This paper proposes a control framework for changing the shape of linear deformable objects (LDOs) with a robotic arm without knowing the object’s properties on a 2D workspace. In particular, we aim to provide a complete methodology that can be used in the future to manipulate agricultural LDOs, such as branches and twigs of vegetables, without damaging them. The first component of our framework is a shape prediction optimal method that obtains a target shape that minimizes the stress along the target’s length. Using this method, the reachability of the target shape can be guaranteed. The second component of our framework is executed later and is based on an indirect optimal controller that automatically drives the objects’ shapes into the target shapes by minimizing a cost function that reduces the error between the targets and the current shapes. To find the relation between the motion of the robotic arm and the object’s shape, a Jacobian matrix is calculated by using the As-Rigid-As-Possible deformation model. Several numerical simulations and real experiments are presented to highlight the performance of the proposed methodology.