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This paper presents a tracking control scheme for an autonomous underwater-manipulator system (UVMS) where the proposed null space controller is not only used to track the given desired path but also allows the use of the self-motion of the vehicle to perform power efficient trajectory because of its kinematically redundant nature. In the proposed scheme, the primary task is to track the given end-effector task space trajectory despite of external disturbances, system uncertainties and internal noises. As the energy savings requirement, the vehicle motion is controlled to be aligned with the estimated ocean current orientation. The performance and effectiveness of the proposed coordinated control motion of the UVMS is demonstrated numerically and confirmed with the specified planar UVMS tasks.