Grasping and manipulation are two of the most important hand functions that allow people to efficiently execute activities of daily living. Over the last years, many robotic devices have been proposed to assist people who suffer from neurological conditions by enhancing their grasping capabilities. In this work, we focus on the development of a robotic exoskeleton glove that can increase the grasp stability and the force exertion capabilities of the user by employing soft, telescopic, inflatable structures on the palmar side of the hand. Also, the proposed design employs a camera and an object identification system to facilitate the development of a shared control scheme that simplifies the operation of the device. The experiments demonstrate that the soft robotic exoskeleton glove can successfully execute semi-autonomous grasps and that the soft telescopic structures can increase the total exerted grasping forces by more than 40% when inflated.