Underactuated systems offer compact design with easy actuation and control but at the cost of limited stable con- figurations and reduced dexterity compared to the directly driven and fully actuated systems. Here, we propose a compact origamibased design in which we can modulate the material stiffness of the joints and thereby control the stable configurations and the overall stiffness in an underactuated robot. The robotic origami, robogami, design uses multiple functional layers in nominally twodimensional robots to achieve the desired functionality. To control the stiffness of the structure, we adjust the elastic modulus of a shape memory polymer using an embedded customized stretchable heater. We study the actuation of a robogami finger with three joints and determine its stable configurations and contact forces at different stiffness settings. We monitor the configuration of the finger using feedback from customized curvature sensors embedded in each joint. A scaled down version of the design is used in a two-fingered gripper and different grasp modes are achieved by activating different sets of joints.