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This paper presents the application of a learning control approach for the realization of a fast and reliable pick-and-place application with a spherical soft robotic arm. The arm is characterized by a lightweight design and exhibits compliant behavior due to the soft materials deployed. A soft, continuum joint is employed, which allows for simultaneous control of one translational and two rotational degrees of freedom in a single joint. This allows us to axially approach and pick an object with the attached suction cup during the pick-and-place application. A control allocation based on pressure differences and the antagonistic actuator configuration is introduced, allowing decoupling of the system dynamics and simplifying the modeling and control. A linear parameter-varying model is identified, which is parametrized by the attached load mass and a parameter related to the joint stiffness. A gain-scheduled feedback controller is proposed, which asymptotically stabilizes the robotic system for aggressive tuning and over large variations of the parameters considered. The control architecture is augmented with an iterative learning control scheme enabling accurate tracking of aggressive trajectories involving set point transitions of 60 degrees within 0.3 seconds (no mass attached) to 0.6 seconds (load mass attached). The modeling and control approach proposed results in a reliable realization of a pick-and-place application and is experimentally demonstrated.