Unlike individual unmanned aerial vehicles (UAVs), integrated aerial platforms (IAPs) containing multiple UAVs do not suffer from underactuation and can move omnidirectionally in six dimensions, providing a basis for constructing aerial manipulation platforms. Compared to single UAVs, multi-UAV IAPs are also advantageous in terms of payload and fault-tolerance capacity, making them promising candidates as platforms with integrated-response, observation, and strike capabilities. Herein, an IAP structure design containing three sub-UAVs connected in a star-like configuration is presented. This form of integration enables the IAP, as a whole, to simultaneously adjust its position and attitude in six dimensions. The dynamics of the overall system of the IAP are modeled. On this basis, an overall system controller is designed. To simplify control, based on stability of cascaded system, the rotational motion of the sub-UAVs is treated as a inner-loop subsystem, whereas the overall motion of the IAP is seen as a outer-loop subsystem. Because the configuration space of the sub-UAVs is non-Euclidean, a controller is designed for the outer-loop subsystem based on model predictive control on the manifold. Subsequently, the stability of the closed-loop system is demonstrated. Fieldbus technology is employed to design a real-time, scalable communication architecture for multiple sub-UAVs, followed by the development of a principle prototype of the multi-UAV IAP that consists of hardware and software systems. The effectiveness of the IAP design and control method is validated through simulation and real-world prototype-based tests. In the simulation and real-world tests, the proposed methodology can make the IAP system converge to the desired configuration at the presence of large initial configuration error. The same test scenario cannot be finished by a baseline PID controller. The advantage of the proposed control scheme in dealing with state and input constraints is shown via such tests.