Advances in open-vocabulary semantic mapping and object navigation have enabled robots to perform an informed search of their environment for an arbitrary object. However, such zero-shot object navigation is typically designed for simple queries with an object name like "television" or "blue rug". Here, we consider more complex free-text queries with spatial relationships, such as "find the remote on the table" while still leveraging robustness of a semantic map. We present DIV-Nav, a real-time navigation system that efficiently addresses this problem through a series of relaxations: i) Decomposing natural language instructions with complex spatial constraints into simpler object-level queries on a semantic map, ii) computing the Intersection of individual semantic belief maps to identify regions where all objects co-exist, and iii) Validating the discovered objects against the original, complex spatial constrains via a LVLM. We further investigate how to adapt the frontier exploration objectives of online semantic mapping to such spatial search queries to more effectively guide the search process. We validate our system through extensive experiments on the MultiON benchmark and real-world deployment on a Boston Dynamics Spot robot using a Jetson Orin AGX. More details and videos are available at https://anonsub42.github.io/reponame/

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