existing methods may compromise between exploration efficiency and safety, increasing the risk of collisions between UAVs.

Current swarm-level avoidance methods have several limitations. First, most methods incorporate collision avoidance as a soft constraint within the optimization [6, 7]: the system attempts to avoid collisions but does not enforce them strictly. Other objectives (such as travel time or trajectory smoothness) can then take precedence, leaving residual collision risk. Second, many approaches rely heavily on real-time communication to exchange planned trajectories. This dependency introduces vulnerability: delays or packet loss may prevent timely responses to teammates’ motion, thereby raising the likelihood of collision.

To address these issues, we propose a distributed swarm exploration framework with an integrated collision avoidance module. The environment is first partitioned into uniform grid cells. Through pairwise interactions, each UAV obtains an assigned sequence of grid cells representing its exploration task. The visiting order is determined by solving a traveling salesman problem (TSP) over the assigned cells, enabling efficient and largely independent exploration. During execution, UAVs share their positions in real time. When the relative distance falls below a threshold, a risk-prediction model based on relative distance and relative velocity determines whether avoidance actions are required. Finally, a height-priority policy triggers either an emergency stop or single-agent trajectory replanning, ensuring safety during swarm exploration. Our main contributions are as follows:

• An improved global exploration strategy: By considering the current UAV position, the spatial location of the task area, and surrounding obstacle distribution, an efficient coverage path is planned to enhance exploration efficiency.

• A novel risk-prediction model: The model fuses relative distance, relative bearing, and relative speed within the swarm to assess motion risk and decide whether to invoke avoidance, effectively balancing safety and timeliness.

• A multi-objective trajectory optimization method: Using the positions of both static obstacles and other UAVs, the method performs collision-aware trajectory optimization that improves flight smoothness and task efficiency while ensuring safety.

The remainder of the paper is organized as follows. Section 2 reviews related works. Section 3 presents the overall system architecture. Section 4 describes the proposed swarm exploration framework. Section 5 details the collision-avoidance strategy. Section 6 reports experimental results and analysis. Section 7 concludes the paper and discusses future directions.

Related work

Autonomous exploration

In recent years, autonomous UAV exploration in unknown environments has become a hot research topic. The commonly used exploration methods are divided mainly into frontier-based methods and sampling-based methods. The frontier-based method, first proposed by [8], involves calculating and selecting the closest frontier region as the next target for exploration to drive the exploration process. Cieslowski et al. [9] achieved efficient environmental coverage by relying on path optimization and spatio-temporall information. However, traditional frontier-based methods typically rely on sensors to perceive the environment [10, 11], and these sensors have a limited effective detection range, which poses challenges for UAVs to adapt to complex and dynamic environments. To overcome this issue, Zhou et al. [12] proposed a hierarchical planning approach that uses global path generation and local path optimization to improve task execution efficiency. However, this method has high computational complexity and still requires further optimization.

Another approach is sampling-based exploration [13], which explores the space by randomly generating viewpoints and evaluating their information gain. Sampling-based methods are closely related to Next Best Viewpoint (NBV), where viewpoints are calculated by repeatedly generating and updating them to fully model the scene. Bircher et al. [14] first introduced the concept of NBV in 3-D exploration and used Rapidly Exploring Random Trees (RRT) [15] to generate paths in free space and perform edges with the most information to achieve effective environmental exploration [16, 17]. However, as the complexity of the task increases, the computational burden of sampling methods also increases.

Multi-robot exploration

Unlike single-agent exploration, multi-robot exploration methods primarily focus on how multiple UAVs can cooperate to efficiently cover large areas [18, 19]. Tian et al. [20] transformed the exploration task into a multi-traveling salesman problem (mTSP) and proposed a multi-agent collaborative path planning method, aiming to assign each UAV a task goal to achieve optimal path allocation. This method can cover the environment within an effective time frame, but due to its reliance on a global task allocation mechanism, it may suffer from reduced efficiency when facing communication delays and environmental complexity [21, 22].

