Paper-Based Robotics with Stackable Pneumatic Actuators

Abstract

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.

Introduction

Paper continues to receive attention as a material for electronics and robotics due to its low cost, recyclability, and foldability. For electronics, many state-of-the-art paper-based devices have included sensors,^1–6 methods of energy storage,^7–9 transistors,^10–13 and electrochemical detectors.^14–16 Paper-based robots benefit from the folding and cutting techniques of paper—origami/kirigami—to achieve large deformation. These techniques apply to other paper-like materials, including plastic sheets, which are thin, foldable, and intrinsically nonstretchable. Like conventional rigid robots, origami and kirigami robots can perform fundamental tasks such as walking, crawling, grasping, and manipulating objects.^17–26 Despite using nonstretchable paper-like materials, these origami and kirigami robots enable motions with large amplitudes using highly deformable structures. These robots are comparable to elastomer-based soft robots, adaptable to their surroundings, and similar in their movements to some living organisms, such as a worm and an octopus.

Previous studies in soft robotics have mainly focused on elastomer-based actuators and origami/kirigami-based actuators. Elastomer-based actuators have multiple modes of operation, including bending, extension, twisting, and rotation^27–39; origami/kirigami-based actuators accomplished similar modes through using highly deformable structures.^{17–26,40,41} However, current origami and kirigami actuators may have limited output force and power. The power-to-mass ratios (PMRs) of many state-of-the-art pneumatic, elastomer-based actuators are several kW/kg at modest pressure (hundreds of kPa),⁴² while only a few origami actuators with airtight layers in previous studies approached this level.^40,41 Martinez et al. presented several soft actuators based on kirigami and origami structures consisting of paper-based skeletons and elastomeric coatings, which could lift loads that are 120 times the weight of the actuator (mass is 8.3 g, PMR of 120).⁴⁰ Li et al. developed artificial muscles by origami-inspired actuators made of PVC films at a negative pressure; the 2.6-g actuator had an output power density of 2 kW/kg and lifted a 3-kg object (PMR of 384).⁴¹ These results suggest that origami and kirigami actuators may produce a higher power-to-mass ratio than human muscle (PMR of 17.6 W/kg⁴³) to perform robotic tasks.

This study presents paper-based robotic systems designed with stackable origami actuators (paper-based actuators [PBAs]), composed of sheets of paper, accordion-like structures, and direct coupling with pressure for extension and bending. We chose standard office paper as the prototyping material, which is cellulose based, decomposable, and foldable. Our approach also applies to other types of paper-like materials, such as foldable plastic sheets. Each PBA is an inflatable structure based on triangulated mesh origami, called Yoshimura patterns.⁴⁴ Over the past two decades, previous work has included the geometric description and kinematic analysis of origami structures with Yoshimura patterns (or Kresling patterns).^18,45–55 The extensive applications have demonstrated the potential of these patterns to contribute to robotics,^18,40,56 architecture,^57,58 and deployable structures.^46,59 This work establishes how PBAs function in robotic systems with simple assembly. To illustrate the stackability of these foldable components, we used them to fabricate a parallel manipulator and a legged locomotor. Although there have been other origami-inspired pneumatic actuators, this study presents a unique approach to design origami robots consisting of stackable actuators. These PBAs may contribute to compliant, lightweight, and disposable robotic systems in the future.

Materials and Methods

Principles of PBAs

The stackable PBAs make use of four principles (Fig. 1). First, the folds of these actuators use hexagonal Yoshimura patterns (see Supplementary Fig. S1 in Supplemental Data). A folded actuator has several sections with repeated patterns and forms a tube with a hexagonal cross-section. Second, these PBAs extend along their axial direction with pressurization. During the process of inflation, a PBA twists at both ends. The angle of rotation is 30° between both ends of each section with full extension. Third, a PBA with original Yoshimura patterns is a helix that rotates along its axial direction (Fig. 1A). To prevent its self-rotation, we reverse triangulated mesh at even-numbered sections. Fourth, by tuning the stiffness of paper on one side, a PBA curves to the opposite stiffer side (Fig. 1B). In this study, we use a coating technique to reinforce regions of the actuators to tailor the resulting curvature.

FIG. 1.

