# Improved Trimming Ant Colony Optimization Algorithm for Mobile Robot Path Planning
## 5 Experimental Simulation and Results
### Verification of the Effectiveness of the ITACO Algorithm  
To validate the feasibility and effectiveness of the proposed ITACO algorithm in mobile robot path planning, simulation experiments were conducted using the parameters listed in Table 1 for both the ACO algorithm and the ITACO algorithm. To eliminate errors caused by experimental randomness, the average values of 20 independent experiments were taken. The experimental data are presented in Table 4, and the experimental results are illustrated in Figure 3.  
From Table 4, it can be observed that the experimental results of the ITACO algorithm are superior to those of the ACO algorithm. * In the 10 \(\times\) 10 grid map, the path lengths of the ITACO algorithm and the ACO algorithm are 13.8995 and 14.4853, respectively. Compared to the ACO algorithm, the ITACO algorithm reduces the path length by 4.04% and the computational time by 13.42%. * In the 20 \(\times\) 20 grid map, the path lengths of the ITACO algorithm and the ACO algorithm are 28.2711 and 33.5563, respectively. The ITACO algorithm reduces the path length by 15.75% and the computational time by 19.23% compared to the ACO algorithm. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Map Scale** & **Algorithm** & **Theoretical Shortest Path** & **Path Length** & **Trimmed Path Length** & **Iterations** & **Computation Time (s)** \\ \hline \multirow{2}{*}{\(10\times 10\)} & ACO & 13.4350 & 14.4853 & - & - & 0.4261 \\  & ITACO & 13.4350 & 13.8995 & 13.8995 & 1 & 0.3689 \\ \hline \multirow{2}{*}{\(20\times 20\)} & ACO & 27.5772 & 33.5563 & - & - & 4.8569 \\  & ITACO & 27.5772 & 28.6274 & 28.2711 & 3 & 3.9229 \\ \hline \multirow{2}{*}{\(30\times 30\)} & ACO & 41.7193 & 116.7107 & - & - & 19.4413 \\  & ITACO & 41.7193 & 50.5269 & 43.3499 & 5 & 15.1451 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of simulation results between ITACO and ACO. In the 30 \(\times\) 30 grid map, the path lengths of the ITACO algorithm and the ACO algorithm are 43.3499 and 116.7107, respectively. The ITACO algorithm reduces the path length by 62.86% and the computational time by 22.1% compared to the ACO algorithm. From Figure 3, it can be observed that the path planned by the ACO algorithm contains numerous sharp turns and significant curvature, which poses considerable challenges in practical path development. In contrast, the path planned by the ITACO algorithm is relatively smooth with fewer sharp turns. Additionally, the ITACO algorithm incorporates triangular pruning to further optimize the planned path, resulting in a shorter path length. A comparison of the path planning results between the two algorithms clearly shows that the path length generated by the ITACO algorithm is significantly shorter than that of the ACO algorithm. Even when the map scale is increased, the ITACO algorithm is still capable of planning an excellent path, demonstrating its stronger adaptability and robustness across different maps. On maps of varying scales, the ITACO algorithm consistently outperforms the ACO algorithm in path planning. Below, we analyze the performance using a 20 \(\times\) 20 map as an example. The convergence curves of the ITACO algorithm and the ACO algorithm are shown in Figure 4.  
From Figure 4, it can be observed that the ACO algorithm requires approximately 70 iterations to converge to the optimal solution, whereas the ITACO algorithm achieves the optimal solution in just two iterations. Furthermore, the convergence curve of the  
Figure 4: Comparison of convergence curves for ITACO and ACO algorithms on 20 \(\times\) 20 grid map. Figure 3: Path planning results for ITACO and ACO algorithms. (**a**) Path planning results on \(10\times 10\) grid map; (**b**) Path planning results on 20 \(\times\) 20 grid map; (**c**) Path planning results on 30 \(\times\) 30 Grid Map. White grids indicate traversable nodes, while black grids represent obstacles. ITACO algorithm is relatively smooth with minimal fluctuations, indicating that the ITACO algorithm significantly improves convergence speed.