Due to communication limitations and robustness issues in centralized methods, distributed coordination methods based on auction mechanisms have gained widespread attention. Zlot et al. [23] proposed using auction mechanisms to resolve conflicts among robots, where each robot bids to acquire tasks or goals. This method effectively addresses resource allocation issues in multi-robot cooperation and reduces conflicts [24, 25]. To further improve multi-agent collaboration efficiency, based on pairwise [26, 27], Zhou et al. [4] proposed the Racer framework, which divides the navigation area into grids and ensures that each UAV explores a different grid path. This method effectively avoids path duplication and improves exploration efficiency. However, its efficiency is still affected by environmental complexity, especially in scenarios with dense obstacles.

Swarm collision avoidance

To address the collision problem between robots, many studies have focused on distributed collision avoidance methods. Early research introduced Velocity Obstacles (VO) [28, 29] to avoid collisions between robots. These methods calculate obstacle regions in the velocity space to ensure robots do not enter collision zones. However, these methods rely solely on velocity for motion planning, which is overly idealized for real-time decision-making in complex and dynamic environments, and they fail to consider additional dynamic constraints, such as acceleration and attitude changes, which may lead to shortcomings in practical applications.

Liu et al. [30] proposed an asynchronous collision avoidance strategy that can handle collisions between robots, obstacles, and other vehicles, particularly in environments with irregular or dynamic obstacles. However, this approach may not fully eliminate uncertainties in dynamic environments, and coordination in large swarms remains a challenge. Zhou et al. [6] extended the gradient-based replanning method to the collaborative collision avoidance problem for UAV swarms. By dynamically adjusting the trajectory of each UAV, this method avoids collisions within the swarm and adapts to the collision avoidance needs of multiple robots. However, its computational complexity is high, and in scenarios with dense obstacles or complex environments, it may lead to insufficient real-time performance and accuracy in trajectory planning.

In summary, although existing UAV swarm exploration and collision avoidance methods have improved exploration efficiency and safety to some extent, the efficiency and safety of swarm exploration are still difficult to guarantee in complex and highly dynamic environments. Our proposed framework considers both the efficiency of path planning in complex scenarios and ensures the safety of swarm flight with limited communication. Experimental results show that the framework demonstrates excellent robustness in various complex environments and effectively balances exploration efficiency and safety.

System overview

Our goal is to build a complete volumetric map of an unknown environment within a bounded region, while jointly emphasizing safety and timeliness. The proposed framework, illustrated in Fig. 2, comprises a cooperative exploration module and a collision-handling module. Before exploration begins, the workspace is partitioned into uniform grid cells. UAVs then perform random pairwise interactions to allocate grid cells, which defines each vehicle’s exploration task and visiting order. Once exploration starts, each UAV constructs a volumetric map using its onboard sensors and continuously broadcasts updated map data, pose estimates, and planned trajectories to the swarm network.

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Figure 2

An overview of the proposed collaborative exploration framework

After task allocation, each UAV first obtains its global tour by solving a TSP. Building on [4], we then propose an exploration strategy tailored to complex, obstacle-dense scenes that effectively reduces detours and backtracking: within each grid, we extract frontiers along the boundaries between known and unknown regions and generate a set of viewpoints, and subsequently plan a locally feasible path that visits these viewpoints sequentially. Each UAV follows its planned path to perform coverage exploration of its assigned area, and its exploration is deemed complete once all assigned grids have been fully explored.

To ensure swarm flight safety, we introduce an emergency state detection mechanism based on relative distance and relative velocity. Once a high-risk state is detected, a priority-based stop/replanning policy is triggered. Specifically, low-priority UAVs immediately hover to avoid further interactions, while high-priority UAVs enter a replanning phase that accounts for the spatial distribution of neighboring teammates and static obstacles, generating a smooth, feasible, and collision-safe new trajectory to quickly exit the danger zone and seamlessly resume normal exploration.

