Multi-degree-of-freedom electrohydraulic origami actuator for highly dynamic shape morphing and robot locomotion

doi:10.21203/rs.3.rs-5165216/v1

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Multi-degree-of-freedom electrohydraulic origami actuator for highly dynamic shape morphing and robot locomotion

https://doi.org/10.21203/rs.3.rs-5165216/v1

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Active origami enabled by soft actuation has demonstrated excellent shape morphing and reconfiguration capability and unleashed great potential in many fields. However, available active origami structures or actuators usually have limited strain and speed, provide few active degrees of freedom or flexibility. Here, we report a multi-degree-of-freedom electrohydraulic origami (EHO) actuator with lightweight, high dynamic performance, flexibility and multi-functionality. We have achieved ultra large actuation strain (3300%) and strain rate (over 23500 % s^-1) for the actuators, and constructed various types of active deployable structures with programmable and rapid shape morphing controlled by the extension, rotation, translation folding or actuation modes of the actuator units. We also demonstrate three origami robots with high-speed bidirectional sliding, multi-directional jumping and crawling respectively based on the reconfiguration and shape morphing of the active origami structures. This study may accelerate the development and application of active origami towards high-speed and agile robotics.

Physical sciences/Engineering/Mechanical engineering

Physical sciences/Materials science/Materials for devices/Actuators

Origami as an ancient art of paper folding has flourished recently in many fields, including robotics^1–5, human-machine interaction^6–8, biomedical applications^9–11, deployable space structures and engineering architectures^12–15, etc. Folding along specific creases and patterns, origami structures can achieve shape morphing or reconfiguration, either from a planar sheet to a 3D architecture, or from a compact folded state to a deployed state, or from a configuration to another. Conventionally, origami structures are folded or actuated mainly by hands^{12, 16, 17}, motors^{1, 6, 18}, or pneumatic actuators^{13, 19–21}. However, the manual folding method is lack of precision and efficiency, and impractical for engineering applications, while motors are often bulky and not applicable for high-speed folding or motion¹⁴. Although pneumatic actuators have the compact and lightweight form such as pouch motors⁸, the operation flexibility and speed are still limited, the noisy and bulky pumps and valves also hinder their portability and integration. On the other hand, the shape programmability and shape-morphing capability determined by the controllable degrees of freedom (DOF) of the origami structures are crucial for developing origami-based functional and autonomous systems (such as origami robots). More DOFs mean better flexibility and compliance for structures or robots to change their shape and adapt to specific tasks and environments, and achieve agility of motion or gain new functionalities^{22, 23}.

Recently, the rising of active origami enabled by the incorporation of active materials or soft actuation further expand the flexibility, functionality and versatility of origami actuators. Active origami structures exhibit appealing advantages such as lightweight, reprogrammable, reconfigurable, capable of remote and selective actuation, even locomotion in response to external stimuli (e.g. electrical, magnetic, temperature, and light, etc.) which hold great promise in active deployable structures and robotics¹⁴. However, the existing active origami structures are not yet able to have metrics of high dynamic and large-range morphing, good flexibility (multi DOFs) and compliance simultaneously. Such as, active origami structures or actuators based on shape memory alloys and polymers (SMAs, SMPs)^{24, 25}, liquid crystal elastomer (LCE)²⁶ usually have slow response speed and high energy consumption, while the soft magnetic^{27, 28} or piezoelectric actuators²⁹ are available for high-DOF and fast origami operation platforms, but the magnetic actuation systems are complex and bulky with limited operation space, and the morphing range and strain are limited in piezoelectric-based origami structures which are also lack of compliance. Recently, dielectric elastomer (DE)³⁰ and electro-origami³¹ both based on electrostatic actuation principle are exploited to construct the active origami due to the superior features of compliant, fast response, lightweight, efficient, low power consumption, and easy to control. Especially the electro-origami has overcome the limitations of strength, speed, and strain of current actuation technologies for active origami structures to some extent³¹, but the open structure appeared to have low actuation speed in complex structures, and the exposed liquid dielectric is also impractical for high dynamic operation and motion³². Another similar actuation technology that couples the electrostatic and hydraulic principles called hydraulically amplified self-healing electrostatic (HASEL) artificial muscles have shown remarkable actuation performance with high speed, high output force and high power density^{33, 34}, but it was once considered unsuitable for actuating high-dynamic origami structures for the limited working strain, nonplanar actuation, and the liquid-filled pouch structures³¹. Although some preliminary attempts have been made³⁵, the results show that this problem has not yet been addressed.

