The convergence of robotics, advanced communication networks, and artificial intelligence (AI) holds the promise of transforming industries through fully automated and intelligent operations. In this work, we introduce a novel co-working framework for robots that unifies goal-oriented semantic communication (SemCom) with a Generative AI (GenAI)-agent under a semantic-aware network. SemCom prioritizes the exchange of meaningful information among robots and the network, thereby reducing overhead and latency. Meanwhile, the GenAI-agent leverages generative AI models to interpret high-level task instructions, allocate resources, and adapt to dynamic changes in both network and robotic environments. This agent-driven paradigm ushers in a new level of autonomy and intelligence, enabling complex tasks of networked robots to be conducted with minimal human intervention. We validate our approach through a multi-robot anomaly detection use-case simulation, where robots detect, compress, and transmit relevant information for classification. Simulation results confirm that SemCom significantly reduces data traffic while preserving critical semantic details, and the GenAI-agent ensures task coordination and network adaptation. This synergy provides a robust, efficient, and scalable solution for modern industrial environments.