Exploration strategy

The improved exploration strategy is based on the framework of Racer [8]. The overall process is as follows: based on the status of the surrounding UAV swarm, one UAV first initiates a request to engage in pairwise interactions with other UAVs for task allocation. Subsequently, each UAV performs global path planning and local path planning based on the allocation results, and continuously updates its path in real-time by considering its current position and the changes in the environment ahead, thereby achieving efficient exploration.

Global path planning

As shown in Fig. 3, the exploration space is divided into uniformly sized grids. The task of the UAVs is to cover these grids without collision. The task allocation is then formulated as a capacitated vehicle routing problem (CVRP), where the objective is to minimize the total path length and balance the workload among all UAVs. Let $cost(a,b)$ denote the pairwise travel cost used in the CVRP distance matrix, defined as $cost(a,b)=\mathrm{len}(P(a,b))$, $P(\cdot ,\cdot )$ denote the feasible path between two points, $\mathrm{len}(\cdot )$ denote the path length, $q_i$ represent the position of the i-th UAV, $gri{d}_j$ represent grid j, and $c_j$ represent the centroid of grid j, then we have:

1

$\text{cost}(q_i,gri{d}_j)=\text{len}(P(q_i,c_j)),$

2

$\text{cost}(gri{d}_m,gri{d}_n)=\text{len}(P(c_m,c_n)).$

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Figure 3

Each UAV achieves the unknown grid allocation through pairwise interaction and plans a coverage path as the global exploration path

The cost matrix used to formulate the CVRP is constructed by considering the distances between the centroids of grid cells and the distances from UAVs to the centroids of the grids. When there are a total of $N_h$ grid cells in the environment, the cost matrix $C_{\text{avrp}}\in {\mathbb{R}}^{(N_h+3)\times (N_h+3)}$ is formulated as:

3

$C_{\text{cvrp}}=\left[\begin{array}{ccc}0& -M_{\mathrm{\infty }}& 0\\ 0& 0& C_{q,h}\\ 0& C_{q,h}^T& C_h\end{array}\right],$ where $C_{q,h}$ represents the pairwise cost between UAVs and grid cells. $C_h$ represents an $N_h\times N_h$ matrix, which represents the connection costs between the grid cells.

To solve the matrix formulation, we use the Lin–Kernighan–Helsgaun (LKH) solver. Given that the problem only involves pairwise interactions, the computational efficiency of the solution is relatively high. The LKH algorithm efficiently handles this problem by transforming it into a standard TSP (Traveling Salesman Problem) and leveraging penalty functions to manage the capacity constraints.

After the task allocation is complete, each UAV generates a path based on its assigned grids, resulting in a global path.

Local path planning

In the process of traversing each grid, we classify the boundary between the known and unknown regions as frontiers. In order to improve the coverage and adapt to the local environmental changes, we compute the views from these frontiers, which will be used as viewpoints for path generation. This step ensures that the UAV’s exploration path is well connected and smooth.

In certain scenarios, such as when large obstacles exist between grids, as illustrated in Fig. 4, the path generated by sequential grid visits may result in unnecessary detours, reducing the exploration speed. To address this detour problem, we introduce a continuity term in the cost function, which considers the distance between the UAV’s current position and the next grid center. This continuity term encourages smoother transitions between grid centers, mitigating the negative impact caused by obstacles and improving efficiency. Specifically, we have:

4

$\begin{array}{rl}\text{cost}(q_i,gri{d}_j)=& \text{len}(P(q_i,c_j))+\text{Con}(q_i,c_j),\end{array}$ where

