We introduce a novel framework for automatic behavior tree (BT) construction in heterogeneous multi-robot systems, designed to address the challenges of adaptability and robustness in dynamic environments. Traditional robots are limited by fixed functional attributes and cannot efficiently reconfigure their strategies in response to task failures or environmental changes. To overcome this limitation, we leverage large language models (LLMs) to generate and extend BTs dynamically, combining the reasoning and generalization power of LLMs with the modularity and recovery capability of BTs. The proposed framework consists of four interconnected modules task initialization, task assignment, BT update, and failure node detection which operate in a closed loop. Robots tick their BTs during execution, and upon encountering a failure node, they can either extend the tree locally or invoke a centralized virtual coordinator (Alex) to reassign subtasks and synchronize BTs across peers. This design enables long-term cooperative execution in heterogeneous teams. We validate the framework on 60 tasks across three simulated scenarios and in a real-world cafe environment with a robotic arm and a wheeled-legged robot. Results show that our method consistently outperforms baseline approaches in task success rate, robustness, and scalability, demonstrating its effectiveness for multi-robot collaboration in complex scenarios.