Analytical and Numerical Study of Underwater Tether Cable Dynamics for Seabed Walking Robots Using Quasi-Static Approximation

In this study, the dynamics of tether cables (TCs) that connect a surface ship and a walking robotic vehicle on the seabed are numerically investigated. The main aim of this study is to develop a reliable prediction model for the dynamic behavior of TCs attached to a seabed walking robot. This system consists of a surface ship, underwater manned seabed walking robot (UMSWR), TC, and winch. The study is comprised of mathematical modeling and numerical simulations of the developed governing equations for the TC dynamics. A relatively simple and efficient mathematical analysis method is proposed to determine the configuration and forces on the TC under a steady state. The problem is solved using the quasi-static technique and lumped mass parameters for discretizing and modeling the dynamics of the TC. Based on the static analysis of the Morrison equation and finite segment method, analytical formulas of the steady-state equation of TC were obtained and solved. The effects of variable water density and variable underwater currents are included in the cable behavior. Consequently, the two-dimensional TC profile and axial tension were estimated in a steady-state configuration. The developed equations were simulated in MATLAB software. Several numerical simulation examples were worked out, demonstrating the accurate performance of the method. Various input parameters of the system and their relationships with the output values were investigated, thereby demonstrating the versatility of the method.