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Robots that can comprehend and navigate their surroundings independently on their own are considered intelligent mobile robots (MR). Using a sophisticated set of controllers, artificial intelligence (AI), deep learning (DL), machine learning (ML), sensors, and computation for navigation, MR's can understand and navigate around their environments without even being connected to a cabled source of power. Mobility and intelligence are fundamental drivers of autonomous robots that are intended for their planned operations. They are becoming popular in a variety of fields, including business, industry, healthcare, education, government, agriculture, military operations, and even domestic settings, to optimize everyday activities. We describe different controllers, including proportional integral derivative (PID) controllers, model predictive controllers (MPCs), fuzzy logic controllers (FLCs), and reinforcement learning controllers used in robotics science. The main objective of this article is to demonstrate a comprehensive idea and basic working principle of controllers utilized by mobile robots (MR) for navigation. This work thoroughly investigates several available books and literature to provide a better understanding of the navigation strategies taken by MR. Future research trends and possible challenges to optimizing the MR navigation system are also discussed.