Optimal Trajectory Tracking of Underwater Vehicle-Manipulator Systems Through the Clifford Algebras and of the Davies Method

The manipulation in singular regions generates an instantaneous reduction in the mechanism mobility which can result in some disturbances in the trajectory tracking. In proximity of the singularities, small velocities in the end-effectors generates high speeds in the joints due to the gradual reduction of the mobility. The phenomenon of kinematic singularity generates a instantaneous instability in torque profile of the redundant robotic systems by the transformation of secondary joints to primary joints. The disturbances of the underwater environment intensifies the effects of the kinematic singularities because the hydrodynamic strongly oppose to torque variations. This work presents a methodology for using dual quaternions in the posture feedback of a Underwater Vehicle-Manipulator System (UVMS) using the Davies method which avoids kinematic singularities and ensures the optimal torque profiles.