Vector Field Path Following of Static Sinusoidal Paths for Underwater Snake Robots

In this paper, a guiding vector field (GVF) approach is applied to solve the path-following problem of a static unbounded sinusoidal path for an underwater snake robot (USR) in the presence of constant irrotational currents. A sliding mode velocity controller for the USR is designed, and the path-following error dynamics for the normalized GVF are analyzed through cascaded systems theory. The cascade is shown to be globally uniformly asymptotically stable (GUAS) when perturbed by a uniformly bounded interconnection term which vanishes with the heading error. Results from a simulation study with a complex USR model are presented, validating the design approach.