In environments where many automated guided vehicles (AGVs) operate, planning efficient, collision-free paths is essential. Related research has mainly focused on environments with static passages, resulting in space inefficiency. We define multi-agent and multi-rack path finding (MARPF) as the problem of planning paths for AGVs to convey target racks to their designated locations in environments without passages. In such environments, an AGV without a rack can pass under racks, whereas an AGV with a rack cannot pass under racks to avoid collisions. MARPF entails conveying the target racks without collisions, while the other obstacle racks are positioned without a specific arrangement. AGVs are essential for relocating other racks to prevent any interference with the target racks. We formulated MARPF as an integer linear programming problem in a network flow. To distinguish situations in which an AGV is or is not loading a rack, the proposed method introduces two virtual layers into the network. We optimized the AGVs' movements to move obstacle racks and convey the target racks. The formulation and applicability of the algorithm were validated through numerical experiments. The results indicated that the proposed algorithm addressed issues in environments with dense racks.

翻译：在大量自动导引车（AGV）运行的环境中，规划高效且无碰撞的路径至关重要。现有研究主要关注具有静态通道的环境，导致空间利用率低下。本文将多智能体与多货架路径规划（MARPF）定义为：在无通道环境中为AGV规划路径，使其将目标货架搬运至指定位置。在此类环境中，未装载货架的AGV可从货架下方通过，而装载货架的AGV为避免碰撞则无法通过。MARPF要求在无碰撞条件下搬运目标货架，同时其他障碍货架无需特定排列。AGV需通过重新布置其他货架来避免对目标货架造成干扰。本文将MARPF建模为网络流中的整数线性规划问题。为区分AGV是否装载货架的不同状态，所提方法在网络中引入两个虚拟层。通过优化AGV运动，实现障碍货架的移动与目标货架的搬运。数值实验验证了算法的可行性及适用性，结果表明该算法可有效解决密集货架环境中的路径规划问题。