Scalable Multi-Agent Path Finding for Delivery Robot Systems with Temporal and Edge Capacity Constraints on Weighted Graphs

The Multi-Agent Path Finding (MAPF) problem on a graph is a fundamental research topic in robotics. This paper formulates a mathematical problem that not only captures path finding in traditional MAPF but also incorporates constraints related to weighted graphs, deadlines, and edge capacity considerations. The feasibility of this formulation is demonstrated and compared with Mixed Integer Linear Programming, Satisfiability Modulo Theories, and OR-Tools, focusing on scalability within a realistic delivery robot system.