An electroadhesive gripping system includes a vacuum-augmented gripper. The gripper can include an electroadhesive surface associated with one or more electrodes and a load-bearing backing structure coupled to the electroadhesive surface. The backing couples to the backside of the electroadhesive surface so as to at least partially define a shape of the electroadhesive surface. The backing is configured to flex between a curled shape and an uncurled shape. A spreading arm is configured to apply force to the backing so as to flex the backing from the curled shape to the uncurled shape. When positioned next to a substrate, the uncurling motion of the backing can cause the electroadhesive surface to become vacuum sealed to the substrate. A power supply can be configured to apply voltage to the electroadhesive surface.