A robot system having a robot with a jamming gripper is disclosed. The jamming gripper may comprise granular material within a deformable membrane configured to phase transition between a malleable state and a rigid state upon modification of its internal pressure. The phase transition of the gripper may allow the robot to engage and/or grasp a target object by conforming to the shape of the target object while in its malleable state, then transitioning to its rigid state in order to firmly grasp the object. In some situations, the robot may be configured to select and/or engage a stencil before engaging the target object, so as to pre-shape the gripper before engagement with the target object.