With the development of e-commerce and intelligent manufacturing, the demand for warehouse automation continues to rise, and collaborative multi-robot handling and picking have become key to improving logistics efficiency. However, with limited picking station resources, increases in robot numbers and order complexity easily lead to congestion and deadlocks near picking stations, affecting system stability and efficiency. To address this problem, this paper proposes a multi-robot scheduling and deadlock prevention method based on a loop path movement mechanism. By establishing a circular buffer zone between picking stations and storage areas, robots are guided to move continuously, thereby reducing queuing and the risk of deadlocks. A finite state machine (FSM) model is introduced to dynamically characterize the operational process, and a loop-path scheduling algorithm is designed to optimize system coordination. Simulation results show that the proposed method can completely avoid deadlocks, and compared with traditional buffer area strategy, shortens the order fulfillment makespan by 68 s and increases average utilization by 11.77%. This study provides a foundation and practical approach for efficient operation and intelligent scheduling of warehouse systems.