In previous research, various types of aerial robots were developed to improve maneuverability or manipulation abilities. However, there was a challenge in achieving both mobility and manipulation capabilities simultaneously. This is because aerial robots with high mobility lack the necessary rotors to perform manipulation tasks, while those with manipulation ability are too large to achieve high mobility. To address this issue, a new aerial robot called TRADY was introduced in this article. TRADY is a tilted-rotor-equipped aerial robot that can autonomously assemble and disassemble in-flight, allowing for a switch in control model between under-actuated and fully-actuated models. The system features a novel docking mechanism and optimized rotor configuration, as well as a control system that can transition between under-actuated and fully-actuated modes and compensate for discrete changes. Additionally, a new motion strategy for assembly/disassembly motion that includes recovery behavior from hazardous conditions was introduced. Experimental results showed that TRADY can successfully execute aerial assembly/disassembly motions with a 90% success rate and generate more than nine times the torque of a single unit in the assembly state. This is the first robot system capable of performing both assembly and disassembly while seamlessly transitioning between fully-actuated and under-actuated models.