This thesis deals with the application of optimization and optimal control for the execution of viticulture related tasks with a mobile manipulator. The focus is on viticultural procedures that require manipulation for their successful execution, namely viticultural spraying and suckering. The central challenge tackled in this thesis is the application of prioritized optimization and optimal control to resolve different kinds of redundancies that arise in the execution of mentioned tasks. Depending on the needs of the specific task, redundancy resolution is performed in various spaces: task space, joint velocity space and joint position space. Viticultural spraying refers to the process of applying a protective spraying agent to grapevine plants. Two variants of the spraying task are considered: applying the spraying agent to the entire plant canopy and to a specific part of the plant. The viticultural suckering task refers to the removal of shoots, buds, and suckers emerging at the lower part of the grapevine plant. Both the robotic tool developed for this task and the accompanying control method are presented. The suckering control method utilizes the torque-sensing capability of the developed tool for tactile exploration, maintaining physical contact with the plant trunk during the suckering process. This enables the robot arm to explore and map the trunk relying solely on tactile feedback, without the need to previously detect its shape.