5

$\text{Con}(q_i,c_j)=\{\begin{array}{cc}\parallel q_i-c_j\parallel ,\hfill & \text{if }{c}_j\text{ is inside the obstacle},\hfill \\ 0,\hfill & \text{if }{c}_j\text{ is outside the obstacle}.\hfill \end{array}$ Intuitively, $\text{Con}(q_i,c_j)$ is a continuity term that penalizes the UAV’s trajectory when the center of grid $c_j$ lies inside an obstacle. In this case, there is no feasible path from the UAV to the grid center, so we define the distance as the Euclidean distance between the UAV’s current position $q_i$ and the grid center $c_j$. In path planning, the UAV prioritizes exploring grids with smaller costs, meaning it first explores grids have lower travel costs. By introducing this continuity term, the UAV is further encouraged to adjust its path planning, effectively changing the order in which grids are explored. This helps to prevent the UAV from staying too long in front of grids blocked by large obstacles, avoiding unnecessary back-and-forth movements. As a result, the UAV can explore more efficiently, bypassing obstacle-occupied grids and reducing the overall exploration time. This modification improves the exploration algorithm’s performance, especially in environments with large or complex obstacles.

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Figure 4

When UAVs explore the grids based on the coverage path, large obstacles spanning across multiple grids in the environment may cause the planned local path to exhibit back-and-forth behavior

Swarm collision avoidance

Potential collisions may occur in UAV swarm flight, as shown in Fig. 5. To enhance the safety of swarm exploration and enable mutual collision avoidance among UAVs, we propose an emergency situation determination method based on relative distance and velocity. This method involves real-time calculation and evaluation of the relative states between UAVs to determine whether collision avoidance measures are necessary. Then, based on the relative altitude of the UAVs, we propose a priority-based stop-and-replan strategy, achieving orderly and safe collision avoidance for the UAV swarm.

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Figure 5

The figure illustrates three possible collision scenarios. The left diagram shows UAVs moving towards each other, the middle diagram represents UAVs moving in the same direction, and the right diagram shows UAVs moving away from each other. Based on the UAVs’ positions at different time instances, the instantaneous velocity of the UAVs is calculated to estimate the collision risk

Collision risk assessment

Collision avoidance detection during UAV flight is illustrated in Algorithm 1. First, UAVs within a certain range are selected as collision avoidance neighbors (lines 2–5), and the collision risk is evaluated using the following formula. In this formula, R represents the overall collision risk, which is a weighted sum of the distance risk ${\hat{r}}_d$, relative orientation risk ${\hat{r}}_{\theta }$, and relative velocity risk ${\hat{r}}_v$, each multiplied by a corresponding weight $w_d$, $w_{\theta }$ and $w_v$. Based on the evaluation, collision avoidance measures are then taken if R exceeds a predefined threshold τ, indicating a high risk of collision (lines 6–15), such as path re-planning or emergency stop:

6

$R=w_d{\hat{r}}_d+w_{\theta }{\hat{r}}_{\theta }+w_v{\hat{r}}_v,R>\tau \Rightarrow \text{trigger action}.$

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Algorithm 1

Collision Avoidance

Let the positions of UAVs i and j be $p_i$ and $p_j$, and their velocities be $v_i$ and $v_j$. The relative position vector between the UAVs is $\mathit{r}={\mathit{p}}_j-{\mathit{p}}_i$, the distance is $d=\parallel \mathit{r}\parallel$, the unit line of sight is $\hat{\mathit{r}}=\frac{\mathit{r}}{d}$, and the relative velocity is ${\mathit{v}}_{\mathrm{rel}}={\mathit{v}}_j-{\mathit{v}}_i$, with the unit relative velocity direction ${\hat{\mathit{v}}}_{\mathrm{rel}}=\frac{{\mathit{v}}_{\mathrm{rel}}}{\parallel {\mathit{v}}_{\mathrm{rel}}\parallel }$. Therefore, the variables in the above equation are defined as follows, The first variable ${\hat{r}}_d$ represents the risk associated with the distance between the UAVs:

7

${\hat{r}}_d=\mathrm{clip}(\frac{d_{\text{safe}}-d}{d_{\text{safe}}},0,1),$ The function $\mathrm{clip}(x,a,b)$ restricts the value of x to lie within the range $[a,b]$, where values less than a are set to a, values greater than b are set to b, and values between a and b remain unchanged. $d_{\text{safe}}$ is the safety distance threshold. When the distance $d\ge d_{\text{safe}}$, the risk is 0; as the distance decreases, the risk approaches 1. The second variable ${\hat{r}}_{\theta }$ represents the risk associated with the relative orientation between the UAVs:

