Conveyor Parcel Routing with Order-Contiguous Arrivals

Automated warehouses face a fundamental trade-off between maximizing storage density and achieving high retrieval throughput. While puzzle-based storage (PBS) architectures increase capacity by eliminating aisles, coordinating multiple robots in these high-density spaces is computationally challenging due to the potential for deadlocks. This paper introduces a novel multi-robot formulation for the ``ordered storage and retrieval problem at maximum capacity''. The focus is on rectangular grids accessible from a single boundary, where loads need to be first stored up to full capacity and then efficiently retrieved, given a planned departure sequence. This work bridges the gap between geometric feasibility and execution efficiency by leveraging the properties of relocation-free arrangements. These properties guide an online, prioritized multi-agent path-finding algorithm, which is the main contribution of this work. Unlike general centralized planners, the approach exploits the specific invariants of the storage arrangement to guarantee completeness and prevent deadlocks, enabling scalability. Experiments demonstrate that the method achieves near-linear improvement in makespan with respect to the number of robots, up to $m = C$, where $C$ is the grid width. Crucially, the algorithmic overhead of supporting robustness is negligible; the system handles uncertainty in departure sequences using robust storage arrangements with no significant penalty in execution speed compared to the non-robust baseline.

Robotic cellular warehousing systems (RCWS) give rise to multi-agent pickup and delivery (MAPD) processes in which robots sequentially collect multiple stock-keeping units (SKUs) for each order. Unlike classical MAPD formulations that assume static tasks, real warehouse operations often involve dynamic order evolution, where new SKUs may be appended to an order while it is being executed. Motivated by this practical requirement, this letter formulates the Dynamic-MAPD problem considering internal order evolution for the first time. Building on the token passing (TP) mechanism, we propose two event-triggered online replanning algorithms. The two strategies target different robot-resource configurations, depending on whether additional robotic resources are available for cooperative assistance. The first, Dynamic-TP, enables an event-triggered dynamic response by allowing robots to replan from their current execution states through priority-aware token acquisition after order updates. The second, Cooperative-TP, further enables reserved robots to assist newly added SKUs while preserving the original order ownership. Simulation results demonstrate that the proposed methods significantly reduce order flowtime compared with static and non-cooperative baselines, thereby improving the order fulfillment efficiency in RCWS.

Multi-agent pathfinding (MAPF) under one-shot planning is a core component of warehouse automation, yet classical formulations typically assume four-connected 2D grids with unit-time moves in four directions. To fill reality gaps while still being trackable with discrete combinatorial search, this work proposes a more practical counterpart tailored to differential-drive AGVs. We term this multi-agent warehouse pathfinding (MAWPF), featured with four constraints: (i) agent actions are restricted to straight motion and in-place rotation; (ii) rotations require multi-step costs; (iii) acceleration and deceleration are considered, and; (iv) follower collisions are prohibited to prevent rear-end crashes. To solve MAWPF efficiently, we adapt representative suboptimal MAPF algorithms-PP, LNS2, PIBT, and LaCAM-and conduct comprehensive benchmarking. Our experiments reveal that PP and LNS2 struggle to solve instances with many agents, while PIBT-based approaches achieve preferable scalability with increased solution cost. We believe that these constitute an important step toward adapting classical gridworld MAPF to operational warehouse setups.