The study done in this paper consists in developing a trajectory control algorithm for a quadcopter in order to follow the movement of a ground mobile object. To achieve the goal, control systems for Pitch and Roll linear speed have been de-signed in a way that allow the drone to a stable flying. The conceptual technical requirements to do this are embodied in the course of control placed in the 6th semester of the Electronic and Automatic Engineering degree. The main part of the current study is devoted to the implementation of the neces-sary algorithms related to the good control of an object in motion. Imaging pro-cessing techniques have been revealed as fundamental in pursuing the former task. The quadcopter used for the experiments was a Parrot AR Drone 2.0. The Drone communicates with the computer using WI-FI network. To establish connection between the computer and the Drone, it was necessary to use two operating sys-tems: Linux and Robot Operating System (ROS). The functions that control the Drone have been implemented by using MATLAB and Simulink Tool. The study is structured in three main parts: the first gathers all the system identi-fication process in order to design the speed linear controllers. The second part refers to the calibration parameters identification and image processing and the final one, is devoted to implement the persecution algorithm and the final results