To broaden and promote the applications of unmanned aerial vehicles (UAVs), UAVs with agile and omnidirectional mobility enabled by full or over actuation are a growing field of research. However, the balance of motion agility and force (energy) efficiency is challenging for a fixed UAV structure. This paper presents the new design of a transformable UAV, which can operate as a coplanar hexacopter or as an omnidirectional multirotor based on different operation modes. The UAV has 100% force efficiency for launching or landing tasks in the coplanar mode. In the omnidirectional mode, the UAV is fully actuated in the air for agile mobility in six degrees of freedom (DOFs). Models and control design are developed to characterize the motion of the transformable UAV. Simulation results are presented to validate the transformable UAV design and the enhanced UAV performance, compared with a fixed structure.