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：在家庭或工业环境中，机器人遵循人类指令执行任务本质要求兼具适应性与可靠性。行为树因其模块化与反应性特性，成为此类场景中合适的控制架构。然而，现有行为树生成方法要么未涉及自然语言理解，要么无法从理论上保证行为树的成功率。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从高层指令中解析目标，再通过最优行为树扩展算法构建高效的目标特定行为树。我们将目标表示为一阶逻辑中的良构公式，有效桥接意图理解与最优行为规划。服务机器人实验验证了大语言模型在生成语法正确且精准解析的目标方面的能力，展示了最优行为树扩展算法在多项指标上优于基准行为树扩展算法，最终确认了本框架的实际可部署性。项目网站为 https://dids-ei.github.io/Project/LLM-OBTEA/。