In this paper we present a methodology that drives and stabilizes a robotic agent moving in a three dimensional environment, to a 2-dimensional manifold embedded in the workspace. Once the agent reaches the manifold, depending on the application, it performs a motion planning or a trajectory tracking task. Appropriately constructed belt-zone vector fields guarantee that the agent will not depart the 2-D manifold proximity area, while carrying out the motion planning or trajectory tracking task. The derived closed form feedback control law guarantees global convergence and collision avoidance. The properties of the proposed algorithm are verified through non-trivial computer simulations.