# Voronoi-GRU-Based Multi-Robot Collaborative Exploration in Unknown Environments
## 5 Conclusions  
This paper presents a novel collaborative exploration strategy (V-R-MATD3) for multiple mobile robots in unknown environments, employing a hierarchical control architecture. The proposed framework specifically contains a hybrid reward function that synergisti  
Figure 9: Comparison of the complete motion trajectories and exploration coverage when using the VRMATD3, MAPPO, RRT, and Cost-based methods. \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**World I**} & \multicolumn{3}{c}{**World II**} & \multicolumn{3}{c}{**World III**} \\ \hline  & **Steps** & **Time (s)** & \begin{tabular}{c} **Overlap** \\ **(\%)** \\ \end{tabular} & **Steps** & **Time (s)** & \
\begin{tabular}{c} **Overlap** \\ **(\%)** \\ \end{tabular} & **Steps** & **Time (s)** &
\begin{tabular}{c} **Overlap** \\ **(\%)** \\ \end{tabular} \\ \hline Ours & 3.65 & 22.41 & 0.02 & 7.72 & 97.04 & 0.24 & 5.42 & 36.87 & 0.13 \\ MATD3 & 7.14 & 38.03 & 0.10 & 12.40 & 106.35 & 0.31 & 8.73 & 50.03 & 0.17 \\ MAPPO & 9.92 & 42.29 & 0.14 & 18.05 & 114.24 & 0.33 & 11.26 & 44.54 & 0.19 \\ RRT & 24.86 & 89.13 & 0.47 & 55.53 & 153.86 & 0.42 & 43.08 & 85.74 & 0.21 \\ Cost & 56.81 & 62.09 & 0.44 & 148.14 & 151.40 & 0.46 & 95.68 & 98.82 & 0.20 \\ \hline \hline \end{tabular}  
* Testing map World II refers to [1], with modifications.  
\end{table} 
Table 3: Results of the MATD3, MAPPO, RRT, and Cost-based methods and our strategy. cally combines coverage completeness, time efficiency, and inter-robot coverage overlap penalties, trained through a multi-robot reinforcement learning toolkit. The high-level decision layer determines the next frontier point for each robot through Voronoi-based task allocation and our enhanced MATD3 algorithm with GRU-enhanced coordination, while the low-level execution layer generates collision-free motion trajectories. Extensive simulation experiments demonstrate significant improvement in exploration efficiency compared to conventional frontier-based methods and other learning-based approaches. Comprehensive ablation studies quantitatively validate the necessity of both Voronoi partitioning and GRU components--their removal induces redundant inter-robot spatial coverage due to task allocation imbalances and severely disrupts cooperative decision-making mechanisms while simultaneously slowing policy convergence during training. These results demonstrate the superiority of our tightly coupled hierarchical framework in addressing the cooperative exploration challenges of multi-robot systems in unknown environments. Nevertheless, there is still room for improvement in our work. Below are the disadvantages of the proposed method, along with potential solutions:  
* Centralized computation limits flexibility in the robotic system: Our approach utilizes a centralized decision-making and distributed execution architecture, which is widely adopted due to its global optimality. However, it faces scalability issues as the number of robots increases and encounters communication bottlenecks. A distributed architecture could address these problems [47], but RL inference has high computational complexity and is resource-intensive. If a distributed approach were adopted, each robot would require high performance [48]. Due to hardware limitations in our lab, we initially chose the centralized decision-making model. Future work will explore the efficiency of distributed solutions in multi-robot systems. * Lack of real-world experiments: Our experiments were conducted in the high-fidelity Gazebo simulation environment [1]. While this environment considers many dynamic factors, it still deviates significantly from the real world. We plan to conduct experiments with real robots in real environments and utilize domain randomization to mitigate the Sim-Real gap [49]. * Insufficient robustness to dynamic obstacles and robot failures: The experiments in this paper were conducted in a static environment, which is ideal and rarely prone to faults.