Uniform Practical Asymptotic Stability for Position Control of Underwater Snake Robots

Abstract

In this article, the 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 sufficient conditions 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 a USR when approaching from such a direction that the USR moves against the current. A simulation study of the controller applied to the ideal case is then studied to investigate how the controller performs. Then, the theoretical results are validated through a high-fidelity simulation study.