Deformable object manipulation is a rapidly evolving field in robotics with applications in various domains such as manufacturing, healthcare, robotics-assisted surgery and rehabilitation. Traditional motion planning algorithms designed for rigid objects are inadequate for deformable objects, necessitating the development of tailored trajectory optimization techniques. This thesis contributes to the field by investigating a model-based technique for deformable object manipulation. The proposed task involves a dynamical movement to be executed by a robotic arm, fixed at the base. This led to assume that the operational space where the end-effector can move is approximated as a sphere, constraining the manipulated mass within this volume.