This article presents a non-linear control system for a robotic arm that will be used for pipeline reparation. It starts with the mechanical description of the arm, its parameters and how the arm will repair the pipelines. This arm needs a control law that is non-linear. The proposed control strategy is obtained through the interpolation of classic feedback quadratic controllers that are computed for each operation point in a trajectory. This design is based on a numerical model that avoids computing an analytical model which is very useful for this kind of application. The technique is validated through simulations.