Coalition Formation Game Approach for Task Allocation in Heterogeneous Multi-Robot Systems under Resource Constraints

This paper studies a case of the multi-robot task allocation (MRTA) problem, where each unmanned aerial vehicle (UAV) is endowed with multiple but limited resources. Completing each task necessitates UAVs to combine different resources through coalition formation, which will incur various costs including flight cost, execution cost, and cooperation cost. To minimize the total cost while maximizing both task completion rate and resource utilization rate, we model the MRTA problem of the UAVs as a leader-follower coalition formation game. In this game, leader UAVs coordinate follower UAVs to fulfill task resource requisites. Meanwhile, follower UAVs select suitable coalitions to join based on the altruistic preference. Theoretical analysis confirms the existence of a Nash stable partition in the coalition formation game. To achieve this stable partition, we propose a coalition formation algorithm. Simulation experiments validate that the proposed algorithm outperforms existing methods for the MRTA problem under resource constraints in terms of both task completion rate and resource utilization rate.