Budget-optimal multi-robot layout design for box sorting

TL;DR

This paper presents an optimization framework for designing cost-effective multi-robot layouts in logistics, abstracting motion constraints to efficiently generate feasible workspace configurations.

Contribution

It introduces a novel subgraph optimization approach that precomputes reachability to simplify layout planning with nonconvex motion constraints.

Findings

Improves memory efficiency over heuristic methods

Successfully validates motion feasibility with task assignment and planning

Demonstrates effectiveness across various grid resolutions

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.