This paper investigates the development and optimization of control algorithms for mobile robotics, with a keen focus on their implementation in Field-Programmable Gate Arrays (FPGAs). It delves into both classical control approaches such as PID and modern techniques including deep learning, addressing their application in sectors ranging from industrial automation to medical care. The study highlights the practical challenges and advancements in embedding these algorithms into FPGAs, which offer significant benefits for mobile robotics due to their high-speed processing and parallel computation capabilities. Through an analysis of various control strategies, the paper showcases the improvements in robot performance, particularly in navigation and obstacle avoidance. It emphasizes the critical role of FPGAs in enhancing the efficiency and adaptability of control algorithms in dynamic environments. Additionally, the research discusses the difficulties in benchmarking and evaluating the performance of these algorithms in real-world applications, suggesting a need for standardized evaluation criteria. The contribution of this work lies in its comprehensive examination of control algorithms' potential in FPGA-based mobile robotics, offering insights into future research directions for improving robotic autonomy and operational efficiency.