LAEA: A 2D LiDAR-Assisted UAV Exploration Algorithm for Unknown Environments

To investigate the effectiveness of the proposed algorithm, three simulation environments were established using the Gazebo simulator. The UAV model used in the simulation had a 500 mm diameter between two diagonal motor shafts, and was equipped with 2D LiDAR and a depth camera. Details of its configuration are presented in Table 2. The geometric controller [21] was implemented to track the generated trajectory. Fiesta [22] was used to construct $V_{high}$ for exploration completeness, and Octomap [23] was used to construct $V_{low}$ for low memory occupation. The following parameters were used for special frontier detection and solving the ATSP: $th{r}_{small}=2.2$ m, $k_1=0.5$, $k_{iso}=15$, $k_{lb}=1.35$, $w_c=0.05$, $w_b=1.0$, $w_s=1.0$, $w_{iso}=1.2$. Adjustments to these parameters can be made with reference to the practical implications described earlier.

The state-of-the-art frontier-based algorithms FUEL [7] and FAEP [8], which currently offer the best autonomous UAV exploration performance, were chosen for comparison. Meanwhile, additional ablation experiments were performed in scenario 1 (Indoor1), where $OUR{S}^{EIG}$ and $OUR{S}^{LiDAR}$ only used EIG strategies and LiDAR data, respectively. To avoid random superiority in a single run, simulations were repeated 10 times in each simulation environment for all three algorithms, with the same settings. The resolutions for $V_{high}$ and $V_{low}$ were set to 0.12 m and 0.15 m, respectively. The initial size of the local map $M_{hybird}$ was 12 × 12 m², and it was adaptively cropped according to the map boundaries to save resources.

(1) Office Rooms: Two typical office rooms were used to investigate the effectiveness of the exploration algorithm. The volume of the Indoor1 scene was 40 × 20 × 3 m³, and that of the Indoor2 scene was 35 × 28 × 3 m³. The simulation results are shown in Table 3 and Figure 8. During exploration, FUEL often missed more frontier clusters, which resulted in obvious repeated exploration motions later, leading to low exploration efficiency. In comparison, based on the depth camera data, FAEP could detect some of the small frontier clusters and reduce their omission. Meanwhile, the boundary constraints of FAEP guided the UAV to explore the map boundary, which also reduced the rate of repeat visits to the explored area to some extent. However, such constraints also caused the omission of isolated frontier clusters that are far from the map boundary, leading to unnecessary repeated exploration, as shown by the trajectory in Figure 8b. In addition, constrained by the limited FOV of the depth camera, many small frontier clusters were not detected properly by FAEP.

Because of the need to cover special frontier clusters with a high risk of repeated exploration, the coverage curves of the proposed LAEA occasionally stagnated briefly, and then, resumed rapid growth, as shown in Figure 8d,e. Comparatively, both FUEL and FAEP also inevitably experienced significant stagnation in the later stages of exploration. Owing to the LiDAR-assisted special frontier cluster detection and EIG optimization strategy, the proposed algorithm can balance exploration gain with the repeated-exploration risk, and its overall exploration efficiency is higher in all three scenes. Compared to FUEL and FAEP, the proposed LAEA reduces the exploration time by 24–28% and 11–22%, respectively, and the path length by 15–21% and 10–20%.

(2) Pillar Forest: Simulations in a forest measuring 48 × 25 × 3 m³ with surrounding walls and uniformly distributed obstacles were also conducted to investigate the stability and efficiency of the proposed algorithm. The results are shown in Table 3 and Figure 8, and demonstrate that the proposed algorithm reduced exploration time by 19% and 13% compared to FUEL and FAEP, respectively. In complex forest environments, because of the lack of boundary guidance, the efficiency of FUEL remains poor, while both FAEP and the proposed LAEA initially guide the UAV around the map boundary, and therefore, are more effective. As depicted in Figure 8c,f, due to the EIG optimization strategy, the proposed LAEA was able to observe more unexplored regions while exploring the boundary, which corresponds to a coverage curve with a faster growth rate. Moreover, as shown in Figure 8c, the boundary constraints of FAEP still tend to miss the small and isolated frontier clusters, leading to undesirable back-and-forth movements. In contrast, the proposed multi-sensor-based hybrid map of LAEA can quickly detect these special frontiers and cover them, which makes exploration more efficient.

