Optimal Trajectory Tracking of the Underwater Robot through a Clifford Algebra

The manipulation in singular regions promotes an instantaneous reduction in mechanism mobility, which can result in some disturbances in the trajectory tracking. In proximity to the singularities, small velocities of the end-effectors generate high speeds in the joints due to the gradual reduction of the mobility. The phenomenon of kinematic singularity promotes 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 intensify the effects of the 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.