We introduce a new problem formulation, Double-Deck Multi-Agent Pickup and Delivery (DD-MAPD), which models the multi-robot shelf rearrangement problem in automated warehouses. DD-MAPD extends both Multi-Agent Pickup and Delivery (MAPD) and Multi-Agent Path Finding (MAPF) by allowing agents to move beneath shelves or lift and deliver a shelf to an arbitrary location, thereby changing the warehouse layout. We show that solving DD-MAPD is NP-hard. To tackle DD-MAPD, we propose MAPF-DECOMP, an algorithmic framework that decomposes a DD-MAPD instance into a MAPF instance for coordinating shelf trajectories and a subsequent MAPD instance with task dependencies for computing paths for agents. We also present an optimization technique to improve the performance of MAPF-DECOMP and demonstrate how to make MAPF-DECOMP complete for well-formed DD-MAPD instances, a realistic subclass of DD-MAPD instances. Our experimental results demonstrate the efficiency and effectiveness of MAPF-DECOMP, with the ability to compute high-quality solutions for large-scale instances with over one thousand shelves and hundreds of agents in just minutes of runtime.
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