Robotic systems are routinely used in the logistics industry to enhance operational efficiency, but the design of robot workspaces remains a complex and manual task, which limits the system's flexibility to changing demands. This paper aims to automate robot workspace design by proposing a computational framework to generate a budget-minimizing layout by selectively placing stationary robots on a floor grid, which includes robotic arms and conveyor belts, and plan their cooperative motions to sort packages from given input and output locations. We propose a hierarchical solving strategy that first optimizes the layout to minimize the hardware budget with a subgraph optimization subject to network flow constraints, followed by task allocation and motion planning based on the generated layout. In addition, we demonstrate how to model conveyor belts as manipulators with multiple end effectors to integrate them into our design and planning framework. We evaluated our framework on a set of simulated scenarios and showed that it can generate optimal layouts and collision-free motion trajectories, adapting to different available robots, cost assignments, and box payloads.

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