I. Introduction
The emergence of mobile robotics has led to a growing interest in developing efficient and safe navigation algorithms for autonomous mobile robots. The mobile robots have been applied widely in warehouses [1], factories [2], [26], hospitals [3], [27], and etc.. In crowded environments, mobile robots must navigate among humans and other mobile robots without causing inconvenience or harm. It requires the development of cooperative navigation strategies that enable robots to coordinate their movements, and adapt to the dynamic environment. Without cooperation, robots may take suboptimal paths or get stuck in crowded areas, leading to congestion and delays. Cooperative navigation of mobile robots in crowded environments is a challenging task that involves addressing issues such as collision avoidance and path planning among robots.