8

${\hat{r}}_{\theta }=\frac{1-cos\theta }{2}.$ Here, $\theta =arccos\left({\hat{\mathit{r}}}^T{\hat{\mathit{v}}}_{\mathrm{rel}}\right)$. In this equation, the symbol ${\hat{\mathit{r}}}^T$ represents the transpose of the unit vector $\hat{\mathit{r}}$. When the relative velocity ${\mathit{v}}_{\mathrm{rel}}$ is aligned with the unit line of sight $\hat{\mathit{r}}$ (moving away from each other), $\theta =0\Rightarrow {\hat{r}}_{\theta }=0$; when completely opposite (approaching), $\theta =\pi \Rightarrow {\hat{r}}_{\theta }=1$. The third variable ${\hat{r}}_v$ represents the risk based on the relative velocity of the UAVs:

9

${\hat{r}}_v=\mathrm{clip}(\frac{\parallel {\mathit{v}}_{\mathrm{rel}}\parallel }{v_{max}},0,1),$ where $v_{max}$ is the maximum allowable relative speed. For UAVs under risk, based on their relative height, higher UAVs perform trajectory replanning, while lower UAVs perform an emergency stop and wait for a period before resuming movement (lines 16–21). In our experiments, we set $w_d=2$, $w_{\theta }=1$, $w_v=1$, $\tau =1.5$, and $d_{\text{safe}}=1.5$ m.

Local trajectory optimization with collision avoidance

When a UAV needs to replan its trajectory to escape a dangerous area, we introduce a trajectory optimization function based on the work in [4], which ensures collision avoidance with other UAVs and static obstacles.

We use uniform B-splines to parameterize the trajectory, with decision variables being the set of control points $Q_{c,b}$ and the node interval $\mathrm{\Delta }{t}_b$. Building on the existing costs for smoothness $J_s$, time T, environmental collision avoidance $J_{c,o}$, and dynamic feasibility $J_v$, $J_a$, and $J_{bs}$, we introduce a peer avoidance cost $J_{\text{peer}}$ for stationary companions. This results in the overall objective:

10

$\begin{array}{rl}& \underset{Q_{c,b},\mathrm{\Delta }{t}_b}{min}{J}_s+w_{t}T+{\lambda }_c{J}_{c,o}+{\lambda }_{c^{`}}{J}_{c,q}\\ & +{\lambda }_d(J_v+J_a)+{\lambda }_{bs}{J}_{bs}+{\lambda }_w{J}_{\text{peer}}.\end{array}$ In the original method, the constraint term $J_{c,q}$ is used as the optimization condition for swarm collision avoidance, considering the temporal distance of the trajectories published by other UAVs. In contrast, we use the actual position of other UAVs when they perform an emergency stop as an optimization constraint. In our design, when the UAV does not need to replan its trajectory, the $J_{c,q}$ term can be retained, and the peer avoidance cost $J_{\text{peer}}$ can be ignored; otherwise, $J_{\text{peer}}$ is used in place of $J_{c,q}$.

Let $\mathcal{N}$ denote the set of peers within the planning horizon, and let $x_j$ be the nominal position of peer j at the current time. To reflect stronger vertical safety margins, we employ an ellipsoidal metric, where $Q_i$ is the i-th B-spline control point:

11

$r_{i,j}=\parallel E^{1/2}(Q_i-x_j)\parallel ,$ where

12

$E=diag(1,1,1/c),c>1,$

The peer-avoidance cost is a one-sided squared hinge accumulated over all control points and peers,

13

$J_{\text{peer}}=\sum _{j\in \mathcal{N}}\sum _i{[max(0,C^{\prime }-r_{i,j})]}^2.$ Here $C^{\prime }$ is a safety margin inflated for uncertainty to counteract network jitter and pose errors,

14

$C^{\prime }=C+v_{\mathrm{r}\mathrm{e}\mathrm{l},\mathrm{m}\mathrm{a}\mathrm{x}}\mathrm{\Delta }+{\sigma }_{\mathrm{loc}},$ where C is the base clearance, Δ is an upper bound of time misalignment, $v_{\mathrm{r}\mathrm{e}\mathrm{l},\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum relative speed, $r_e$ bounds the tracking error, ${\sigma }_{\mathrm{loc}}$ models localization uncertainty.