Schematics of PBAs. (A) The design of PBAs and their tunable stiffness. A PBA can curve to one side by tuning the stiffness of paper on the opposite side. (B) The rotatable and nonrotatable actuators. A PBA with original Yoshimura patterns rotates with deployment. By reversing triangulated meshes at specified sections, the ends of a PBA can elongate without relative rotation. (C) PBAs in series. An example of PBAs in series is an S-shaped actuator which consists of a top PBA with a stiffer right side and a bottom PBA with a stiffer left side. (D) PBAs in parallel. An example of a parallel manipulator has two PBAs stacked next to each other. PBAs, paper-based actuators. Color images are available online.

Like mechanical springs, PBAs can stack in series or parallel. For serial stacks, PBAs connect with each other from end to end and share the same internal pneumatic channel. By stacking actuators in succession, we combine the motion of multiple PBAs, creating an actuator with new functionality. For example, if we connect one PBA with a stiff left side and the other with a stiff right side in series, they can curve to an S-shape upon inflation (Fig. 1C). For parallel stacks, the motions of the PBAs couple with each other by sharing the top and bottom ends. We can manipulate parallel stacks of PBAs by inflating separate channels. For example, the parallel stack of two PBAs tilts right with the left actuator inflated; otherwise, the stack tilts left with the right actuator inflated (Fig. 1D).

Design and fabrication of PBAs

These PBAs are simple to cut, fold, and seal. Supplementary Figure S1 shows two types of Yoshimura patterns. First, we use a commercial printer to mark cutting and folding patterns for a hexagonal tube on a piece of office paper of 5 g. Then, we use liquid glue (Elmer's Liquid School Glue) to seal the sides and attach two pieces of cardboard at both ends. Among the six sections of the folding patterns, four in the middle are extensible, while the first and sixth sections stay attached to the top and bottom pieces of cardboard. We punch a hole in the bottom piece of cardboard and insert a plastic tube fitting as an inlet for pressurized air. In this work, the basal edge a and basal angle α of the folds are 24 mm and 30°, respectively; the corresponding cross-sectional area of each actuator is 15 cm². The mass of a PBA with the tube fitting is 5 g. The original height of the PBA is 9 mm in the compressed state. When folded patterns expand fully, a PBA elongates 80 cm and rotates 120°. It is worth noting that these PBAs are not airtight, so air leaks from these actuators during inflation.

In this work, we use bendable PBAs as fingers of a gripper. To tune the stiffness of paper, we brush 0.6 mL of M-bond 200 adhesive on one side of an actuator. The liquid adhesive permeates paper and reinforces regions of the actuators after the adhesive cures. We reduce the outer diameter of a PBA from 48 to 30 mm and increase the number of sections from 6 (Fig. 2A) to 12 (Fig. 3) for making a thin and long actuator. In addition, we use the folding patterns of nonrotatable PBAs to prevent sliding between grasped objects and the actuators. While curing, we sandwich a group of bendable PBAs between two steel bars and compress both ends of the tubes with the uncured adhesive to a length of 30 mm for setting their initial length. The cure time is 24 h at room temperature.

FIG. 2.

The experiment and simulation of the deployment of PBAs. (A) The experimental setup of the characterization of PBAs. A tube supported the actuator for avoiding buckling. The figure shows that a PBA lifted 200 g of mass at 44.8 kPa. (B) The process of the deployment of a rotatable PBA. The color scale shows the first principal strain on the shell. (C) The comparison of the elongation and rotation of a rotatable PBA between experiment and simulation. The simulated results are the average elongation and rotation of six vertices at the top plane of the actuator. (D) The relationship between payload and pressure. The pressure in the y-axis is the minimum pressure for lifting the payload to the highest position. The test was repeated thrice. Color images are available online.

FIG. 3.

The experiment and demonstration of bendable PBAs and a paper gripper. (A) The characterization of a bendable PBA. Angle θ is the angular displacement of the top piece of cardboard. Vector d is the displacement of the actuator in a horizontal direction. (B) The design and characterization of the gripper. The chart on the right side shows the relationship between the mass of payload and the minimum pressure for lifting the payload. (C) The demonstration of the gripper. The figure shows that the gripper lifted plush toys and snack food.

