# Voronoi-GRU-Based Multi-Robot Collaborative Exploration in Unknown Environments
## 4 Experiments and Discussion
### Ablation Study
#### 4.3.2 Testing Process  
Ultimately, in order to validate the average performance across repeated experiments, we applied these three methods to three different maps. In our evaluation protocol, the single task terminated when either the motion steps exceeded 20 or the map coverage rate surpassed 90%. Figure 7 presents the simulation process at different step stages under the V-R-MATD3 strategy, including the state information of robot1 and robot2, as well as their merged map. More details are provided in the caption of Figure 7. For instance, Figure 7e illustrates the local map and trajectory information of robot2 in the third step. In the Rviz visualization, the red and green right-angle arrows indicate the robot's poses, the black lines represent the detected obstacles, and the purple bar-shaped regions surrounding them denote the inflation radii within which the robot moves more slowly. The purple curve depicts the robot's trajectory, the white area on the right shows the explored region, the black areas on the left and bottom represent completely unknown regions, and the bluish-green area indicates regions that are reachable but not yet explored. Figure 7 clearly demonstrates each robot's exploration process, showing that the areas explored by the two robots are relatively separated, with the exploration task completed in a total of six steps. In Figure 8a-c, the exploration process under the MATD3 strategy is shown, with the task completed in nine steps, while Figure 8d-f display the exploration under the R-MATD3 strategy, which completes the task in eight steps. Our V-R-MATD3 strategy not only requires fewer steps to complete the task but also results in less repetitive exploration trajectories. Figure 6: Average episode reward of strategies: (**a**) MATD3, (**b**) GRU-based MATD3, (**c**) V-R-MATD3, and (**d**) comparisons. In our study, we adopted both the mean absolute error (MAE) of the exploration rate and the number of exploration time steps to provide a comprehensive analysis of exploration efficiency. The MAE describes the difference between the measured exploration coverage of each iteration by the robot and the expected coverage. Therefore, using the absolute error better reflects the extent to which the task achieves its intended goal. However, we also noticed an issue. On the World II map, both V-R-MATD3 and R-MATD3 achieved an average map coverage exceeding 90%, with V-R-MATD3 exhibiting a larger absolute error relative to the expected 90%. However, in our exploration task, the robot may not always perfectly explore 90%. By observing the robot's movement process, we found that, under the R-MATD3 strategy, the robot exhibited a significant amount of redundant exploration, resulting in slower overall exploration rate growth and a longer exploration time, though the final exploration rate was closer to 90%. In contrast, with the Voronoi-based V-R-MATD3 strategy, the overall exploration rate grew faster. There may be instances where the exploration rate of the previous step is below 90% but that of the next step exceeds 90% by a large margin, and the exploration time is shorter. Clearly, this represents a more efficient exploration strategy. Figure 7: The motion trajectories and exploration coverage of robot1 and robot2 at different stages when using the VRMATD3 strategies. As shown in Table 2, V-R-MATD3 has the lowest number of time steps on all maps and achieves superior mapping completion rates of 90.3% on average across all environments, outperforming both R-MATD3 (88.9%) and MATD3 (78.9%). While V-R-MATD3 demonstrates particular advantages on World I and World II, its slightly inferior performance on World III (compared to that of R-MATD3) may be attributed to the map's unique topological features, with certain peripheral areas remaining persistently unexplored due to limitations in our Voronoi-based partitioning approach.