Motion control design plays a crucial role in autonomous vehicles. Mainly, these systems operate in conditions of under-actuation, which make the control a serious task especially in presence of practical constraints. The main objective within this paper is to ensure the tracking of 3D reference trajectory overcoming some of the issues related to the control of multi-rotor vehicles (such as underactuation, robustness, limited power, accuracy, overshoot, etc.). Therefore, a control scheme for Vertical Take Off and Landing (VTOL) multi-rotor Unmanned Aerial Vehicle (UAV) is designed, applying the Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) technique. As reference model based technique, the control specifications are readily met by fixing a desired dynamic model, which is a major advantage of the technique. Moreover, a port −controlled Hamiltonian representation is exploited in order to point out the physical properties of the system such as its internal energy. This latter is exploited, as a fitness function for an optimization algorithm, in order to decrease the consumed energy especially at the take-off step and allows the tuning of the controller parameters. The numerical simulations have shown satisfactory results that support the claims using nominal system model or disturbed model. The designed controller has been implemented on a real vehicle for which one demonstrates, in an indoor area manipulation, the effectiveness of the proposed control strategy.