## 4 Experiments and Results
### Communication Topology Mutation Experiment  
In order to further evaluate the swarm robustness under the control of the IDGCNs-based strategy, we design a communication topology mutation experiment, where we assume that some robots are destructed due to the attacks or their own reasons and new robots merge into the swarm during the flocking process. The strategies are verified whether they can avoid swarm splitting while maintaining the swarm consistency during the dynamic change of the swarm scale and the sudden change of the communication topology.  
The experiment also assumes that the swarm is composed of seven robots and the initial form of the swarm is a regular hexagon. The positions and velocities of individuals are attached with Gaussian noise and the maximum velocity of the robot is set to 2 m/s. The test results on the test set are shown in Table 7.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Strategy** & **VR** & **DR** & **GIE** & **SR** \\ \hline IDGCNs-based strategy & \(-\)**229.239** & \(-\)351.562 & **1.868** & **0.995** \\ DAGNNs-based strategy & \(-\)243.937 & \(-\)372.027 & 1.862 & 0.99 \\ Distributed APF strategy & \(-\)235.586 & \(-\)**178.002** & 1.729 & 0.845 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Evaluation results of the three distributed strategies in the following experiment.  
The quantitative results show that the velocity and one-hop distance consistency obtained under the control of the three strategies are at the same level. However, the control strategy based on IDGCNs has better performance in the GIE and SR, which means that the swarms controlled by the IDGCNs-based strategy achieve higher robustness.  
Figure 9 plots the motion trajectories and some intermediate forms under the control of the three strategies in a specific episode. The breaking point of each trajectory indicating the failure position of the corresponding robot and the start point of each trajectory indicating the departure position of a new robot which is ready to merge into the swarm.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Strategy** & **VR** & **DR** & **GIE** & **SR** \\ \hline IDGCNs-based strategy & \(-1178.36\) & \(-552.709\) & \(1.802\) & \(0.815\) \\ DAGNNs-based strategy & \(-1169.61\) & \(-695.476\) & \(1.763\) & \(0.56\) \\ Distributed APF strategy & \(-1211.969\) & \(-659.868\) & \(1.614\) & \(0.725\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Evaluation results of the three distributed strategies in the communication topology mutation experiment.  
Figure 8: Motion trajectories and intermediate forms of the swarm in the following experiment. (**a**) Trajectories and intermediate forms of the IDGCNs-based strategy. (**b**) Trajectories and intermediate forms of the DAGNNs-based strategy. (**c**) Trajectories and intermediate forms of the distributed APF strategy.  
From the motion trajectory of the swarm, it can be seen that the IDGCNs-based strategy can maintain the consistency during the dynamic change of the swarm scale and can constantly adjust the swarm morphology according to scale to achieve a balanced distribution of graph importance, which can help to improve the swarm robustness. Considering the trajectories and intermediate forms under the control of the distributed APF strategy and the DAGNNs-based strategy, it can be found that both of them achieve various morphology because they do not consider the consistency of graph importance, which directly leads to lower swarm robustness and is reflected in the lower success rate of avoiding swarm splitting.