An improved multi-agent path finding algorithm based on the conflict search algorithm is proposed for the path planning problem of picking-delivery with mobile robot clusters in the smart storage environment. In terms of the model, a mathematical planning model with the objective of minimizing the picking-delivery time and the invalid path ratio is established by using multi-carrier robots instead of KIVA robots. In terms of the algorithm, firstly a priority rule-based multi-intelligent conflict resolution acceleration strategy is proposed. Then a single-robot picking sequence optimization algorithm based on dynamic planning is designed. Finally, an enhanced A* algorithm with the consideration of turning penalty is proposed to search for the optimal robot path. The experimental results show that the proposed model is superior to the KIVA system. The proposed algorithm can effectively shorten the picking-delivery time and reduce the invalid path time.