# Virtual Pheromone Based Network Flow Control For Modular Robotic Systems
## 4 Experiments and Results
### Virtual pheromone-Based Routing Algorithm
Similarly, high evaporation rate enables to switch communication paths according to users's behaviours but creates fluctuation because of the conflict between deposition and evaporation. In contrast, low evaporation rate could reduce flexibility of communication paths since the virtual pheromone concentration is still maintained even when the selected communication path is not used for a while. Selection of deposition and evaporation rates is an important issue for a specific application. To illustrate the real time analysis of the virtual pheromone concentration, we collected data from the module \(t\) and displayed through the Matlab graphical user interface (GUI). Using the basic parameters in Table 3, the virtual pheromone concentration levels on three physical communication channels was presented as in Figure 8. A video demonstration of this experiment can be found in the link ([[https://youtu.be/ph2a8](https://youtu.be/ph2a8)]([https://youtu.be/ph2a8](https://youtu.be/ph2a8))[ShHDk). Figure 8: Demonstration of the virtual pheromone based network data flow control in _Phonic Game_ using the Matlab GUI. Virtual pheromone levels are real-time visualized in continuous lines and bar graphs. \begin{table}
\begin{tabular}{l r} \hline \hline
**Parameters** & **Value** \\ \hline Maximum ant rate & 1 ants/second \\ \hline Deposition rate \(d\) & 2 unit/ant \\ \hline Evaporation rate \(e\) & 0.5 unit/second \\ \hline Delay & 25 \(ms\) / module \\ \hline Concentration upper limit & 95\% \\ \hline Concentration lower limit & 5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Virtual pheromone parameters. One research question would be posed: _What happens if the deposition rate is not constant?_ To answer this, we implemented _three deposition functions_ in terms of _pseudo-linear, pseudo-quadrature, pseudo-logarithm functions_. Figure 9 shows the virtual pheromone concentration of these deposition functions measured on the same system for comparative analysis. First, we applied the pseudo-step function for the modular robotic system. Pseudo-linear function can be seen as one-step response function enabling the virtual pheromone concentration to reach the threshold with only one step. Second, the pseudo-quadrature function slowly increased the virtual pheromone concentration by a little amount for the first few steps, then quickly got up to the maximum value. In a dynamic network where a dominant path is not clear, using the pseudo-quadrature function ensures that a desired communication path is achievable. Meanwhile, the pseudo-logarithm function showed fast reaction to the network reconfiguration. The virtual pheromone concentration quickly raised to the high level, and then slowed down to keep the channel stable when it reached the threshold. This pseudo-logarithm function is helpful for switchability of communication paths but might introduce turbulence when the distinction between paths are not clear. Hence, system performance can be adjusted according to the selected deposition rate. In particular, we found that this step function is suitable for our _Phonic_ game because any request from any branches can be immediately activated due to the fast switching between communication paths at the threshold of 95%. In addition, if we set the upper threshold to 100% and the lower threshold to 0%, probability of choosing communication paths by randomness did not exist according to user's point of view. The flexibility of system was secured by the evaporation rate because the virtual  
Figure 9: Different functions of deposition rate measured at the intersection block on different physical channels using Equations (7) and (8): _Range 1, 2_: Pseudo-linear deposition rate creates linear growth of the virtual pheromone concentration on the selected channels. When no data packets were transmitted over this channel, the pheromone concentration was slowly decreased to the initial values by the evaporation. _Range 3_: Pseudo-quadrature deposition functions with slow increasing rate at the beginning.