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The goal of achieving 'universal grasping' where many objects can be handled with minimal control input is the focus of much research due to potential high impact applications ranging from grocery packing to recycling. However, many of the grippers developed suffer from limited sensing capabilities which can prevent handing of both heavy bulky items and also lightweight delicate objects which require fine control when grasping. Sensorizing such grippers is often challenging due to the highly deformable surfaces. We propose a novel sensing approach which uses highly flexible latex bladders. By measuring changes in the air pressure of the bladders, normal force and longitudinal strain can be measured. These sensors have been integrated into a 'Magic Ball' origami gripper to provide both tactile and proprioceptive sensing. The sensors show reasonable sensitivity and repeatability, are durable and low-cost, and can be easily integrated into the gripper without affecting performance. When the sensors are used for classification, they enabled identification of 10 objects with over 90% accuracy, and also allow failure to be detected through slippage detection. A control algorithm has been developed which uses the sensor feedback to extend the capabilities of the gripper to include both delicate and strong grasping. It is shown that this closed loop controller enables delicate grasping of potato chips; 80% of those tested were grasped without damage. © 2020 IEEE.