This paper addresses task planning problems for language-instructed robot teams. Tasks are expressed in natural language (NL), requiring the robots to apply their capabilities (e.g., mobility, manipulation, and sensing) at various locations and semantic objects. Several recent works have addressed similar planning problems by leveraging pre-trained Large Language Models (LLMs) to design effective multi-robot plans. However, these approaches lack mission performance and safety guarantees. To address this challenge, we introduce a new decentralized LLM-based planner that is capable of achieving high mission success rates. This is accomplished by leveraging conformal prediction (CP), a distribution-free uncertainty quantification tool in black-box models. CP allows the proposed multi-robot planner to reason about its inherent uncertainty in a decentralized fashion, enabling robots to make individual decisions when they are sufficiently certain and seek help otherwise. We show, both theoretically and empirically, that the proposed planner can achieve user-specified task success rates while minimizing the overall number of help requests. We demonstrate the performance of our approach on multi-robot home service applications. We also show through comparative experiments, that our method outperforms recent centralized and decentralized multi-robot LLM-based planners in terms of in terms of its ability to design correct plans. The advantage of our algorithm over baselines becomes more pronounced with increasing mission complexity and robot team size.

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