In the realm of robot action recognition, identifying distinct but spatially proximate arm movements using vision systems in noisy environments poses a significant challenge. This paper studies robot arm action recognition in noisy environments using machine learning techniques. Specifically, a vision system is used to track the robot's movements followed by a deep learning model to extract the arm's key points. Through a comparative analysis of machine learning methods, the effectiveness and robustness of this model are assessed in noisy environments. A case study was conducted using the Tic-Tac-Toe game in a 3-by-3 grid environment, where the focus is to accurately identify the actions of the arms in selecting specific locations within this constrained environment. Experimental results show that our approach can achieve precise key point detection and action classification despite the addition of noise and uncertainties to the dataset.