# Path Planning of Mobile Robots with an Improved Grey Wolf Optimizer and Dynamic Window Approach
## 1 Introduction  
With the rapid development of robotics, robots are increasingly deployed in various fields, and path planning, one of the fundamental challenges for mobile robots, has gradually attracted widespread attention [1]. Path planning refers to the process by which mobile robots use algorithms to plan paths that satisfy task requirements, with evaluation metrics such as path distance, number of turns, and running time [2]. Path planning can typically be divided into two categories: global and local path planning. Traditional approaches in global path planning often involve algorithms such as [PERSON]'s algorithms [3], the A* algorithms [4], and the RRT algorithms [5], and local path planning includes the dynamic window approach (DWA) [6] and the artificial potential field (APF) algorithm [7]. In path planning, researchers worldwide have proposed many algorithms and made significant contributions. [PERSON] et al. [8] proposed an autonomous path planning method capable of dynamically adjusting coverage paths and priorities, by introducing a dynamic weightmatrix to [PERSON]'s algorithm, thereby generating cost-optimal paths rather than merely the shortest paths. To address vehicle path safety in uncertain dynamic obstacle environments, [PERSON] et al. [9] calculated the Wasserstein distance between the distributions of vehicle and obstacle states, improved the RRT algorithm through the incorporation of a dynamic distribution model, and provided safe paths that are probabilistically guaranteed. [PERSON] et al. [10] added a risk penalty to the evaluation function of the A* algorithm, making the improved algorithm more suitable for practical situations, and combined the A* algorithm with the DWA, which allows the DWA to traverse the A* path points, thus endowing the algorithm with dynamic path planning capability. [PERSON] et al. [11] employed a beetle antennae search algorithm to address the optimization issues of the APF algorithm. They dynamically adjusted the search step size based on the distance between the robot and the target point, thereby achieving a balance between path generation speed and planning accuracy. To address the suboptimal path problem of the DWA algorithm due to fixed weights in complex environments, [PERSON] et al. [12] improved the velocity cost function. They input the distances between the robot, obstacles, and the target point into a fuzzy control module, thus enabling the robot to adapt to environmental changes. Although traditional global path algorithms and local path algorithms perform well in many applications, they also have limitations in addressing optimization problems. For example, the A* algorithm is subject to computational complexity in high-dimensional environments, which results in poor dynamic capability. The APF can result in path planning failures due to local minima problems and is computationally intensive, requiring considerable time. In recent years, with the development of intelligent optimization algorithms, such as ant colony optimization (ACO) [13], genetic algorithm (GA) [14], sine cosine algorithm (SCA) [15], and particle swarm optimization (PSO) [16], these algorithms have also been widely applied to path planning problems. [PERSON] et al. [17] enhanced the ACO by employing several heterogeneous ant colonies to enhance solution diversity and optimize UAV task allocation through task insertion boundaries and random interruption mechanisms. [PERSON] et al. [18] introduced a differential update strategy into the SCA, where different strategies are chosen to update candidate solutions, thereby enhancing the diversity of the algorithm. [PERSON] et al. [19] incorporated adaptive weighted delayed velocity in the PSO algorithm to improve convergence stability and proposed quartic Bezier curves for smoothing the paths, thereby reducing abrupt turns in robot motion. [PERSON] et al. [20] combined GA with deep learning, and the trained deep neural networks can quickly generate planning results, which significantly reduces the running time.