# An Artificial Plant Community Algorithm for Collision-Free Multi-Robot Aggregation
## 6 Benchmark Data and Experiments
### Benchmark Test Results
The maximum travel distance in Figure 7 is \(\max\{D_{Ta,Tb}^{travel}\}=440\) m, and the minimum travel distance is \(\min\{D_{Ta,Tb}^{travel}\}=\)300 m, while the total travel distance \(D_{T}^{travel}\) is 5800 m.  
After 300 tests, the statistics of the benchmark test are summarized in Table 6, where the results demonstrate that the proposed APC algorithm can help us to search for the optimal solution to the collision-free multi-robot aggregation problem. It can be seen that the minimum value of makespan \(k_{T}^{make}\) presented an increase of about 14.55% compared to the maximum value, the total travel distance \(D_{T}^{travel}\) (m) had an increase of about 6.90% compared to the maximum value, and the minimum value of travel energy consumption \(e_{T}^{travel}\) had an increase of 6.90% compared to the maximum value. There is a positive correlation between the total robot energy consumption (kWh) and the maximum travel distance (m) and the travel speed (m/s) in Table 5, where the total processing energy (kWh) of robots was 430.33-462.24 times greater than the travel energy consumption (kWh). The statistical data indicate the total collision time \(k_{T}^{coll}=0.0\) h, verifying that the collision-free objective was satisfied in the multi-robot aggregation problem. Figure 8 shows the convergence curves of the proposed APC algorithm, including the average fitness of the APC population and the best fitness of the optimal solution. The benchmark test results in Figures 6 and 7 were calculated with a maximum number of iterations equal to 200. It can be observed, from Figure 8, that the optimal solution can be obtained by the proposed APC algorithm after about 140 iterations, showing the good convergence performance of the proposed APC algorithm in solving the collision-free multi-robot aggregation problem. Figure 6: The processing time for the collision-free multi-robot aggregation problem solution (the same color is used for the same operations in each task, and different operations are randomly assigned different colors). Figure 7: The travel time for the collision-free multi-robot aggregation problem solution (the same color is used for the same tasks of different operations, and different tasks are randomly assigned different colors). To delve deeper into the entangled factors affecting the collision-free multi-robot aggregation problem, the benchmark results under changing parameters are shown in Figure 9a,b, describing how variations in the parameters affected the main metrics (i.e., the makespan \(k_{T}^{make}\), total collision time \(k_{T}^{coll}\), total travel distance \(D_{T}^{thread}\), and total energy consumption \(e_{T}^{total}\)). To present the different variation curves in the same graph, all data were normalized. The trends of the four main metrics with different distances between tasks are shown in Figure 9a. It can be observed that the the collision-free goal of \(k_{T}^{coll}=0.0\) h is reached, where a greater distance between tasks increased the makespan \(k_{T}^{make}\), total travel distance \(D_{T}^{travel}\), and the total energy consumption \(e_{T}^{total}\). When the distance between tasks was in the range of 90-150 m, the makespan \(k_{T}^{make}\) rapidly increased. Maintaining the distance between tasks in the range of 50-90 m is helpful to balance the makespan \(k_{T}^{make}\) and the energy consumption \(e_{T}^{total}\), as the total travel distance \(D_{T}^{travel}\) will decrease and less time will be consumed for aggregation. The trends of the four main metrics under different robot velocities are shown in Figure 9b. It can be seen that a greater robot velocity is helpful to decreasing the makespan \(k_{T}^{make}\) when the collision-free goal of \(k_{T}^{coll}=0.0\) h is achieved. However, a greater robot velocity will increase the total energy consumption \(e_{T}^{total}\), while the total travel distance \(D_{T}^{travel}\) remains stable. When the robot velocity is in the range of 1.0-2.0 m/s, the total energy consumption \(e_{T}^{total}\) will rapidly increase.