# Path Planning of Mobile Robots with an Improved Grey Wolf Optimizer and Dynamic Window Approach
## 7 Conclusions  
This paper proposes a new algorithm, PAGWO-IDWA, to solve the path planning problem. First, to improve the quality of the initial population, the Piecewise chaotic mapping is used to initialize the Grey Wolf population. Second, a nonlinear convergence factor is introduced to balance global and local search capabilities. Then, the EPD strategy is applied, and dynamic weights are introduced, enhancing the algorithm's ability to escape local optima and accelerate the convergence speed. Finally, combining PAGWO with IDWA addresses the issues of path smoothness and dynamic obstacle avoidance in the PAGWO algorithm.  
The algorithm's performance is verified through both static and dynamic obstacle avoidance experiments. PAGWO outperforms GA, SCA, PSO, and GWO in path planning performance across three static maps with varying complexity. Compared with the standard GWO, the improved PAGWO reduces the path length, number of turns, and running time by 9.39%, 14.08%, and 13.81%, respectively, in map 1. In map 2, the improvements are 10.61%, 50.78%, and 38.55%, respectively, and in map 3, they are 8.73%, 34.62%, and 38.57%. Dynamic obstacle avoidance experiments further demonstrate that PAGWO-IDWA  
Figure 14: Dynamic Obstacle Avoidance Experiment 4. (**a**) Global optimal path; (**b**) the robot stops to avoid the obstacles; (**c**) the robot proceeds toward the goal; (**d**) the robot is bypassing to the right; (**e**) the robot is bypassing to the left; (**f**) the robot reaches the goal.  
generates efficient, smooth paths in complex dynamic environments, safely bypassing dynamic obstacles or waiting for them to pass, according to the obstacle avoidance strategy. This progression verifies its strong global path planning and dynamic obstacle avoidance capabilities.  
While our current conflict avoidance strategy has enhanced the mobile robot's obstacle avoidance performance compared to the original approach, limitations still remain. In the future, we plan to explore predictive techniques, such as Reinforcement Learning, to allow the robot to anticipate obstacle trajectories and proactively adjust its path. We expect that these improvements will further enhance both the safety and efficiency of path planning in highly dynamic environments. Additionally, our simulations presently model the mobile robot as a point, with a fitness function that primarily minimizes path length while applying a basic obstacle-avoidance penalty. However, practical applications necessitate a more comprehensive consideration of factors such as the robot's physical dimensions, obstacle sizes, and necessary safety margins to account for localization errors. In subsequent studies, we intend to integrate these real-world constraints into our optimization framework. By combining predictive techniques with a more realistic model, we aim to further improve the robustness and applicability of the PAGWO-IDWA algorithm for mobile robot path planning.  
Conceptualization, W.C. and L.L.; methodology, W.C. and L.L.; software, W.C., L.L. and L.Z.; validation, W.C., L.L., L.Z., Z.L., J.C. and D.H.; formal analysis, W.C. and L.L.; investigation, W.C. and L.L.; resources, W.C. and L.L.; data curation, W.C., L.L., Z.Z., L.J.C. and D.H.; writing--original draft, W.C. and L.L.; writing--review and editing, W.C., L.L., L.Z. and Z.L.; visualization, W.C. and L.L.; supervision, W.C. and L.L.; project administration, W.C. and L.L. All authors have read and agreed to the published version of the manuscript. The research in this paper was funded by the Fujian University Industry-University-Research Joint Innovation Project (2022H6005) and the Fujian University Industry-University Cooperation Science and Technology Program (2022N5020). Not applicable. Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy. The authors declare no conflicts of interest.