In the context of Industry 4.0, Autonomous Mobile Robots (AMRs) have emerged as essential components of modern industrial automation. This case study investigates the pivotal role of the Robot Operating System (ROS) in driving technological advancements within the realm of AMRs. Through an exploration of practical use cases, it elucidates how ROS facilitates the development and implementation of AMRs, reshaping various industrial processes. This case study illustrates the integration of ROS into the design and operation of AMRs, enabling enhanced autonomy, adaptability, and efficiency in industrial applications. It scrutinizes instances where ROS-powered AMRs have revolutionized tasks such as material handling, warehouse logistics, and autonomous navigation, resulting in significant improvements in productivity and cost-effectiveness. Furthermore, the study explores into the challenges and opportunities presented by ROS in the Industry 4.0 landscape, addressing topics like sensor fusion, machine learning, and human-robot collaboration. It underscores ROS's critical role in bridging the gap between traditional manufacturing methods and the evolving requirements of the fourth industrial revolution.