Over the last years, the development and control of Autonomous Underwater Vehicles with attached robotic manipulators, also called Underwater Vehicle Manipulator System (UVMS), has gained significant research attention. In such applications, feedback controllers which guarantee that the end-effector of the UVMS is fulfilling desired complex tasks should be designed in a way that state and input constraints are taken into consideration. Furthermore, due to their complicated structure, unmodeled dynamics as well as external disturbances may arise. Complex tasks can be conveniently given in the so-called Linear Temporal Logic (LTL). Motivated by this, the authors develop a combined abstraction and control synthesis framework in which, given the uncertain kinematics/dynamics of the UVMS, a workspace divided into Regions of Interest and a desired LTL task, a sequence of feedback control laws that probably guarantee the LTL formula is provided. The proposed controller falls within the tube-based non-linear model predictive control methodology and can handle the rich expressivity of LTL in both safety and reachability specifications. Numerical simulations verify the validity of the proposed framework.