Coordinating heterogeneous multi-robot systems (MRS) for complex, long-horizon tasks requires both flexible high-level reasoning and efficient low-level scheduling. Existing LLM-based approaches address the reasoning side but introduce two critical bottlenecks: (1) repeated LLM inference during execution, which inflates latency with agent count, and (2) offline, pre-committed scheduling, which forces robots to idle while waiting for sequentially ordered predecessors even when independent work is available. This paper presents OSDAG, a novel framework that integrates LLM-based task reasoning with Directed Acyclic Graph (DAG) representation and constraint-aware online scheduling. The LLM is invoked once to decompose a natural-language instruction into a dependency-annotated task graph, and a lightweight online scheduler then allocates ready tasks to idle agents in real time. The DAG representation encodes both precedence and resource constraints, ensuring correctness while exposing all available parallelism. Experiments across five benchmark scenarios demonstrate that OSDAG achieves 5-15x faster reasoning time compared to dialogue-based methods, reduces makespan by up to 38% over sequential baselines, and maintains competitive success rates. Both simulation and real-world experiments on dual-arm manipulation tasks validate the effectiveness and practicality of the proposed approach for efficient multi-robot coordination. The website and resources are available at http://thanhnguyencanh.github.io/LLM_DAG4MultiRobot

翻译：协调异构多机器人系统（MRS）完成复杂、长期任务需要兼顾高层推理的灵活性与低层调度的效率。现有基于大语言模型（LLM）的方法虽能处理推理问题，但引入两个关键瓶颈：（1）执行过程中需反复调用LLM推理，导致延迟随智能体数量增加而膨胀；（2）采用离线预分配调度策略，即使存在可独立执行的任务，机器人也需等待前序任务的串行完成。本文提出OSDAG——一种集成LLM任务推理、有向无环图（DAG）表征与约束感知在线调度的新型框架。该框架仅需单次LLM调用即可将自然语言指令分解为含依赖标注的任务图，随后通过轻量级在线调度器实时将就绪任务分配给空闲智能体。DAG表征编码了先后顺序与资源双重约束，在确保正确性的同时显式暴露所有可并行计算。在五个基准场景的实验表明：相比对话式方法，OSDAG推理速度提升5-15倍；相比串行基线方案，总完成时间缩短最多38%；同时保持具有竞争力的任务成功率。双臂操作任务的仿真与实物实验均验证了该方法对高效多机器人协调的有效性与实用性。项目网站及资源详见http://thanhnguyencanh.github.io/LLM_DAG4MultiRobot