Robotic Path Following in 3D Using a Guiding Vector Field

Path following serves as one of the most basic functions for industrial or mobile robots used in different scenarios. In this paper, a general 3D guiding vector field (GVF) is analyzed rigorously that extends the existing results on 2D GVFs. The desired 3D path is described by the intersection of two zero-level surfaces in their implicit forms, which can be used to describe various desired paths. Although the same path can be represented by the intersection of different surfaces, convergence to the path is not always guaranteed. However, under some mild assumptions, the existence of solutions and the local and global convergence results are proved rigorously for both bounded and unbounded desired paths. Examples and counter-examples from simulations further validate the theoretical results.