3D trajectory tracking of underactuated non-minimum phase underwater vehicles

Abstract

This paper studies the 3D trajectory tracking problem for a class of torpedo-type underwater vehicles which are a typical underactuated and also non-minimum phase systems. Two spherical coordinate transformations are introduced to transform the vehicles’ tracking model into a certain three-input-three-output form which, unfortunately, is not in a strict-feedback form. To avoid possible singularity problem in the recursive control design, an exponential modification of orientation (EMO) concept is introduced and forces the vehicles to track this modified trajectory instead of directly tracking the reference one. As for the non-minimum phase problem, since the input matrix in the transformed three-input-three-output form is always invertible, this problem can be easily handled in this paper. Numerical studies are also carried out to verify the effectiveness of the proposed tracking scheme.