To solve the above problem and challenge, we introduce a new design and actuation method for creating powerful and multifunctional active origami combined with high dynamic actuation, flexibility, and compliance. As shown in Fig. 1, we have designed a hexagonal origami actuator based on four HASEL actuators which can be actuated to morph and reconfigure in three different modes corresponding to its three degrees of freedom (respectively, the extension, rotation, and translation modes). The resulted multi-DOF electrohydraulic origami (EHO) actuator can act as an elementary reconfigurable and morphing unit to construct active deployable structures and origami robots with highly dynamic shape morphing or agile locomotion abilities. Specifically, via the different reconfiguration of EHO actuators, four types of active deployable structures (garland-type, honeycomb-type, palisade-type, and bellow-type) and three kinds of locomotion origami robots (bi-directional vibration-driven locomotion, multi-directional jumping and crawling) are fabricated and demonstrated. Based on the high dynamic and multi-DOF actuation of individual actuator unit and the selective and distributed actuation in multi-unit origami systems, rapid and programmable shape morphing can be achieved which further enables the fast and highly maneuverable locomotion for the origami robots.

Design and working principle

The EHO actuator is designed to be a hexagonal configuration which encompasses four active origami folding joints and two passive ones as shown in Fig. 2a. Every joint is a single DOF rigid origami structure composed of two rigid panels separated by a compliant hinge, forming a crease structure. Folding only occurs at the compliant hinges which is accompanied by the flexion of joints. Four Peano-HASEL actuators are bonded to the joints symmetrically to form the four active origami joints which can fold with different angles in response to independent excited voltages (V_a, V_b, V_c, V_d) and a common ground. The Peano-HASEL actuator is a liquid-filled flexible pouch partially covered by flexible electrodes on opposing sides and operates on electrostatic and hydraulic principles^{34, 36}. When a high voltage is applied across the electrodes, the electrostatic zipping is induced to pressurize and displace the liquid dielectric in the pouch. As the fluid is pumped into the non-electrode region, the increased hydraulic pressure inside makes this region bulge and rotates the attached origami joint through this rigid-flexible coupling structural characteristics³⁷. As voltage increases from V₁ to V₂, a quicker zipping motion is induced by the larger Maxwell stress, thus resulting in larger hydraulic pressure in the actuator, finally faster and stronger actuation can be achieved.

The active origami joints share similar hydraulic actuation principle with spider joints and also exhibit similar high dynamic output performance which can enable the leap motion³⁷. As shown in Fig. 2b, the hexagonal configuration of the actuator also can be seen as a plane six-bar linkage mechanism if we consider the hinges as revolute pairs and the panels as linkages. The mobility of this closed-loop mechanism can be calculated as F = 3n-2p₅ = 3×5 − 2×6 = 3, where n=(N-1) = 5 is the number of moving links when designating the bottom link as the fixed one, while N = 6 and p₅ = 6 are the numbers of links and lower pairs, respectively. According to the condition for mechanism with definite motion, that the number of actuators should be equal to the degree of freedom F, we need three actuators for this six-bar linkage. Here, four Peano-HASEL actuators are deployed, so the EHO actuator can be seen as a redundantly actuated mechanism. While when coupling with the elastic hinges and structural constraint, the EHO actuator can also have specific configurations controlled by more or less active joints.

Benefiting from the motion transmission and transformation of the origami mechanism, the limited actuation strain of the Peano-HASEL actuators can be amplified, the simple rotation motion of the joints also can be transformed to multi-DOF agile motions for the EHO actuators. Three-DOF motion within the xoy plane corresponding to three actuation modes can be achieved (Fig. 2b and Supplementary Movie 1), respectively translation in y direction (extension mode), rotation in plane (bending mode), and coupled translation in x and y directions (translation mode), the different control voltages for different actuation modes are also shown. Due to the gravity, the upper and bottom panels and pouches are initially approaching to each other with the two passive origami joints in folded state and the four active ones in unfolded state. The initial height y₀ is codetermines by the stiffness of the hinges, the preload, and the self-weight of the actuator. Assuming four active origami joints have same characteristics and the structure is totally symmetry, when the four joints are activated together by same magnitude of voltage (V_a=V_b=V_c=V_d>0), the upper panel will move upward horizontally along the y axis by the simultaneously rotation actuation of the four active origami joints, meanwhile the initial folded passive joints on both sides unfold for the motion transmission; when applying voltage only on two joints on the same side, (V_a=V_d>0, V_b=V_c=0) or (V_a=V_d=0, V_b=V_c>0), the upper panel will rotate clockwise or counterclockwise with tilting angle θ, and the other joints rotate passively, finally the actuator appears as a axisymmetric configuration; when the two diagonal active origami joints are activated, (V_a=V_c>0, V_b=V_d=0) or (V_a=V_c=0, V_b=V_d>0), the upper panel will move towards top right or top left, we label this translational motion with midpoint coordinates (x, y) of the top surface of the upper panel, the other joints also rotate passively, finally the actuator appears as a centrosymmetric configuration.

