# Multirobot Task Planning Method Based on the Energy Penalty Strategy
## 5 Simulation Experiment Analysis  
### MRTA Optimization  
To prove the effectiveness of the penalty mechanism in the algorithm, the proposed algorithm in this paper is compared with the basic GA through simulation experiments. Assuming that all robots have sufficient initial energy, the initial parameters are set as follows: with energy consumption per unit distance \(A\) as a constant value, take \(A=1.5\) J, \(\alpha=4\%\), population size \(M=80\), \(P_{\rm c}=0.8\), \(P_{m}=0.1\), and iterations \(T=1000\). In addition, the computational characteristics of the computer used for all experiments are as follows: DELL G3 3590, Intel(R) Core(TM) i7-9750H CPU @ 2.60 GHz, 16.0 GM (RAM), and the software is MATLAB R2019a. **Experiment 1:** We set the number of tasks \(m=30\) (the task nodes are represented by 1-30 serial numbers). When the number of robots is \(n=3\) and \(n=4\), the proposed algorithm and the basic GA are used to realize the task planning. Given the same barrier-free task environment, multiple robots begin to perform other tasks from starting point 1 (  
The optimal task sequence (TS) and task number (TN) of the algorithm in this paper (Figure 9a,c, respectively) are shown below. \[Opt(TS)_{m=30,n=3}= \begin{cases}R_{1}:\left\{(1),12,3,21,6,11,10,28,18\right\},&TN _{1}=8\\ R_{2}:\left\{(1),24,2,8,20,22,19,13,6,9,29,16\right\},&TN_{2}=11\\ R_{3}:\left\{(1),26,7,17,23,30,4,27,25,15,14\right\},&TN_{3}=10\end{cases} \]  
\[Opt(TS)_{m=30,n=4}= \begin{cases}R_{1}:\left\{(1),24,6,11,14,2,15,8\right\},&TN _{1}=7\\ R_{2}:\left\{(1),7,17,23,30,3,21,12\right\},&TN_{2}=7\\ R_{3}:\left\{(1),26,10,28,9,29,16\right\},&TN_{3}=6\\ R_{4}:\left\{(1),4,27,25,18,5,13,19,22,20\right\},&TN_{4}=9\end{cases} \]  
It can also be seen from the energy consumption iteration curve of the robot (Figure 10a-d) that the GA of the energy penalty strategy improves the convergence speed of genetic iteration with lower total energy consumption and better energy balance. The experimental data of the robot energy consumption and standard deviation \(\sigma\) are shown in Table 1.  
The results indicate that when \(n=3\) and \(n=4\), the total energy consumption rates of the proposed algorithm are 2.3% and 12.6% lower than those of the basic GA (without penalty mechanism), and the standard deviations are 65.6% and 83.8% lower, respectively. Therefore, compared with the basic GA (Figure 9b,d), the task allocation of the proposed algorithm (Figure 9a,c) is more reasonable. Furthermore, the task groups are relatively centralized, which ensures the balance of each robot's movement distance and energy consumption. Thus, genetic optimization based on the energy penalty strategy can not only  
Figure 10: Iterative curve of robot energy consumption from Experiment 1: (**a**) algorithm in this paper (\(m=30\), \(n=3\)); (**b**) basic genetic algorithm (\(m=30\), \(n=3\)); (**c**) algorithm in this paper (\(m=30\), \(n=4\)); (**d**) basic genetic algorithm (\(m=30\), \(n=4\)). The optimal TS and TN of the algorithm in this paper (Figure 11a,c) are shown below. \[Opt(TS)_{m=40,n=3}= \begin{cases}R_{1}:\{(1),13,27,38,28,30,2,14,10,4,33,9,12,19,25 \},&TN_{1}=14\\ R_{2}:\{(1),20,35,6,21,3,26,16,31,23,24,22,29,5,18\},&TN_{2}=14\\ R_{3}:\{(1),11,32,17,34,15,8,36,40,37,39,7\},&TN_{3}=11\end{cases} \]  
\[Opt(TS)_{m=40,n=4}= \begin{cases}R_{1}:\{(1),3,26,21,17,34,15,8,36,40\},&TN_{1}= 9\\ R_{2}:\{(1),13,38,27,32,11,6,35,20,24\},&TN_{2}=9\\ R_{3}:\{(1),21,14,9,12,25,19,18,22,23,31,16\},&TN_{3}=11\\ R_{4}:\{(1),29,5,33,4,10,28,30,39,37,7\},&TN_{4}=10\end{cases} \]  
When the number of robots increases, similar to the result of Experiment 1, the optimal scheme of the MRTA is more reasonable than the basic GA. It can be seen from the energy consumption iteration curve (Figure 12) that it still has a better effect in terms of convergence speed and energy consumption.