## 1 Introduction
In this paper, the concept of a deep deterministic policy gradient (DDPG) [27] in the design of multi-agent path-finding is an improved algorithm based on the policy gradient (PG) [28] and deterministic policy gradient (DPG) [29]. The DDPG is a type of off-policy algorithm and can be regarded as a DQN that realizes a great action in explore space. To increase the robustness of DRL in different environments, this paper relied on the observation information required for reinforcement learning in robot simulation environments. It improved multi-agent research results in the path planning of multiple robot applications. In response to the other novel study, an experience replay training method is verified to achieve more smooth learning, reduce correlations, and facilitate offline training [30]. It is an indispensable tool for tackling a wide range of DRL challenges. In this study, a simple and efficient one-step experiment reply will be established. This experience replay is also a key focus of our future research in the development of mobile robot path planning application. Currently, a lot of research has been conducted in robotics based on the Gazebo simulator [31; 32]. Therefore, the Gazebo simulator can be regarded as a stable and reliable experimental platform. Due to the higher system requirements of the Gazebo simulator, reinforcement learning takes about 0.4 microseconds for each step of the Gazebo training. This results in a higher training time for more learning experiences to occur; therefore, this training simulation uses OpenAI's multi-agent particle environment to modify and design the required training model [33; 34]. The sampling time for the training in this study was about 0.01 s to complete the simulation of the discrete action of the subsequent multi-agent. In this study, the simple particle multi-agent simulator uses its own robot position to capture a fixed-size field of view (FOV) as input to the neural network instead of using an occupation grid map of the entire domain and imports the local environment as observed from your local field of view. In addition to significantly reducing the computational burden of neural networks, it also helps the networks to be smoothly implemented in real robots. Section 2 will explain the reinforcement learning and training environment development, the basic design of multi-agent path-finding will be explained in Section 3, a path-finding design with multi-agent deep deterministic policy gradients in Section 4, and experimental results and analyses in Section 5. Finally, conclusions and future works are discussed in the last section. The main contributions of this paper are as follows:  
1. This study is a multi-agent reinforcement learning architecture combining centralized training and decentralized execution. In centralized training, a self-developed reward function can enhance the multi-agent to complete the information aggregation of the training environment and effectively achieve the purpose of loss convergence. 2. The current design of training methods for multi-agent path-finding. Five different training environments combine the simple-to-complex schedule to enhance the learning efficiency. Based on the experimental results, the designed training schedule can effectively learn different environmental information and improve the capability of multi-agents.