UC Berkeley

As e-commerce expands, warehouse systems face new challenges, leading to the development of robotic warehouses. These warehouses typically employ part-to-picker systems, where mobile robots and stationary human workers collaborate. To improve the performance of these systems, we proposed new performance evaluation models and operational strategies. We also proposed innovative designs aimed at fully robotic warehouses in the foreseeable future.

Performance prediction and evaluation are crucial in designing and operating robotic warehouses, especially given the highly stochastic and complex nature of robot traffic congestion. We introduced a new evaluation model that accounts for robot congestion by initially modeling the system as a closed queueing network (CQN) with blocking. Simulation observations led us to propose a congestion mechanism and simplify the system to a CQN without blocking. Demonstrating the asymptotic Poisson properties of robot arrivals enabled us to further approximate the simplified CQN as a transportation network. This approach allowed us to estimate congestion delays as closed-form functions of traffic flow. We integrated these estimated delays with the CQN model and developed an iterative algorithm to estimate the system throughput. Our numerical experiments confirmed that this method could accurately predict throughput under transportation congestion when the system was stable.

Effective real-time robotic warehouse operation requires strategic decisions regarding workstation assignments and collision-free robot path planning. To improve system efficiency, we developed an integrated method for task assignment and path planning, implemented in both offline and online phases. In the offline phase, based on our evaluation model, we estimated an approximated optimal steady-state traffic assignment, while the online phase guided robots according to offline traffic patterns using a decentralized and computationally efficient algorithm. The simulation results indicated that our method achieved 5-10% higher throughput and required much less computational time compared to current industrial implementations.

The advent of robotic arms has made fully robotic warehouses feasible. We proposed a new layout design that positions workstations, called internal workstations, equipped with robotic arms within the storage area to minimize transportation costs. We introduced a batching pool mechanism using special pods to collect and transport assembled totes in batches from internal to external workstations. This system was evaluated using an open queueing network (OQN), which led to a closed-form queue delay approximation. We found an upper bound for the relative error in the sojourn time estimation using this approximation and showed that our approximation is accurate. Using this approximation, we developed a location-allocation-queuing model, which can be transformed into mixed integer second-order conic programming (MISOCP) for efficient solving, to find the optimal workstation locations and pod-to-workstation allocation plans. This model demonstrated a significant reduction in transportation costs and an improvement in the robot machine time of 10-20% for large or deep systems in our simulations.