Modeling of PBAs

To understand the mechanical performance of the foldable PBAs under applied pressure, we build a numerical model of the actuator in COMSOL. To simulate the pressurization of the PBA, we apply linearly increasing pressure in quasi-static steps to the inner surface of each triangular face. As a result, the model simulates the unfolding process of inflation of a PBA (see Supplementary Video S2 in Supplementary Data). We describe the geometric formulation and modeling of a PBA in the Supplementary Data S1 (Supplementary Fig. S2).

Figure 2B shows the deployment of rotatable Yoshimura patterns in the simulation. With the increase of pressure, the creases unfold so that the structure elongates and rotates about the central axis. To verify the model, we compare the numerical results to experimental data. In the experiment, we recorded the relationships between the elongation and rotation of a PBA to describe the unfolding process (see Supplementary Fig. S3 in Supplementary Data for the experimental setup). Figure 2C shows that the simulated unfolding process of the folding patterns agrees with the experimental data.

The numerical model of the actuators has some limitations. First, the model does not consider the leakage of air. The air pressure required to stretch the actuator in the simulation is much less than that in the experiment. In the experiment, some air leaks out of the PBA, demanding the injection of more compressed air to stretch the actuator. In addition, a higher set pressure in the experiment drove leaky flow under pressure, which likely possessed a nonlinear relationship between the payload and the set pressure. Second, the model assumes that the creases and the triangular faces have the same material properties. Despite the simplifications in our numerical simulations, the model qualitatively predicts the outputs of the PBA (such as the distribution of stress and the process of deployment) as a function of dimensional specifications, folding patterns, and nominal material properties.

Results

Characterization of PBAs

We characterized the mechanical performance of the PBAs experimentally. A rotatable PBA without reinforcement coating lifted 200 g of mass at 82.7 kPa (12 psi) in 0.5 s (Fig. 2A), achieving a PMR of 80.7 W/kg, which is more than four times that of human muscle (PMR of 17.6 W/kg⁴³). Not surprisingly, the PMR of these PBAs without an airtight layer is lower than those of less leaky actuators reported in the literature, among which the highest PMR of an origami actuator was 2 kW/kg.³⁸ In addition, our paper-based manipulator is lighter and, thus, has a lower absolute output power than the human hand.

To characterize the mechanical performance of PBAs, we tested two rotatable and two nonrotatable PBAs. In the experiment, we increased the pressure of compressed air until a PBA lifted the payload to its highest position. During three repeated tests, we inflated each actuator >60 times. Figure 2D shows that two actuators with the same folding patterns had similar behavior, suggesting that PBAs have a repeatable mechanical performance. Furthermore, the mechanical performance of rotatable and nonrotatable actuators is similar, as there is an insignificant difference between the corresponding curves of payload to pressure. The simulation results in Supplementary Figure S4 also illustrated the similarity of these two types of actuators. After repeated inflation, small cracks (length of 1 mm) appeared at most of the exterior vertices of the PBAs where the cellulose-based fibers broke. Although air began to leak from these cracks, the curves in Figure 2D did not change. Therefore, the new damage that occurred during the repeated tests had an insignificant effect on the mechanical performance of our actuators. For more details, see Supplementary Data S1.

To characterize the bending and loading capabilities of the bendable PBAs, we used graph paper and a camera to record the position of the actuators as a function of pressure (Fig. 3A). We fixed the base of a bendable actuator on a test rig and measured the tilt angle θ of the top piece of cardboard relative to ground and the horizontal elongation of the PBAs (i.e., the displacement d of Point P in the horizontal direction). When the pressure increased from 0 to 28 kPa, angle θ changed from 55° to 95°, and the displacement d was 12 mm. In the example shown in Figure 3B, the gripper consisted of four bendable PBAs. We characterized the loading capability of the gripper in Figure 3B (see Supplementary Data S1 for more details). In the demonstration shown in Figure 3C, we used the gripper to grasp and lift small household objects, such as plush toys, a tape dispenser, and a packaged snack food (see Supplementary Video S1 in Supplementary Data).

