We develop a natural language interface for human robot interaction that implements reasoning about deep semantics in natural language. To realize the required deep analysis, we employ methods from cognitive linguistics, namely the modular and compositional framework of Embodied Construction Grammar (ECG) [Feldman, 2009]. Using ECG, robots are able to solve fine-grained reference resolution problems and other issues related to deep semantics and compositionality of natural language. This also includes verbal interaction with humans to clarify commands and queries that are too ambiguous to be executed safely. We implement our NLU framework as a ROS package and present proof-of-concept scenarios with different robots, as well as a survey on the state of the art.