An underwater vehicles dynamics in the presence of noise and Fokker-Planck equations

Abstract

In systems and control literature, underwater vehicles are studied extensively. The translational equations of motion coupled with rotational equations, which encompass the evolution of linear velocity vector in combination with angular velocity vector, describe the equation of motion of underwater vehicles. As a result of this, the underwater vehicle dynamics assumes the structure of a six-dimensional ordinary differential equation. Ocean current circulations influence stochastically the motion of underwater vehicles. In this paper, first we account the underwater vehicle-ocean current interaction in the stochastic framework that leads to a multi-dimensional Stochastic Differential Equation (SDE). Secondly, we accomplish the noise analysis of underwater vehicles using the Fokker-Planck technique. This paper will be of interest to mechanists, control theorists, naval scientists looking for research in autonomous systems under noise influence. Further research on stochastically perturbed underwater vehicles will refine existing results available in literature.