In our experiments, we set ${\lambda }_w=20$, $\mathrm{\Delta }=0.01$ s, and ${\sigma }_{\mathrm{loc}}=0.05$ m. With this design, the UAV can plan a safe trajectory that satisfies multiple constraint conditions.

Experiment

To comprehensively verify the proposed method, we conducted experiments in both simulation and real-world environments. In this section, firstly, we compare the proposed exploration strategy with two existing methods. Then, we compare the success rate of swarm exploration with and without the integrated collision avoidance module. Lastly, we demonstrate the performance of the swarm exploration framework in real-world scenarios. Additional details of the experiments, including the demonstration video featuring both simulation and real-world test results, can be found in Online Resource 1.

Exploration strategy comparison

The experiments in Sects. 6.1 and 6.2 were conducted in a simulation environment on a machine equipped with an Intel i7-14700HX processor and 32 GB memory, running ROS on the Ubuntu 18.04 system. We selected three different maps (Office 1, Office 2, Office 3) to compare the exploration strategy and swarm collision avoidance, validating the superiority of the proposed framework. The environment resolution was 0.1 m, the sensor’s field of view (FOV) was set to ${80}^{\circ }\times {60}^{\circ }$, and the maximum detection range was 4.5 m. In all simulation experiments, we assumed perfect UAV localization and swarm communication.

We compared the proposed method with the distributed swarm exploration frameworks Role [2] and Racer [4]. The Role method assigns each UAV two modes, “Explorer” and “Collector”, enabling rapid advancement into unknown areas and precise scanning of narrow regions through mode switching. The Racer method achieves task balance among UAVs through interactive grid allocation and explores unknown grid areas based on coverage paths. We compared the minimum, average, maximum values, and standard deviation of the longest time and longest exploration distance for 2, 4 and 6 UAVs. All UAV parameters were set to $v_{\text{max}}=1.5\text{m/s}$ and $acc=1.0{\text{m/s}}^2$, and each method was executed 20 times from the same initial position. The simulation results are shown in Table 1, and the experiments demonstrate that our method outperforms both Role and Racer in the vast majority of cases.

Table 1. Exploration Strategy Comparison

Drones	Scene	Method	Exploration time(s)				Total path length(m)
			Min	Avg	Max	Std	Min	Avg	Max	Std
2	Office 1	Role	77.5	88.5	103.2	7.25	96.7	120.5	147.7	12.42
		Racer	53.2	75.8	92.4	8.87	48.8	92.5	120.4	14.43
		Ours	36.7	65.2	83.0	11.13	40.5	78.9	103.7	13.29
	Office 2	Role	81.1	92.9	111.4	8.93	80.0	126.2	159.1	18.73
		Racer	49.7	69.4	89.5	12.12	53.0	84.0	108.5	15.15
		Ours	41.4	72.1	90.7	13.03	54.6	86.1	116.0	13.68
	Office 3	Role	81.8	105.7	127.6	12.02	130.5	151.8	187.6	16.27
		Racer	99.8	140.4	179.4	28.93	131.2	193.3	253.1	43.15
		Ours	84.4	98.9	118.9	11.84	113.8	133.5	166.6	16.60
4	Office 1	Role	45.7	57.8	82.4	10.04	64.7	79.7	108.8	10.18
		Racer	33.8	43.6	58.4	6.89	39.7	54.2	75.6	9.17
		Ours	37.5	45.8	62.1	7.89	36.1	54.0	69.6	8.76
	Office 2	Role	40.5	58.9	73.9	9.21	56.5	81.5	114.0	14.73
		Racer	31.2	47.2	61.6	8.21	42.1	56.4	74.7	10.59
		Ours	25.3	43.3	66.7	9.69	32.2	51.6	83.8	13.16
	Office 3	Role	51.7	72.5	128.7	16.51	76.0	101.9	138.7	16.27
		Racer	56.9	71.2	100.8	12.97	74.9	96.1	143.6	20.60
		Ours	41.3	56.3	77.0	11.12	30.4	53.9	76.5	12.51
6	Office 1	Role	37.0	48.7	69.3	9.90	48.7	65.5	97.8	13.52
		Racer	22.2	38.7	63.2	10.89	25.3	46.2	83.2	15.39
		Ours	20.3	30.1	40.3	6.11	19.2	34.1	54.7	8.76
	Office 2	Role	31.7	46.4	63.3	8.19	42.0	61.3	87.2	12.95
		Racer	24.6	34.3	57.7	7.25	21.6	38.1	60.9	7.82
		Ours	25.8	32.2	44.9	5.76	24.9	35.9	52.0	6.40
	Office 3	Role	44.5	57.9	87.8	11.47	56.1	78.4	117.3	16.56
		Racer	38.0	47.6	60.8	6.61	48.0	63.7	85.2	11.45
		Ours	30.8	37.8	54.7	6.91	37.9	50.0	67.0	8.12