We established the respective kinematic models corresponding to the three-DOF motions for this six-bar linkage (Supplementary Notes), under different structural symmetry assumptions, the planar motion of the upper panel and the actuator configuration related with different actuation angles can be predicted (Supplementary Fig. 1). Besides, we also find that the fabricated actuators demonstrate remarkable dynamic performance, as shown in Fig. 2c, d, an EHO actuator sample with short arm length (L = 2.5 cm) can leap about 7.8 cm off the ground (over 8.5 times its body height) by a 9-kV excitation voltage, and a sample with longer arm length (L = 10 cm) exhibits a ultra-large and ultra-fast extension actuation with strain of about 3300% and strain rate of over 23500% s^− 1 which are larger than most of the existing soft actuators (Supplementary Movie 2, Fig. 2e, and Supplementary Table 1).

Characterization

Axial extension actuation performance

We fabricated and tested several EHO actuator samples with different arm lengths (L = 2.5, 5, 10 cm) and hinge thicknesses (t_d =30, 50, 70 µm). The detailed materials and fabrication process for actuator samples can be found in Materials and Methods, and Supplementary Figs. 2 and 3. We first characterized the extension actuation performance of the EHO actuators, Fig. 3a shows the maximum axial extension displacements gradually increases and converges with the increase of voltage, the maximum extension displacements are respectively 5.44 cm, 10.5 cm, and 20.6 cm corresponding to the actuators with arm lengths 2.5 cm, 5 cm, and 10 cm under an 8-kV excited voltage. The maximum displacements corresponded to the fully unfolded states of the actuators, the measured values were slighter more than twice the arm length of every actuator, including the thickness of top and bottom panels and the length of hinges. Larger voltage was needed for reaching the maximum extension corresponding to the actuator with longer arm panel. EHO actuator sample with arm length of 10 cm can achieve larger extension, as shown in Fig. 3b, its strain and strain rate both increase with the voltage, reach about 3300% and 23500%/s respectively under 8-kV voltage. However, once the voltage exceeds 6 kV, the strain hardly increases due to geometric limitations of arm panels. Conversely, the strain rate continues to increase with rising voltage because the higher actuation voltage, the lager output torque of electrohydraulic actuators, causing a faster unfolding of the EHO actuator. Through the experimental observation, we can reasonably speculate that the measured maximum strain and strain rate were not the achievable extrema for the EHO actuator, actuator with longer arm under higher voltage may achieve larger extension strain, but the extreme value should be ultimately limited by the actuation torque.

Figure 3c shows the displacement versus voltage curves for EHO actuators with different hinge thicknesses (t_d= 30, 50, 70 µm). The results show that the extension displacement increases rapidly as voltage amplitudes increase from 1 to 4 kV, and when the values of the actuation voltage exceed 4 kV, the displacement will converge as voltage increases. Additionally, the values of the convergence displacements increase as the hinge thickness decreases, while the initial resting vertical displacement or the gap y₀ between top and bottom panels, which is determined by the flexible hinge deformation caused by the bonding process of Peano-HASEL actuator and actuator’s self-weight, decreases as the hinge thickness decreases. When the voltage exceeds 4 kV, the arm length become a key factor limiting the output displacement. The thicker hinges provide stronger elastic restoring force, therefore, the maximum displacement of EHO actuator with t_d= 70 µm is slightly smaller than that with t_d= 30 µm. The effect of hinge thickness on extension displacement was modeled and analyzed for the actuator (Supplementary Notes), as shown in Supplementary Fig. 4, the experimental data show the same tendency with the theoretical curves. In addition, hinges made of thicker PET tapes have more robust bonding strength and lateral stiffness, thus preventing buckling of the joints under large external loads and extending the lifetime of actuators. Therefore, a 50 µm thick hinge was chosen for general use.

The dynamic extension performance of the EHO actuator with L = 2.5 cm, t_d= 50 µm under different square-wave voltages with frequency varying from 0.5 Hz to 24 Hz are shown in Fig. 3d and Supplementary Fig. 5. The amplitude of the output displacement decreases with the increase of frequency under 3 kV, while it increases first and then decreases as actuation frequency increases under 7 kV, and the maximum amplitude occurred at 4-Hz. The EHO actuator exhibits different dynamic behaviors at different voltages, due to the charge retention which may cause EHO actuators difficult to restore to its initial state after turning off the voltage. The charge retention becomes more pronounced with longer durations of applied high voltage. Therefore, compared to 7 kV voltage with 4-Hz frequency, the voltage with 0.5 Hz has a longer period of energization, thus a smaller amplitude.