Design and demonstration of a parallel manipulator

The PMR of PBAs (81 W/kg) reported in this work is higher compared with human muscle (PMR of 17.6 W/kg), so PBAs have the potential to handle and transfer lightweight objects graspable by a single human hand. To show the potential applications of PBAs, we present a robotic arm consisting of a paper-based gripper (Fig. 3B) and a parallel manipulator (Fig. 4A). We arranged three actuators into an equilateral triangle pattern and sandwiched them between two pieces of cardboard. We call the top and bottom pieces of cardboard the platform and the substrate, respectively (Fig. 4B). If the platform and substrate of three PBAs were to rotate relative to each other, the manipulator would lock because the twisting actuators would jam with each other. To avoid this jamming behavior, we stacked two rotatable PBAs with mirrored symmetry in series. The upper PBA rotated clockwise, while the lower PBA rotated counterclockwise. As a result, the twists of the two rotatable PBAs canceled each other.

FIG. 4.

The demonstration of a manipulator consisted of PBAs. (A) The direction of bending of a parallel manipulator. The green hexagon is the inflated actuator. The red arrow is the direction of bending. (B) Schematics of a manipulator. We placed three actuators in a triangle pattern. The figure shows the definition of the coordinate of the manipulator. (C) The demonstration of a manipulator. The manipulator transferred a ball from Point A to B.

A LabVIEW interface with multichannel solenoid valves allows selective inflation of the actuators. We use a pneumatic regulator to set the pressure of compressed air and mount the substrate of the manipulator on a test rig. Seven combinations of inflated actuators corresponded to seven directions of bending, which are 0°, ±60°, ±120°, ±180°, and a vertical direction (Fig. 4A). When we tested the manipulator, we noticed two difficulties in the deflation of the actuators. First, some triangular faces were unable to collapse to their original positions. Second, even if all the faces collapsed, the deflation was time consuming. To overcome the slow deflation and collapse the actuators to their original heights, we applied vacuum in the demonstration shown in Figure 4C.

We mounted a paper-based gripper onto the platform of a manipulator (see Supplementary Video S3 in Supplemental Data). We used three solenoid valves to control the manipulator and one valve to control the gripper. To speed up the collapse of folding patterns, we connected the inlets to a vacuum pump with a pressure of −88.3 kPa and kept the pump on during the whole demonstration. We increased the pressure of compressed air to 103 kPa to neutralize the suction of the continuously applied vacuum. As shown in Figure 4C, the manipulator bent to the left for a Ping-Pong ball, grasped the ball, bent to the right, and dropped the ball in a container. This demonstration shows that the manipulator was capable of performing a pick-and-place operation.

Design and demonstration of a legged locomotor

The second application is a legged locomotor with four feet (Fig. 5). We attached feet on both ends of the Left and Right Actuators. On the bottom of each foot, we attached a rubber film of Mold Star 30 (Smooth-On, Inc.) and used a piece of tape (Gorilla Heavy Duty Packing Tape) to cover the front half of the attached rubber film. Qualitatively, the tape had a lower coefficient of friction than the exposed rubber film.

FIG. 5.

The design and demonstration of a legged locomotor. (A) The diagram of a locomotor. The arrows show the direction of rotation of each PBA. (B) The demonstration and photographs of the locomotor. The red arrow is the direction of pressurized air. The blue arrow is the direction of vacuum. (C) The relationship between time and the position of the locomotor in three cases. When we used vacuum to deflate PBAs and used a support stand to hold the ends of pneumatic lines, the walking velocity increased significantly. Color images are available online.

As shown in Figure 5A, the locomotor consists of two parallel actuators: the Left Actuator and the Right Actuator. Each actuator consists of two rotatable PBAs with mirrored symmetry in series (Fig. 5A). During inflation, the actuators elongate and transition to placing the attached feet on both ends flush against the ground. During deflation, the actuators contract and transition to placing the attached feet on both ends into a tilted configuration. By alternating the inflation and deflation of the Left and Right actuators, the translation, rocking, and tilting motions of the feet result in forward motion. The portions of the rubbery feet making contact with the ground keep the robot from moving backward.

