The goal of the Object Disambiguation using Locative Prepositions project is to improve human-robot interaction by developing models for how humans use prepositional phrases to identify objects in a cluttered space. When using only words to reference one of many objects located together, it is hard to avoid misunderstanding, even between human coworkers. To reduce uncertainty, humans often use prepositional phrases that describe the target object in reference to the most easily distinguished nearby objects. This research makes human-robot interactions of this sort more effective by developing a new system for object disambiguation in cluttered environments based on probabilistic models of unique object features and spatial relationships. It builds on prior models of spatial relationship semantics by collecting and encoding empirical data from a series of crowdsourced studies to better understand how and when people use locative prepositions, how reference objects are chosen and how to model prepositional geometry in 3D space. The project also introduces new techniques for responding to compound locative phrases of arbitrary complexity and proposes a new metric for disambiguation confidence. Experiments demonstrate that these methods can improve accuracy and performance over existing approaches.