Oe. Fjellstad et Ti. Fossen, POSITION AND ATTITUDE TRACKING OF AUVS - A QUATERNION FEEDBACK APPROACH, IEEE journal of oceanic engineering, 19(4), 1994, pp. 512-518
A position and attitude tracking control law for autonomous underwater
vehicles (AUV's) in 6 degrees of freedom (DOF) is derived. The 4-para
meter unit quaternion (Euler parameters) is used in a singularity-free
representation of attitude. Global convergence of the closed-loop sys
tem is proven. In addition, several 3-parameter representations in ter
ms of the Euler parameters are discussed with application to the same
control law. These schemes contain singularities, and only local conve
rgence can therefore be proven. The proposed control scheme is simulat
ed with Euler parameters and Euler angles.