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This work presents a unique approach to the design, fabrication, and characterization of paper-based origami robotic systems consisting of stackable pneumatic actuators. These paper-based actuators (PBAs) use materials with high elastic modulus-to-mass ratios, accordion-like structures, and direct coupling with pneumatic pressure for extension and bending. The study contributes to the scientific and engineering understanding of foldable components under applied pneumatic pressure by constructing stretchable and flexible structures with intrinsically nonstretchable materials. Experiments showed that a PBA possesses a power-to-mass ratio greater than 80 W/kg, which is more than four times that of human muscle. This work also illustrates the stackability and functionality of PBAs by two prototypes: a parallel manipulator and a legged locomotor. The manipulator consisting of an array of PBAs can bend in a specific direction with the corresponding actuator inflated. In addition, the stacked actuators in the manipulator can rotate in opposite directions to compensate for relative rotation at the ends of each actuator to work in parallel and manipulate the platform. The locomotor rotates the PBAs to apply and release contact between the feet and the ground. Furthermore, a numerical model developed in this work predicts the mechanical performance of these inflatable actuators as a function of dimensional specifications and folding patterns. Overall, we use stacked origami actuators to implement functionalities of manipulation, gripping, and locomotion as conventional robotic systems. Future origami robots made of paper-like materials may be suitable for single use in contaminated or unstructured environments or low-cost educational materials.