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The convergence of Artificial Intelligence (AI) and robotics has brought about a fresh period of autonomous systems able to execute sophisticated jobs in changing and unpredictable settings. Although significant advancements have been achieved, a multitude of unresolved mathematical issues limit the use of AI-driven robots in safety-critical and real-world uses. Focusing on robustness, safety, learning, Human-Robot Interaction (HRI), and complicated system management, this study investigates several significant unresolved concerns at the crossroads of AI, control theory, and mathematics. Creating intelligent, dependable, and trustworthy autonomous robots depends on addressing these obstacles. Several influential open problems are introduced within the folds of this paper, with final thoughts on mathematizing AI-driven robot control.
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