In the near future many tasks could be performed by swarms of flying robots. To successfully implement multiple of these swarms in the same airspace they will have to be decentralised, autonomously cope with high densities and even resolve conflicting objectives of other swarms, while remaining controllable by operators through high-level objectives. This article introduces a novel swarming approach dubbed "Velocity Templates" based on artificial potential fields. These global fields represent the objectives of the swarm, which are balanced with local interaction. Different fields are considered leading to still or sustained motion swarms where conflicting objectives between sub-groups or multiple swarms are gracefully resolved. The approach is implemented on groups of 2 and 4 Parrot Bebop UAVs, using an efficient on-board vision algorithm to locate neighbours and a motion tracking system for guidance. The experiments show promising results for further outdoor tests assessing the scalability of the proposed approach.