# Task Planning of Space-Robot Clusters Based on Modified Differential Evolution Algorithm
## 5 Experimental Results
### Comparison Experiment of Optimal-Path Model Optimization  
#### 5.2.1 Experimental Comparison  
In the process of task planning, it is necessary to reasonably consider the relationship between the paths between clusters and the number of points within the clusters--and then to complete the optimization of the robot clusters revenue and energy consumption under a certain energy. In this experiment, under the condition of certain energy, the newly proposed optimal-path model of space-robot cluster and the shortest-path model of space-robot cluster are compared. The optimal path is solved by the modified differential evolution algorithm, and the total number, revenue and completion rate of the maintenance tasks under the condition of certain energy are compared. In order to simplify problem solving, it is assumed that each space robot's movement consumption \(\alpha_{k}\) and maintenance failure point consumption \(\beta_{k}\) a are the same, set \(\alpha_{k}\!=\!5,\ \beta_{k}\!=\!1,\ \mathrm{k}\!=\!1,2,3,4,5\). In this experiment, the corresponding parameters are set as: \(\mathrm{NP}\!=\!500,\ \mathrm{ng}\!=20,\ \gamma\!=\!0.9,\ \mathrm{CR}\!=\!0.1,\ \mathrm{F}_{0}\!=\!0.4,\ \lambda_{1}=\lambda_{2}=\lambda_{3}=\lambda_{4}=0.25,\ gMax=10,000\). The clustering results of 800 maintenance points are taken as the target node to be planned in this experiment. The charging piles in each space are the starting point of each space robot. The space robots are required to return to the starting position after repairing each target node according to the design path. The initial positions of the five space robots are, respectively (0, 0), (-90, 30), (-90, -30), (90, 30), (90, -30). In this experiment, the total battery capacity of the space-robot cluster is set to 5000, 6000 and 7000, respectively. The energy of each robot is shown in Table 2. Considering the optimal-path model and the shortest-path model of the robot cluster, the maximum number, the maximum revenue and the task completion rate of the space-robot cluster maintenance solar array are calculated. The maintenance path and completed tasks are shown in Tables 3-5, respectively. In this experiment, the safety factor, maintenance revenue weight, maintenance cost weight and penalty function coefficients are set as \(\xi=0.8,\ \omega_{1}=1,\ \omega_{2}=-0.5,\ \varrho=-400\). Consumption is the energy consumption of each space robot. Income is the total income of repair points on the repair path. Number of tasks is the number of tasks completed by the space-robot cluster at a given energy. Income rate is the ratio of the income completed by the space-robot cluster and the total task income. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type** & **Robot** & **Consumption** & **Income** & **Number of Tasks** & **Income Rate** \\ \hline \multirow{4}{*}{Multirobot optimal-path} & R\({}_{1}\) & 1184.51 & & & \\ \cline{2-6}  & R\({}_{2}\) & 890.12 & & & \\ \cline{2-6}  & R\({}_{3}\) & 888.59 & 12,640 & 632 & 79.65\% \\ \cline{2-6}  & R\({}_{4}\) & 899.01 & & & \\ \cline{2-6}  & R\({}_{5}\) & 896.14 & & & \\ \hline \multirow{4}{*}{Multirobot shortest-path} & R\({}_{1}\) & 1184.70 & & & \\ \cline{2-6}  & R\({}_{2}\) & 865.95 & & & \\ \cline{2-6}  & R\({}_{3}\) & 845.31 & 9160 & 466 & 57.84\% \\ \cline{2-6}  & R\({}_{4}\) & 843.96 & & & \\ \cline{2-6}  & R\({}_{5}\) & 880.99 & & & \\ \hline \hline \end{tabular} Note: The total energy of robot cluster is 6000, the energy of each robot are \([1500,\,1125,\,1125,\,1125]\), the available energies are \([1200,900,900,900,900]\).  
\end{table} 
Table 2: Space-robot capacity information. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Robot Number** & **Robot 1** & **Robot 2** & **Robot 3** & **Robot 4** & **Robot 5** \\ \hline Total capacity 5000 & 1200 & 950 & 950 & 950 & 950 \\ Total capacity 6000 & 1500 & 1125 & 1125 & 1125 & 1125 \\ Total capacity 7000 & 1800 & 1300 & 1300 & 1300 & 1300 \\ \hline \hline \end{tabular}
\end{table}