## 5 Simulation Results  
To verify the validity of the improved algorithm, this paper uses MATLAB to build three kinds of \(20\times 20\) m grid maps with different complexity. The test is to observe whether the robot could find a feasible optimal path in an environment with static obstacles. The results of the improved ant colony optimization (IACO) and basic ant colony optimization (ACO) are compared and analyzed. The main parameters of the algorithm are shown in Table 2.  
The two algorithms are compared and tested with the same parameters and environment in the experiments. Due to that the algorithm convergence time is positively correlated with the convergence iteration times, the experiments use the best path and convergence iteration times to measure the performance of the algorithm. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Parameter** & \(m\) & \(\alpha_{0}\) & \(\beta_{0}\) & \(Q\) & \(\rho_{0}\) & \(N\) & \(A\) & \(B\) & \(C\) \\ \hline Value & 80 & 1 & 9 & 1 & 0.5 & 100 & 2 & 66 & 0.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Initial parameter setting of the algorithm. Figure 7: Flow chart of the improved ACO. Figure 8 shows the optimal path of the mobile service robot. The left picture is the result of basic ACO. The right picture is the result of IACO, proposed in this paper. Figure 9 is a comparison of the convergence curves between the two algorithms. Figure 8: Comparison of global path planning results between ACO (**left**) and IACO (**right**). In Map 1, there is little difference in the iteration times when finding the optimal path between ACO and IACO. The optimal path by IACO is shorter than ACO, and the convergence speed of IACO is faster. IACO optimizes the pheromone mechanism. First, the IACO determines the initial pheromone according to the distribution of obstacles on the map. It can greatly accelerate the searchability of the algorithm in the early stage. Then, IACO takes a subsection method to update the pheromone. It only updates the pheromone on the optimal path in the later stage of the algorithm. It can be seen from Figure 7(a) that the optimal path solution of ACO is unstable at the end of the iterations. IACO can keep the optimal path solution due to the new pheromone mechanism. IACO introduces the fuzzy algorithm to dynamically adjust the key parameters \(\alpha\) and \(\beta\) of ACO. \(\alpha\) and \(\beta\) can be adaptively adjusted by the quality of the path solution after each iteration. The dynamic adjustment of the parameter \(\rho\) increases the randomness of the algorithm. IACO finds the shortest path earlier than ACO algorithm in Map 2. In the later stage of the map 2 experiment, the sub-best solution quickly takes advantage based on the high pheromone concentration of the sub-best path. The ACO falls into the local optimal problem, which is difficult to escape. The IACO algorithm reduces the dependence on the pheromone concentration by dynamically adjusting the parameters \(\alpha\) and \(\beta\). This avoids the local optimal problem and obtains the best path solution. In Map 3, the basic ACO finds the optimal path and remains stable, but IACO uses fewer iterations. The iteration times are reduced, and the algorithm runtime is shortened. Map 4 is randomly generated by the mapping algorithm. The data shows that IACO finds the shortest path after 13 iterations, which verifies that the algorithm has stronger stability and adaptability than the traditional ACO algorithm. The experimental results are shown in Table 3. In the three maps, the IACO algorithm can get a better optimal path solution and has a faster convergence speed than the ACO  
Figure 9: Convergence curves of ACO and IACO. algorithm. There are some limitations in the IACO algorithm. The fusion of the fuzzy algorithm in IACO needs to determine a suitable fuzzy rule. This point increases the computational complexity of the algorithm and requires higher hardware performance. The simulation results verify the effectiveness of the algorithm.