Multi-agent pathfinding and its reliable execution in stochastic environments represent a critical challenge for real-world applications, demanding both the planning of efficient paths and the formal assurance of safe, conflict-free operation. This paper introduces a novel methodology framework to address this dual requirement. To maximize operational efficiency, we introduce a strategy for optimal goal allocation for team collaboration, integrating it with the conflict-based search algorithm to minimize the total move counts required for mission completion. The second component is an integrated verification process grounded in probabilistic model checking. We model the multi-agent path execution process under stochastic uncertainties using a Markov decision process. By leveraging the probabilistic model checker and probabilistic computation tree logic, the framework formally verifies critical safety properties, ensuring conflict-free and deadlock-free path execution. Furthermore, it evaluates the effectiveness of proposed behavioral constraints designed to mitigate stochastic delays, thereby verifying the overall system safety. By fusing multi-agent planning, probabilistic reasoning, and formal logic-based verification, the proposed framework establishes a foundation amenable to natural extension for addressing multi-agent decision-making and uncertainty estimation. Case study results demonstrate that our methodology effectively selects the pathfinding solution with the minimum move count while significantly enhancing overall system safety through these formally verified behavioral constraints.
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