(3) Further Evaluation: To more clearly demonstrate the contribution of the proposed algorithm, a simple and effective comparison test was designed. As shown in Figure 9d, FAEP missed a number of special frontier clusters and caused several unnecessary back-and-forth motions during its exploration, which is mainly related to Parts 1–3. The details of the special clusters missed by FAEP in Parts 1–3 are shown in Figure 9a–c, and these omissions were partly limited by the restricted FOV of the depth camera. In particular, since FAEP relies heavily on boundary constraints during exploration, this inevitably leads to low access rights to frontier clusters far from the map boundary. In contrast, as shown in Figure 9e–g, the proposed LAEA, with the help of LiDAR data information, can efficiently acquire environmental contour information to quickly detect unexplored closed regions (isolated frontier clusters) and regions with low potential for information gain (small frontier clusters). From the detected special frontier clusters, either the next target or the middle yaw angle of the EIG optimization strategy is then selected for fast coverage.

(4) Ablation Study: The results of the ablation experiments are shown in Table 3 and Figure 10. It is clear that both $OUR{S}^{EIG}$ and $OUR{S}^{LiDAR}$ are more effective than FAEP and FUEL. As in Figure 10, thanks to the flexible yaw motion, $OUR{S}^{EIG}$ can achieve additional coverage of nearby frontier clusters as it travels to the next target, and can maintain high coverage per unit time. However, due to the lack of environmental contour information at the frontier clusters, many back-and-forth motions are still seen in the later stages of the exploration flight to cover missed isolated and small frontier clusters; thus, the coverage per unit time decays dramatically. Meanwhile, thanks to the prioritized access to the detected isolated and small frontier clusters, $OUR{S}^{LiDAR}$ has a relatively slow but steadily increasing trend of coverage per unit time, outperforming FAEP and FUEL. In contrast, the proposed LAEA, incorporating the advantages of both $OUR{S}^{EIG}$ and $OUR{S}^{LiDAR}$, achieves superior efficiency to FAEP and FUEL.

Real-world experiments were also carried out in two different scenarios to investigate the effectiveness of the proposed algorithm at reducing repeated exploration. As shown in Figure 11, we used a customized quadrotor platform measuring 380 mm in diameter between two diagonal motor shafts, which was equipped with an RGB-D camera (D435, Intel, Santa Clara, CA, USA), 2D LiDAR (LD19, LdRobot, Nanshan District, Shenzhen, China) and an Nvidia onboard computer (Xavier, Nvidia, Santa Clara, CA, USA). In addition, an Intel T265 camera was used for UAV position estimation. The dynamic motion limits were set to $v_{max}=0.75$ m/s, $a_{max}=0.75$ m/s and ${\theta }_{max}=0.75$ rad/s in the outdoor scene, and $v_{max}=0.5$ m/s and $a_{max}=0.5$ m/s in the indoor scene.

Experiments were first conducted in a courtyard with an exploration map size of 27 × 16 × 2.1 m³, and the results are shown in Figure 12a–c. Due to the branches and weeds in the scene, the detection threshold $th{r}_{small}$ for small areas was set to 1.0 m. The exploration time of the whole process was 190 s, and the total length of the flight path was 120 m. During the exploration process, the multi-sensor-based hybrid map quickly detected and covered the special frontier areas, which ensured steady growth of the coverage curve shown in Figure 12c. Subsequently, experiments were also carried out in an indoor environment with map dimensions of 22 × 10 × 1.8 m³, as illustrated in Figure 12d–f; the exploration time was 100 s, and the flight path length was 42 m. The experimental results show that the proposed algorithm was able to quickly cover the special frontier region of detection in different scenarios, demonstrating efficient exploration of the unknown environment.

It is worth noting that our preset minimum height for the exploration area was $-0.1$ m, and due to the uneven topography of the courtyard and the presence of large low-lying areas and visual localization drift, many visually blank areas (no point cloud) appeared in Figure 12b,e. In contrast, the local hybrid map enables better visualization of whether areas are covered or not, as shown in Figure 13. The hybrid map is moved according to the current position of the UAV and is adaptively cropped according to the map boundaries. More details of the experiment can be seen in the demonstration video provided in Figure 8.