# A Bacterial Chemotaxis-Inspired Coordination Strategy for Coverage and Aggregation of Swarm Robots
## 5 Simulations and Discussion
### Comparison for Coverage  
In this section, BCCS and A1 are compared with the bacteria-inspired controller in Reference [27], where A1 is the BCCS without chaotic preprocessing. First, we consider an extreme case where all the robots are at the same point (\(30,30\)), and compare A1 with other bacteria-inspired controller. Also, the case of BCCS is studied. Figure 10 shows the iteration series of the robot positions for A1 and the controller in Reference [27], where the stars in different colors represent different robots. The environment is 60 units \(\times\) 60 units. The number of robots is 9, and the radius of the red circle is \(Rs\). The maximum number of iterations is 120. In Figure 10, the robot distribution based on A1 is more uniform than that based on the controller in Reference [27] after 60 iterations. After 80 iterations, the position of each robot based on A1 is fine-tuned. One can see the same scenario in Figure 10, which causes A1 to have a higher performance. Figure 11 shows the evolution of the performance measure \(F_{i}\) of each robot over iterations. We can conclude that the \(F_{i}\) of each robot increases as the number of iterations increases for two methods at the beginning of the coverage. In Figure 11a, the \(F_{i}\) of some robots oscillates over a wide range for the existing bacteria-inspired controllers. As shown in Figure 11b, \(F_{i}\) of each robot for A1 gradually converges after 80 iterations. It is because the robot evaluates the neighbors' positions when performing rotating. In fact, the robot moves far away from its neighbors, and direction is calculated by Equation (8). The smaller the oscillation amplitude for all the robots is, the more stable the swarm robotic system is. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline  & 60 units \(\times\) 60 units, \\ Environments, \(E\) & 80 units \(\times\) 80 units, \\  & 100 units \(\times\) 100 units \\ Cell size, \(k\) & 1 unit \(\times\) 1 unit \\ Number of robots, \(n\) & 9, 16, 25 \\ Velocity of robot, \(v\) & 1 unit/iteration \\ Maximum iterations, \(\mathit{Imax}\) & 2L \\ Covered radius, \(Rs\) & 10 units \\ Sense radius, \(Ri\) & 20 units \\ Logistic equation iterations, \(I_{c}\) & 500 \\ Rotation range, \(\theta\) & 0–360\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter settings of the swarm robotic system. Figure 10: Simulation results for coverage in noise free environment: (**a–f**) The controller in Reference [27]; (**g–l**) A1. Next, we consider the noise, and the background noise is fixed at \(\sigma_{k}\) = 0.005. \(\chi^{\prime}\) (t + 1) = x (t + 1) + \(\sigma_{k}\) is the actual moving position of robot at time \(t+1\). Figure 12 shows the evolution of \(F\) for all the robots with and without noise. For the noise free environment, although the robot based on the existing bacteria-inspired controller is more exploratory at the first 50 iterations, due to the randomness of the robot's initial motion direction, the robot based A1 can quickly adjust their motion planning as the number of iterations increases. In Figure 12, although the noise reduces the stability of change of \(F\) for A1, the performance is better than that for the controller in Reference [27]. Meanwhile, after 60 iterations, the covered area of the environment for A1 is larger than that for the existing bacteria-inspired controller as the number of iterations increases, as shown in Figure 13.  
Next, we also consider chaotic preprocessing, which improves the diversity of positions of robots and the convenience of individual deployment. Some simulations are presented under different numbers of robots in different sizes of noise free environments. Each robot can cover 316 cells. To evaluate iteration consumption, we defined that the condition meets \(S/(316n)\)\(\geq\)95%, which means coverage is successfully completed, and record the current number of iterations. The robots' initial positions for the controller in Reference [27], and A1 are randomly generated and the same.