One-to-many bipartite matching based coalition formation for multi-robot task allocation

In this paper, we study the NP-Hard problem of multi-robot coalition formation for task allocation. To tackle this notoriously difficult problem, we model it as a variant of classical bipartite matching, which we call One-To-Many Bipartite Matching (OTMaM). Unlike the classical bipartite matching techniques used for matching a unique robot to a unique task, in the OTMaM problem, we let multiple robots to be matched to a single task while restricting the opposite. To this end, we propose a novel heuristic algorithm that allocates robots to tasks by finding mutually best robot-task pairs. Our algorithm provides a similar theoretical worst-case approximation ratio and guarantees a better worst-case time complexity than a comparable algorithm from the literature. The proposed approach in this paper is proved to be deterministic and the resultant matching is perfect. Simulation results also demonstrate the scalability of the presented algorithm (taking less than 1 millisecond with 100 robots and 10 tasks).