Budget-optimal multi-robot layout design for box sorting

TL;DR

The paper tackles budget-aware design of multi-robot workspaces for box sorting by placing stationary robots on a floor grid to minimize hardware cost while ensuring delivery from an input to multiple outputs. It introduces a decoupled approach that precomputes a kinematic reachability graph $G=(V,A)$ to abstract motion constraints and then solves a minimum-cost connected subgraph extraction via a commodity-flow MILP over arc-selection variables $s_a$ and flows $f_{a,i}$. Extensions include modeling conveyor belts with junctions and enforcing payload constraints, with memory-efficient, orders-of-magnitude faster performance than a heuristic baseline in grid-resolution and output-count studies. Limitations include RAM constraints at fine grid densities and the absence of dynamic task allocation or throughput optimization, suggesting future work on separation oracles and multi-objective tradeoffs for budget-throughput balancing.

Abstract

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 to sort packages from given input and output locations. Finding a good layout that minimizes the hardware budget while ensuring motion feasibility is a challenging combinatorial problem with nonconvex motion constraints. We propose a new optimization-based approach that models layout planning as a subgraph optimization problem subject to network flow constraints. Our core insight is to abstract away motion constraints from the layout optimization by precomputing a kinematic reachability graph and then extract the optimal layout on this ground graph. We validate the motion feasibility of our approach by proposing a simple task assignment and motion planning technique. We benchmark our algorithm on problems with various grid resolutions and number of outputs and show improvements in memory efficiency over a heuristic search algorithm.

Figures (12)

• Figure 1: Multi-robot logistic layouts generated using our approach: (a) before and (b) after adding an output location.
• Figure 2: Non-reachable robot pairs due to collisions (a) and kinematic limits (b), and a reachable robot pair (c)
• Figure 3: The ground set and the corresponding graph (a) of the layout, where each grid point is assigned with two potential robots, and a feasible subgraph (b, red) extracted from it. We use hollow vertices to denote input/output locations and solid vertices to denote robots.
• Figure 4: Three types of junctions to connect belt segments
• Figure 5: A feasible layout with conveyor belts (a) and its corresponding graph representation (b), where the arc representing the inline junction is highlighted.