The maximum output force of the actuator is also an important performance index for the EHO actuators. We tested the maximum output force of the actuators with different arm lengths L and initial axial offsets y₀ under different applied voltages (Supplementary Fig. 6a), Fig. 3e shows that for EHO actuator with the same arm length and 8-kV applied voltage, the larger the axial offset, the smaller the output force, EHO actuator with L = 2.5 cm and y₀ = 1 cm can output a maximum force of 2.16 N. Figure 3f shows the output force versus applied voltage for EHO actuator with L = 2.5 cm and y₀ = 2 cm, the actuation force increases with the voltage. The results for other cases are shown in Supplementary Fig. 6b, c, showing the same tendency with Fig. 3f. The different initial axial offsets were set as y₀ = 2 cm, 3 cm, 6 cm, corresponding to the initial free stress states of actuators with different arm lengths L = 2.5 cm, 5 cm, 10 cm. Figure 3g shows the controllable extension displacement of EHO actuator as a function of applied voltage under both 0 and 20 g external loads.

Rotation and translation actuation performance

When two active joints on one side or diagonal positions in the EHO actuator are activated, a rotation or a translation deformation can be generated, as shown in Fig. 4a, b, the actuator can response to the excited voltage within 20 ms and deform rapidly. Figure 4c shows the maximum rotation angle versus voltage curves for EHO actuators with 50-µm hinge thickness and different arm lengths. When a lower voltage is applied to EHO actuators with different arm lengths, the shorter the arm length (the moment arm of electrohydraulic actuator's output torque), the larger a support force can be generated at the flexible hinge between two arms, resulting in a larger rotation angle. Conversely, when a higher voltage is applied, the electrohydraulic actuator can output great enough torque, and the geometric constraints between the rigid panels become the primary factor limiting the rotation angle of the actuator. Moreover, the longer the arm length, the larger the rotation angle at the same joint angle. The corresponding kinematic modeling is provided in Supplementary Notes. Figure 4d shows the rotation angle of EHO actuators with L = 2.5 cm and different hinge thicknesses versus voltage. The thinner the hinge, the larger the angle of actuators under the same actuation voltage, and the EHO actuator with t_d= 50 µm can output a rotation angle of 27.8° under an 8-kV voltage.

Figure 4e, f show the displacements along the x and y directions of the surface center of the actuator’s top panel versus voltage in translation actuation, respectively. Due to the excellent dynamic performance of the EHO actuators, the joint angle θ₁ may exceed 90° when a high actuation voltage is applied, as indicated by the dashed lines in the figures for actuators with L = 5 cm and L = 10 cm. Furthermore, the EHO actuator with L = 5 cm can return to its initial flat state when power is cut off, because of the elastic force generated by the flexible hinge. In contrast, the actuator with L = 10 cm cannot recover to its initial state, this is because when the joint angle θ₁ exceeds 90°, the actuator gravity causes the joint angle θ₁ to gradually increase and tend towards 180°, causing the actuator to transition from one stable state to another, hence its corresponding curve is represented by a dashed line with higher transparency, and the data itself does not carry an actual meaning. When the joint angle is less than 90°, EHO actuator's displacement in the x-direction is positively correlated with that in the y-direction, while when the joint angle is greater than 90°, the relation is negatively, and the curve of the 5-cm-arm-length actuator has an extreme point at the voltage of 6 kV. The translation displacements of the actuators with different hinge thicknesses varying with voltage are shown in Supplementary Fig. 7. The translation actuation performance of the EHO actuators with L = 2.5 cm and different hinge thicknesses was also tested and theoretically modeled (Supplementary Notes), as shown in Supplementary Fig. 7d, the theoretical curve can accurately predict the translation configuration of the actuator with different hinge thicknesses.

Highly dynamic shape morphing

After charactering the three-DOF EHO actuators, we then designed and fabricated several types of active deployable structures based on the actuators with short arm length (L = 2.5 cm) to demonstrate the modularity, flexibility, and scalability. Although the actuator with longer arm exhibits larger shape morphing range and deployable space (see Figs. 3 and 4), we chose actuator with short arm length for it has larger output force and more compact and robust structure. As shown in Fig. 5, we used the same EHO actuator as the elementary structural and shape morphing unit, four types of active deployable structures were fabricated by assembling different numbers of actuators in different array configurations. For example, a honeycomb-type structure and a garland-type structure combined by six actuators can rapidly unfolding within 70 ms when activating all active origami joints in the actuators simultaneously by a 7-kV voltage (Fig. 5a, b). The periodic folding and unfolding morphing process excited by a 2-Hz square-wave voltage can be seen in Supplementary Movie 3.

