This paper introduces a novel framework for integrating sensing and decision-making functionalities in healthcare robotics, focusing on AI-driven COVID-19 detection through chest X-rays using Convolutional Neural Networks (CNNs). The proposed system combines an optimized pre-trained CNN model with a real-time data processing pipeline embedded in a robotic healthcare system. Our contributions include the design and implementation of an end-to-end system for autonomous diagnosis, reducing reliance on human oversight, the integration of sensory data processing with decision-making capabilities to enhance robotic autonomy, and the identification and mitigation of key integration challenges, such as real-time data throughput and system reliability. Evaluation results show the system achieves a diagnostic accuracy of 97%, with a latency reduction of 40% compared to standalone CNN implementations, demonstrating its feasibility for real-time clinical applications. Additionally, our robotic framework improves decision-making consistency by 20% in edge cases compared to human operators. These findings highlight the potential of combining AI and robotics to address critical healthcare challenges, paving the way for more autonomous and efficient diagnostic tools.