# Integrated Robotic and Network Simulation Method
## 4 A Case-Study Illustrating the Use of the IRoNS Method
### Study Case--Experimentation and Data Analysis  
After making any needed adjustments in the Base Simulation, we defined 15 different initial conditions (samples) and obtained results each factor combination. For each sample, factor combination results are transformed in factor and cross-factor impact. The last step is to compute the mean and variance of the 15 samples of each impact factor and cross-factor to finally build their confidence intervals (CI). The CIs were built with confidence of 99% using (1), with \(\alpha=0.01\) and \(\mathrm{t}_{14,0.995}=2.977\), leading to the three CIs shown in Figure 3. \begin{table}
\begin{tabular}{c c} \hline \hline  & **Fixed Topology** \\ \hline
**MPC–CI 99\%—Tf** & [\(-0.016\); \(0.041\)] \\ \hline
**MPC–CI 99\%—Df** & [\(-0.013\); \(0.0298\)] \\ \hline
**Average–CI 99\%—Tf** & [\(-0.01\); \(0.021\)] \\ \hline
**Average–CI 99\%—Df** & [\(-0.013\); \(0.022\)] \\ \hline
**Circumcenter–CI 99\%—Tf** & [\(-0.021\); \(0.016\)] \\ \hline
**Circumcenter–CI 99\%—Df** & [\(-0.023\); \(0.018\)] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Base simulation validation with confidence intervals. Figure 3: Differences in convergence time between the rendezvous techniques with 99% confidence intervals. Figure 3 shows what happens to the rendezvous completion time when changing from the first technique X to a second technique Y (\(\mathrm{(X\times Y)}\), without any message losses and using a fixed topology control. In the first and last case, A \(\times\) MPC and MPC \(\times\) C respectively, confidence intervals do not include zero, indicating a significant performance difference. In particular, the convergence time increases when using MPC over an average rendezvous and decreases when using the circumcenter algorithm instead of the MPC. The confidence interval of the A \(\times\) C experiment includes zero, meaning that these techniques do not have a statistically significant difference, which is consistent with the other two comparisons (A \(\times\) MPC and MPC \(\times\) C). On the other hand, even the difference in convergence time between A or C and MPC is small, just around 1s, which may be considered negligible when compared with the absolute convergence times that varied between 20 and 50 s. With this information, we can conclude that changing between these rendezvous techniques does not impact significantly the convergence time under these network parameters, which is consistent with the Matlab simulation, too. In the second part of the experiments we considered the robots deployed in an environment with network interference affecting the quality of robots communication through message losses. To create this effect in the simulation framework, we added a fixed node in the simulation environment that generates bursts of messages with a periodicity of 300 ms and duration of 100 ms, causing collisions with the robots messages. We used the same 15 initial conditions of the previous experiment to build another comparison study between the first experiment, labelled 'Ideal' case, and the results achieved under message collisions, labelled 'Collision' case. Moreover, we considered that each robot can hold a message for 200 ms (one communication cycle memory), thus tolerating one message loss. However, if two or more consecutive messages are lost, the communication link is disabled until the robot receives a new message from that neighbor (source). The resulting CIs between control strategies in a network with message losses are shown in Figure 4 and the comparison for each technique between the cases of without and with losses is shown in Figure 5.  
Figure 4: Differences in convergence time between the rendezvous techniques with 99% confidence intervals and message losses, with one communication cycle memory. Figure 5: Differences in convergence time for each rendezvous technique with and without message losses, with one communication cycle memory, and with 99% confidence intervals.