Figure 5c shows a bellow-type structure connected by five EHO actuators in series not only can extend along the axis direction but also can oscillate like a fish tail under different control strategies. Activating all active origami joints in the five actuators simultaneously can induce the extension morphing, applying voltage on only one side of the joints can induce the rotation or bending towards the opposite direction. The highly dynamic shape morphing with different modes of this bellow-type structure can be showed through a ping-pong game, the coming ball can be quickly hit back towards three different directions (Fig. 5d, Supplementary Fig. 8 and Supplementary Movie 4), the maximum rolling speed of the hit ball can reach about 0.88 m/s. Figure 5e plots the periodic bi-directional rotation angle of the bellow-type structure with 1-Hz frequency. This periodic oscillation is controlled by two coordinated square-wave voltage signals with 7-kV amplitude for the two side groups of the active origami joints (Supplementary Movie 4). Figure 5e shows the snapshots of the corresponding configurations at different moments during the oscillation process, an anticlockwise rotation angle of 58.3° appears at 1.27 s and a clockwise rotation angle of 47.3° appears at 3.77 s. We can see this series configuration with five actuator units gains remarkably increase in the total extension range and rotation angle compared with the single unit (Figs. 3a and 4c). We also demonstrate the fast shape morphing ability of a palisade-type structure enabled by the translation mode of the EHO actuator, four different unfolding configurations corresponding to different control voltage strategies are shown in Fig. 5g and Supplementary Movie 5, the morphing response time are all less than 50 ms under a 7-kV excitation voltage.

Highly dynamic origami robots

Besides the highly dynamic shape morphing enabled by the different combination types of actuator units, we also designed and demonstrated three origami robots with different locomotion modes, either based on a sole actuator or multiple actuators connected in series. Figure 6a shows a vibration-driven locomotion robot which is legless and only relies on internal actuation torque and external isotropic friction to achieve movement. When putting an EHO actuator on the ground, the dynamic rotation shape morphing of the actuator can be translated into the sliding motion based on the stick-slip effect between the actuator and the ground. Theoretically the bidirectional rotation shape morphing can control the robot moving towards two opposite directions. The underlying vibration-driven locomotion mechanism is modeled and analyzed (Supplementary Notes, Supplementary Fig. 9). The robot moved about 8.6 cm within 2 s with a speed of 4.3 cm/s under periodic square-wave control signal with 7-kV amplitude and 8-Hz frequency, relying on only one body actuator and isotropic friction (Fig. 6a, Supplementary Fig. 9, Supplementary Movie 6).

Based on the highly dynamic multi-DOF shape morphing of the EHO actuator, we designed a multi-directional jumping origami robot which simply consists of an EHO actuator and a support leg (Fig. 6b, Supplementary Fig. 10). The leg is mounted on the bottom panel of the actuator and make the actuator tilt with β ≈ 8° on the ground, thus the horizontal and vertical components of the inertial force induced by the dynamic folding of the actuator can accelerate the robot to jump up and forward. The robot can realize straight jumping based on the extension actuation of the actuator, and turning jumping based on the rotation or bending actuation mode. The anticlockwise rotation actuation corresponds to the left jumping, and the clockwise corresponds to the right jumping. The corresponding modeling and analysis for the multi-directional jumping locomotion can be found in Supplementary Notes and Supplementary Fig. 11. We tested the multi-directional jumping performance (Supplementary Figs. 12 and 13, Supplementary Movie 7), the robot can realize continuous jumping with an average speed of 15.3 cm/s (3.8 BL/s) and 3.97-cm height (3.45 body height) under 7-kV and 3-Hz voltage, the turning speed is about 63.7°/s for left jumping and 38.2°/s for right jumping. We also tested the terrain adaptability for the robot (Fig. 6c, d, Supplementary Fig. 14, Supplementary Movie 7), the robot can easily cross the simulated unstructured environments like greensward (grass height: 3–6 mm) and gravel (size: 3 to 6 mm).

