The convergence of Artificial Intelligence (AI) and the Internet of Things (IoT) has paved the way for the Internet of Robotic Things (IoRT), where autonomous robotic systems leverage AI capabilities to operate seamlessly in interconnected ecosystems. However, traditional IoRT architectures reliant on cloud computing face critical challenges, including data privacy risks, latency, and bandwidth limitations. This paper proposes a novel AI-driven distributed system, AI \(\tilde{o }\) RT, that utilizes edge computing to distribute computational resources closer to robotic devices, enabling reduced response times and enhanced data security. The system employs layered architecture integrating edge AI, heterogeneous edge-split federated learning, and FPGA-accelerated binary compressive sensing (BinCSNet) for efficient model training and data processing. This design optimizes resource usage, supports real-time decision-making, and facilitates scalable deployment across heterogeneous networks. The system also demonstrated its scalability at the robot service level through humanoid robot-based application cases, gait emotion recognition and human depression detection, highlighting its potential to advance autonomous systems in sustainable and secure environments.