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This research introduces a fully-actuated multirotor flight system utilizing the T3 (Tilting Thruster Type)-Multirotor, a new type of fully-actuated multirotor platform that enables six controllable degrees-of-freedom (DOF) flight with minimal structural deformation to existing multirotor design. This new multirotor platform consists of upper and lower parts (or thruster and fuselage parts), with a unique kinematic structure and dedicated servomechanism that controls the relative attitude between the two parts. With the new mechanism, the fuselage of the T3-Multirotor can control the translational and rotational motions independently of each other, allowing 6-degrees of freedom motion that was not possible with conventional multirotors. A dedicated robust control algorithm is developed based on a thorough analysis of system dynamics to derive accurate 6-degrees of freedom motion of the platform. The flight control performance of the platform is validated through simulations and actual experiments. Several flight tasks are also performed to demonstrate the potential of the T3-Multirotor in overcoming the limitations of conventional multirotors.