Based on the bellow-type active deployable structure and its multimodal shape morphing, we designed and demonstrated a multi-directional crawling origami robot as shown in Fig. 6e-h. The structural composition and crawling mechanism are shown in Fig. 6e and Supplementary Fig. 15, only three EHO actuator units were connected in series for constructing the robot body, two purpose built friction feet (Supplementary Fig. 10) were mounted on the front and rear ends of the body, two elastic bands made of silicone elastomer were wrapped around the body actuators to improve the recovery speed of morphing, the total robot length is about 4 cm. The stick slip effect induced by the feet with anisotropic friction can convert the periodic folding and unfolding of the bellow-type body actuator to continuous crawling locomotion. The extension mode can control the straight crawling and the rotation mode can control the turning crawling (Supplementary Notes, Supplementary Fig. 15). Figure 6f shows the fast straight crawling of a robot prototype on a PVC plate under 3-Hz and 6-kV voltage with an average speed of 17.1 cm/s (4.3 BL/s), the robot moves 37.6 cm within 2.2 s, within the first two actuation cycles, the robot only took 0.6 s to move about 16.8 cm, the instantaneous crawling speed achieved 28 cm/s (7.0 BL/s) (Supplementary Fig. 15d, Supplementary Movie 8). Figure 6g shows the continuous turning crawling, the robot took 5.4 s to turn 155° with average speed of 28.7°/s, and 16.2 s to turn 347.5° with average speed of 21.5°/s at 3 Hz and 6 kV (Supplementary Movie 8). We also demonstrate an untethered crawling origami robot as shown in Fig. 6h and Supplementary Movie 9. A miniature high voltage control system which can provide a bipolar square-wave signal with 6-kV amplitude and tunable frequency and duty cycle (Supplementary Fig. 16) is integrated with the robot. The untethered robot can crawl stably on a wood table with a speed of 3.2 cm/s (0.8 BL/s) under 6-kV and 1-Hz square-wave voltage, which is faster than most of the reported untethered robots capable of continuous locomotion on land and driven by soft actuators (Supplementary Table 2).

In this study, we have reported a multi-DOF origami actuator based on HASEL actuators with high dynamic performance, flexibility and multi-functionality. The resulted EHO actuator is a compact and lightweight hexagonal configuration with rigid-flexible coupling characteristics and has three DOFs and corresponding three actuation or folding modes (extension, rotation, and translation). Three control strategies were proposed for controlling the four HASEL-based active origami joints in the EHO actuator corresponding to the three actuation modes. More DOFs can be obtained by the combination of more actuator units, such as two orthogonal EHO actuators connected in series have five DOFs in total (Supplementary Fig. 17). The compliant origami structure and rigid-flexible coupling feature of the EHO actuator not only amplifiers the limited actuation strain, but also enriches the actuation modes of the conventional HASEL actuators. A ultra-large actuation strain (3300%) and corresponding ultra-fast strain rate (over 23500% s^− 1) were achieved, superior to most of the existing soft actuators, the EHO actuator can even leap about 7.8 cm off the ground (over 8.5 times its body height). We also fabricated several EHO actuator samples with different geometry parameters (hinge thickness and arm length) and investigated their quasi-static and dynamic actuation performance under different excited voltages for different modes and load conditions theoretically and experimentally.

Based on the multimodal and powerful dynamic actuation, the active deployable origami structures assembled by different types of EHO actuator array can rapidly unfold and achieve periodic shape morphing with response time less than 50 ms. Programmable and multimodal shape morphing or reconfiguration for the origami structures also can be easily realized by selectively actuating different EHO units and switching between different folding modes in one unit. Three tethered origami robots with different locomotion mechanism were then designed and fabricated based on the highly dynamic and multi-DOF actuators, they all demonstrate agile and fast-moving abilities. The legless bidirectional vibration-driven locomotion robot can achieve continuous and bidirectional locomotion relying on only one body actuator and isotropic friction; the multi-directional jumping origami robot also can realize continuous straight and turning jumping based on only one body actuator without additional energy-storing and demonstrates excellent terrain adaptability and jumping performance; the multi-directional crawling robot also demonstrates a high moving speed and good mobility. Furthermore, we developed the first untethered land locomotion robot driven by HASEL actuators which shows potential for fast untethered moving.

Due to the manual fabrication and assembly error, the consistency and symmetry of the actuator samples are not perfect yet. Standardizing the fabrication process³⁶ or using 3D-printing technology⁶³ may solve the problem to obtain more robust and consistent actuators and robot prototypes. The performance inconsistency of the four active origami joints in one actuator may also affect their desired actuation modes and the straight locomotion of the origami robots, while through individually adjusting the excited voltages of the four joints can minimize the deviation. Moreover, the charge retention of the HASEL actuators can cause the performance degradation during dynamic actuation, and the high excited voltage may increase the complexity and cost of the control circuit, however recent advances in the dielectric materials^{38, 64} and low-cost high-voltage circuits⁶⁵ suggests those are not insurmountable impedes and challenges for the realistic application. But modeling and prediction of the dynamic characteristics are still challenge for the strong nonlinearity of electromechanical-fluid-structure coupling and the rigid-flexible coupling in the EHO actuators⁶⁶, and the closed-loop precision control based on capacitance self-sensing⁶⁷ for the actuators is also an important research topic in the future.

