## 6 Simulative Experiments and Analysis
### Simulation Experiment on Multi-Robot Coordination  
To verify the efficacy of the multi-robot cooperative planning algorithm presented in this paper within complex circumstances, taking into account the time expenditure, this study carried out a simulation experiment on a 20 \(\times\) 20 grid map. The experiment mimicked a situation where three robots performed their individual tasks in the same environment. The experimental setting encompassed dynamic obstacles and unknown static ones to heighten the complexity and difficulty of path planning. Each robot was allocated an independent starting point and destination, and the path needed to be adjusted dynamically during task execution to prevent conflicts with other robots and obstacles. The yellow grid indicates dynamic obstacles, the gray grid represents unknown static obstacles, and the black grid stands for known static obstacles. The simulation outcomes are presented in Figure 11, where the triangle indicates the starting point of the robot, and T1, T2, and T3 respectively denote the target points of Robot 1, Robot 2, and Robot 3.  
At t = 0, a node conflict emerged between Robot 1 and Robot 2. Since Robot 1 had already passed through the intersection where the goal point of Robot 2 was located, Robot 1 was automatically assigned a higher priority. Moreover, as Robot 2 had no alternative route to bypass [PERSON] in the narrow section, Robot 2 stopped and waited. Robot 1 proceeded along its original path. Once it was safe, Robot 2 resumed its forward movement.  
At t = t1, Robot 3 detected the existence of unknown static obstacles on the original path, while Robot 2 was on the verge of reaching the target point, thus Robot 2 was automatically assigned a higher priority. At this point, Robot 3 assessed the feasibility of the current path ahead and determined that proceeding further would lead to an inability  
Figure 10: Comparative analysis of fusion algorithms in a dynamic environment. (**a**) The fusion algorithm presented in [25]. (**b**) The integrated algorithm presented in this article.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Path Length (m)** & **Time (s)** \\ \hline Algorithm from [25] & — & — \\ \hline Algorithm in this paper & 30.37 & 146 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The results obtained from the fusion algorithm.  
to bypass the obstacle or collide with Robot 2, resulting in a path deadlock. Consequently, Robot 3 chose to re-plan the path, and Robot 2 continued its forward movement.  
At \(t=t2\), the three robots managed to evade obstacles successfully and reached their respective target points concurrently via coordinated path planning. This process showcases the ability of multi-robot systems to collaborate effectively in complex environments.  
As depicted in Figure 12a,b, the curves of the velocity and angular velocity of the robots are presented. When Robot 3 encountered a moving obstacle for the first time, it opted to halt and wait since the obstacle met the distance threshold and angle threshold; thus, its linear velocity was zero. Once the obstacle passed, Robot 3 resumed its movement. Due to the fact that the priority of Robot 2 was higher than that of Robot 3, Robot 3 undertook path replanning, and its linear velocity tended to zero. Robot 2 had a linear velocity of zero because it needed to avoid Robot 1. In conclusion, this validates that the algorithm proposed in this paper can effectively address the conflict issue between robots. The algorithm is capable of generating global paths efficiently in complex environments and flexibly circumventing dynamic and unknown static obstacles through local path planning to ensure the safe operation of the robots. The actual trajectories of the multiple robots in the complex dynamic environment demonstrate the effectiveness and viability of the proposed algorithm in optimizing paths, improving obstacle avoidance, and facilitating cooperation in multi-robot systems.  
Figure 11: Multi-robot path planning.  
Figure 12: Robot parameters.