Sub-1.5 Time-Optimal Multi-Robot Path Planning on Grids in Polynomial Time

Abstract

It is well-known that graph-based multi-robot path planning (MRPP) is NP-hard to optimally solve. In this work, we propose the first low polynomial-time algorithm for MRPP achieving 1-1.5 asymptotic optimality guarantees on solution makespan (i.e., the time it takes to complete a reconfiguration of the robots) for random instances under very high robot density, with high probability. The dual guarantee on computational efficiency and solution optimality suggests our proposed general method is promising in significantly scaling up multi-robot applications for logistics, e.g., at large robotic warehouses.