Artificial Intelligence (AI) has revolutionized the field of robotics, enabling the development of sophisticated robotic mechanisms that can perform complex tasks with high precision and autonomy. This article explores the integration of AI in robotic systems, focusing on the advancements in perception, decision-making, and control. By leveraging machine learning algorithms, computer vision, and natural language processing, AI-powered robots can interact with their environment and make real-time decisions. The main part of this article delves into the mathematical foundations of AI in robotics, presenting key equations and models that underpin these technologies. The conclusion highlights the potential future applications and challenges of AI-powered robotic mechanisms.