As shown in Fig. 6, in a complex indoor environment, Role is prone to more circling and repetitive phenomena. This is mainly because the algorithm cannot balance the mode selection in an environment with a large number of obstacles, causing the unmanned aerial vehicle to repeatedly switch between rapid advancement and fine exploration, resulting in the flight trajectory wandering. Racer performs well overall, but there are instances of trajectory overlap, which pose potential collision risks for the UAVs. In contrast, the proposed exploration framework, when combined with the collision avoidance strategy, results in more dispersed exploration trajectories, which reduces the overlap of the perception fields and helps speed up the exploration process. Additionally, in scenarios with large obstacles (such as in Office 3), the framework effectively avoids the occurrence of backtracking, ensuring both exploration efficiency and flight safety.

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Figure 6

Comparison of four UAVs’ collaborative exploration in three different environments. From left to right in each group: Role, Ours, Racer. The far-right image shows a comparison of the exploration progress curves of each method

Collision avoidance comparison

To verify the reliability of the proposed collision avoidance strategy, the following test conditions were set: the relative distance between UAVs was monitored, and if the distance between two UAVs became less than 0.4 m during exploration, a collision was considered to have occurred and the exploration failed. We tested the success rate of exploration with and without the collision avoidance module on three maps, with UAVs’ speeds set to $v=1.5\text{m/s}$, $acc=1.0{\text{m/s}}^2$ and $v=1.0\text{m/s}$, $acc=0.8{\text{m/s}}^2$ for 4 and 8 UAVs in the swarm. Each method was run 50 times in each scenario. The results are shown in Fig. 7 where the success rate of exploration significantly increased after integrating the collision avoidance module, fully demonstrating the safety of the proposed collision avoidance strategy. Furthermore, at lower speeds, the success rate is higher, mainly because more time is left for the UAVs to plan safe paths and avoid collisions. Even in the most complex environment (Office 3), which has narrower passageways and more complex exploration routes, our strategy greatly ensured the safety of exploration. Lastly, experiments with an 8-UAV swarm further validate the reliability of the proposed collision avoidance strategy in large-scale UAV clusters. The success rate remained consistently high across various scenarios, confirming that the algorithm can effectively handle the increased complexity and coordination required in larger groups.

