This paper presents a solution to the problem of robust allocation of Unmanned Aerial Vehicles (UAVs) to targets under environmental uncertainty. A framework is developed to allocate heterogeneous UAVs with different exploration and exploitation abilities to targets. This framework can handle different types of uncertainties, and thus goes beyond existing frameworks that only handle Gaussian uncertainty. The ability to handle a wider class of uncertainties is useful because target scores cannot always be modeled using a Gaussian distribution. Two methods of assigning UAVs are compared: the decoupled approach considers allocating UAVs with heterogeneous abilities independently of each other; and the coupled approach considers allocating heterogeneous UAVs simultaneously. The decoupled and coupled approaches are implemented using the fully decentralized and scalable Consensus-Based Bundle Algorithm (CBBA). Experiments are performed on a hardware testbed where targets have categorical uncertainties. The experiments show that the coupled approach encourages cooperation between UAVs and thus has better performance than the decoupled approach.