# Integrated Robotic and Network Simulation Method
## 4 A Case-Study Illustrating the Use of the IRoNS Method
### Study Case--Experimentation and Data Analysis
These results show an interesting behavior change when comparing the rendezvous techniques with (Figure 4) and without (Figure 3) message losses. Now MPC takes significantly less time to converge than A or C, as the resulting CIs from A \(\times\) MPC and MPC \(\times\) C indicate. Again, the difference between A and C is not statistically significant, which is also consistent with the other two comparisons. When comparing each technique without and with message losses (Ideal - I \(\times\) Collision - C) (Figure 5), we see an increase of the convergence time for the three rendezvous techniques, being much stronger for A and C, indicating that these techniques are more sensitive to message losses. This explains the change in behavior observed when comparing the three techniques with and without message losses (Figure 3 versus Figure 4). It is important to note that these results could not be obtained with a simple robot control simulation in Matlab. Given the observed impact of message losses, we carry out another comparison to answer the following question: What is the impact of, upon losses, keeping using the information of the last received message for a longer time (more communication cycles), thus tolerating more consecutive losses? Another set of simulations were carried out using similar parameters as before, except for an extended memory capacity, or in other words, when messages are lost, the last message information is used for up to two communication cycles, i.e., messages were kept for up to 300 ms. The results are shown in Figures 6 and 7. When comparing results of a longer information lifetime, from one cycle memory in Figure 4 to two cycles memory in Figure 6, we observe that an increased lifetime reduces the differences in convergence times to values closer to the case without message losses (Figure 3), meaning that the different techniques exhibit closer behaviors. Moreover, the relative behavior among the three rendezvous techniques with increased information lifetime is still the same in the two cases with  
Figure 6: Differences in convergence time between the rendezvous techniques with 99% confidence intervals and message losses, with two communication cycles memory. Figure 7: Differences in convergence time for each rendezvous technique with and without message losses, with two communication cycles memory, and with 99% confidence intervals. message losses, i.e., MPC takes less time to converge. However, there is now a more significant difference between A and C, in favor of the Circumcenter (C) technique, and consequently a less significant difference between MPC and C (note that the CI now includes zero). This reduction in the impact of message losses is observed in Figure 7 too, when we compare again each technique without and with message losses but now with longer information lifetime. Both average and circumcenter rendezvous techniques show a moderate increase in convergence time, slightly more pronounced for A, while the impact on the MPC technique is not statistically significant (CI includes zero). To further show how the method can be modular and how these parameters can affect the results, we made a simulation case in which we increase the number of robots and use the change in the topology (Linear \(\times\) Grid, as indicated in Figure 8) as factor \(e1\) and the change in control algorithm (Average \(\times\) Circumcenter) as factor \(e2\). The results are presented in Figure 9, where we can clearly observe that the increasing number of robots also increases the convergence time. Figure 8: Fixed communication topologies for 20 robots. Figure 9: Results of varying the number of robots with two different control algorithms (Average \(\times\) Circumcenter) and two fixed communication topologies (Linear \(\times\) Grid). There is a notable difference between the linear and grid topologies results.