Uniform Practical Asymptotic Stability for Position Control of Underwater Snake Robots

In this paper, Lyapunov theory for uniform practical asymptotic stability (UPAS) is presented and utilized to solve the problem of position control of a planar underwater snake robot (USR). First, a precise definition of UPAS is presented, which imposes that, locally, all solutions converge to the origin up to a steady-state error that can be arbitrarily reduced by a convenient parameter tuning. Additionally, a sufficient condition for UPAS of a time-varying nonlinear system and a theorem for UPAS of cascaded systems are presented. These are then utilized to design controllers that stabilize the position of an USR when approaching from such a direction that the USR moves against the current. Results from numerical simulations are then investigated to validate the theoretical results.