# A Bacterial Chemotaxis-Inspired Coordination Strategy for Coverage and Aggregation of Swarm Robots
## 5 Simulations and Discussion
### Comparison for Aggregation  
We employ the BCCS given by Equations (5), (6) and (10)-(12) for aggregation. We assume that the systems for the controller in Reference [27] and BCCS are distributed, and the robots are not connected by a graph \(G\). The simulation configuration is the same as that used for coverage. Figure 14 shows the iteration series of the robot positions for the controller in Reference [27], and BCCS, where robots have dispersed initial positions, as shown in Table 4. In Figure 14, the controller in Reference [27] faces the problem of the slow aggregation process. Although the robots aggregate locally, the fusion of sub-aggregations is a very slow process. After the maximum number of iterations, there are three sub-aggregations in the environment, which means the aggregation failure. However, the robots based on BCCS aggregated in a common place at 60 iterations. From 60 iterations to 120 iterations, the aggregation structure is stable. This is because the BCCS can balance cohesive swarms and exploration of individuals when performing rotating. The \(w_{2}\) helps a sub-aggregation explore space and search other sub-aggregations. The higher \(w_{2}\) means the more obvious the exploration capability of the robot in a sub-aggregation. When the robot senses the others with \(Ri\), \(w_{2}\) is zero, and the robot loses the exploration capabilities and quickly gathers to its neighbors. Figure 15 shows the evolution of the performance measure \(F_{i}\) of each robot over iterations for two methods. In Figure 15b, the \(F_{i}\) of each robot for BCCS gradually converges after 60 iterations. In fact, each robot will not escape from its current aggregation because the \(w_{2}\) of each robot is zero. Figure 13: The \(S\) evolution of two methods without and with noise for coverage. The red and purple lines are for the controller without and with noise in Reference [27], respectively. The blue and green lines are for A1 without and with noise, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**The Controller in Reference [27]** & \multicolumn{3}{c}{**A1**} & \multicolumn{3}{c}{**BCCS**} & \multicolumn{3}{c}{**\#Robots**} & \multicolumn{1}{c}{**\#Environment**} \\ \hline
**Avg** & **Std** & **Succ (\%)** & **Avg** & **Std** & **Succ (\%)** & **Avg** & **Std** & **Succ (\%)** & & **(Unit \(\times\) Unit)** \\ \hline
84 & 10.88 & 93.33 & 73 & 9.35 & 100 & 55 & 8.81 & 100 & 9 & 60 \(\times\) 60 \\
117 & 17.19 & 76.67 & 98 & 13.17 & 93.33 & 71 & 8.47 & 100 & 16 & 80 \(\times\) 80 \\
162 & 15.88 & 60.00 & 126 & 19.55 & 90.00 & 108 & 22.88 & 100 & 25 & 100 \(\times\) 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance comparison results. Avg = average of iterations. Std = standard deviation of iterations. Succ = success rate. 354 at 60 iterations. That is to say, BCCS is robust to noise, and all robots rendezvous in a common place. Table 5 shows the simulation results of two methods for aggregation in a noise free environment. It is worth mentioning that the initial positions of robots for the two methods are randomly generated in local space and the same. Although all simulation results are probabilistic for two methods, we find the superiority of BCCS through some simulations. The completion condition of aggregation is \(S/316\ \leq\ 1.5\), which means all robots rendezvous in a common place. The simulation results are that BCCS has a significant performance comparing with the existing controller for all schemes. For example, the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Robot** & \(x_{i,1}\) & \(x_{i,2}\) \\ \hline
1 & 10 & 10 \\
2 & 30 & 10 \\
3 & 50 & 10 \\
4 & 10 & 30 \\
5 & 30 & 30 \\
6 & 50 & 30 \\
7 & 10 & 50 \\
8 & 30 & 50 \\
9 & 50 & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Robots’ initial positions. Figure 16: The \(F\) evolution of two methods without and with noise for aggregation. The red and purple lines are for the controller without and with noise in Reference [27], respectively.