Integrated networks of mobile robots, personal smart devices, and smart spaces can provide for a more accurate data for user assistance than if the former are used individually. We call this network of personal and smart space devices and robots " Robots-Assisted Ambient Intelligence " (RAmI). Additionally , with the application of distributed network optimization, not only can we improve the assistance of an individual user, but we can also minimize conflict or congestion created when multiple users in large installations use the limited resources of RAmI that are spatially and temporally constrained. The emphasis of RAmI is on the efficiency and effectiveness of multiple and simultaneous user assistance and on the influence of individual robot actions on the desired sys-tem's performance. In this paper, we model RAmI as a multi-agent system with AmI and robot agents. Moreover, we propose a modular three-layer architecture for each robot agent and discuss its application and communication requirements with the emphasis on interaction between robots, humans, and AmI agents to facilitate efficient usage of limited RAmI resources. Our approach is showcased by means of a case study where we focus on meal and medicine delivery to patients in large hospitals.