# Research on Path Planning Multiple Mobile Robots Based on the LAPGWO Algorithm
## 2 Related Work  
Centralized path planning refers to a full-information collaborative planning approach. Under the premise that the central controller has comprehensive access to environmental information (including obstacle distribution, agent positions, and task objectives), it generates collision-free travel routes for multiple agents through a global optimization model. The planning accuracy of this approach depends on the worldwide modeling ability of the central processor for the environment and the efficiency of multi-objective optimization. Typical algorithms include conflict-based search (CBS) [14], rapidly exploring random trees [15], and hybrid heuristic algorithms [16]. Distributed path planning refers to a collaborative mechanism in which a multi-robot system generates collision-free paths through autonomous decision making based on local environmental perception and neighborhood information interaction without the coordination of a central controller. Its core advantages lie in reducing communication dependence and enhancing adaptability to dynamic environments. Typical methods include distributed model predictive control (DMPC) [17], auction algorithms [18], and swarm intelligence optimization algorithms. The grey wolf optimization (GWO) [19] algorithm is a new type of bio-inspired algorithm with the advantages of a simple structure, few parameters to set, and easy implementation in experimental coding. In recent years, it has gradually emerged in various fields. However, the traditional GWO algorithm has certain defects, such as the lack of diversity in the initial population, the imbalance between global exploration and local exploitation, the tendency to become trapped in local extrema, and low search efficiency. [PERSON] [20] proposed a framework that combines GWO with the dynamic window approach (DWA). DWA searches for and optimizes the algorithm's balance by dynamically adjusting the nonlinear convergence factor. [PERSON] [21] proposed an improved GWO algorithm for the complex three-dimensional environment of vertical farms. Introducing a grid map hierarchical mechanism and a dynamic priority assignment strategy solves the path conflict problem in multi-robot and multi-task scenarios. [PERSON] [22] proposed a route planning method for military transport aircraft based on the grey wolf optimization (GWO) algorithm. An aviation network model is established by applying the relevant knowledge of graph theory. Then, the GWO algorithm is introduced to optimize the flight path on the constructed aviation network for the route planning of military transport aircraft, resulting in faster convergence speed and higher efficiency. [PERSON] [23] optimized the GWO algorithm. An optimized numerical intelligent representation of multi-UAV cooperative trajectories using a variable-length coding method is adopted, which reduces the GWO algorithm's search workload and improves the optimization search's efficiency. However, the generated path has many redundant paths and is not the optimal one. [PERSON] [24] proposed a smoothing DGWW global planning method based on the BAS algorithm to optimize the GWO algorithm. This method integrates the optimal search method in the BAS algorithm using the two tentacles of the beetle's head into the GWO algorithm, thus avoiding local optimization. However, it increases the calculation time and reduces the search efficiency. [PERSON] [25] combined the traditional grey wolf optimization (GVO) algorithm with the Coati optimization algorithm (COA) to form the LM-GWO composite algorithm, which successfully planned the best route in a complex marine environment full of obstacles. However, it has a long search time and is prone to becoming trapped in local optima. [PERSON] [26] proposed a multi-population grey wolf optimization (LM-GWO) algorithm based on Levy flight. It combines the idea of multi-population, and clusters individual grey wolves into different populations through the Bi-K-means clustering algorithm.