As societies face the growing challenge of caring for elderly individuals and people living with chronic conditions, there is an increasing need for intelligent systems that can monitor daily routines while preserving privacy and autonomy. In this context, the convergence of generative Artificial Intelligence and the Internet of Things opens new possibilities for understanding human behavior through natural language. This work proposes a distributed architecture that enables the local execution of lightweight Large Language Models on affordable edge devices to interpret sensor data and generate readable activity summaries. Rather than depending on cloud services, the system follows a conceptual framework designed to scale across real-world homes, adapting to their complexity. A functional prototype was developed and validated using real activity data. Results show that, given the characteristics of the models suitable for small computing units and their extensive use of hardware resources, distributing tasks across devices becomes essential. The proposed architecture contributes to more human-centered monitoring solutions for ambient assisted living environments, while preserving privacy.