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BT planning, an emerging field, provides theoretical guarantees for the automated generation of reliable BTs. However, BT planning typically assumes that a well-designed BT system is already grounded -- comprising high-level action models and low-level control policies -- which often requires extensive expert knowledge and manual effort. In this paper, we formalize the BT Grounding problem: the automated construction of a complete and consistent BT system. We analyze its complexity and introduce CABTO (Context-Aware Behavior Tree grOunding), the first framework to efficiently solve this challenge. CABTO leverages pre-trained Large Models (LMs) to heuristically search the space of action models and control policies, guided by contextual feedback from BT planners and environmental observations. 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