Foundation models provide robots with the ability to interpret natural language and reason about environmental context, yet most language-conditioned policies assume that goals are well-specified and that task-relevant information is provided upfront via a prior map. Operating in unfamiliar environments with underspecified tasks entails high contextual uncertainty: the robot must jointly infer what constitutes task success, what constitutes relevant information, and where (or whether) that information exists. We address these limitations via CLUE (Closed-Loop contextual Uncertainty rEsolution), a framework for actively resolving contextual uncertainty given underspecified tasks in natural language. CLUE uses an LLM-derived policy to hypothesize task-relevant concepts and potential plans. It then uses a language-embedded map, which is constructed online, to ground these hypotheses into actions. The policy sequentially evaluates hypotheses via closed-loop environment interaction and refines its plans as it gathers new information. We deploy CLUE on a Boston Dynamics Spot across three real indoor and outdoor environments spanning 15 tasks that require object disambiguation, functional inference, and occlusion reasoning. CLUE achieves a success rate within 7 percentage points of an oracle policy and outperforms an LLM-enabled planner without closed-loop feedback by a 4x margin. Supporting experiments demonstrate that simply building and then querying a language-enriched map is insufficient to resolve complex contextual planning tasks; these approaches achieve roughly one third the success rate of CLUE while requiring over 10x more VLM tokens. We provide additional information at https://zacravichandran.github.io/CLUE.

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