In the demonstration, we powered the locomotor through pneumatic tubes (Fig. 5B). Two airlines connected to the Left and Right Actuators for inflation and deflation; three airlines connected to two solenoid valves for compressed air and a vacuum pump for negative pressure. In this setup, the applied vacuum increased the rate of deflation of the Left/Right Actuators, which permitted fast cycling between inflation and deflation to increase the speed of walking. To track the position of the locomotor, we attached a piece of red tape to the top of the framework and extracted the position of the red tape through image processing.

We tested the locomotor in three cases. In the first case, a support stand held one end of pneumatic lines above the table, and we used vacuum to deflate the actuators. In the second case, a support stand held one end of pneumatic lines above the table, but we did not use vacuum. In the third case, there was no support stand to hold the pneumatic lines above the table, and we did not use vacuum. Supplementary Figure S5 shows the configuration of a support stand for holding pneumatic lines. As shown in Supplementary Video S4 in the Supplementary Data, the locomotor in the first case walked 11 cm in 20 s (Fig. 5B). Figure 5C shows the relationship between time and the position of the locomotor in each case. The average velocity was 5.2, 2.9, and 1.7 mm/s in the first, second, and third cases, respectively. In the first case, the average velocity of the locomotor was close to 7 mm/s in the first 10 s. As the locomotor walked away from the support holding the tubes, the amount of tubing that dragged on the table increased, which resulted in a reduced walking speed. Overall, robotic systems consisting of PBAs in series and parallel can implement complex motions, although a single PBA can only elongate and rotate.

Discussion

This work provides a unique method of designing origami robots made of paper-like materials. We stacked PBAs to implement a series of specific and complex motions. To understand the mechanical performance of PBAs, we experimentally characterized the actuators and numerically simulated their inflation. The experimental results suggest that the power-to-mass ratio of a PBA is more than four times that of human muscle. The simulated results of the numerical model matched well with the experimental data. The model has the potential to guide the design of origami actuators made of paper or other thin-sheet materials. Two robotic systems illustrated potential applications of these stackable actuators. These paper-based robots with highly deformable structures showed similar properties to elastomer-based robots, even though paper is not stretchable.⁶⁰ Similarities include: (1) an underactuated gripper that adapts to the shape of its targeted objects; (2) a manipulator that exhibits tentacle-like behavior; and (3) a locomotor that moves like earthworms, which extend/contract their body when moving forward. This study may have an impact on the structural design and choice of materials for compliant robots.

Furthermore, these robots are lightweight, low cost, and recyclable. In the future, paper-based manipulators have the potential to transfer and manipulate lightweight and fragile objects, such as medical/biomedical samples in health care facilities. The primary material of the robot is paper so that users can recycle or burn them for sterilization after use. In addition, paper-based locomotors have the potential to inspect unstructured quarters and transport tether-like payloads, such as signal wires and flexible tubing. A robot with folded components may also be capable of navigating channels, cavities, or chambers with narrow cross-sectional regions. The low-cost and accessible nature of paper may facilitate the use of paper-based robotics for educational demonstrations and learning in the classroom.

Finally, this approach for assembling actuators is applicable to origami robots made of materials other than paper. Nonetheless, cellulose-based paper is suitable for prototyping robots or educational purposes, but this type of paper may be inappropriate for applications that require high power or need to be airtight. Plastic sheets are alternatives, which have been widely used in origami/kirigami structures.^{17,21,26,41,61,62} In the future, the application of origami robots may require the development of new polymer-based materials. As a functional requirement, the material should be foldable like paper because origami actuators require high flexibility at the creases of folding patterns. The material should also resist damage due to fatigue and fracture, especially at tight folds or vertices. Addressing these issues would potentially enable new origami-based robots for commercial and household use.

Footnotes

Acknowledgments

The authors acknowledge the support from the Rutgers School of Engineering and the Rutgers New Brunswick Honors College. X.Z. and T.L. acknowledge fellowships from the China Scholarship Council. M.A. acknowledges support from the IP@Leibniz program.

Authors' Contributions

X.Z., T.L., M.A., and A.D.M. designed the research; X.Z., M.Y., C.L., S.S., B.W., S.H., and A.D.M. performed the research; X.Z., T.L., and A.D.M. analyzed the data; and X.Z., M.A., E.G., and A.D.M. wrote the article.

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This article is independent research funded by the National Science Foundation Award Nos. 1610933 and 1653584.

Supplementary Material

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