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This paper focuses on the modeling and control of a flying robot. The complete system, composed of a quadrotor unmanned aerial vehicle and a custom-made manipulator, has been designed for remote inspection by contact of industrial plants. The goal of this paper is to show the dynamical characteristics of the flying robot during tasks that require physical interaction, and to determine a control strategy that allows to safely interact with unknown environments. The methodology has been implemented on a real prototype and tested in an indoor area. Experimental results validate the proposed controller and show its effectiveness.