Overall, the new design and actuation method are reported here for creating powerful and multifunctional electrohydraulic origami actuators which also demonstrates excellent dynamic performance, flexibility, compliance, and scalability. The delicate combination of compliant origami mechanism and soft electrohydraulic actuation makes remarkable contributions in both fields, the resulted prominent properties of highly dynamic folding shape morphing or reconfiguration with multi-DOF for the EHO actuators provides more possibility in developing agile and fast-moving locomotion robots and active deployable structures. It will also inspire diverse applications in shape changing and reconfigurable robots, deployable space structures, active metamaterials, and safe human-machine interactions.

Materials

The liquid-filled pouches of electrohydraulic actuators in EHO actuators were made by heat-sealing two 20-µm-thick polyethylene terephthalate (PET) films (GD-09MP300-LG, Gude, China), the filled silicone oil (PMX-200, Dow Corning) has a viscosity of 1 cSt. The PET film has a heat-sealable layer on one side and the other side is treated with corona to promote conductive ink adhesion. The electrodes were screen printed on both sides of the pouches using conductive inks (LN-GCI-3, Jining Leadernano Tech., China). We chose single-wall corrugated cardboard with 1.5-mm thickness and surface density of ~0.4 kg/m² (Triple E 40×40 cm, Zhiying, China) here as the material of the actuator’s hexagonal frame. The support leg of the jumping robot was made from 0.4 mm-thick PET sheet (Dupont, United States), which was then bonded to commercial syringe needles (0.45×16 RW LB, Conpuvon Co.) using cyanoacrylate glue (HJ-402, Huiju, China) to form the anisotropic friction foot of the crawling robot. The elastic silicone bands were made of Ecoflex 00-30 (Smooth-on, United States).

Fabrication of EHO actuators

The detailed fabrication process of EHO actuator is shown in Supplementary Fig. 2. (a) The PET films were sealed into pouches using a 3D printer (F350, Snapmaker, China), with the heat-sealable layers pressed together and sandwiched between 25 μm thick Kapton films (RS-PI001, Runhai, China) to prevent the printer nozzle from damaging the PET films and distribute the heat. (b) Electrode patterns were created in CAD software (Solidworks 2022) and produced on a 200-mesh oil-based screen board. A screen-printing machine (3024, Deliou, China) was used to print conductive ink on both sides of the heat-seal pouches. (c) Each pouch was filled with 1.15 ml silicone oil with a viscosity of 1 cSt. (d) Sealing filling ports with a soldering iron, and adhering a narrow piece of PET tape between the electrodes to reduce the mutual effect of electrostatic induction during individual actuation of the two joints. Each pouch was trimmed along the seal edge, leaving 5-mm excess ‘skirt’ on the sides. (e) Using laser cutting technology to precisely cut the corrugated cardboards into the shapes for the substrates and the origami arms, as shown in Supplementary Fig. 3. A substrate panel and two origami arms were aligned and bonded together using a piece of double-sided PET tape (Darit tape, China) with the thickness of t_d, then the electrohydraulic actuator was adhered to it to accomplish the half assembly of an EHO actuator. (f) The previous steps were repeated to fabricate the complementary half of the EHO actuator. The two halves of the actuator were then connected together by the same double-sided PET tape and strengthen by the Scoatch tape (3M, United States) as shown in Fig. 2a, thereby completing the whole fabrication of the EHO actuator. The EHO actuators, with arm lengths of 2.5 cm, 5 cm, and 10 cm, have respective masses of 8.1 g, 9.3 g, and 11.8 g. Supplementary Table 3 lists the basic parameters of the EHO actuator.

Fabrication of active deployable structures and origami robots

The EHO actuators with an arm length of 2.5 cm can be connected in series or parallel using double-sided adhesive tape for various configurations like honeycomb, garland, bellow and palisade types.

The jumping origami robot was assembled by taping a support leg to a 2.5 cm-arm-length EHO actuator. The fabrication of the support leg was shown in Supplementary Fig. 10, and the mass of the prototype is 8.5g. The crawling origami robot's body consisted of three 2.5 cm-arm-length EHO actuators in series, connected with 50-µm PET double-sided tape. The dimensions of the outermost substrates were modified, as shown in Supplementary Fig. 3. The elastic silicone bands, 150 µm thick and 2 mm wide, were made from silicone Ecoflex 00-30, they were clamped into the corresponding grooves of the outermost two substrates, and secured with adhesive tape. Two 3D-printed support platforms were fixed on the robot's outer substrates to attach anisotropic friction feet and support control system. A 3.8 cm × 0.5 cm × 0.9 cm rectangular platform with a 3.6 cm × 0.7 cm × 0.8 cm groove was fixed to the front, while a 3.8 cm × 0.5 cm × 0.9 cm rectangular platform with a 3.6 cm × 0.3 cm × 0.8 cm groove was at the rear. The friction feet were glued to the outermost sides of both support platforms, respectively. The circuit board was placed into the front platform's groove and taped to the substrate. The crawling robot prototype had a base mass of 30.1 g, which increased to 56.1 g upon assembly with the control system.

