Complex and cluttered urban environments are subject to rapidly increasing energy and time costs of transportation through jam-packed urban road networks, making aerial delivery an effective solution. Even in developing countries, road networks either do not exist or are inaccessible for significant parts of the year due to seasonal rain, flood, and snow. The introduction of inexpensive micro unmanned aerial vehicles (UAV) in recent years provides a novel opportunity for easy aerial transportation of loads. While most aerial load transportation research considers the load rigidly attached to a single aerial vehicle, this presents a single point of failure, and moreover the rigid connection of the load dramatically increases the inertia of the system making the system sluggish and incapable of quickly responding to perturbations, which is critical in an urban environment. Our research contributes to the foundations of constrained geometric feedback control through the study of the tight dynamical coupling between the multiple aerial robots and the shared load, dynamics on manifolds, unilateral cable tension constraints, multiple hybrid modes, and physical system limits.