Optimal leader allocation in UAV formation pairs under costly switching

We study the leader allocation problem in UAV formation pairs when switching the lead incurs a fuel cost. While in formation, UAVs are assumed to adhere to a notion of epsilon-cooperativeness. The problem is formulated as the combination of a non-convex and a discrete optimization problem where the leader allocations are constrained to those that induce cooperation between UAVs. A equivalent formulation of the problem allows us to express the constraint set as a family of equality and inequality constraints. By restricting our search to solutions of a specific form, we replace the non-convex problem with a convex one while preserving the optimal value of the original problem. A necessary and sufficient condition is obtained which is used to verify a solution to the discrete problem. The results are combined to design the OPTIMAL COST ALGORITHM, which efficiently solves the original problem. Our results are verified in simulation.