Robots executing tasks following human instructions in domestic or industrial environments essentially require both adaptability and reliability. Behavior Tree (BT) emerges as an appropriate control architecture for these scenarios due to its modularity and reactivity. Existing BT generation methods, however, either do not involve interpreting natural language or cannot theoretically guarantee the BTs' success. This paper proposes a two-stage framework for BT generation, which first employs large language models (LLMs) to interpret goals from high-level instructions, then constructs an efficient goal-specific BT through the Optimal Behavior Tree Expansion Algorithm (OBTEA). We represent goals as well-formed formulas in first-order logic, effectively bridging intent understanding and optimal behavior planning. Experiments in the service robot validate the proficiency of LLMs in producing grammatically correct and accurately interpreted goals, demonstrate OBTEA's superiority over the baseline BT Expansion algorithm in various metrics, and finally confirm the practical deployability of our framework. The project website is https://dids-ei.github.io/Project/LLM-OBTEA/.

翻译：机器人在家庭或工业环境中执行人类指令任务时，本质上需要兼具适应性与可靠性。行为树（BT）因其模块化特性与反应能力，成为适用于此类场景的理想控制架构。然而，现有的行为树生成方法要么未能融入自然语言理解，要么无法在理论上保证行为树的执行成功率。本文提出一种两阶段行为树生成框架：首先利用大语言模型（LLMs）从高层级指令中解析目标，随后通过最优行为树扩展算法（OBTEA）构建针对特定目标的高效行为树。我们将目标表征为一阶逻辑中的合式公式，从而有效衔接意图理解与最优行为规划。在服务机器人场景中的实验验证表明：大语言模型能够生成语法正确且解析精准的目标描述；OBTEA算法在多项指标上均优于基准行为树扩展算法；最终证实了本框架具备实际部署能力。项目网站详见 https://dids-ei.github.io/Project/LLM-OBTEA/。