Optimal leader allocation in UAV formation pairs under no-cost switching

This paper considers a group of UAVs that travel from origin to destination locations. Individual agents can choose to either fly directly to their destination or pair with other agents into a leader-follower formation to conserve fuel. In the latter case, only the follower experiences a cost benefit, and hence UAVs must negotiate how to fairly allocate the task of leading. We show that selfish agents cannot reach satisfactory collaboration agreements, which leads us to propose the notion of ϵ-cooperativeness. For this class of UAVs, we introduce the partition refinement algorithm to strategically schedule alternating leading and following intervals that induce cooperation. We show that the proposed strategy is guaranteed to find leader allocations with the minimum number of leader-follower switches. Moreover, these allocations are optimal with regards to the cost that UAVs can attain while collaborating with other UAVs. Several simulations illustrate our results.