3D path following with no bounds on the path curvature through surface intersection

The article proposes a new feedback control model which is suited for path following in a 3 Dimensional Cartesian space. Differently from other methods in literature, the method proposed neither requires to compute a projection of the robot´s position on the path, nor it needs considering a moving virtual target. In spite of this: i) it guarantees asymptotic stability for every 3D curve which can be represented through a couple of intersecting surfaces f₁(X, Y, Z) = 0, f2(X, Y, Z) = 0; ii) it does not put any bounds on the initial position of the vehicle depending on the path´s curvature.