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Figure 7

Comparison of exploration success rates for (a) 4 UAVs and (b) 8 UAVs, with and without the integrated Collision Avoidance module (CA), under different speeds and scenarios

Real world exploration tests

To further validate the performance of the proposed method in real-world environments, we conducted extensive experiments in both outdoor and indoor settings. The UAV platform used is equipped with an Intel NUC13 i7-1370P processor and a Livox-Mid360 LiDAR for positioning and mapping. The positioning framework is based on the method described in [31]. To simulate the depth camera’s mapping effect, the LiDAR’s horizontal FOV was restricted to 86^∘ and its vertical FOV to −10^∘ to 60^∘. The speed was limited to $v_{\text{max}}=1.0\text{m/s}$ and $acc=0.8{\text{m/s}}^2$ to achieve better collision avoidance. All UAVs performed task allocation and exploration in a distributed manner, with no centralized control used during the experiments.

First, four UAVs explored a $12\times 30\times 1.6{\text{m}}^3$ indoor environment with multiple columns and a large exhibition board as obstacles. The UAVs efficiently and quickly completed the exploration task through cooperation. Next, three UAVs were tested in the $12\times 20\times 2{\text{m}}^3$ forests. The results are shown in Fig. 1 and Fig. 8. The swarm excelled in the more complex environment and successfully completed the exploration task, achieving collision avoidance between UAVs.

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Figure 8

(a) shows exploration experiments conducted in the forests. (b) shows the complete mapped environment and the UAV swarm’s exploration trajectory

These indoor and outdoor experiments demonstrate that the proposed distributed swarm system achieves efficient exploration and robust safety in complex real-world scenarios. Across both structured indoor environments and unstructured forested terrain, our method exhibits strong robustness.

Additionally, the bandwidth usage during the experiments was carefully monitored. With 6 UAVs in the swarm, the average data transmission required for real-time tracking and map updates was approximately 10.25 MB/second, as calculated from the rosbag data. The rosbag data recorded during the experiments included several key components: the UAVs’ real-time position and trajectory data, the simplified grid map data used for exploration and navigation, and the UAVs’ internal status and sensor readings. The moderate bandwidth usage ensured that the UAVs were able to perform coordinated exploration and task allocation without noticeable network delays or performance degradation. This confirms that the proposed distributed swarm system is not only efficient in terms of task execution but also effectively utilizes network resources, making it feasible for practical deployment in both indoor and outdoor settings.

Conclusion

This paper proposes an exploration framework for UAV swarms that effectively balances safety and timeliness in unknown environments. Through grid-based task allocation and hierarchical exploration planning strategies, the exploration process is significantly accelerated. To ensure safety, the swarm predicts collision risks based on position sharing and takes priority-based collision avoidance measures, effectively safeguarding the UAVs’ safe flight. Experimental results demonstrate that the framework constructs a complete volumetric map while ensuring safety without compromising efficiency, showing good robustness.

Future work will focus on scaling the framework to larger clusters operating in complex dynamic environments, with emphasis on: (1) Robust collision avoidance for high-density UAV swarms; (2) Timely target search and exploration amidst moving obstacles.

Acknowledgements

The authors would like to express their sincere gratitude to the Shanghai Research Institute for Intelligent Autonomous Systems for its strong support. The Institute’s provision of critical experimental facilities and computational resources was instrumental in the successful completion of this research.

Author contributions

YB: writing original draft, methodology, experiments and analysis. SD, QJ, YL: assisting in the experiments. MX, BZ, GW, QL: manuscript review and revision. All authors read and approved the final manuscript.

Funding information

This work was supported in part by the National Key Research and Development Program of China under Grant No. 2022YFA1004700; in part by the National Natural Science Foundation of China under Grant Nos. 62301308, 62305019, 62371342, and 62071334; in part by the Shanghai Municipal Science and Technology Major Project under Grant No. 2021SHZDZX0100; in part by the Shanghai Municipal Commission of Science and Technology Project under Grant No. 19511132101; in part by the Aeronautical Science Foundation of China under Grant No. 20230007308001; in part by the Fundamental Research Funds for the Central Universities under Grant No. 22120210543; and in part by Tianjin Transportation Science and Technology Project under Grant No. 2025-76.

Availability of data and material

The dataset used in this research is available under the public domain.

Code availability

Due to the confidentiality requirements of the research, the code is not available for public release.

Declarations

Competing interests

The research has no conflicts of interest.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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