Collision- and Reachability-Aware Multi-Robot Control with Grounded LLM Planners

Large language models (LLMs) have demonstrated strong performance in various robot control tasks. However, their deployment in real-world applications remains constrained. Even state-ofthe-art LLMs, such as GPT-o4mini, frequently produce invalid action plans that violate physical constraints, such as directing a robot to an unreachable location or causing collisions between robots. This issue primarily arises from a lack of awareness of these physical constraints during the reasoning process. To address this issue, we propose a novel framework that integrates reinforcement learning with verifiable rewards (RLVR) to incentivize knowledge of physical constraints into LLMs to induce constraints-aware reasoning during plan generation. In this approach, only valid action plans that successfully complete a control task receive positive rewards. We applied our method to two small-scale LLMs: a non-reasoning Qwen2.5-3B-Instruct and a reasoning Qwen3-4B. The experiment results demonstrate that constraint-aware small LLMs largely outperform large-scale models without constraints, grounded on both the BoxNet task and a newly developed BoxNet3D environment built using MuJoCo. This work highlights the effectiveness of grounding even small LLMs with physical constraints to enable scalable and efficient multi-robot control in complex, physically constrained environments.