This paper implements robust decentralized model predictive control (DMPC) for a team of cooperating uninhabited aerial vehicles (UAVs). The problem involves vehicles with independent dynamics but with coupled constraints to capture required cooperative behavior. Using a recently-developed form of DMPC, each vehicle plans only for its own actions, but feasibility of the sub-problems and satisfaction of the coupling constraints are guaranteed throughout, despite the action of unknown but bounded disturbances. UAVs communicate relevant plan data to ensure that decisions are consistent across the team. Collision avoidance is used as an example of coupled constraints and the paper shows how the speed, turn rate and avoidance distance limits in the optimization should be modified in order to guarantee robust constraint satisfaction. Integer programming is used to solve the non-convex problem of path-planning subject to avoidance constraints. Numerical simulations compare computation time and target arrival time under decentralized and centralized control and investigate the impact of decentralization on team performance. The results show that the computation required for DMPC is significantly lower than for its centralized counterpart and scales better with the size of the team, at the expense of only a small increase in UAV flight times.