# Path Planning of Mobile Robots with an Improved Grey Wolf Optimizer and Dynamic Window Approach
## 6 Experiments Simulation and Analysis
### Global Path Planning Experiment  
To validate the efficacy of the PAGWO algorithm, the mobile robot is simplified as a point on a two-dimensional network and compared with four algorithms, GA, SCA, PSO, and GWO, in the three simulation maps described above. The black squares in the figure represent obstacles, and the red dots and squares indicate the start and goal positions, respectively (the start is located at the bottom-left corner, and the goal is at the top-right corner). The evaluation metrics are path length, number of turns, and running time. In the experiment, the population size for all algorithms is set to 50, and the number of iterations is set to 1000. The simulation results for map 1 are presented in Figure 6, which illustrates the paths generated by each algorithm and their convergence behaviors. Among the five algorithms compared--namely, GA, SCA, PSO, GWO, and PAGWO, PAGWO produces the shortest path with the fewest turns, indicating that PAGWO approaches the target location faster while avoiding static obstacles. This is due to incorporating strategies such as Piecewise chaotic mapping and nonlinear convergence factors, which make PAGWO more effective in path planning algorithms. Specifically, in Figure 6a, GA exhibits redundant path segments in the early stage of the route. In Figure 6b, SCA generates the highest number of path deviations. In Figure 6c,d, PSO and GWO perform well, demonstrating fewer deviations and shorter path lengths. However, further improvements are needed to achieve optimality. In Figure 6f, PAGWO is observed to converge faster toward the minimum, quickly finding the optimal solution during the iterative process, indicating that it outperforms other algorithms in global planning and convergence efficiency. For further verification of the performance of the PAGWO algorithm in this study, the second set of experiments was conducted in simulation environment 2. Compared with the first set of experimental maps, the obstacle distribution in the second set is more complex, demanding higher path planning capabilities from the algorithm. The comparison of path  
Figure 6: Path Planning Comparison of Different Algorithms in Simulation Map 1. (**a**) GA; (**b**) SCA; (**c**) PSO; (**d**) GWO; (**e**) PAGWO; (**f**) convergence curve comparison. planning results is shown in Figure 7. For example, both GA and PSO exhibited moderate performance by navigating into the U-shaped obstacle twice in succession. However, SCA and GWO performed poorly in this path planning, generating paths with a large number of redundant segments. In contrast, PAGWO not only avoids the U-shaped obstacles but also performs exceptionally well in terms of path smoothness, with a notable reduction in the number of turns, indicating its ability to effectively avoid redundant steering and improve the smoothness of the path. From Figure 7f, PAGWO is shown to be the most effective in both convergence accuracy and speed, having converged after 200 iterations, outperforming other algorithms. The computational efficiency and path planning stability of PAGWO in complex environments are further verified. To further verify the generalizability of the PAGWO algorithm, path planning simulation experiments were performed in simulation environment 3, which has the most complex obstacle distribution. The results of the experiment are presented in Figure 8. Both GA and SCA exhibit significant path redundancy in the early stages of their routes, characterized by unnecessary detours into the interior U-shaped obstacles. Additionally, PSO becomes trapped in a local optimum, resulting in a suboptimal path, while GWO produces a path with multiple turns in its middle section, compromising overall path quality. In contrast, the PAGWO algorithm generates a path with significantly fewer turns and a smoother trajectory, demonstrating a practical improvement in path smoothing and efficiency when handling complex obstacle distributions.