Characterization of EHO actuators

In all actuation performance tests, the voltage signals had a duty cycle of 50%, and all actuation signals operated at a frequency of 0.5 Hz, with the exception of dynamic tests. The EHO actuator was affixed to a horizontal plane and the motion was captured using a camera (FDR-AX700, Sony) with tunable frame rate such as 50, 100, and 500 fps. Kinovea (version 0.9.5) was used to process the videos and the maximum displacement or angle was measured for each cycle. The dynamic performance of EHO actuator was tested using a laser displacement sensor (LK-G150, Keyence), and the sampling frequency was set to 1000 Hz. Output force was measured using a load cell (LSB200, Futek) and the maximum force output was measured for each cycle. The top and bottom substrates were bonded to the stage fixed on the horizontal slide and the load cell, respectively. EHO actuators' initial extension displacement can be altered by adjusting the slide. Each test was repeated five times and the average and standard deviation of the results were recorded.

Characterization of active deployable structures and origami robots

All side edges of the panels in the actuators were brushed by fluorescent pigment for better observing and recording the dynamic shape morphing of the active deployable structures.The different types of deployable structures were positioned on an acrylic board with smooth surface in turn, and the camera was at a top-down angle to capture the dynamic shape morphing of these them in a dark environment.

The power-on time of the vibration driven locomotion robot and multi-directional jumping robot in each cycle was 10 ms. By applying a pulsed voltage, residual charge effects on the robot were mitigated, ensuring stable and continuous motion of the robots. The crawling robot was driven by a signal with a duty cycle of 50%. The camera was set at the top or side of the motion space to record the robot locomotion.

High voltage control circuits and signals

Amplified the voltage from the DC power supply (UTP1306S, Uni-trend Co.) using a high-voltage amplifier module with a power rating of 15 W (H101p, EMCO) and output a signal resembling a square wave through an H-bridge circuit made up of four high-voltage relays (CRSTHV-20KV-A, CRST Co.) (Supplementary Fig. 18). The polarity was reversed to alleviate charge retention. An NI DAQ (NI USB-6363) took voltage signals generated by custom NI LabVIEW (version 2021) and fed them into the H-bridge circuit to output voltages with controlled duty cycle and frequency, and the amplitude of the output voltages can be modified by altering the input voltages of the DC power supply.

Miniature high voltage control system

The system was powered by a low-voltage battery (3.7 V) and can output up to 6 kV through a high-voltage amplifier module (A60P-5, XP Power). A high-voltage H-bridge circuit constructed with four specially-made miniature high-voltage optocouplers by HV Opto-diodes (OZ100SG, VMI) can output a bipolar square wave with an adjustable duty cycle range of 10%-90% and a tunable frequency range of 1-10 Hz. The control system has a total mass of approximately 26 g, with dimensions measuring 57 mm in length, 41 mm in width, and 8 mm in height. The PCB layout diagram and the completed circuit can be found in Supplementary Fig. 16b, c. Supplementary Table 4 lists the main components containing in the circuit.

Competing interest Statement

The authors declare no Competing Financial or Non-Financial Interests.

Data availability

All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Information. Additional data related to this paper may be requested from the authors.

Code availability

The code used in this paper is available upon any reasonable request.

Author Contribution Statement

W.L. conceived the project and designed the actuators. Y.Z. and W.L. fabricated the actuators. Y.Z. and W.L. developed the theoretical model for the actuators and conducted the analysis. W.L. and Y.Z. designed the experiments and built the experimental setup. Y.Z. and W.L. conducted the experiments. W.L. and Y.Z. analyzed the results and wrote the manuscript. G.L., H.L., K.T., W.Z., and J.X. discussed and revised the manuscript. J.X. supervised the research.

Acknowledgments

We thank Y. Zhai, F. Fang and H. Chen for discussion about different soft actuators and the figures. This work was supported by the Fundamental Research Funds for the Central Universities, China (W.L.), Shanghai Gaofeng Project for University Academic Program Development (W.L.), Research Project of State Key Laboratory of Mechanical System and Vibration (Grant no. MSV202407 (W.L.)), National Natural Science Foundation of China (Grant no. 12002204 (W.L.), 12102398 (G. L.)).

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Multi-degree-of-freedom electrohydraulic origami actuator for highly dynamic shape morphing and robot locomotion

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Introduction

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Design and working principle

Characterization

Axial extension actuation performance

Rotation and translation actuation performance

Highly dynamic shape morphing

Highly dynamic origami robots

Discussion

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